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Here`s - The Brian spiking neural network simulator

1. Postsynaptic neurons noisy coincidence detectors eqs post dv dt n v tau cd 1 dn dt n tau_n sigmax 2 tau_n 5 xi 1 vee postneurons NeuronGroup Ndur nneurons model eqs_post threshold 1 reset 0 C Connection neurons postneurons Divide into subgroups each group corresponds to one postsynaptic neuron with all stimulus duratio postgroup for i in range nneurons postgroup append postneurons subgroup Ndur Connections according to the synchrony partition group for i in range N group append neurons subgroup Ndur group i tauK tauK i group i gmax gmax i group i tau tau i group i duration linspace 100 ms l second Ndur if group number i 0 C connect one to one group i postgroup group number i weight 1 count group number i spikes SpikeCounter postneurons run rest_timet l 1 second report text Figure 2C window 100 5 smoothing window rate zeros Ndur window totrate zeros Ndur window for i in range nneurons display tuning curve for each neuron in grey count spikes count ixNdur i 1 Ndur Smooth for j in range 0 len count window rate j mean count j j window totratet rate if i 5 plot only 5 individual curves plot group 0 duration window 2 window 2 ms rate grey linewidth 1 Mean tuning curve plot group 0 duration window 2 window 2 ms totrate nneurons k linewidth 2 xlim 100 600
2. Dependencies can be specified explicitly or are automatically extracted as the words in string cond and re solved can be specified explicitly or by default is set codeitems class brian experimental codegen2 CodeItem An item of code can be anything from a single statement corresponding to a single line of code right up to a block with nested loops etc Should define the following attributes default values are provided 368 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 resolved The set of dependencies which have been resolved in this item including in items contained within this item Default value the union of selfresolved and subresolved Elements of the set should be of type Dependency i e Read or Write selfresolved The set of dependencies resolved only in this item and not in subitems Default value set subresolved The set of dependencies resolved in subitems default value is the union of item dependencies for each item in this item Requires the CodeItem to have an iterator i e amethod iter dependencies selfdependencies subdependencies As above for resolved but giving the set of dependencies in this code The default value for dependencies takes the union of selfdependencies and subdependencies and removes all the symbols in resolved This structure of having default implementations allows several routes to derive a class from here e g Block Simply defines a
3. 4 Optionally insert additional data into the namespace of the Code object 5 Use the Code object via code namel vall name2 val2 where the name val are to be inserted into the namespace before the code is called This process is very clearly illustrated in the source code for CodeGenStateUpdater Structure of the package The following are the main elements of the code generation package Code This is the output of the code generation package a compilable compiled code fragment along with a names pace in which it is executed Language Used to specify which language the output should have CodeItem Before code is converted into a specific language it is stored in a language invariant format consisting of CodeItem objects which can in turn contain other Code It em objects The main derived classes from this are Block and Statement The first can contain a series of statements or it can be a for loop an if block etc A Statement can bea MathematicalStatement or CodeStatement The former is for things like x y z and the latter for things like x arr index Symbol resolve A CodelItem with unresolved dependencies needs to be resolved by the function resolve Each unresolved depdendency should correspond to a Symbol which knows how to modify a CodeItem in order to resolve itself For example a NeuronGroupStateVariableSymbol will in sert the NeuronGroup state variable value into the namespace create a new array
4. bandpass filter third order gammatone filters bandpass_nonlinear2 ApproximateGammatone compression center_frequencies_nonlinear bandwidth_nonlinear order order_nonlinear low pass filter cutoff_frequencies_nonlinear center_frequencies_nonlinear order_lowpass_nonlinear 2 lp nl LowPass bandpass nonlinear2 cutoff frequencies nonlinear lowpass nonlinear Cascade bandpass nonlinear2 lp nl 3 fadding the two pathways dnrl filter lowpass linear lowpass nonlinear dnrl dnrl filter process figure imshow flipud dnrl T aspect auto show Example IIRfilterbank hears Example of the use of the class IIRFilterbank available in the library In this example a white noise is filtered by a bank of chebyshev bandpass filters and lowpass filters which are different for every channels The centre frequencies of the filters are linearly taken between 100kHz and 1000kHz and its bandwidth or cutoff frequency increases linearly with frequency from brian import x from brian hears import sound whitenoise 100xms ramp sound level 50 dB example of a bank of bandpass filter tees ttt nchannels 50 center frequencies linspace 200 Hz 1000 Hz nchannels fcenter frequencies bw linspace 50 Hz 300 Hz nchannels bandwidth of the filters The maximum loss in the passband in dB Can be a scalar or an array of length nchannels gpass 1 dB The minimum attenuation in
5. 4 10 Analysis and plotting Most plotting should be done with the PyLab commands all of which are loaded when you import Brian See http matplotlib sourceforge net matplotlib pylab html for help on PyLab The scientific library Scipy is also automatically imported by the instruction from brian import The most useful plotting instruction is the Pylab function plot A typical use with Brian is plot t ms vm mV where t is a vector of times with units ms and vm is a vector of voltage values with units mV To display the figures on the screen the function show must be called once this should be the last line of your script except when using IPython with the Pylab mode ipython pylab Brian currently defines just two plotting functions of its own raster plot andhist plot In addition the StateMonitor object has a plot method 4 10 1 Raster plots Spike trains recorded by a 5pikeMonitor can be displayed as raster plots S SpikeMonitor group raster plot S Usual options of the plot command can also be passed to raster plot One may also pass several spike monitors as arguments 210 Chapter 4 User manual Brian Documentation Release 1 4 1 4 10 2 State variable plots State values recorded by a Stat eMonitor can also be plotted as follows M StateMonitor group V record 0 1 2 M plot 4 10 3 Realtime plotting Both raster plot and StateMonitor plot have real time versions
6. 60 mV v I_synE I_synI I_b 10 nS 20 ms volt I_synE 3 nS gex Q mV v amp I_synI 30 nS gix 80 mV v amp Id amp dge dt ge 5 ms iod dgi dt gi 10 xms FD EEF P NeuronGroup 10000 eqs threshold 50 mV refractory 5 ms reset 60 xmV Pe P subgroup 8000 Pi P subgroup 2000 Ce Connection Pe P ge weight 1 sparseness 0 02 Cie Connection Pi Pe gi weight 1 sparseness 0 02 Cii Connection Pi Pi gi weight 1 sparseness 0 02 eqs stdp dpre dt pre 20 xms 130 dpost dt post 20 ms 1 0 EELZ nu 0 1 learning rate alpha 0 12 controls the firing rate stdp STDP Cie eqs eqs_stdp pre pre 1 wt nu post alpha post post 1 wt nuxpre wmin 0 wmax 10 M PopulationRateMonitor Pe bin 1 P I_b 200 pA set the input current run 10 second P I_b 600 x pA increase the input and see how the rate adapts run 10 second 98 Chapter 3 Getting started Brian Documentation Release 1 4 1 plot M times 0 1 second M rate 0 1 show Example PierreYger twister Pierre Yger s winning entry for the 2012 Brian twister from brian import x import numpy os pylab mmm An implementation of a simple topographical network like those used in Mehring 2005 or Yger 2011 Cells are aranged randomly on a 2D plane and connected according to a gaussian profile P r exp d 2 2 sigma 2
7. These two lines reset the clock to 0 and clear any remaining data so that memory use doesn t build up over multiple runs reinit default clock clear True EES eqs dv dt getgi v 49 mV 20 ms volt dge dt ge 5 ms volt dgi dt gi 10 ms volt P NeuronGroup 4000 eqs threshold 50 mV reset 60 x mV 3 2 Examples 85 Brian Documentation Release 1 4 1 P v 60 mV 10 mV x rand len P Pe P subgroup 3200 Pi P subgroup 800 Ce Connection Pe P ge Ci Connection Pi P gi Ce connect random Pe P 0 02 weight excitatory weight Ci connect random Pi P 0 02 weight 9 mV M SpikeMonitor P run 100 ms return M nspikes if name main Note that on Windows platforms all code that is executed rather than just defining functions and classes has to be in the if name main block otherwise it will be executed by each process that starts This isn t a problem on Linux pool multiprocessing Pool uses num cpu processes by default weights linspace 0 3 5 100 mV args w volt for w in weights results pool map how many spikes args launches multiple processes plot weights results show Example multiple_runs_with_gui multiprocessing A complicated example of using multiprocessing for multiple runs of a simulation with different parameters using a GUI to monitor and control the runs
8. This function returns an appropriate Stat eUpdater object and a list of the dynamic variables of an Equations object It uses methods of the Equations object to do this such as Equations is linear The Equations object can be constructed in various ways It can be constructed from a multi line string or by adding concatenating other Equations objects Construction by multi line string is done by pattern matching The four forms are 1 dx dt f unit differential equation 2 x f unit equation 3 x y alias 4 x unit parameter Differential equations and parameters are dynamic variables equations and aliases are just computed and substituted when necessary The f patterns in the forms above are stored for differential equations and parameters For the so lution of nonlinear equations these patterns are executed as Python code in the evaluation of the state update For example the equations dV dt V V 10xms 1landdW dt cos W 20xms Llarenumer ically evaluated with an Euler method as the following code generated from the list of dynamic variables and their defining strings V W P S V tmp W tmp P dS V tmp V V 10 ms W tmp cos W 20 ms P S dt P dS This code generation is done by the Eguations forward euler family of methods In the case where the equations are linear they are solved by a matrix exponential using the code in get linear equa
9. print table results The two remote machines would run the Playdoh server 5 7 Brian hears Brian hears is an auditory modelling library for Python It is part of the neural network simulator package Brian but can also be used on its own To download Brian hears simply download Brian Brian hears is included as part of the package Brian hears is primarily designed for generating and manipulating sounds and applying large banks of filters We import the package by writing from brian import x from brian hears import Then for example to generate a tone or a whitenoise we would write soundl tone 1 kHz 1 second sound2 whitenoise 1 second These sounds can then be manipulated in various ways for example sound soundl1 sound2 sound sound ramp If you have the pygame package installed you can also play these sounds sound play We can filter these sounds through a bank of 3000 gammatone filters covering the human auditory range as follows cf erbspace 20 Hz 20 kHz 3000 fb Gammatone sound cf output fb process 236 Chapter 5 The library Brian Documentation Release 1 4 1 The output of this would look something like this Zoomed into one region 20000 Frequency Hz 20 38 40 42 44 46 48 Time ms Alternatively if we re interested in modelling auditory nerve fibres we could feed the output of this filterbank directly into a group of neurons define
10. valuesv valuesh array M _values array Mh _values criterion 10 mV ms criterion for spike threshold for i in range N v valuesv i h valuesh i onsets spike onsets v criterion defaultclock dt criterion vc 35 mV threshold extend v onsets logh extend log h onsets log g onsets threshold array threshold mV logh array logh log 10 for display Voltage trace with spike onsets subplot 311 v valuesv 0 onsets spike onsets v criterion defaultclock dt criterion vc 35 mV t M times onsets ms plot M times ms M 0 mV k plot t v onsets mV r xlabel t ms ylabel V mV Distribution of Vm and spike onsets subplot 312 hist threshold 30 normed 1 histtype stepfilled alpha 0 6 facecolor r hist valuesv flatten mV 100 normed 1l histtype stepfilled alpha 0 6 facecolor k 38 Chapter 3 Getting started Brian Documentation Release 1 4 1 xlabel V mV xlim 80 40 Relationship between h and spike threshold subplot 313 slope intercept 3 1 54 linear regression for the prediction of threshold pl p2 min logh max logh plot logh len logh 10 threshold len logh 10 k plot pl p2 intercept slope array pl p2 10g 10 r xlabel h ylabel Threshold mvV ylim 55 40 xticks 0 10og 5e 1 10g 10 1 10g 5e 2 109g 10 1 5e 1 1e 1 5e 2 xlim 0 1 5 don t show everything show Example
11. 05 0 5 mV recurrent Connection layer2 layer2 sparseness 5 weight lateralmap spikes SpikeMonitor layer2 run l second subplot 211 raster_plot spikes subplot 223 imshow feedforward W todense interpolation nearest origin lower title Feedforward connection strengths subplot 224 imshow recurrent W todense interpolation nearest origin lower title Recurrent connection strengths show Example HodgkinHuxley misc Hodgkin Huxley model Assuming area 1 cm 2 from brian import x from brian library ionic currents import x Z defaultclock dt 01 ms more precise El 10 6 mV K 12 mV Na 120 mV qs MembraneEquation l uF leak current 3 msiemens El eqs K_current_HH 36 msiemens EK Na_current_HH 120 msiemens ENa eqs Current I amp E n 3 2 Examples 167 Brian Documentation Release 1 4 1 neuron NeuronGroup 1 eqs implicit True freeze True trace StateMonitor neuron vm record True run 100 ms neuron I 10 uA run 100 ms plot trace times ms trace 0 mV show Example spikes_io misc This script demonstrates how to save load spikes in AER format from inside Brian from brian import x HeHHA AHHH H AEE EHH AEE EEH SAVING HHIS2ATHISIATREHISHIHSRTETHHE First we need to generate some spikes N 1000 g PoissonGroup N 200 Hz A
12. 126 Chapter 3 Getting started Brian Documentation Release 1 4 1 def product xargs Simple and inefficient variant of itertools product that works for Python 2 5 directly returns a list instead of yielding one item at a time pools map tuple args result for pool in pools result x y for x in result for y in pool return result def gen_tone freq level CEE Little helper function to generate a pure tone at frequency freq with the given level The tone has a duration of 50ms and is ramped with two ramps of 2 5ms kx freq float freq Hz level float level dB return tone freq duration ramp when both duration 2 5 ms inplace False atlevel level freqs 500 1100 2000 4000 levels np arange 10 100 1 5 cf level product freqs levels steady state start 10 ms samplerate end 45 ms xsamplerate For Figure 7 we have manually adjusts the gain for different CFs otherwise the RMS values wouldn t be identical for low CFs Therefore try to estimate suitable gain values first using the lowest CF as a reference f tone gen tone freqs 0 levels 0 out reference TanCarneySignal MiddleEar ref tone gain 1 freqs 0 update interval 1 process flatten A Hoch sh Gh ref rms np sqgrt np mean F out reference start end np mean F out reference start end 2 gains np linspace 0 1 1 50 for higher CFs we need lower g
13. 3 2 Examples 73 Brian Documentation Release 1 4 1 Example params frompapers computing with neural synchrony duration selectivity Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Duration selectivity parameters from brian import x Simulation control Npulses 5000 Ntest 20 record period 15 second rest time 200 ms Encoding neurons Vt 2 55xmV Vr 70 mV El 2 35 xmV EK 90xmV Va Vr ka 5xmV gmax2 2 tauK2 300 ms N 100 number of encoding neurons Nout 30 number of decoding neurons ginh max 5 tauK spread 200 ms tau Spread 20 ms minx 1 7 range of gmax for K maxx 2 5 Coincidence detectors sigma 0 1 noise s d tau_cd 5 ms tau_n tau_cd slow noise refractory 0 ms Connections Nsynapses 5 synapses per neuron wO lambda i j rand STDP factor 0 05 a pre 06 factor b post 1l factor b pre 0 1 factor tau pre tau cd 3 2 4 frompapers computing with neural synchrony olfaction Example Fig11B olfaction stdp testing frompapers computing with neural synchrony olfaction Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 11B Learning to recognize odors Caption Fig 11B After learning responses of postsynaptic neurons ordered by tuning ratio to odor A blue and odor B red with an increasing concentration
14. brian log level debug Shows log messages only of level DEBUG or higher including INFO WARNING and ERROR levels 6 8 Logging 255 Brian Documentation Release 1 4 1 256 Chapter 6 Advanced concepts CHAPTER SEVEN EXTENDING BRIAN TODO Description of how to extend Brian add new model types and maybe at some point how to upload them to a database share with others etc For the moment see the documentation on Projects with multiple files or functions 257 Brian Documentation Release 1 4 1 258 Chapter 7 Extending Brian CHAPTER EIGHT REFERENCE For an overview of Brian see the User manual section 8 1 SciPy NumPy and PyLab See the following web sites http www scipy org Getting Started http www scipy org Documentation e http matplotlib sourceforge net matplotlib pylab html 8 2 Units system brian have same dimensions obj obj2 Tests if two scalar values have the same dimensions returns a bool Note that the syntax may change in later releases of Brian with tighter integration of scalar and array valued quantities brian is dimensionless obj Tests if a scalar value 1s dimensionless or not returns a bool Note that the syntax may change in later releases of Brian with tighter integration of scalar and array valued quantities exception brian DimensionMismatchError description dims Exception class for attempted operations with inconsistent dimensions
15. end def depress_C n len G1 248 Chapter 6 Advanced concepts Brian Documentation Release 1 4 1 m len G2 code for int i 0 i n i for int j 0 j lt m j C matrix i j depression factor rire weave inline code C matrix np mp depression factor type converters weave converters blitz compiler gcc extra compile args 03 The first time you run this it will be slower because it compiles the C code and stores a copy but the second time will be much faster as it just loads the saved copy The way it works is that Weave converts the listed Python and NumPy variables C matrix n mand depression factor into C compatible data types n and m are turned into int s depression factor is turned into a double and C matrix is turned into a Weave Array class The only thing you need to know about this is that elements of a Weave array are referenced with parentheses rather than brackets i e C_matrix i 4 rather than C matrix i j In this example I have used the gcc compiler and added the optimisation flag 03 for maximum optimisations Again in this case it s much simpler to just use the C matrix depression factor NumPy expression but in some cases using inline C might be necessary and as you can see above it s very easy to do this with Weave and the C code for a snippet like this is often almost as simple as the Python code would be 6 2 Compiled code C
16. w f write join str x for x in group number f close show Example Fig1D duration selectivity frompapers computing with neural synchrony duration selec tivity Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 1C D Duration selectivity takes about 1 min Caption Fig 1C D A postsynaptic neuron receives inputs from A and B It is more likely to fire when the stimulus in the synchrony receptive field of A and B from brian import x Parameters and equations of the rebound neurons Vt 55 mV Vr 70 mV El 2 35 xmV EK 90 mV Va Vr ka 5 mV gmax2 2 tau 20 ms ginh_max 5 tauK2 100 ms N 10000 number of neurons different durations rest_time l second initial time tmin rest_time 20 ms for plots tmax rest_time 600 ms IP eqs dv dt El v gmax gK gmax2 gK2 ginh EK v tau volt dgK dt gKinf gK tauK 1 IKLT dgK2 dt gK2 tauK2 1 Delayed rectifier gKinf 1 1 exp Va v ka 1 duration second ginh ginh max t rest time amp t rest time cduration 1 tauK ms gmax 1 theta volt 4 threshold EEF neurons NeuronGroup 2 N model eqs threshold v gt theta reset v Vr gK2 1 neurons v Vr neurons theta Vt neurons gK 1 1 exp Va El ka Neuron A duplicated to simulate multiple input durations simultaneously 72 Chapter 3 Gett
17. 1 0e9 1 0e10 tau 1 ms 50 ms print_table results Warning Windows users should read the section Important note for Windows users The model is defined by equations an Equations object reset a scalar value or a set of equations as a string and threshold a scalar value or a set of equations as a string The target spike trains are defined by data a list of pairs neuron index spike time ora list of spike times if there is only one target spike train The input is specified with input a vector containing the time varying signal and dt the time step of the signal The input variable should be I in the equations although the input variable name can be specified with input_var The number of particles per target train used in the optimization algorithm is specified with popsize The total number of neurons is popsize multiplied by the number of target spike trains The number of iterations in the algorithm is specified with maxiter Each free parameter of the model that shall be fitted is defined by two values param_name min max param_name should correspond to the parameter name in the model equations min and max specify the initial interval from which the parameter values will be uniformly sampled at the beginning of the optimization algorithm A boundary interval can also be specified by giving four values param_name bound_min min max bound_max The parameter values will be forced to stay insi
18. Brian Documentation Release 1 4 1 xlabel label for the x axis ylabel label for the y axis title title for the plot 8 13 Variable updating 8 13 1 Timed Arrays class brian TimedArray args kwds An array where each value has an associated time Initialisation arguments arr The values of the array The first index is the time index Any array shape works in principle but only 1D 2D arrays are supported other shapes may work but may not The idea is to have the shapes T or T N for T the number of time steps and N the number of neurons times A ID array of times whose length should be the same as the first dimension of arr Usually it is preferable to specify a clock rather than an array of times but this doesn t work in the case where the time intervals are not fixed clock Specify the times corresponding to array values by a clock The t attribute of the clock is the time of the first value in the array and the time interval is the dt attribute of the clock If neither times nor clock is specified a clock will be guessed in the usual way see Clock start dt Rather than specifying a clock you can specify the start time and time interval explicitly Tech nically this is useful because it doesn t create a Clock object which can lead to ambiguity about which clock is the default If dt is specified and start is not start is assumed to be 0 Note that if the clock or start time and dt of the array should be
19. Example barrelcortex synapses Late Emergence of the Whisker Direction Selectivity Map in the Rat Barrel Cortex Kremer Y Leger JF Goodman DF Brette R Bourdieu L 2011 J Neurosci 31 29 10689 700 Development of direction maps with pinwheels in the barrel cortex Whiskers are deflected with random moving bars N B network construction can be long In this version STDP is faster than in the paper so that the script runs in just a few minutes Original time 4m13 s without construction With Synapses 4m36 s from brian import x import time Uncomment if you have a C compiler set global preferences useweave True usecodegen True usecodegenweave True usenewpropagate True use tl time time PARAMETERS Neuron numbers M4 M23exc M23inh 22 25 12 side of each barrel in neurons NA N23exc N23inh M4 2 M23exc 2 M23inh 2 f neurons per barrel barrelarraysize 5 Choose 3 or 4 if memory error Nbarrels barrelarraysize 2 Stimulation stim_change_time 5 ms Fmax 5 stim_change_time maximum firing rate in layer 4 5 spike stimulation Neuron parameters taum taue taui l10 ms 2 ms 25 ms E1l 70 mV Vt vt inc tauvt 55 mV 2xmV 50 ms adaptive threshold STDP taup taud 5 ms 25x ms Ap Ad 05 04 EPSPs IPSPs EPSP IPSP 1 mV 1l mvV EPSC EPSP taue taum taum taue taum IPSC IPSP taui taum taum taui taum Ap Ad Ap EPSC Ad EPSC Mod
20. I1 0 Odor B increasing concentration for I2 in intensity exp linspace log 1 log 10 20 run 1 second report text Figure 11B spikes array S2 spikes i t n t spikes 0 spikes 1 subplot 211 Raster plot plot t n k subplot 212 Odor concentrations semilogy linspace 0 20 20 exp linspace log 1 log 10 20 b semilogy linspace 20 40 20 exp linspace 10g 1 109g 10 20 r 76 Chapter 3 Getting started Brian Documentation Release 1 4 1 plot 0 40 1 1 k show Example Fig11B olfaction stdp learning frompapers computing with neural synchrony olfaction Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 11B Learning to recognize odors long simulation Caption Fig 11B After learning responses of postsynaptic neurons ordered by tuning ratio to odor A blue and odor B red with an increasing concentration 0 1 to 10 where 1 is odor concentration in the learning phase After this script run the other file Fig11B olfaction stdp testing py from brian import x from params import x from brian experimental connectionmonitor import import numpy bmin bmax 7 1 def odor N Returns a random vector of binding constants return 10 rand N bmax bmin bmin def hill function c K 1 n 23 oF a Hill function C concentration K half activation constan
21. Index Brian Documentation Release 1 4 1 RestructureFilterbank 49 83 109 120 run 26 31 33 35 39 41 43 45 46 49 50 53 54 56 57 60 63 65 66 68 69 72 74 77 79 82 84 91 93 95 99 102 106 109 115 125 128 130 132 135 144 147 174 176 187 sequence 125 128 set default samplerate 113 114 125 126 128 set global preferences 128 silence 128 SimpleCustomRefractoriness 102 sin 108 118 166 sinh 108 118 Sound 49 83 109 114 125 126 128 spike triggered average 161 SpikeCounter 40 49 63 68 72 83 99 109 155 186 SpikeGeneratorGroup 54 63 163 168 177 179 183 184 SpikeMonitor 31 39 43 45 50 53 56 57 60 65 69 74 77 79 82 84 97 102 103 106 115 128 131 136 137 140 152 154 156 158 164 167 170 173 176 187 sqrt 50 52 60 63 99 108 111 126 StateMonitor 35 41 43 45 50 56 57 65 72 79 82 84 91 93 95 97 102 125 128 132 135 139 142 143 147 150 153 155 159 162 164 167 170 171 173 174 177 179 181 182 185 187 StateSpikeMonitor 26 STDP 31 66 77 98 106 130 stop 159 STP 131 132 Synapses 135 144 147 153 TanCarney 113 125 128 TimedArray 82 137 166 185 tone 111 115 123 125 128 VanRossumMeetric 170 whitenoise 49 83 108 109 111 113 115 117 118 120 123 124 ZhangSynapse 125 128 execute brian RemoteControlClient method 303 exp example usage 40 46 65 66 68
22. The string must be an expression which evaluates to a boolean It can contain variables from the neuron group units and any variable defined in the namespace e g tau as for equations Be aware that if a variable in the namespace has the same name as a neuron group variable then it masks the neuron variable The way it works is that the expression is evaluated with the neuron variables replaced by their vector values values for all neurons so that the expression returns a boolean vector 194 Chapter 4 User manual Brian Documentation Release 1 4 1 Functional threshold The generic method to define a custom threshold condition is to pass a function of the state variables which returns a boolean true if the threshold condition is met for example eqs p dv dt v tau volt dw dt v w tau volt EXE group NeuronGroup 100 model eqs reset 0 mV threshold lambda v w v gt w Here we used an anonymous function 1ambda keyword but of course a named function can also be used In this example spikes are generated when v is greater than w Note that the arguments of the function must be the state variables with the same order as in the Equations string Thresholding another variable It is possible to specify the threshold variable explicitly group NeuronGroup 100 model eqs reset 0 mV threshold Threshold 0xmV state w Here the variable w is checked Using another variable as the threshold value The same
23. The three arguments are the number of repeats before joining the joining type serial or interleave and the number of tilings after joining See below for details Initialise arguments source Input source or list of sources numrepeat 1 Number of times each channel in each of the input sources is repeated before mixing the source channels For example with repeat 2 an input source with channels AB will be repeated to form AABB type serial The method for joining the source channels the options are serial to join the channels in series or interleave to interleave them In the case of interleave each source must have the same number of channels An example of serial if the input sources are abc and def the output would be abcdef For interleave the output would be adbecf numtile 1 The number of times the joined channels are tiled so if the joined channels are ABC and numtile 3 the output will be ABCABCABC indexmapping None Instead of specifying the restructuring via numrepeat type numtile you can directly give the mapping of input indices to output indices So for a single stereo source input indexmapping 1 0 would reverse left and right Similarly with two mono sources indexmapping 1 0 would have channel 0 of the output correspond to source and channel 1 of the output corresponding to source 0 This is because the indices are counted in order of channels starting from the first source and continu
24. You can access an HRTF by index via hrtfset index or by its coordinates via hrtfset coordl vall coord2 val2 Initialisation data An array of shape 2 num indices num samples where data 0 is the left ear and data 1 is the right ear num indices is the number of HRTFs for each ear and num samples is the length of the HRTF samplerate The sample rate for the HRTFs should have units of Hz coordinates A record array of length num indices giving the coordinates of each HRTF You can use make coordinates to help with this class brian hears HRTFDatabase samplerate None Base class for databases of HRTFs Should have an attribute subjects giving a list of available subjects and a method load_subject subject which returns an HRTFSet for that subject The initialiser should take optional keywords samplerate The intended samplerate resampling will be used if it is wrong If left unset the natural samplerate of the data set will be used brian hears make_coordinates kwds Creates a numpy record array from the keywords passed to the function Each keyword value pair should be the name of the coordinate the array of values of that coordinate for each location Returns a numpy record array For example coords make coordinates azimuth 0 30 60 0 30 60 elevation 0 0 0 30 30 30 print coords azimuth class brian hears IRCAM_LISTEN basedir compensated False samplerate N
25. brian experimental codegen2 statements from codestring code eqs None defined None in fer_definitions False Generate a list of statements from a user defined string code The input code string a multi line string which should be flat no indents eqs A Brian Equations object which is used to specify a set of already defined variable names if you are using infer_definitions defined A set of symbol names which are already defined if you are using infer_definitions infer definitions Set to True to guess when a line of the form a b should be inferred to be of type a b as user specified code may not make the distinction between a b and a b The rule for definition inference is that you scan through the lines and a set of already defined symbols is maintained starting from eqs and defined if provided and an op is changed to if the name on the LHS is not already in the set of symbols already defined brian experimental codegen2 c data type dtype Gives the C language specifier for numpy data types For example numpy int32 maps to int32 t inC Perhaps this method is given somewhere in numpy but I couldn t find it stateupdater class brian experimental codegen2 CodeGenStateUpdater group method language clock None State updater using code generation supports Python C GPU Initialised with group The NeuronGroup that this will be used in 378 Chapter 11 Developer s guide Brian Documentat
26. legend show class brian RecentStateMonitor P varname duration 5 0 msecond clock None record True timestep 1 when end StateMonitor that records only the most recent fixed amount of time Works in the same way as a Stat eMonitor except that it has one additional initialiser keyword duration which gives the length of time to record values for the record keyword defaults to True instead of False and there are some different or additional attributes values values_ times times_ These will now return at most the most recent values over an interval of maximum time duration These arrays are copies so for faster access use unsorted_values etc unsorted values unsorted values unsorted times unsorted times The raw ver sions of the data the associated times may not be in sorted order and if duration hasn t passed not all the values will be meaningful current time index Says which time index the next values to be recorded will be stored in varies from 0 to M 1 has looped Whether or not the current time index has looped from M back to 0 can be used to tell whether or not every value in the unsorted values array is meaningful or not they will only all be meaningful when has looped True i e after time duration 8 11 Monitors 293 Brian Documentation Release 1 4 1 The getitem method also returns values in sorted order To plot do something like plot M times M values il class brian AERSp
27. myconnection_fast Connection groupl group2 ge delay l ms myconnection_slow Connection groupl group2 ge delay 5 ms For a highly heterogeneous set of delays initialise the connection with delay True set a maximum de lay with for example max delay 5xms and then use the delay keyword in the connect random and connect full methods myconnection Connection groupl group2 ge delay True max_delay 5 ms myconnection connect_full group1l group2 weight 3 nS delay 0 ms 5xms The code above initialises the delays uniformly randomly between Oms and 5ms You can also set delay to be a function of no variables where it will be called once for each synapse or of two variables i j where it will be called once for each row as in the case of the weights in the section above Alternatively you can set the delays as follows myconnection delay i j 3 ms See the reference documentation for Connection and DelayConnection for more details 4 3 Connections 197 Brian Documentation Release 1 4 1 4 3 3 Connection structure The underlying data structure used to store the synaptic connections is by default a sparse matrix If the connections are dense it is more efficient to use a dense matrix which can be set at initialisation time myconnection Connection groupl group2 ge structure dense The sparse matrix structure is fixed during a run new synapses cannot be added or delet
28. run the simulation Remember that the controler are at th nd of the chain and the output of the whole path comes from them signal control process figure imshow flipud signal T aspect auto show Example gammatone hears Example of the use of the class Gammat one available in the library It implements a fitlerbank of IIR gammatone filters as described in Slaney M 1993 An Efficient Implementation of the Patterson Holdsworth Auditory Filter Bank Apple Computer Technical Report 35 In this example a white noise is filtered by a gammatone filterbank and the resulting cochleogram is plotted from brian import x from brian hears import x from matplotlib import pyplot sound whitenoise 100 ms ramp sound level 50 dB nbr_center_frequencies 50 bl 1 019 factor determining the time constant of the filters center frequencies with a spacing following an ERB scale center_frequencies erbspace 100 Hz 1000 Hz nbr_center_frequencies gammatone Gammatone sound center frequencies b b1 gt mon gammatone process figure imshow gt mon T aspect auto origin lower left extent 0 sound duration ms center frequencies 0 center frequencies 1 pyplot yscale log title Cochleogram ylabel Frequency Hz xlabel Time ms show Example cochleagram hears Example of basic filtering of a sound with Brian hears This example imp
29. state updates This step might be avoided and replaced by eval calls It might actually be a little simpler because arguments would be replaced by namespace It seems to be faster with the current implementation but the string could be compiled with compile then evaluated in the relevant namespace Besides with the way it is currently evaluated in the Euler update S var for var in f func code co varnames itis not faster than direct evaluation in the namespace 356 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 Checking units This is done by the check_units method First the static equations are ordered see next section To check the units of a static equation one calls the associated function giving the RHS where the arguments are units e g 1 volt for v etc and adds the units of the LHS A dimension error is raised if it is not homogeneous Cur rently the message states The differential equation is not homogeneous but it should be adapted to non differential equations One problem with this way of checking units is that the RHS function may not be defined at the point it is checked Differential equations are checked in the same way with two specificities the units of RHS should be the units of the variable divided by second dx dt and noise xi has units of second 5 this is put in the globals of the function which might not be a very clean way to do it Ordering static
30. swapped channels which means repeating them num indices times first hrtfset fb hrtfset filterbank Repeat swapped channels num indices Now we apply cochlear filtering logically this comes before the HRTF filtering but since convolution is commutative it is more efficient to 3 2 Examples 49 Brian Documentation Release 1 4 1 do the cochlear filtering afterwards cfmin cfmax cfN 150 Hz 5 kHz 40 cf erbspace cfmin cfmax cfN We repeat each of the HRTFSet filterbank channels cfN times so that for each location we will apply each possible cochlear frequency gfb Gammatone Repeat hrtfset_fb cfN tile cf hrtfset_fb nchannels Half wave rectification and compression cochlea FunctionFilterbank gfb lambda x 15 clip x 0 Inf 1 0 3 0 Leaky integrate and fire neuron model eqs dv dt I V 1xms 0 1 xi 0 5xms x x 5 1 de ey d CEF G FilterbankGroup cochlea I eqs reset 0 threshold 1 refractory 5 ms The coincidence detector cd neurons cd NeuronGroup num indices cfN qs reset 0 threshold 1 clock G clock Each CD neuron receives precisely two inputs one from the left ear and one from the right for each location and each cochlear frequency C Connection G cd V for i in xrange num indices cfN C i i 0 5 from right ear C i num indices cfN i 0 5 from left ear We want to just count the number of CD spikes counter SpikeCounter cd
31. xkwds which returns a Connect ionMat rix object of the appropriate type class brian DenseConstructionMatrix val kwds Dense construction matrix Essentially just numpy ndarray The connection matrix method returns a DenseConnectionMatrix object The setitem method is overloaded so that you can set values with a sparse matrix class brian SparseConstructionMatrix arg kwds SparseConstructionMatrix is converted to SparseConnectionMatrix class brian DynamicConstructionMatrix arg kwds DynamicConstructionMatrix is converted to DynamicConnectionMatrix 8 7 3 Connection vector types class brian ConnectionVector Base class for connection vectors just used for defining the interface Connection Vector objects are returned by ConnectionMatrix objects when they retrieve rows or columns At the moment there are two choices sparse or dense This class has no real function at the moment class brian DenseConnectionVector Just a numpy array class brian SparseConnectionVector Sparse vector class A sparse vector is typically a row or column of a sparse matrix This class can be treated in many cases as if it were just a vector without worrying about the fact that it is sparse For example if you write 2 v it will evaluate to a new sparse vector There is one aspect of the semantics which is potentially confusing In a binary operation with a dense vector such as sv dv where sv is sparse and dv is dense the result will be a
32. 44 Chapter 3 Getting started Brian Documentation Release 1 4 1 zeros len spikes b title s d spikes second uncorrelated inputs correlated inputs i len M spiketimes i show Example Diesmann et al 1999 frompapers Synfire chains M Diesmann et al 1999 Stable propagation of synchronous spiking in cortical neural networks Nature 402 529 533 from brian import x Neuron model parameters Vr 70 mV Vt 55 mV taum 10 ms taupsp 0 325 ms weight 4 86 mV Neuron model eqs Equations dV dt V Vr x 1 taum volt dx dt x y x 1 taupsp volt dy dt y 1 taupsp 25 27 mV ms N 39 24 mV msxx0 5 xi volt pee Neuron groups P NeuronGroup N 1000 model eqs threshold Vt reset Vr refractory 1 ms Pinput PulsePacket t 50 ms n 85 sigma 1 ms The network structure Pgp P subgroup 100 for i in range 10 C Connection P P y for i in range 9 C connect full Pgp i Pgp i 1 Cinput Connection Pinput Pgp 0 Cinput connect full weight weight Record the spikes Mgp SpikeMonitor p for p in Pgp Minput SpikeMonitor Pinput monitors Minput Mgp Setup the network and run it P V Vr rand len P Vt Vr run 100 ms Plot result raster plot showgrouplines True monitors show weight y Example Wang Buszaki 1996 frompapers W
33. 60 mV EK 90 mV ENa 50 mV g_na 100 msiemens cm 2 area g kd 30 msiemens cm x 2 area VT 63 mV Time constants taue 5 ms taui 10 ms Reversal potentials Ee 0 mV Ei 80 mV we 6 x nS excitatory synaptic weight voltage wi 67 x nS inhibitory synaptic weight The model eqs Equations dv dt gl El v gex Ee v gix Ei v g na m mxm h v ENa N g_kd n xn n n v EK Cm volt dm dt alpham 1 m betam m 1 dn dt alphan 1 n betan n 1 dh dt alphahx 1 h betah h 1 dge dt gex 1 taue siemens dgi dt gix 1 taui siemens alpham 0 32 mV 1 13 mV v VT exp 13 mV v VT 4 mV 1 ms Hz betam 0 28 mV x 1 v VT 40xmV exp v VT 40xmV 5xmV 1 ms Hz alphah 0 128 exp 17 mV v4VT 18xmV ms Hz betah 4 1 exp 40 mV v VT 5 mV ms Hz alphan 0 032 mV x 1 15 mV v VT exp 15 mV v VT 5 mV 1 ms Hz betan 5xexp 10 mV v VT 40 mV ms Hz PES P NeuronGroup 4000 model eqs threshold EmpiricalThreshold threshold 20 mV refractory 3 ms implicit True freeze True Pe P subgroup 3200 P subgroup 800 Connection Pe P ge weight we sparseness 0 02 C Connection Pi P gi weight wi sparseness 0 02 Initialization P v El randn len P 5 5 mV P P Q U HO H
34. A few simple synaptic models are implemented in the module synapses from brian library synapses import All the following functions need to be passed the name of the variable upon which the received spikes will act and the name of the variable representing the current or conductance The simplest one is the exponential synapse eqs exp_synapse input x tau 10 ms unit amp output x_current It is equivalent to eqs Equations dx dt x tau amp X out x FEY Here x is the variable which receives the spikes and x current is the variable to be inserted in the membrane equation since it is a one dimensional synaptic model the variables are the same If the output variable name is not defined then it will be automatically generated by adding the suffix out to the input name Two other types of synapses are implemented The alpha synapse x t alphax t tau exp 1 t tau where alpha is a normalising factor is defined with the same syntax by eqs alpha_synapse input x tau 10 ms unit amp and the bi exponential synapse is defined by x t tau2 tau2 taul exp t taul exp t tau2 up to a normalising factor eqs biexp_synapse input x taul 10 ms tau2 5 ms unit amp For all types of synapses the normalising factor is such that the maximum of x t is 1 These functions can be used as in the following example 5 1 Library models 225 Brian Documentation Re
35. Ce 0 1 x ms Re eqs Equations dvm dt glxvm i inj Cm volt I amp edd qs electrode 6 Re Ce eqs current clamp vm v el i inj i cmd i cmd I Re 4 Re Ce Ce setup NeuronGroup 1 model eqs clock myclock board AEC setup v rec I clock rec recording StateMonitor board record record True clock myclock soma StateMonitor setup vm record True clock myclock 96 Chapter 3 Getting started Brian Documentation Release 1 4 1 run 50 ms board command 5 nA run 200 ms board command 0 nA run 150 ms board start_injection tl time run l second t2 time print Duration t2 tl 7e board stop injection run 100 ms board estimate print Re sum board Ke ohm board switch_on run 50 ms board command 5 nA run 200 ms board command 0 nA run 150 ms board switch off figure plot recording times ms recording 0 mV b plot soma times ms soma 0 mV r figure plot board Ke show 3 2 9 twister Example QuentinPauluis twister Quentin Pauluis s entry for the 2012 Brian twister from brian import x taum 20 ms membrane time constant taue 5 ms excitatory synaptic time constant taui 10 ms inhibitory synaptic time constant Vt 50 mV spike threshold Vr 60 mV reset value El 49 mV rest
36. SpikeGeneratorGroup N spiketimes where N is the number of neurons in the group and spiketimes is a list of pairs i t indicating that neuron i should fire at time t In fact spiketimes can be any iterable container or generator but we don t cover that here see the detailed documentation for 5pikeGeneratorGroup In our case we want to create a group with two neurons the first of which neuron 0 fires at times 1 ms and 4 ms and the second of which neuron 1 fires at times 2 ms and 3 ms The list of spiketimes then is spiketimes 0 1 ms 0 4 ms 1 2 ms 1 3 x ms and we create the group as follows Gl SpikeGeneratorGroup 2 spiketimes Now we create a second group with one neuron according to the model we defined earlier G2 NeuronGroup N 1 model eqs threshold Vt reset Vr Connections In Brian a Connection from one NeuronGroup to another is defined by writing C Connection G H state Here G is the source group H is the target group and st ate is the name of the target state variable When a neuron i in G fires Brian finds all the neurons j in H that i in Gis connected to and adds the amount C i j to the specified state variable of neuron j in H Here C i j is the i j th entry of the connection matrix of C which is initially all zero To start with we create two connections from the group of two directly controlled neurons to the group of one neuron with th
37. ax None The axis to set or uses gca if None freqs None Override the default frequency locations with your preferred tick locations See also 10g frequency yaxis labels Note with log scaled axes it can be useful to call axis tight before setting the ticks 328 Chapter 8 Reference Brian Documentation Release 1 4 1 brian hears log frequency yaxis labels ax None freqs None Sets tick positions for log scale frequency x axis at sensible locations Also uses scalar representation rather than exponential i e 100 rather than 10 2 ax None The axis to set or uses gca if None freqs None Override the default frequency locations with your preferred tick locations See also 1og frequency yaxis labels Note with log scaled axes it can be useful to call axis tight before setting the ticks 8 21 8 HRTFs class brian hears HRITF hrir l hrir_r None Head related transfer function Attributes impulse response The pair of impulse responses as stereo Sound objects fir The impulse responses in a format suitable for using with FIRFilterbank the transpose of impulse response left right The two HRTFs mono Sound objects samplerate The sample rate of the HRTFs Methods apply sound Returns a stereo Sound object formed by applying the pair of HRTFs to the mono sound input Equiva lently you can write hrt f sound for hrtf an HRTF object filterbank source kwds Returns an FIRFilterb
38. brian experimental codegen2 GPUManager method 374 run brian experimental codegen2 PythonCode method 370 example usage 125 128 sound 239 sequence brian hears Sound static method 313 sequence in module brian hears 316 set brian RemoteControlClient method 303 set default samplerate example usage 113 114 125 126 128 set default samplerate in module brian hears 311 set dt brian Clock method 262 set duration brian Clock method 262 set end brian Clock method 262 set global preferences example usage 128 set global preferences in module brian 254 set group var by array in module brian 299 set t brian Clock method 262 shifted brian hears Sound method 313 silence example usage 128 silence brian hears Sound static method 312 silence in module brian hears 316 SimpleCustomRefractoriness example usage 102 SimpleCustomRefractoriness class in brian 267 SimpleFunThreshold class in brian 269 simulation control 213 update schedule 213 sin example usage 108 118 166 sinh example usage 108 118 SliceIndex class in brian experimental codegen2 381 Sound example usage 49 83 109 114 125 126 128 sound 239 aiff 239 dB 240 316 398 Index Brian Documentation Release 1 4 1 decibel 316 level 240 316 multiple channels 240 sequence 239 stereo 240 wav 239 Sound class in brian hears 311 source brian hears
39. class brian IdentityConnection args kwds A Connection between two groups of the same size where neuron i in the source group is connected to neuron i in the target group Initialised with arguments source target The source and target NeuronGroup objects state The target state variable weight The weight of the synapse must be a scalar delay Only homogeneous delays are allowed The benefit of this class is that it has no storage requirements and is optimised for this special case 8 7 1 Connection matrix types class brian ConnectionMatrix Base class for connection matrix objects Connection matrix objects support a subset of the following methods get row i get col i Returns row col i as a DenseConnectionVector Or SparseConnectionVector as appropriate for the class set row i val set col i val Sets row col with an array DenseConnectionVector or SparseConnectionVector if supported get element i j set element i j val Gets or sets a single value get_rows rows Returns a list of rows should be implemented without Python function calls for efficiency if possible get cols cols Returns a list of cols should be implemented without Python function calls for efficiency if possible insert i j x remove i j For sparse connection matrices which support it insert a new entry or remove an existing one getnnz Return the number of nonzero entries todense Return the matrix as a dense array The
40. eqs current_clamp vm v_el i inj i comd bridge Re capa_comp CC setup NeuronGroup N model eqs setup I 0 nA setup v 0 x mV setup Rbridge linspace 0 Mohm 60 Mohm N setup CC linspace 0 Ce Ce N recording StateMonitor setup v rec record Tru run 50 ms setup I 5 nA run 200 ms setup I 0 nA run 150 ms for i in range N plot recording times ms i 400 recording i show Example SEVC electrophysiology Voltage clamp experiment SEVC from brian import x from brian library electrophysiology import x i cmd I Re 4 Re Ce Ce mV k 3 2 Examples 91 Brian Documentation Release 1 4 1 defaultclock dt 01 ms taum 20 ms membrane time constant gl 1 50 Mohm leak conductance Cm taum gl membrane capacitance Re 50 Mohm electrode resistance Ce 0 1 ms Re electrode capacitance eqs Equations dvm dt gl vmti_inj Cm volt I amp PARES eqs current clamp i cmd I Re Re Ce Ce setup NeuronGroup 1 model eqs ampli SEVC setup v rec I 1 kHz gain 250 nS gain2 50 nS ms recording StateMonitor ampli record record True soma StateMonitor setup vm record True ampli command 20 mV run 200 ms figure plot recording times ms recording 0 nA k figure plot soma times ms soma 0 mV
41. for i in range len groupl for j in range len group2 myconnection i j 1 cos i j 2 nS but it is much faster because the construction is vectorised i e the function is called for every i with j being the entire row of target indexes Thus the implementation is closer to for i in range len groupl myconnection i j 1 cos i arange len group2 2 nS The method connect random also accepts functional arguments for the weights and connection probability For that method it is possible to pass a function with no argument as in the following example myconnection connect random groupl group2 0 1 weight lambda rand nS Here each synaptic weight is random between 0 and 1 nS Alternatively the connection probability can also be a function e g myconnection connect random groupl group2 0 1 weight 1 nS sparseness lambda i j exp abs i j 1 The weight or the connection probability may both be functions with 0 or 2 arguments 4 3 2 Delays Transmission delays can be introduced with the keyword delay passed at initialisation time There are two types of delays homogeneous all synapses have the same delay and heterogeneous all synapses can have different delays The former is more computationally efficient than the latter An example of homogeneous delays myconnection Connection groupl group2 ge delay 3 ms If you have limited heterogeneity you can use several Connection objects e g
42. print Network construction time time time start time seconds print len P neurons in the network print Simulation running run l msecond start_time time time run l second duration time time start_time print Simulation time duration seconds print Me nspikes excitatory spikes print Mi nspikes inhibitory spikes plot M times ms M smooth_rate 2 ms gaussian show Example gap_junctions misc Network of noisy IF neurons with gap junctions from brian import x N 300 v0 5 x mV tau 20 ms sigma 5 mV vt 10 mV vr 0 mV g_gap 1 N beta 60 mV 2 ms delta vt vr eqs TEF dv dt v0 v taut tg_gaps u N v tau volt du dt N v0 u tau volt input from other neurons COE def myreset P spikes P v spikes vr reset P v g gap beta len spikes spike effect P u delta len spikes group NeuronGroup N model eqs threshold vt reset myreset Qnetwork operation def noise cl 3 2 Examples 173 Brian Documentation Release 1 4 1 x randn N sigma cl dt tau 5 group v x group u sum x trace StateMonitor group v record 0 1 spikes SpikeMonitor group rate PopulationRateMonitor group run l second subplot 311 raster_plot spikes subplot 312 plot trace times ms trace 0 plot trace times ms trace 1 subplot 313 plot rate
43. update namespace brian experimental codegen2 ArraySymbol method 381 update namespace brian experimental codegen2 Symbol method 380 V values brian StateSpikeMonitor method 291 VanRossumMetric example usage 170 VanRossumMetric class in brian 295 variable reset 266 threshold 268 VariableReset class in brian 266 VariableThreshold class in brian 268 vectorisation 247 efficient code 247 vowel brian hears Sound static method 313 W wav sound 239 white noise 264 whitenoise example usage 49 83 108 109 111 113 115 117 118 120 123 124 whitenoise brian hears Sound static method 312 whitenoise in module brian hears 315 word substitute n brian experimental codegen2 371 Write class in brian experimental codegen2 371 write brian experimental codegen2 ArraySymbol method 381 write brian experimental codegen2 Symbol method 380 brian experimental codegen2 ArraySymbol method 381 module write_c to matrix brian synapses synapticvariable S ynaptic Variablerite python brian experimental codegen2 ArraySymbol method 284 method 381 to sympy expression brian experimental model_documentation DocumentWriter static method 342 tone example usage 111 115 123 125 128 tone brian hears Sound static method 312 tone in module brian hears 315 total correlation in module brian 300 U Unit class in brian 260 unit tes
44. 0 0 sin w0 2 filt_b 1 0 0 filt_b 2 0 sin w0 2 filt a 0 0 ltalpha filt a 1 0 2xcos w0 filt a 2 0 1 alpha the filter which will have time varying coefficients bandpass filter LinearFilterbank sound filt b filt a the updater 3 2 Examples 119 Brian Documentation Release 1 4 1 updater CoeffController bandpass filter the controller Remember it must be the last of the chain control ControlFilterbank bandpass filter fc generator bandpass filter updater update interval time varying filter mon control process figure 1 pxx freqs bins im specgram squeeze time varying filter mon NFFT 256 Fs samplerate noverlap 240 imshow flipud pxx aspect auto show Example ircam_hrtf hears Example showing the use of HRTFs in Brian hears Note that you will need to download the IRCAM_LISTEN database from brian import x from brian hears import Load database hrtfdb IRCAM_LISTEN r F HRTF IRCAM hrtfset hrtfdb load_subject 1002 Select only the horizontal plane hrtfset hrtfset subset lambda elev elev 0 Set up a filterbank sound whitenoise 10 ms fb hrtfset filterbank sound Extract the filtered response and plot img fb process T img_left img img shape 0 2 img right img img shape 0 2 subplot 121 imshow img left origin lower left aspect auto extent 0 soun
45. 1000993 Techniques for online computation are discussed below in the section Online computation Brian hears consists of classes and functions for defining sounds filter chains cochlear models neuron models and head related transfer functions These classes are designed to be modular and easily extendable Typically a model will consist of a chain starting with a sound which is plugged into a chain of filter banks which are then plugged into a neuron model The two main classes in Brian hears are Sound and Filterbank which function very similarly Each consists of multiple channels typically just 1 or 2 in the case of sounds and many in the case of filterbanks but in principle any number of channels is possible for either The difference is that a filterbank has an input source which can be either a sound or another filterbank All scripts using Brian hears should start by importing the Brian and Brian hears packages as follows from brian import x from brian hears import x 238 Chapter 5 The library Brian Documentation Release 1 4 1 To download Brian hears simply download Brian Brian hears is included as part of the package See Also Reference documentation for Brian hears which covers everything in this overview in detail and more List of examples of using Brian hears 5 7 1 Sounds Sounds can be loaded from a WAV or AIFF file with the 1 oadsound function and saved with the savesound function or Soun
46. 20xms would correspond to bins with intervals 0 10ms 10 20ms and 20 ms Has properties bins The bins array passed at initialisation count An array of length len bins counting how many ISIs were in each bin This object can be passed directly to the plotting function hist plot class brian PopulationRateMonitor source bin None Monitors and stores the time varying population rate 294 Chapter 8 Reference Brian Documentation Release 1 4 1 Initialised as PopulationRateMonitor source bin Records the average activity of the group for every bin Properties rate rate_ An array of the rates in Hz times times_ The times of the bins bin The duration of a bin in second class brian VanRossumMet ric source tau 2 0 msecond van Rossum spike train metric From M van Rossum 2001 A novel spike distance Neural Computation Compute the van Rossum distance between every spike train from the source population Arguments source The group to compute the distances for tau Time constant of the kernel low pass filter Has one attribute distance A square symmetric matrix containing the distances class brian CoincidenceCounter source data spiketimes_offset None spikedelays None coin cidence_count_algorithm exclusive onset None delta 4 0 msecond Coincidence counter class Counts the number of coincidences between the spikes of the neurons in the network model spikes a
47. 314 ramped brian hears Sound method 314 raster plotting 296 raster plot example usage 31 39 45 56 60 79 82 84 97 102 106 115 131 136 137 140 152 154 156 159 160 162 164 167 170 173 176 178 185 187 raster_plot in module brian 296 Read class in brian experimental codegen2 371 read brian experimental codegen2 Symbol method 379 read atf in module brian 302 read neuron dat in module brian 302 RealtimeConnectionMonitor class in brian experimental realtime monitor 341 recall in module brian 289 RecentStateMonitor example usage 99 160 174 RecentStateMonitor class in brian 293 Refractoriness example usage 170 prepare gpu func brian experimental codegen2 GPUKerrg fractoriness class in brian 266 method 372 print table in module brian library modelfitting 306 process brian hears Filterbank method 332 progress reporting 304 ProgressReporter class in brian utils progressreporting 304 refractory 266 RegularClock class in brian 262 reinit example usage 63 reinit brian Clock method 261 reinit in module brian 288 reinit default clock propagate brian experimental codegen2 CodeGenConnection example usage 43 54 128 168 method 370 PSO class in brian library modelfitting 307 pulse packet 271 PulsePacket example usage 45 140 183 PulsePacket class in brian 271 pylab plotting 189 210 259 296 PythonCode class
48. 315 53 54 56 57 60 63 65 66 68 69 72 74 TT plot brian StateMonitor method 292 79 82 84 91 93 95 99 102 106 109 130 plotting 210 296 132 135 144 147 160 162 164 167 169 histogram 297 174 177 182 184 187 pylab 189 210 259 296 NeuronGroup class in brian 264 raster 296 NeuronGroupStateVariableSymbol class in poisson brian experimental codegen2 381 group 270 396 Index Brian Documentation Release 1 4 1 input 270 PoissonGroup example usage 46 99 130 131 135 136 139 142 144 151 157 158 161 162 165 167 168 176 177 180 PoissonGroup class in brian 270 PoissonInput example usage 43 PoissonInput class in brian 270 PoissonThreshold example usage 160 186 PopulationRateMonitor example usage 39 54 98 102 130 131 141 143 151 152 160 165 172 173 181 183 PopulationRateMonitor class in brian 294 PopulationSpikeCounter example usage 141 156 162 172 PopulationSpikeCounter class in brian 291 powerlawnoise brian hears Sound static method 312 powerlawnoise in module brian hears 315 precompute offsets brian SpikeQueue method 285 predict in module brian library modelfitting 307 preferences 254 prepare brian experimental codegen2 GPUKernel method 372 brian experimental codegen2 GPUManager method 373 prepare array 260 Quantity class in brian 260 R ramp brian hears Sound method
49. Decoder neurons M 200 taud 8 ms sigma 15 eq_decoders dv dt v taud sigmax 2 taud 5 xi 1 CF decoders NeuronGroup 2 M model eq_decoders threshold 1 reset 0 First M neurons encode odor A next M neurons encode odor B Synapses syn Connection receptors decoders v Connectivity according to synchrony partitions bhalf 5 bmint tbmax select only those that are well activated u 2 x log cl1 log 10 bhalf bmax bmin normalized binding constants for odor A for i in range M which u gt i l M amp u lt itl 1 M we divide in M groups with similar values if sum which gt 0 w 1 sum which total synaptic weight for a postsynaptic neuron is 1 syn i w xwhich u 2 log c2 log 10 bhalf bmax bmin for i in range M normalized binding constants for odor B which u gt i l M amp u i 1 x 1 M if sum which gt 0 w 1 sum which syn 2 M 1 1i w which Record odor concentration and output spikes O StateMonitor plume y record True S SpikeMonitor receptors S2 SpikeMonitor decoders print Odor A I1 12 intensity 0 run 2 second print Odor B I1 12 0 intensity run 2 second 80 Chapter 3 Getting started Brian Documentation Release 1 4 1 print Odor B x2 I1 1220 2x intensity run 2 second print Odor A odor C Il I2 intensity intensity old c2 2c2 c2 odor N different odor run 2 second print Odor A
50. Example jeffress synapses Jeffress model adapted with spiking neuron models A sound source white noise is moving around the head Delay differences between the two ears are used to determine the azimuth of the source Delays are mapped to a neural place code using delay lines each neuron receives input from both ears with different delays 3 2 Examples 137 Brian Documentation Release 1 4 1 Romain Brette from brian import from time import time defaultclock dt 02 ms dt defaultclock dt Sound sound TimedArray 10 randn 50000 white noise Ears and sound motion around the head constant angular speed sound speed 300 metre second interaural distance 20 cm big head max delay interaural distance sound speed print Maximum interaural delay max delay angular speed 2 pi x radian second 1 turn second tau ear 1 x ms Sigma ear 1 eqs ears dx dt sound t delay x tau eartsigma ear 2 tau ear x 5 xxi 1 delay distancexsin theta second distance second distance to the centre of the head in time units dtheta dt angular_speed radian CFE ears NeuronGroup 2 model eqs_ears threshold 1 reset 0 refractory 2 5 ms ears distance 5 max delay 5 max delay traces StateMonitor ears x record True Coincidence detectors N 300 tau 1 ms sigma 1 yer eqs neurons dv dt v tautsigmax 2 tau 5
51. If there is only one variable or if you have a variable named one of V Vm v or vm it will be used If reset is a string it should be a series of expressions which 264 Chapter 8 Reference Brian Documentation Release 1 4 1 are evaluated for each neuron that is resetting The series of expressions can be multiline or separated by a semicolon For example reset Vt 5 mV V Vt Statements involving if constructions will often not work because the code is automatically vectorised For such constructions use a function instead of a string refractory 0 ms min_refractory max_refractory A refractory period used in combination with the reset value if it is a scalar For constant resets only you can specify refractory as an array of length the number of elements in the group or as a string giving the name of a state variable in the group In the case of these variable refractory periods you should specify min_refractory optional and max_refractory required level 0 See Equations for details clock A clock to use for scheduling this NeuronGroup if omitted the default clock will be used order 1 The order to use for nonlinear differential equation solvers TODO more details implicit False Whether to use an implicit method for solving the differential equations TODO more details max_delay 0 ms The maximum allowable delay larger values use more memory This doesn t usually need to be specified because Connections
52. Lansner Rochel Vibert Alvarez Muller Davison El Boustani and Destexhe Journal of Computational Neuroscience 23 3 349 98 Benchmark 2 random network of integrate and fire neurons with exponential synaptic currents Clock driven implementation with exact subthreshold integration but spike times are aligned to the grid R Brette Oct 2007 Brian is a simulator for spiking neural networks written in Python developed by R Brette and D Goodman http brian di ens fr from brian import x import time start_time time time taum 20 ms taue 5 ms taui 10 x ms Vt 50 mV Vr 60 mV El 49 x mV eqs Equations dv dt getgi v El taum volt dge dt ge tau volt dgi dt gi taui volt em P NeuronGroup 4000 model eqs threshold Vt P v Vr P ge 0 mV P gi 0 x mV Pe P subgroup 3200 Pi P subgroup 800 as reset Vr refractory 5 ms 172 Chapter 3 Getting started Brian Documentation Release 1 4 1 we 60 0 27 10 mV excitatory synaptic weight voltage wi 20 4 5 10 mV inhibitory synaptic weight Ce Connection Pe P ge weight we sparseness 0 02 Ci Connection Pi P gi weight wi sparseness 0 02 P v Vr rand len P Vt Vr Record the number of spikes Me PopulationSpikeCounter Pe Mi PopulationSpikeCounter Pi A population rate monitor M PopulationRateMonitor P
53. Plot result raster plot showgrouplines True monitors show DEFAULT PARAMATERS FOR SYNFIRE CHAIN Approximates those in Diesman et al 1999 model params Parameters Simulation parameters dt 0 1 ms duration 100 x ms Neuron model parameters taum 10 ms taupsp 0 325 ms Vt 55 x mV Vr 70 mV abs refrac 1 x ms we 34 7143 wi 34 7143 psp peak 0 14 mV Noise parameters noise neurons 20000 noise exc 0 88 noise inh 0 12 noise exc rate 2 Hz noise inh rate 12 5 Hz computed model parameters noise mu noise neurons noise exc noise exc rate noise inh noise inh rate psp peak noise sigma noise neurons noise exc noise exc rate noise inh noise inh rate 5 x mmm MODEL FOR SYNFIRE CHAIN Excitatory PSPs only def Model p equations Equations dV dt V p Vr x 1 p taum dx dt x y x x 1 p taupsp dy dt yx 1 p taupsp 25 27 mV ms 39 24 mV ms 0 5 xi rrt return Parameters model equations threshold p Vt default_params Parameters Network parameters num_layers 10 reset p Vr volt VOLE volt refractory p abs_refrac 28 Chapter 3 Getting started Brian Documentation Release 1 4 1 neurons_per_layer 100 neurons_in_input_layer 100 Initiating burst parameters initial_burst_t 50 ms initial_burst_a 85 initial burst sigma 1 ms these values are rec
54. Python is a fast language but each line of Python code has an associated overhead attached to it Sometimes you can get considerable increases in speed by writing a vectorised version of it A good guide to this in general is the Performance Python page Here we will do a single worked example in Brian Suppose you wanted to multiplicatively depress the connection strengths every time step by some amount you might do something like this 247 Brian Documentation Release 1 4 1 C Connection Gl G2 V structure dense network_operation when end def depress_C for i in range len G1 for j in range len G2 C i j C i j depression factor This will work but it will be very very slow The first thing to note is that the Python expression range N actually constructs a list 0 1 2 N 1 each time it is called which is not really necessary if you are only iterating over the list Instead use the xrange iterator which doesn t construct the list explicitly for i in xrange len G1 for j in xrange len G2 C i j C i jl depression factor The next thing to note is that when you call C i j you are doing an operation on the Connect ion object not directly on the underlying matrix Instead do something like this C Connection Gl G2 V structure dense C matrix asarray C W Qnetwork operation when end def depress_C for i in xrange len G1 for j in xrange le
55. Run the simulation giving a report on how long it will take as we run run sound duration report stderr We take the array of counts and reshape them into a 2D array which we sum across frequencies to get the spike count of each location specific assembly count counter count count shape num_indices cfN count sum count axis 1 count array count dtype float amax count Our guess of the location is the index of the strongest firing assembly index guess argmax count Now we plot the output using the coordinates of the HRTFSet coords hrtfset coordinates azim elev coords azim coords elev scatter azim elev 100xcount plot azim index elev index r ms 15 mew 2 plot azim index_guess elev index guess xg ms 15 mew 2 xlabel Azimuth deg ylabel Elevation deg xlim 5 350 ylim 50 95 show Example Platkiewicz Brette 2011 frompapers Slope threshold relationship with noisy inputs in the adaptive threshold model Fig 5E F from Platkiewicz J and R Brette 2011 Impact of Fast Sodium Channel Inactivation on Spike Threshold Dynamics and Synaptic Integration PLoS Comp Biol 7 5 e1001129 doi 10 1371 journal pcbi 1001129 from brian import x from scipy import stats optimize 50 Chapter 3 Getting started Brian Documentation Release 1 4 1 from scipy stats import linregress rectify lambda x clip x volt 0
56. Si delay rand ms P v Vr rand len P Vt Vr Record the number of spikes Me PopulationSpikeCounter Pe Mi PopulationSpikeCounter Pi A population rate monitor M PopulationRateMonitor P print Network construction time time time start time seconds print len P neurons in the network print Simulation running 3 2 Examples 141 Brian Documentation Release 1 4 1 run l msecond start_time time time run l second duration time time start time print Simulation time duration seconds print Me nspikes excitatory spikes print Mi nspikes inhibitory spikes plot M times ms M smooth_rate 2 ms gaussian show Example gapjunctions synapses Neurons with gap junctions from brian import x N 10 v0 1 05 tau 10 ms ET eqs dv dt v0 v Igap tau 1 Igap 1 gap junction current vee neurons NeuronGroup N model eqs threshold 1 reset 0 neurons v linspace 0 1 N trace StateMonitor neurons v record 0 5 S Synapses neurons model w 1 gap junction conductance Igapz w v pre v post 1 S True neurons Igap S Igap S w 02 run 500 ms plot trace times ms trace 0 plot trace times ms trace 5 show Example STDP1 synapses Spike timing dependent plasticity Adapted from Song Miller and Abbott 2000 and Song and Abbott 2001 This simulation takes a long time
57. The idea is that it can be used at various levels of abstraction without the steep learning curve of software like Neuron where you have to learn their own programming language to extend their models As a language Python is well suited to this task because it is easy to learn well known and supported and allows a great deal of flexibility in usage and in designing interfaces and abstraction mechanisms As an interpreted language and therefore slower than say C Python is not the obvious choice for writing a computa tionally demanding scientific application However the SciPy module for Python provides very efficient linear algebra routines which means that vectorised code can be very fast Here s what the Python web site has to say about themselves Python is an easy to learn powerful programming language It has efficient high level data structures and a simple but effective approach to object oriented programming Python s elegant syntax and dynamic typing together with its interpreted nature make it an ideal language for scripting and rapid application development in many areas on most platforms The Python interpreter and the extensive standard library are freely available in source or binary form for all major platforms from the Python Web site http www python org and may be freely distributed The same site also contains distributions of and pointers to many free third party Python modules programs and tools and additional
58. This example features An indefinite number of runs with a set of parameters for each run generated at random for each run A plot of the output of all the runs updated as soon as each run is completed A GUI showing how long each process has been running for and how long until it completes and with a button allowing you to terminate the runs A simpler example is in examples multiprocessing multiple runs simple py We use Tk as the backend for the GUI and matplotlib so as to avoid any threading conflicts import matplotlib matplotlib use TkAgg from brian import x import Tkinter time multiprocessing os from brian utils progressreporting import make text report from Queue import Empty as QueueEmpty class SimulationController Tkinter Tk ra ifa GUI uses Tkinter and features a progress bar for each process and a callback function for when the terminate button is clicked Kor def init self processes terminator width 600 Tkinter Tk init self None self parent Non self grid 86 Chapter 3 Getting started Brian Documentation Release 1 4 1 button Tkinter Button self text Terminate simulation command terminator button grid column 0 row 0 self pb_width width self progressbars for i in xrange processes can Tkinter Canvas self width width height 30 can grid column 0 row 1 i can create rectangle 0 0 width 30 fill aaaaaa r can c
59. bandpass or bandstop filter of type Chebyshef Example IIRfilterbank Elliptic etc hears Butterworth Bank of low high bandpass or bandstop Butterworth filters Example butterworth hears LowPass Bank of lowpass filters of order 1 Example cochleagram hears Second the library provides linear auditory filters developed to model the middle ear transfer function and the fre quency analysis of the cochlea Class Description Example MiddleEar Linear bandpass filter based on middle ear Example tan_carney_simple_test frequency response properties hears tan_carney_2003 Gammatone Bank of IIR gammatone filters based on Slaney Example gammatone hears implementation ApproximateGamBankofUR gammatone filters based on Hohmann Example approximate_gammatone implementation hears LogGammachirp Bank of IIR gammachirp filters with logarithmic Example log_gammachirp hears sweep based on Irino implementation LinearGammachfi Bank of FIR chirp filters with linear sweep and Example linear_gammachirp gamma envelope hears LinearGaborchfi Bank of FIR chirp filters with linear sweep and gaussian envelope Finally Brian hears comes with a series of complex nonlinear cochlear models developed to model nonlinear effects such as filter bandwith level dependency two tones suppression peak position level dependency etc Class Description Example DRNL
60. black B red and C blue in 25 trials with a signal to noise ratio SNR of 10 dB shared vs private Bottom left The shuffled autocorrelogram of neuron A indicates that spike trains are not reproducible at a fine timescale Botto right Nevertheless the average cross correlogram between A and B shows synchrony at a millisecond timescale which does not appear between A and C from brian import x Inputs N 100 number of trials tau 10 ms sigma 0 7 eqs input dx dt x taut 2 tau 5 xi 1 PRT input NeuronGroup N 2 eqs_input shared input N different in all trials but common to all neurons stimulusl input N N 1 identical in all trials stimulus2 input N 1 identical in all trials Neurons taum 10 ms sigma_noise 05 duration 3000 ms sigma sigmarsqrt 2 SNRdB 10 SNR 10 SNRdB 10 Z sigmaxsqrt taumttau taux SNR 2 1 normalizing factor print Z Z SNR Z sigmaxsqrt 1 SNR 2 1 eqs neurons dv dt Z SNR I n v taum 1 dn dt n taut 2 tau 5 xi 1 i 4 por y neuron NeuronGroup 3 N eqs_neurons threshold 1 reset 0 neuronA neuron N neuronB neuron N 2 N neuronC neuron 2 N neuron n randn len neuron Qnetwork operation 3 2 Examples 61 Brian Documentation Release 1 4 1 def inject neuronA I shared x stimulusl x neuronB I shared x stimulusl x neuronC I shared x stimulus2 x spikes SpikeMonitor neuron run
61. can do an arbitrary transformation of the input CodeItem but typically it will either do something like load item save Or something like for name in array item See the reference documentation for Symbol resolve and the documentation for the most important symbols SliceIndex ArraySymbol ArrayIndex NeuronGroupStateVariableSymbol convert to This step is relatively straightforward each CodeItem object has its convert to method called iteratively The important one is in MathematicalStatement where the left hand side usage is replaced by Symbol write and the right hand side usage is replaced by Symbol read In addition at this stage the syntax of mathematical statements is corrected e g Python s x y is replaced by C s pow x y using sympy 11 5 3 Code generation in Brian The four objects used for code generation in Brian are CodeGenStateUpdater Used for numerical integration see above and reference documentation CodeGenThreshold Used for computing a threshold function CodeGenReset Used for computing post spike reset CodeGenConnection Used for synaptic propagation Numerical integration An integration scheme is generated from an Equations object using themake integration step function See reference documentation for that function for details This is carried out by CodeGenStateUpdater which can be used as a Brian brian StateUpdater object in brian NeuronGroup As an
62. compensated trace parameters where parameters is an array of the best parameters one column slice If True return a dict with the following keys Vcompensated Vneuron Velectrode params params instance where instance in the ElectrodeCompensation object docompensation True if False does not perform the optimization and only return an ElectrodeCompen sation object instance to take full control over the optimization procedure eparams a list of initial parameters for the optimization in the following order R tau Vr Re taue Best results are obtained when reasonable estimates of the parameters are given brian library electrophysiology find spikes v vc None dt 0 1 msecond refrac tory 5 0 msecond check quality False Find spikes in an intracellular trace 310 Chapter 8 Reference Brian Documentation Release 1 4 1 evc None separatrix in volt If None a separatrix will be automatically detected using the method described in the paper edt 0 1 ms timestep in the trace inverse of the sampling frequency erefractory 5 ms refractory period minimal duration between two successive spikes echeck_quality False if True will check spike detection quality using signal detection theory The function then returns a tuple spikes scores where scores is a dict brian library electrophysiology get trace quality v l full False Compute the quality of a compensated trace v a compensated intracellular tra
63. fc Bank of 1st order lowpass filters The code is based on the code found in the Meddis toolbox It was implemented here to be used in the DRNL cochlear model implementation Initialised with arguments source Source of the filterbank fc Value list or array with length number of channels of cutoff frequencies class brian hears AsymmetricCompensation source f b 1 0189999999999999 c I ncas cades 4 Bank of asymmetric compensation filters Those filters are meant to be used in cascade with gammatone filters to approximate gammachirp filters Unoki et al 2001 Improvement of an IIR asymmetric compensation gammachirp filter Acoust Sci amp Tech They are implemented a a cascade of low order filters The code is based on the implementation found in the AIM MAT toolbox Initialised with arguments source Source of the filterbank f List or array of the cut off frequencies b 1 019 Determines the duration of the impulse response Can either be a scalar and will be the same for every channel or an array with the same length as cf c 1 The glide slope when this filter is used to implement a gammachirp Can either be a scalar and will be the same for every channel or an array with the same length as cf ncascades 4 The number of time the basic filter is put in cascade 8 21 4 Auditory model library class brian hears DRNL source cf type human paramz Implementation of the dual resonance nonlinear DRNL filte
64. from brian import x from time import time N 1000 taum 10 ms taupre 20 ms taupost taupre 142 Chapter 3 Getting started Brian Documentation Release 1 4 1 Ee O mV vt 54 x mV vr 60 mV El 74 x mV taue 5 ms F 15 Hz gmax 01 dApre 01 dApost dApre taupre taupost 1 05 dApost gmax dApre gmax eqs neurons dv dt ge Ee vr El v taum volt the synaptic current is linearized dge dt ge taue 1 rrt input PoissonGroup N rates F neurons NeuronGroup l model eqs neurons threshold vt reset vr S Synapses input neurons model w l1 Apre 1 Apost t pre gec w Apre Aprexexp lastupdate t taupre dApre Apost Apost exp lastupdate t taupost w clip wtApost 0 gmax post Apre Aprexexp lastupdate t taupre Apost Apost exp lastupdate t taupost dApost w clip wtApre 0 gmax neurons v vr S True S w rand gmax rate PopulationRateMonitor neurons start_time time run 100 second report text print Simulation time time start_time subplot 311 plot rate times second rate smooth rate 100 ms subplot 312 plot S w gmax subplot 313 hist S w gmax 20 show Example weightmonitor synapses Monitoring synaptic variables STDP example from brian import from time import time N 10
65. i C connect one to one weight A SE stp STP C taud 1 ms tauf 100 ms U 1 facilitation stp STP C taud 100 ms tauf 10 ms U 6 depression trace StateMonitor neuron v record 0 N 1 run 1000 ms subplot 211 plot trace times ms trace 0 mV title Vm subplot 212 plot trace times ms trace N 1 mV title Vm show 3 2 13 modelfitting Example modelfitting groups modelfitting Example showing how to fit a single model with different target spike trains several groups from brian import loadtxt ms Equations second from brian library modelfitting import if name main model Equations dV dt R I V tau 1 pL i R 1 tau second oe input loadtxt current txt spikesO loadtxt spikes txt spikes for i in xrange 2 spikes extend i spikexsecond 5x ixms for spike in spikes0 results modelfitting model model reset 0 threshold 1 data spikes 3 2 Examples 133 Brian Documentation Release 1 4 1 input input dt 1lx ms popsize 1000 maxiter 35 cpu 1 delta 4xms R 1 0e9 9 0e9 tau 10 ms 40xms delays 10xms 10 ms ll print table results Example modelfitting machines modelfitting Model fitting example using several machines Before running this example you must start the Playdoh server on the remote machines from brian
66. input NeuronGroup 1 model dx dt x tau_noiset 2 tau_noise 5 xi 1 The noisy neurons receiving the same input independent noise tau 10 ms SNR 3 signal to noise ratio sigma 5 total input amplitude Z sigma sqrt tau_noise tau tau_noisex SNR 2 1 normalizing factor eqs neurons dx dt Z x SNR I u x tau 1 du dt u tau noise 2 tau noise x 5xxi 1 mq pay neurons NeuronGroup 25 model eqs_neurons threshold 1 reset 0 refractory 5 ms neurons x rand 25 random initial conditions neurons I linked_var input x spikes SpikeMonitor neurons run 2 second Figure raster_plot spikes show 60 Chapter 3 Getting started Brian Documentation Release 1 4 1 Example Fig6 shared variability frompapers computing with neural synchrony coincidence de tection and synchrony Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 6 Shared variability This example shows that synchrony may be reproducible without individual responses being reproducible because of shared variability here due to a common input Caption Fig 6 Neurons A and B receive the same stimulus driven input neuron C receives a different one The stimuli are identical in all trials but all neurons receive a shared input that varies between trials Each neuron also has a private source of noise Top Responses of neurons A
67. layer23exc recurrent inh w IPSC 146 Chapter 3 Getting started Brian Documentation Release 1 4 1 Stimulation stimspeed 1 stim_change_time speed at which the bar of stimulation moves direction 0 0 stimzonecentre ones 2 barrelarraysize 2 stimcentre stimnorm zeros 2 zeros 2 stimradius ll stim_change_timexstimspeed 1 5 stimradius2 stimradius 2 def new_direction global direction direction rand 2 pi stimnorm cos direction sin direction stimcentre stimzonecentre stimnorm stimradius Qnetwork operation def stimulation global direction stimcentre stimcentre stimspeed stimnorm defaultclock dt if sum stimcentre stimzonecentre 2 gt stimradius2 new direction for i j b in barrels4 iteritems whiskerpos array i j dtype float 0 5 isactive abs dot whiskerpos stimcentre stimnorm lt 5 if barrels4active i j isactive barrels4active i j isactive b rate float isactive tuning layer4 selectivity barrelindices i j direction new direction t2 time time print Construction time t2 tl s run 5 second report text figure Preferred direction perhaps we need to add presynaptic and postsynaptic with 2D 3D access selectivity array mean array feedforward w feedforward synapses post il exp layer4 selectivity o selectivity arctan2 selectivity imag selectivity real 2 pi 180
68. len source p np tile p self nsamples 1 freqs frange 0 p 1 p frange 1 del p times linspace O ms duration self nsamples reshape self nsamples 1 times np tile times 1 len source self sounds np sin 2 np pi freqs times self init mixer def propagate self spikes if len spikes data np sum self sounds spikes axis 1 x array 2 15 1 clip data amax data 1 1 dtype int16 x shape x size Make sure pygame receives an array in C order x pygame sndarray make sound np ascontiguousarray x x play def init mixer self global mixer status if mixer status 1 1 or mixer status 0 1 or mixer status self samplerate pygame mixer quit pygame mixer init int self samplerate 16 1 _mixer_status 1 self samplerate def test_cuba The CUBA example with sound taum 20 ms taue 5 ms 104 Chapter 3 Getting started Brian Documentation Release 1 4 1 def taui 10 ms Vt 50 mV Vr 60 x mV El 49 x mV eqs Equations dv dt getgi v El taum volt dge dt ge taue volt dgi dt gi taui volt C P NeuronGroup 4000 model eqs threshold Vt reset Vr P v Vr P ge 0 mV P gi 0 x mV Pe P subgroup 3200 Pi P subgroup 800 we 60 0 27 10 wi 20 4 5 10 Ce Connection Pe P Ci Connection Pi P P v Vr rand len P
69. linspace 0 1 len layerl abstract position between 0 and 1 layer2 NeuronGroup N model eqs threshold 10 mV reset 0 mV layer2 x linspace 0 1 len layer2 Generic connectivity function topomap lambda i j x y sigma exp abs x i y j sigma feedforward Connection layerl layer2 sparseness 5 weight lambda i j topomap i j layerl x layer2 x 3 3 mV recurrent Connection layer2 layer2 sparseness 5 weight lambda i j topomap i j layerl x layer2 x 2 5 mV spikes SpikeMonitor layer2 run l second subplot 211 raster_plot spikes subplot 223 imshow feedforward W todense interpolation nearest origin lower title Feedforward connection strengths subplot 224 imshow recurrent W todense interpolation nearest origin lower title Recurrent connection strengths show Example correlated_inputs misc An example with correlated spike trains From Brette R 2007 Generation of correlated spike trains from brian import x N 100 input HomogeneousCorrelatedSpikeTrains N r 10 Hz c 0 1 tauc 10 ms c 2 nu linspace 1 Hz 10 Hz N P c dot nu reshape N 1 nu reshape 1 N mean nu 2 tauc 5 ms spikes mixture process nu P tauc 1 second spikes i t second for i t in spikes input SpikeGeneratorGroup N spikes S SpikeMonitor input S2 PopulationRateMo
70. refractory The refractory period in second If it s a single value the same refractory will be used in all the simulations If it s a list or a tuple the fitting will also optimize the refractory period see x params below Warning when using a refractory period you can t use a custom reset only a fixed one data A list of spike times or a list of several spike trains as a list of pairs index spike time if the fit must be performed in parallel over several target spike trains In this case the modelfitting function returns as many parameters sets as target spike trains input var I The variable name used in the equations for the input current input A vector of values containing the time varying signal the neuron responds to generally an injected current dt The time step of the input the inverse of the sampling frequency xparams The list of parameters to fit the model with Each parameter must be set as follows param name bound min min max bound max where bound min and bound max are the boundaries and min and max specify the interval from which the parameter values are uniformly sampled at the beginning of the optimization algorithm If not using boundaries set param name min max Also you can add a fit parameter which is a spike delay for all spikes add the special parameter delays in x params for example modelfitting delays 10 ms 10 ms You can also add fit the refractory period by spe
71. reset 0 refractory 2 5 ms ears distance 5 max delay 5 max delay traces StateMonitor ears x record True Coincidence detectors N 300 tau 1 ms sigma 05 eqs neurons dv dt v tauc sigma x 2 tau x x 5 xi 1 Fr neurons NeuronGroup N model eqs neurons threshold 1 reset 0 synapses Connection ears neurons v structure dense delay True max delay 1 1 max delay 82 Chapter 3 Getting started Brian Documentation Release 1 4 1 synapses connect_full ears neurons weight 5 synapses delay 0 linspace 0 ms 1 1 max delay N synapses delay 1 linspace 0 ms 1 1 x max delay N 1 Spikes SpikeMonitor neurons run 1000 ms raster plot spikes show Example Fig12A Goodman Brette 2010 frompapers computing with neural synchrony hearing Sound localization with HRTFs Goodman DF and R Brette 2010 Spike timing based computation in sound localization PLoS Comp Biol 6 11 e1000993 doi 10 1371 journal pcbi 1000993 Corresponds to Fig 12A in Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Simplified version of the ideal sound localisation model The sound is played at a particular spatial location indicated on the final plot by a red Each location has a corresponding assembly of neurons whose summed firing rates give the sizes of the blue circles in
72. run sound duration raster_plot M show Example drnl hears Implementation example of the dual resonance nonlinear DRNL filter with parameters fitted for human as described in Lopez Paveda E and Meddis R A human nonlinear cochlear filterbank JASA 2001 3 2 Examples 115 Brian Documentation Release 1 4 1 A class called DRNL implementing this model is available in the library The entire pathway consists of the sum of a linear and a nonlinear pathway The linear path consists of a bank of bandpass filters second order gammatone a low pass function and a gain attenuation factor g in a cascade The nonlinear path is a cascade consisting of a bank of gammatone filters a compression function a second bank of gammatone filters and a low pass function in that order The parameters are given in the form 10 p0 mlog10 cf from brian import x from brian hears import x Simulation duration 50 ms samplerate 50 kHz level 50 dB level of the input sound in rms dB SPL sound whitenoise simulation duration samplerate ramp sound level level nbr_cf 50 number of centre frequencies center frequencies with a spacing following an ERB scale center frequencies erbspace 100 Hz 1000 Hz nbr_cf conversion to stape velocity which are the units needed by the following centres sound sound 0 00014 Linear Pathway bandpass filter second order gammatone filter c
73. they do not have durations e g in the case of Onl ineSound 332 Chapter 8 Reference Brian Documentation Release 1 4 1 buffersize 32 The size of the buffered segments to fetch as a length of time or number of samples 32 samples typically gives reasonably good performance For example to compute the RMS of each channel in a filterbank you would do def sum_of_squares input running_sum_of_squares return running_sum_of_squares sum input 2 axis 0 rms sqrt fb process sum_of_squares nsamples Alternatively the buffer interface can be used which is described in more detail below Filterbank also defines arithmetical operations for x where the other operand can be a filterbank or scalar Details on the class This class is a base class not designed to be instantiated A Filterbank object should define the interface of Bufferable as well as defining a source attribute This is normally a Buf ferable object but could be an iterable of sources for example for filterbanks that mix or add multiple inputs The buffer_fetch_next samples method has a default implementation that fetches the next input and calls the buffer_apply input method on it which can be overridden by a derived class This is typically the easiest way to implement a new filterbank Filterbanks with multiple sources will need to override this default implementation There is a default init__ method that can be called by a derived class t
74. with delays depending linearly on the distances Note that the exact number of synapses per neuron is not fixed here To avoid any border conditions the plane is considered to be toroidal Script will generate an Synchronous Irregular SI slow regime with propagating waves that will spread in various directions wandering over the network In addition an external layer of Poisson sources will stimulates some cells on the network with a wiring scheme such that the word BRIAN will pop up External rates can be turned off to observed ti spontaneous activity of the 2D layer One can observe that despite the inputs is constant the netwo is not always responding to it The script will display while running the spikes and Vm of the excitatory cells Varying sigma will show the various activity structures from a random network s lat 1 to a very locally connected one s lat 0 1 mmm We are setting the global timestep of the simulation Clock 0 1 ms Cell parameters tau m 20 ms Membrane time constant cm 0 2 nF Capacitance tau exc 3 ms Synaptic time constant excitatory tau_inh 7 ms Synaptic time constant inhibitory tau ref 5 x ms Refractory period El 80 x mV Leak potential Ee 0 mV Reversal potential excitation Ei 70 mV Reversal potential inhibition vt 50 mV Spike Threhold Vr 60 mV Spike Reset Equation for a Conductanc
75. ylim 0 0 5 xlabel Duration ms ylabel Spiking probability show 3 2 Examples 69 Brian Documentation Release 1 4 1 Example Fig2A_synchrony_partition frompapers computing with neural synchrony duration se lectivity Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 2A Synchrony partition for duration selective neurons Caption Fig 2A Decoding synchrony patterns in a heterogeneous population Color represents the latency of the spike produced by each neuron responding to the stimulus white if the neuron did not spike Thus neurons with the same color are synchronous for that specific stimulus duration The population can be divided in groups of synchronous neurons i e with the same color forming the synchrony partition Circled neurons belong to the same synchronous group This script calculates and displays the synchrony partition for one particular duration It also saves the results in file that is required by the script Fig2C_decoding_synchrony The synchrony partition is calculated empirically by simulating the responses of the neurons at the specific inhibitory duration and grouping neurons that respond in synchrony 2 ms from brian import x from numpy random import seed from params import x from pylab import cm Graphics radius 15 selected_neuron 7 Parameters ginh_max 5 Nx 5 number of ne
76. 0 1 alpha In the present example the time varying filter is a LinearFilterbank therefore we must initialise the filter coefficients the one used for the first buffer computation w0 2 pixfc_init samplerate BW 2 arcsinh 1 2 Q 1 44269 alpha sin w0 sinh log 2 2 BW xw0 sin w0 filt_b zeros nchannels 3 1 filt_a zeros nchannels 3 1 filt b 0 0 sin w0 2 filt b 1 0 0 filt b 2 0 sin w0 2 filt a 0 0 ltalpha filt a 1 0 2xcos W0 filt a 2 0 1 alpha the filter which will have time varying coefficients bandpass filter LinearFilterbank sound filt b filt a the updater updater CoeffController bandpass_filter the controller Remember it must be the last of the chain control ControlFilterbank bandpass_filter noise_generator bandpass_filter updater update_interval time varying filter mon control process figure 1 pxx freqs bins im specgram squeeze time varying filter mon NFFT 256 Fs samplerate noverlap 240 imshow flipud pxx aspect auto show Example sound_localisation_model hears Example demonstrating the use of many features of Brian hears including HRTFs restructuring filters and integration with Brian Implements a simplified version of the ideal sound localisation model from Goodman and Brette 2010 The sound is played at a particular spatial location indicated on the final plot
77. 0 n exc im set clim El Vt fig2 set ylabel v pylab colorbar im manager pylab get current fig manager print Running network for time in xrange int simtime sim step ms run sim step figl cla figl set title t bg s sim step time ms idx s exc count gt 0 if numpy sum idx gt 0 im figl scatter all_cells position n_exc 0 idx all cells position n exc 1 idx c S exc count numpy zeros n exc We reset the spike counter figl set xlim 0 size figl set ylim 0 size figl set ylabel spikes im set clim 0 1 setp figl xticks yticks fig2 cla im fig2 scatter all cells position n exc 0 all cells position n exc 1 c v exc values fig2 set xlim 0 size fig2 set ylim 0 size 3 2 Examples 101 Brian Documeniation Release 1 4 1 fig2 set ylabel v im set clim El Vt setp fig2 xticks yticks manager canvas draw manager canvas flush events ioff To leave the interactive mod Example MicheleGiugliano twister Michele Giugliano s entry for the 2012 Brian twister Figure5B from Giugliano et al 2004 Journal of Neurophysiology 92 2 977 96 implemented by Eleni Vasilaki lt e vasilaki sheffield ac uk gt and Michele Giugliano lt michele giugliano ua ac be gt A sparsely connected network of excitatory neurons interacting via current based synaptic interactions and incorporating spike frequency adapta
78. 0 1 to 10 where 1 is odor concentration in the learning phase 74 Chapter 3 Getting started Brian Documentation Release 1 4 1 Run the other file first Fig11B_olfaction_stdp_learning py from brian import x from params import x import numpy from scipy sparse import lil matrix bmin bmax 7 1 Loads information from the STDP simulation t odor numpy load stimuli npy T W numpy load weights npy Spikes out numpy load spikesout npy weights W 1 final weights Analyze selectivity at the end of the STDP simulation ispikes spikes out 0 indexes of neurons that spiked tspikes spikes out 1 spike timings Select only the end of the STDP simulation end tspikes 8 max tspikes ispikes ispikes end tspikes tspikes end odors odor digitize tspikes t 1 odor 0 1 presented at the time of spikes tuning zeros 30 Tuning ratio of the postsynaptic neurons n0Q nl zeros 30 zeros 30 number of spikes for odor 0 and for odor 1 for k in range len tuning o odors ispikes k nO k sum o 0 nl k sum o 1 tuning k nO X 1 n0 k n1 k Sort the postsynaptic neurons by odor tuning weights weights argsort tuning TRL Run the simulation Ky def odor N Returns a random vector of binding constants return 10 rand N gt bmax bmin bmin def hill function c K 1 n 23 Kr Hill function C concentration K n ERE half activation con
79. 1 reset 0 refractory 2 ms traces StateMonitor receptors x record True sound StateMonitor receptors sound record 0 Coincidence detectors min freq 50 Hz max freq 1000 Hz N 300 tau 1 x ms sigma 1 eqs_neurons dv dt v tautsigmas 2 tau 5 xi 1 yop pg neurons NeuronGroup N model eqs neurons threshold 1 reset 0 synapses Connection receptors neurons v structure dense max delay 1 1 max delay delay T synapses connect full receptors neurons weight 5 synapses delay 1 1 exp linspace log min freq Hz log max freq Hz N spikes SpikeMonitor neurons run 500 ms raster plot spikes ylabel Frequency yticks 0 99 199 299 array 1 synapses delay todense 1 0 99 199 299 dtype int show 3 2 6 multiprocessing Example multiple runs simple multiprocessing Example of using Python multiprocessing module to distribute simulations over multiple processors The general procedure for using multiprocessing is to define and run a network inside a function and then use multi processing Pool map to call the function with multiple parameter values Note that on Windows any code that should only run once should be placed inside an if name main block from brian import x import multiprocessing This is the function that we want to compute for various different parameters def how many spikes excitatory weight
80. 1 vt 1 spike threshold vee neurons NeuronGroup N model eqs threshold v gt vt s d on the membrane potential reset v 0 refractory tau cd neurons vt linspace 0 3 N spike threshold varies across neurons counter SpikeCounter neurons Inputs are regular spikes starting at TO input SpikeGeneratorGroup 1 0 n T TO for n in C Connection input neurons v weight w Calculate the false alarm rate run TO report text FR tau cd counter count 1 TO0 Calculate the hit rate counter reinit run Nspikes T report text HR counter count 1 Nspikes FR T tau cd tau cd Prediction based on Gaussian statistics FRpred spike probability neurons vt sigmav HRpred spike probability neurons vt w sigmav Figure plot FR 100 HR 100 k simulations range Nspikes plot FRpred 100 HRpred 100 r theoretical predictions plot 0 100 0 100 k plot 0 100 50 50 k xlim 0 100 ylim 0 100 xlabel False alarm rate ylabel Hit rate show 64 Chapter 3 Getting started Brian Documentation Release 1 4 1 3 2 3 frompapers computing with neural synchrony duration selectivity Example Fig1A rebound neurons frompapers computing with neural synchrony duration selec tivity Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 1A B Caption Fig 1A B
81. 100 v0 5 x mV sigma 4 mV group NeuronGroup N model dv dt v0 v tau sigmaxxi tau 5 volt threshold 10 mV reset 0 mV C Connection group group v weight lambda i j 4 mV cos 2 pi x i j 1 N S SpikeMonitor group R PopulationRateMonitor group group v rand N 10 mV run 5000 ms subplot 211 raster plot S subplot 223 imshow C W todense interpolation nearest title Synaptic connections subplot 224 plot R times ms R smooth rate 2 ms filter flat title Firing rate show 3 2 Examples 181 Brian Documentation Release 1 4 1 Example multipleclocks misc This example demonstrates using different clocks for different objects in the network The clock simclock is the clock used for the underlying simulation The clock monclock is the clock used for monitoring the membrane potential This monitoring takes place less frequently than the simulation update step to save time and memory Finally the clock inputclock controls when the external current Iext should be updated In this case we update it infrequently so we can see the effect on the network This example also demonstrates the network_operation decorator A function with this decorator will be run as part of the network update step in sync with the clock provided or the default one if none is provided from brian import x define the three clocks simclock Clo
82. 2 5 eqs neurons dv dt ge Ee vr El v taum volt the synaptic current is linearized dge dt ge taue 1 EEF input PoissonGroup N rates F neurons NeuronGroup 1 model eqs_neurons threshold vt reset vr synapses Connection input neurons ge weight rand len input len neurons gmax structure dense neurons v vr stdp ExponentialSTDP synapses tau pre tau post dA pre dA post wmax gmax update mixed rate PopulationRateMonitor neurons start_time time run 100 second report text print Simulation time time start time subplot 311 plot rate times second rate smooth rate 100 ms subplot 312 plot synapses W todense gmax subplot 313 hist synapses W todense gmax 20 show Example short_term_plasticity plasticity Example with short term plasticity model Neurons with regular inputs and depressing synapses from brian import x tau_e 3 ms taum 10 ms A SE 250 pA Rm 100 Mohm N 10 eqs rra 132 Chapter 3 Getting started Brian Documentation Release 1 4 1 dx dt rate 1 rate Hz ae J A input NeuronGroup N model eqs threshold 1 reset 0 input rate linspace 5 Hz 30 Hz N eqs neuron dv dt Rm i v taum volt di dt i tau e amp vee neuron NeuronGroup N model eqs_neuron C Connection input neuron
83. 32 Chapter 3 Getting started Brian Documentation Release 1 4 1 SETSHTESHSAEHSE RHRHHATHAEHSTH EEHATHSEHSETEHS9EA TEAHHE Make plots E heds eee es teats teat tea ta ted ta te dtd te HT E te subplot 211 raster plot sm ms 1 title Before xlabel xlim 0 8 1e3 1x1e3 subplot 212 raster plot sm ms 1 title After xlim simtime 0 2 second le3 simtimexle3 show Example Guetig_Sompolinsky_2009 frompapers Implementation of the basic model no speech recognition no learning described in Gutig and Sompolinsky 2009 Time Warp Invariant Neuronal Processing PLoS Biology Vol 7 7 e1000141 from brian import x class TimeWarpModel object r A simple neuron model for testing the time warp invariance with conductance based or current based synapses The neuron receives balanced excitatory and inhibitory input from a random spike train The same spike train can be fed into the model with different time warps ERE def init self conductance_based True y Wr Create a new model with conductance based or current based synapses Lr Model parameters 5 1 _L 0 g_L 1 100 0 msecond tau syn lx ms N_ex 250 N_inh 250 self N N_ex N_inh ti _e ME zi p Equations if conductance based Irr eqs dv dt V EL g_L I syn I_syn I_ge I_gi secondxx 1 I_ge V E_e g_e sec
84. 4 1 run l second print M nspikes Having run the network we simply use the raster_plot function provided by Brian After creating plots we have to use the show function to display them This function is from the PyLab module that Brian uses for its built in plotting routines raster plot show Woo oW o dod ob a a a a a HERB EES BoBOB B BOB NOB HOS BOB OG Neuron number oo BoRot ooo BOB Bom Bos Hom so b L WEGREG x EO ta ow o some em x a o o3 o4 OE OR Q boR B ROB B B BON HO HO How s a Peet Pot 9o 9 oR box B RR B RB B 3 n b Bom titan ob T B te Pete ee g uh y am Rok 20 A 1HM3S538 0 A e 3 3 S0 X 100 Time in ms As you can see despite having introduced some randomness into our network the output is very regular indeed In the next part we introduce one more way to plot the output of a network Tutorial 1b Counting spikes In the previous part of the tutorial we looked at the following Importing the Brian module into Python Using quantities with units Defining a neuron model by its differential equation Creating a group of neurons Running a network In this part we move on to looking at the output of the network The first part of the code is the same 3 1 Tutorials 17 Brian Documentation Release 1 4 1 from brian import x tau 20 msecond membrane time constant Vt 50 mv
85. 69 72 74 77 79 84 120 125 144 153 161 187 exp euler in module brian experimental codegen2 375 exponential Euler numerical integration 217 ExponentialSTDP example usage 46 131 ExponentialSTDP class in brian 280 Expression class in brian experimental codegen2 371 extended brian hears Sound method 313 extending brian contained objects protocol 251 338 derived classes 251 338 magic functions 250 337 magic register 250 337 magic return 250 337 external variables equations 215 F FileSpikeMonitor class in brian 294 filter 240 filter bank 240 Filterbank class in brian hears 332 filterbank brian hears HRTF method 329 filterbank brian hears HRTFSet method 329 FilterbankGroup example usage 49 83 109 115 FilterbankGroup class in brian hears 328 filtering control path 241 find spikes in module brian library electrophysiology 310 finish brian ProgressReporter method 304 FIRFilterbank class in brian hears 317 firing rate example usage 179 firing rate in module brian 299 fixed points equations 219 flattened docstring in module brian experimental codegen2 371 FloatClock class in brian 262 ForBlock class in brian experimental codegen2 367 forget in module brian 289 format equation brian experimental model_documentation LaTeXDocun static method 342 freeze with equations in module brian experimental codegen2 371 freezing diff
86. A When neuron A is hyperpolarized by an inhibitory input top its low voltage activated K channels slowly close bottom which makes the neuron fire when inhibition is released neuron models are used in this and other figures B Spike latency is negatively correlated with the duration of inhibition black line from brian import x Parameters and equations of the rebound neurons Vt 2 55xmV Vr 70 mV El 2 35 mV EK 90 mV Va Vr ka 5xmV gmax 1 gmax2 2 tau 20 ms ginh_max 5 tauk 400 ms tauK2 100 ms N 100 number of neurons different durations for plot 1B plotted_neuron N 4 rest time 1 second initial time to start at equilibrium tmin rest time 20 ms for plots tmax rest_time 600 ms ey And eqs dv dt El v gmax gK gmax2 gK2 ginh EK v tau volt dgK dt gKinf gK tauK 1 IKLT dgK2 dt gK2 tauK2 1 Delayed rectifier gKinf 1 1 exp Va v ka 1 duration second duration of inhibition varies across neurons ginh ginh max t rest time amp t lt rest_timetduration 1 EOD neurons NeuronGroup N model eqs threshold v gt Vt reset v Vr gK2 1 neurons v Vr neurons gK 1 1 exp Va E1 ka neurons duration linspace 100 ms 1 second N M StateMonitor neurons v record plotted neuron Mg StateMonitor neurons gK record plotted neuron spikes SpikeMonitor neurons run rest_time 1 1 second M insert_spikes spi
87. Brunel Hakim 1999 frompapers Dynamics of a network of sparsely connected inhibitory current based integrate and fire neurons Individual neu rons fire irregularly at low rate but the network is in an oscillatory global activity regime where neurons are weakly synchronized Reference Fast Global Oscillations in Networks of Integrate and Fire Neurons with Low Firing Rates Nicolas Brunel amp Vincent Hakim Neural Computation 11 1621 1671 1999 from brian import x N 5000 Vr 10 mV theta 20 mV tau 20 ms delta 2 ms taurefr 2 ms duration 1 second C 1000 sparseness float C N J 1 mV muext 25 mV sigmaext 1 mV eqs wey dv dt V muext sigmaext sqrt tau xi tau volt wwe group NeuronGroup N eqs threshold theta reset Vr refractory taurefr group V Vr conn Connection group group state V delay delta weight J sparseness sparseness M SpikeMonitor group LFP PopulationRateMonitor group bin 0 4 ms run duration subplot 211 3 2 Examples 39 Brian Documentation Release 1 4 1 raster_plot M xlim 0 duration ms subplot 212 plot LFP times_ ms LFP rate xlim 0 duration ms show Example Sturzl et al 2000 frompapers Adapted from Theory of Arachnid Prey Localization W Sturzl R Kempter and J L van Hemmen PRL 2000 Poisson inputs are replaced by integrate and fire neurons Romain Brette fr
88. Chapter 6 Advanced concepts Brian Documentation Release 1 4 1 gcc options ffast math Defines the compiler switches passed to the gcc compiler For gcc ver sions 4 2 we recommend using march native By default the ffast math optimisations are turned on if you need IEEE guaranteed results turn this switch off openmp False Whether or not to use OpenMP pragmas in generated C code If supported on your compiler gcc 4 24 it will use multiple CPUs and can run substantially faster However if you are already running several simulations in parallel this will not improve the speed and may even slow it down In addition for smaller networks or for simpler neuron models the parallelisation overheads can make it take longer usecodegen False Whether or not to use experimental code generation support usecodegenweave False Whether or not to use C with experimental code generation support usecodegenstateupdate True Whether or not to use experimental code generation support on state up daters usecodegenreset False Whether or not to use experimental code generation support on resets Typically slower due to weave overheads so usually leave this off usecodegenthreshold True Whether or not to use experimental code generation support on thresholds usenewpropagate False Whether or not to use experimental new C propagation functions usecstdp False Whether or not to use experimental new C STDP brianhears usegpu
89. Dual resonance nonlinear filter as described in Example drnl hears Lopez Paveda and Meddis JASA 2001 DCGC Compressive gammachirp auditory filter as described in Example dcgc hears Irino and Patterson JASA 2001 TanCarney Auditory phenomenological model as described in Tan Example tan carney simple test and Carney JASA 2003 hears tan carney 2003 ZhangSynapMEdel of an inner hair cell auditory nerve synapse Example tan carney simple test Zhang et al JASA 2001 hears tan carney 2003 5 7 8 Head related transfer functions You can work with head related transfer functions HRTFs using the three classes HRTF a single pair of left right ear HRTFs HRTF Set a set of HRTFs typically for a single individual and HRTFDatabase for working with databases of individuals At the moment we have included only one HRTF database the TRCAM LISTEN public HRTF database However we will add support for the CIPIC and MIT KEMAR databases in a subsequent release There is also one artificial HRTF database HeadlessDatabase used for generating HRTFs of artifically introduced ITDs An example of loading the IRCAM database selecting a subject and plotting the pair of impulse responses for a particular direction hrtfdb IRCAM_LISTEN r F HRTF IRCAM hrtfset hrtfdb load_subject 1002 hrtf hrtfset azim 30 lev 15 plot hrtf left plot hrtf right show 244 Chapter 5 The library Brian Docum
90. Example of the use of the cochlear models DRNL DCGC and TanCarney available in the library from brian import x from brian hears import Simulation duration 50 ms set default samplerate 50 kHz sound whitenoise simulation duration sound sound atlevel 50 dB level in rms dB SPL cf erbspace 100 Hz 1000 Hz 50 centre frequencies interval 16 update interval of the time varying filters DNRL param_drnl Zparam drnl lp nl cutoff m 1 1 drnl_filter DRNL sound cf type human param param drnl fout drnl filter processY DCGC param_dcgc param_dcgc cl 2 96 dcgc_filter DCGC sound cf interval param param_dcgc fout dcgc_filter process Tan and Carney 2003 tan_filter TanCarney sound cf interval out tan filter process figure imshow flipud out T aspect auto show Example approximate_gammatone hears Example of the use of the class ApproximateGammatone available in the library It implements a filterbank of approximate gammatone filters as described in Hohmann V 2002 Frequency analysis and synthesis using a Gammatone filterbank Acta Acustica United with Acustica In this example a white noise is filtered by a gammatone filterbank and the resulting cochleogram is plotted from brian import x from brian hears import x 3 2 Examples 113 Brian Documentation Release 1 4 1 level 50 dB level of the
91. False Whether or not to use the GPU if available in Brian hears Support is experi mental at the moment and requires the PyCUDA package to be installed magic useframes True Defines whether or not the magic functions should search for objects defined only in the calling frame or if they should find all objects defined in any frame This should be set to False if you are using Brian from an interactive shell like IDLE or IPython where each command has its own frame otherwise set itto True 6 8 Logging Brian uses the standard Python logging package to generate information and warnings All messages are sent to the logger named brian or loggers derived from this one and you can use the standard logging functions to set options write the logs to files etc Alternatively Brian has four simple functions to set the level of the displayed log see below There are four different levels for log messages in decreasing order of severity they are ERROR WARN INFO and DEBUG By default Brian displays only the WARN and ERROR level messages Some useful information is at the INFO level so if you are having problems with your program setting the level to INFO may help brian log level error Shows log messages only of level ERROR or higher brian log level warn Shows log messages only of level WARNING or higher including ERROR level brian log level info Shows log messages only of level INFO or higher including WARNING and ERROR levels
92. Filterbank attribute 332 SparseConnectionMatrix class in brian 277 SparseConnection Vector class in brian 279 SparseConstructionMatrix class in brian 279 SparseMatrixSymbols class in brian experimental codegen2 370 SparseMatrixSymbols SynapseIndex class in brian experimental codegen2 370 SparseMatrixSymbols TargetIndex class in brian experimental codegen2 370 SparseMatrixSymbols Value class in brian experimental codegen2 371 spectrogram brian hears Sound method 314 spectrum brian hears Sound method 315 speed vectorisation 247 spike triggered average example usage 161 spike triggered average in module brian 300 SpikeCounter example usage 40 49 63 68 72 83 99 109 155 186 SpikeCounter class in brian 290 SpikeGeneratorGroup example usage 54 63 163 168 177 179 183 184 SpikeGeneratorGroup class in brian 272 SpikeMonitor example usage 31 39 43 45 50 53 56 57 60 65 69 74 77 79 82 84 97 102 103 106 115 128 131 136 137 140 152 154 156 158 164 167 170 173 176 187 SpikeMonitor class in brian 290 SpikeQueue class in brian synapses spikequeue 284 Spikes aer file 301 spikes direct control 272 spikes brian StateSpikeMonitor attribute 291 sqrt example usage 50 52 60 63 99 108 111 126 start brian ProgressReporter method 304 state brian NeuronGroup method 265 state brian Synapses method 282 StateHistogramMonitor class i
93. For example 3 mvolt 2xamp raises this exception The purpose of this class is to help catch errors based on incorrect units The exception will print a representation of the dimensions of the two inconsistent objects that were operated on If you want to check for inconsistent units in your code do something like Cry your code here except DimensionMismatchError inst cleanup code here e g print Found dimension mismatch details inst 259 Brian Documentation Release 1 4 1 brian check_units au Decorator to check units of arguments passed to a function Sample usage check_units I amp R ohm wibble metre result volt def getvoltage I R k return I R You don t have to check the units of every variable in the function and you can define what the units should be for variables that aren t explicitly named in the definition of the function For example the code above checks that the variable wibble should be a length so writing getvoltage lxamp 1 ohm wibble 1 would fail but getvoltage l amp 1xohm wibble 1 metre would pass String arguments are not checked e g get voltage wibble hello would pass The special name result is for the return value of the function An error in the input value raises a DimensionMismatchError and an error in the return value raises an AssertionError because it is a code problem rather than a value problem Notes This decor
94. T2 The result the rate of coincidences in each bin returned as an array e Autocorrelogram autocorrelogram TO width 20 ms bin 1 ms T None is the same as correlogram TO T0O width 20 ms bin l ms T None e Cross correlation function CCF T1 T2 width 20 ms bin 1l ms T None returns the cross correlation function of T1 and T2 which is the same as the cross correlogram divided by the bin size which makes the result independent of the bin size 4 10 Analysis and plotting 211 Brian Documentation Release 1 4 1 Autocorrelation function ACF TO width 20 ms bin 1 ms T None same as CCF TO TO width 20 ms bin l1 ms T None e Cross covariance function CCVF T1 T2 width 20xms bin 1 xms T None is the cross correlation function of T1 and T2 minus for the cross correlation of independent spike trains with the same rates product of rates Auto covariance function ACVF TO width 20 ms bin 1l ms T None is the same as CCVF TO TO width 20 ms bin 1 ms T None Total correlation coefficient total correlation T1 T2 width 20 ms T None is the integral of the cross covariance function divided by the rate of T1 typically but not always between 0 and 1 e Vector strength vector strength spikes period returns the vector strength of the given spike train with respect to the period If each spike time with phase phi is represented by a vector with angle phi then the vector strength is the length of t
95. Vt Vr Record the number of spikes M SoundMonitor P run 10 second test_synfire from brian import x Neuron model parameters Vr 70 mV Vt 55 mV taum 10 ms taupsp 0 325 ms weight 4 86 mV Neuron model eqs Equations dV dt V Vr x 1 taum volt dx dt x y 1 taupsp volt dy dt y 1 taupsp 25 27 mV ms N 39 24xmV msx 0 5 xi volt Amy Neuron groups P NeuronGroup N 1000 model eqs threshold Vt reset Vr refractory 1 ms Pinput PulsePacket t 50 ms n 85 sigma l1 ms The network structure Pgp P subgroup 100 for i in range 10 C Connection P P y for i in range 9 C connect full Pgp i Pgp i 1 weight Cinput Connection Pinput Pgp 0 y Cinput connect full weight weight monitor SoundMonitor P Setup the network and run it refractory 5 ms x mV excitatory synaptic weight voltage mV inhibitory synaptic weight ge weight we sparseness 0 5 gi weight wi sparseness 0 5 3 2 Examples 105 Brian Documentation Release 1 4 1 P V Vr rand len P Vt Vr run 1 second Plot result show if name main__ test synfire Example FriedemannZenke twister Friedemann Zenke s winning entry for the 2012 Brian twister FEISSSTESEHAESAHTRHSRSASAATEHATTEE HSEAHSSESSATHSATE Inhibitory synaptic plasticity in a recurrent networ
96. a successful installation there are some optimisations you can make to your Brian installation to get it running faster using compiled C code We do not include these as standard because they do not work on all computers and we want Brian to install without problems on all computers Note that including all the optimisations can result in significant speed increases around 30 These optimisations are described in detail in the section on Compiled code 2 3 Testing 7 Brian Documentation Release 1 4 1 8 Chapter 2 Installation CHAPTER THREE GETTING STARTED 3 1 Tutorials These tutorials cover some basic topics in writing Brian scripts in Python The complete source code for the tutorials is available in the tutorials folder in the extras package 3 1 1 Tutorials for Python and Scipy Python The first thing to do in learning how to use Brian is to have a basic grasp of the Python programming language There are lots of good tutorials already out there The best one is probably the official Python tutorial There is also a course for biologists at the Pasteur Institute Introduction to programming using Python NumPy SciPy and Pylab The first place to look is the SciPy documentation website To start using Brian you do not need to understand much about how NumPy and SciPy work although understanding how their array structures work will be useful for more advanced uses of Brian The syntax of the Numpy and Pylab
97. allow remote control use portnumber authkey The authentication key to allow access change it from brian if you are allowing access from outside otherwise you allow others to run arbitrary code on your machine Use a RemoteControlServer on the simulation you want to control Has the following methods execute code Executes the specified code in the server process If it raises an exception the server process will catch it and reraise it in the client process evaluate code Evaluate the code in the server process and return the result If it raises an exception the server process will catch it and reraise it in the client process set name value Sets the variable name a string to the given value can be an array etc Note that the variable is set in the local namespace not the global one and so this cannot be used to modify global namespace variables To do that set a local namespace variable and then call execute with an instruction to change the global namespace variable pause Temporarily stop the simulation in the server process continue simulation with the meth go method go Continue a simulation that was paused stop Stop a simulation equivalent to execute stop Example usage Main simulation code includes a line like this 8 17 Remote control 303 Brian Documentation Release 1 4 1 server RemoteControlServer In an Python shell you can do something l
98. and two rules to specify what should happen when a presynaptic neuron fires pre and when a postsynaptic neuron fires post The equations should be standard set of equations in the usual string format The pre and post rules should be a sequence of statements to be executed triggered on pre and post synaptic spikes The sequence of statements can be separated by a or by using a multiline string The reserved symbol w can be used to refer to the synaptic weight of the associated synapse This framework allows you to implement most STDP rules Specifying differential equations and pre and post synaptic event code allows for a much more efficient implementation than specifying for example the spike pair weight modification function but does unfortunately require transforming the definition into this form There is one restriction on the equations that can be implemented in this system they need to be separable into independent pre and post synaptic systems this is done automatically In this way synaptic variables and updates can be stored per neuron rather than per synapse Example eqs stdp n dA pre dt A pre tau pre gii dA post dt A post tau post 1 num stdp STDP synapses eqs eqs stdp pre A pre r delta A pre wt A_post post A post t delta A post wt A_pre wmax gmax STDP variables You can access the pre and post synaptic variables as follows stdp STDP print stdp A_pre Alternatively
99. array_name index_name resolve_python read write vectorisable item namespace If vectorisable it will prepend one of these two forms to item name array_name name array_name start end where start end array_slice if provided If not vectorisable it will return a for loop over either array name or array name start end supported languages python c gpu brian experimental codegen2 language_invariant_symbol_method basemethname langs fall back None doc None Helper function to create methods for Symbo1 classes Sometimes it is clearer to write a separate method for each language the Symbo1 supports This function can generate a method that can take any language and calls the desired method For example if you had defined two methods 1oad python and 1oad c then you would define the load method as follows load language invariant symbol method iloaGd python 1load python c load c The fallback gives a method to call if no language specific method was found A docstring can be provided to doc brian experimental codegen2 get neuron group symbols group language in dex neuron index pre fix Returns a dict of NeuronGroupStateVariable from a group Arguments group The group to extract symbols from language The language to use index The name of the neuron index by default neuron index prefix An optional prefix to add to each symbol 11 5 Code
100. as a time or a number of samples The updater The updater argument can be either a function or class instance If it is a function it should have a form like A single input def updater input Two inputs def updater inputl input2 Arbitrary number of inputs def updater xinputs Each argument input to the function is a numpy array of shape numsamples numchannels where numsamples is the number of samples just computed and numchannels is the number of channels in the corresponding filterbank The function is not restricted in what it can do with these inputs Functions can be used to implement relatively simple controllers but for more complicated situations you may want to maintain some state variables for example and in this case you can use a class The object updater should be an instance of a class that defines the call method with the same syntax as above for functions In addition you can define a reinitialisation method reinit which will be called when the buffer init method is called on the filterbank although this is entirely optional Example The following will do a simple form of gain control where the gain parameter will drift exponentially towards target rms rms with a given time constant This class implements the gain see Filterbank for details class GainFilterbank Filterbank def __init__ self source gain 1 0 Filterbank init self source self gain gain def buffer apply
101. attribute means that clock first will always be evaluated before clock second 4 12 1 Other clocks The default clock uses an underlying integer representation This behaviour was changed in Brian 1 3 from earlier ver sions which used a float representation To recover the earlier behaviour if it is important you can use FloatClock or NaiveClock You may want to have events that happen at regular times but still want to use the default clock for all other objects in which case you can use the EventClock for a network operation and it will not create any clock ambiguities e g from brian import x G NeuronGroup N eqs Qnetwork operation clock EventClock dt 1 second def do_something 4 13 Simulation control 4 13 1 The update schedule When a simulation is run the operations are done in the following order by default 4 13 Simulation control 213 Brian Documentation Release 1 4 1 1 Update every NeuronGroup this typically performs an integration time step for the differential equations defining the neuron model 2 Check the threshold condition and propagate the spikes to the target neurons 3 Update every Synapses this may include updating the state of targeted NeuronGroup objects 4 Reset all neurons that spiked 5 Call all user defined operations and state monitors The user defined operations and state monitors can be placed at other places in this schedule by using the key word w
102. autonomous 218 numerical integration 216 parameter 192 stochastic 217 time dependent 218 Equations class in brian 263 EquationsContainer class in brian experimental codegen2 375 erbspace example usage 49 83 109 111 113 115 120 123 124 erbspace in module brian hears 328 Euler numerical integration 217 euler in module brian experimental codegen2 375 evaluate brian RemoteControlClient method 303 EventClock example usage 66 77 EventClock class in brian 262 exact numerical integration 216 example usage AERSpikeMonitor 168 ApproximateGammatone 113 115 arcsinh 108 118 arctan 40 AsymmetricCompensation 120 Butterworth 112 Cascade 115 clear 168 click 128 Clock 96 99 165 181 Compartments 177 Connection 31 39 40 45 46 49 54 63 66 68 74 TT 79 82 84 97 99 102 106 109 130 132 154 156 158 160 162 164 165 167 170 172 174 177 179 181 185 187 ControlFilterbank 108 118 120 correlogram 60 cos 40 108 118 Current 155 167 177 180 CV 179 EmpiricalThreshold 174 Equations 43 45 91 93 95 97 99 133 134 141 156 171 172 174 erbspace 49 83 109 111 113 115 120 123 124 EventClock 66 77 exp 40 46 65 66 68 69 72 74 77 79 84 120 125 144 153 161 187 ExponentialSTDP 46 131 FilterbankGroup 49 83 109 115 firing rate 179 FunctionFilterbank 49 83 108 109 115 118 123 gain 115 186 Gammatone
103. b show Example compensation ex1 electrophysiology Example of L p electrode compensation method Requires binary files current npy and rawtrace npy Rossant et al A calibration free electrode compensation method J Neurophysiol 2012 import os from brian import x import numpy as np from brian library electrophysiology import working dir os path dirname __file__ load data dt 0 1 ms current np load os path join working dir current npy 10000 long vector 1s duration rawtrace np load os path join working dir trace npy 10000 long vector 1s duration t linspace 0 1 len current launch compensation r Lp_compensate current rawtrace dt p 1 0 full True print best parameters print Best parameters R tau Vr Re taue print r params plot traces subplot 211 plot t current k 92 Chapter 3 Getting started Brian Documentation Release 1 4 1 subplot 212 plot t rawtrace k f raw trace plot t x UVt uLlW full model trace neuron and electrode plot t r Vcompensated g compensated trace show Example compensation ex3 quality electrophysiology Example of quality check method Requires binary files current npy and rawtrace npy Rossant et al A calibration free electrode compensation method J Neurophysiol 2012 import os from brian import x import numpy as np from brian library electro
104. be a divisor of the original number 316 Chapter 8 Reference Brian Documentation Release 1 4 1 Note that higher order filters are often numerically unstable Notes These notes adapted from scipy s 1filter function The filterbank is implemented as a direct II transposed structure This means that for a single channel and element of the filter cascade the output y for an input x is defined by a 0 y m b 0 x m b 1 x m 1 b m x 0 a 1 v m 1 a m xy 0 using the following difference equations yli b 0 x i z 0 i 1 z 0 i b 1 x i z2 1 i 1 a 1 y i z m 3 i b m 2 x i z m 2 i 1 a m 2 xy i z m 2 i b m 1 x i a m 1 y i where i is the output sample number The rational transfer function describing this filter in the z transform domain is 1 nb b 0 b 1 z b m z I na a 0 a 1 z alm z class brian hears FIRFilterbank source impulse response use linearfilterbank False mini mum buffer size None Finite impulse response filterbank Initialisation parameters source Source sound or filterbank impulse response Either a 1D array providing a single impulse response applied to every input channel or a 2D array of shape nchannels ir length forir length the number of samples in the impulse response Note that if you are using a multichannel sound x as a set of impulse responses the array should be impulse respo
105. be defined as const specify this if only reading the value and not writing to it 11 5 Code generation 377 Brian Documentation Release 1 4 1 class brian experimental codegen2 MathematicalStatement var op expr dtype None A single line mathematical statement The structure is var op expr var The left hand side of the statement the value being written to a string op The operation can be any of the standard Python operators including etc or a special operator which means you are defining a new symbol whereas means you are setting the value of an existing symbol expr A string or an Expression object giving the right hand side of the statement dtype If you are defining a new variable you need to specify its numpy dtype If op then this statement will resolve var otherwise it will add a Write dependency for var The other dependencies come from expr convert to language symbols tabs 0 namespace When converting to a code string the following takes place If the LHS variable is in the set of symbols then the LHS is replaced by sym write The expression is converted with Expression convert to elf the operation is definition op then the output is language dependent For Python it is 1hs rhs and for C or GPU itis dtype lhs rhs elf the operation is not definition the statement is converted to lhs op rhs elf the language is C GPU the statement has appended
106. be the same size although subgroups can be used if they are not the same size Arguments source The group from which values will be taken var The state variable of the source group to take values from func An additional function of one argument to pass the source variable values through e g func lambda x clip x 0 Inf to half rectify the values when The time in the main Brian loop at which the copy operation is performed as explained in Net work clock The update clock for the copy operation by default it will use the clock of the target group 8 14 Analysis 8 14 1 Statistics of spike trains brian firing rate spikes Rate of the spike train brian CV spikes Coefficient of variation 8 14 Analysis 299 Brian Documentation Release 1 4 1 brian correlogram Tl T2 width 20 0 msecond bin 1 0 msecond T None Returns a cross correlogram with lag in width width and given bin size T is the total duration optional and should be greater than the duration of T1 and T2 The result is in Hz rate of coincidences in each bin N B units are discarded TODO optimise brian autocorrelogram T0 width 20 0 msecond binz 1 0 msecond T None Returns an autocorrelogram with lag in width width and given bin size T is the total duration optional and should be greater than the duration of T1 and T2 The result is in Hz rate of coincidences in each bin N B units are discarded brian CCF T1 T2
107. because multiple synapses can exist for a given pair or pre and post synaptic neurons In this case the state values for all the synapses between neurons i and j are aggregated in the 1 j position of the matrix This is done according to the multiple synapses keyword argument which can be changed mutiple synapses last default takes the last value mutiple synapses first takes the first value mutiple synapses min takes the min of the values mutiple synapses max takes the max of the values mutiple synapses sum takes the sum of the values Please note that this function should be used for visualization and should not be used to store or reload synaptic variable values If you want to do so refer to the documentation at Synapses save connectivity class brian synapses synapticvariable SynapticDelayVariable data synapses name A synaptic variable that is a delay The main difference with SynapticVariable is that delays are stored as integers timebins but accessed as absolute times in seconds TODO pass the clock as argument class brian synapses spikequeue SpikeQueue source synapses delays max delayz0 0 sec ond maxevents 1 precompute_offsets True Spike queue Initialised with arguments source The neuron group that sends spikes synapses A list of synapses synapses i array of synapse indices for neuron i delays An array of delays delays k delay of synapse k max del
108. by MagicNetwork objects created after clearing will still be collected If erase is True then it will also delete all data from these objects This is useful in for example ipython which stores persistent references to objects in any given session stopping the data and memory from being freed up If all True then all Brian objects will be cleared See also forget brian forget objs Forgets the list of objects passed Forgetting means that MagicNetwork will not pick up these objects but all data is retained You can pass objects or lists of objects Forgotten objects can be recalled with xeca11 See also clear brian recall objs Recalls previously forgotten objects See forget and clear class brian MagicNetwork verbose False level 1 Creates a Network object from any suitable objects Initialised as MagicNetwork The object returned can then be used just as a regular Net work object It works by finding any object in the execution frame i e in the same function script or section of module code where the MagicNetwork was created derived from NeuronGroup Connection or NetworkOperation Sample usage G NeuronGroup C Connection Qnetwork operation def f net MagicNetwork Each of the objects G C and f are added to net Advanced usage MagicNetwork verbose False level 1 with arguments verbose Setto True to print out a list of objects that were added to the ne
109. c c2 definition of the pole of the asymmetric comensation filters p0 2 pl 1 7818 1 0 0791 b2 1 0 1655 abs c2 p2 0 5689 1 0 1620 b2 1 0 0857 abs c2 ll 3 2 Examples 121 Brian Documentation Release 1 4 1 ll 0 2523 1 0 0244 b2 1 0 0574xabs c2 1 0724 p3 p4 definition of the parameters used in the control path output levels computation see IEEE paper for details decay tcst 5 ms order 1 lev weight 5 level ref 50 level pwrl 1 5 level pwr2 5 RMStoSPL 30 fratO 2330 fratl 005 exp deca val exp 1 decay_tcst samplerate log 2 level min 10 RMStoSPL 20 definition of the controller class What is does it take the outputs of the first and second fitlerbanks of the control filter as input compute an overall intensity level for each frequency channel It then uses those level to update the filter coefficient of its target the asymmetric compensation filterbank of the signal path class CompensensationFilterUpdater object def init self target self target target self levell prev 100 self level2 prev 100 def call self input valuel input 0 1 value2 input 1 1 the current level value is chosen as the max between the current output and the previous one decreased by a decay levell maximum maximum valuel 0 self levell prev exp deca val level2 maximum maximum value2
110. channel 1 params None A FilterbankGroup that represents an IHC AN synapse according to the Zhang et al 2001 model The source should be a filterbank producing V_ihc e g TanCarney CF specifies the characteristic frequencies of the AN fibers params overwrites any parameters values given in the publication The group emits spikes according to a time varying Poisson process with absolute and relative refractoriness probability of spiking is given by state variable R The continuous probability of spiking without refractoriness is available in the state variable s The n per channel argument can be used to generate multiple spike trains for every channel 8 21 Brian hears 327 Brian Documentation Release 1 4 1 If all you need is the state variable s you can use the class ZhangSynapseRate instead which does not simulate the spike generating Poisson process For details see Zhang X M G Heinz I C Bruce and L H Carney A Phenomenological Model for the Responses of Auditory nerve Fibers I Nonlinear Tuning with Compression and Suppression The Journal of the Acoustical Society of America 109 2001 648 8 21 5 Filterbank group class brian hears FilterbankGroup filterbank targetvar args kwds Allows a Filterbank object to be used as a NeuronGroup Initialised as a standard NeuronGroup object but with two additional arguments at the beginning and no N number of neurons argument The number of neurons
111. class EquallySpacedSpikeGroup SpikeGeneratorGroup def init self N t spikes 0 i dt for i in range N SpikeGeneratorGroup init self spikes You would use these objects in the following ways obj1 equally spaced spike group 100 10x ms obj2 EquallySpacedSpikeGroup 100 10 ms For simple examples like the one above there s no particular benefit to using derived classes but using derived classes allows you to add methods to your derived class for example which might be useful For more experienced Python programmers or those who are thinking about making their code into an extension for Brian this is probably the preferred approach Finally it may be useful to note that there is a protocol for one object to contain other objects That is suppose you want to have an object that can be treated as a simple NeuronGroup by the person using it but actually instantiates several objects perhaps internal Connection objects These objects need to be added to the Network object in order for them to be run with the simulation but the user shouldn t need to have to know about them To this end for any object added to a Net work if it has an attribute contained objects then any objects in that container will also be added to the network 6 3 Projects with multiple files or functions 251 Brian Documentation Release 1 4 1 6 4 Connection matrices A Connection object has an attribute W which is its
112. code may be used by someone else or if you want to make it into an extension to Brian 250 Chapter 6 Advanced concepts Brian Documentation Release 1 4 1 6 3 2 Use the magic return decorator or magic_register function The magic return decorator is used as follows Qmagic return def f return obj Any object returned by a function decorated by magic return will be considered to have been instantiated in the execution frame that called the function In other words the magic functions will find that object even though it was really instantiated in a different execution frame In more complicated scenarios you may want to use the magic register function For example def f magic register obj1l obj2 return obj1 obj2 This does the same thing as magic return but can be used with multiple objects Also you can specify a level see documentation on magic register for more details 6 3 3 Use derived classes Rather than writing a function which returns an object you could instead write a derived class of the object type So suppose you wanted to have an object that emitted N equally spaced spikes with an interval dt between them you could use the 5pikeGeneratorGroup class as follows Qmagic return def equally spaced spike group N dt spikes 0 i xdt for i in range N return SpikeGeneratorGroup spikes Or alternatively you could derive a class from SpikeGeneratorGroup as follows
113. common model of cochlear filtering is to apply a bank of gammatone filters and then half wave rectify and compress it for example with a 1 3 power law This can be achieved in Brian hears as follows for 3000 channels in the human hearing range from 20 Hz to 20 kHz cfmin cfmax cfN 20 Hz 20 kHz 3000 cf erbspace cfmin cfmax cfN sound Sound test wav gfb GammatoneFilterbank sound cf ihe FunctionFilterbank gfb lambda x clip x 0 Inf 1 0 3 0 The erbspace function constructs an array of centre frequencies on the ERB scale The GammatoneFilterbank source cf class creates a bank of gammatone filters with inputs coming from source and the centre frequencies in the array cf The FunctionFilterbank source func creates a bank of filters that applies the given function func to the inputs in source Filterbanks can be added and multiplied for example for creating a linear and nonlinear path e g sum path fb 0 1 linear_path_fb 0 2 nonlinear_path_fb A filterbank must have an input with either a single channel or an equal number of channels In the former case the single channel is duplicated for each of the output channels However you might want to apply gammatone filters to a stereo sound for example but in this case it s not clear how to duplicate the channels and you have to specify it explicitly You can do this using the Repeat Tile Join and Interleave filterbanks For example if the input is a
114. computationally expensive operation running at a lower frequency 8 3 1 The Clock class class brian Clock args kwds An object that holds the simulation time and the time step Initialisation arguments dt The time step of the simulation t The current time of the clock order If two clocks have the same time the order of the clock is used to resolve which clock is processed first lower orders first makedefaultclock Setto True to make this clock the default clock The times returned by this clock are always off the form n dt offset for integer n and float dt and offset For example for a clock with dt 10 ms setting t 25 ms will set n 2 and of fset 5x ms For a clock that uses true float values for t rather than underlying integers use F1oatClock although see the caveats there In order to make sure that certain operations happen in the correct sequence you can use the order attribute clocks with a lower order will be processed first if the time is the same The condition for two clocks to be considered as having the same time is abs t1 t2 epsilonxabs t1 a standard test for equality of floating point values For ordinary clocks based on integer times the value of epsilonis 1e 14 and for float based clocks it is 1e 8 The behaviour of clocks was changed in version 1 3 of Brian if this is causing problems you might try using FloatClock or if that doesn t solve the problem NaiveClock Methods reinit rz0 seco
115. documentation As an example of the ease of use and clarity of programs written in Brian the following script defines and runs a randomly connected network of 4000 integrate and fire neurons with exponential currents from brian import x eqs dv dt ge gi v 49xmV 20xms volt dge dt ge 5 ms volt dgi dt gi 10 ms volt Fay P zNeuronGroup 4000 model eqs threshold 50 mV reset 60 mV P v 60 xmV Pe P subgroup 3200 Pi P subgroup 800 Ce Connection Pe P ge weight 1 62xmV sparseness 0 02 Ci Connection Pi P gi weight 9 mV sparseness 0 02 M SpikeMonitor P run 1 second raster_plot M show As an example of the output of Brian the following two images reproduce figures from Diesmann et al 1999 on synfire chains The first is a raster plot of a synfire chain showing the stabilisation of the chain Brian Documentation Release 1 4 1 Synfire chain raster plot 0 20 40 1 60 BO 100 Time in mas The simulation of 1000 neurons in 10 layers each all to all connected to the next using integrate and fire neurons with synaptic noise for 100ms of simulated time took 1 second to run with a timestep of 0 1ms on a 2 4GHz Intel Xeon dual core processor The next image is of the state space figure 3 2 Chapter 1 Introduction Brian Documentation Release 1 4 1 0 5 Lo 1 3 zu Z0 KAT m ims The figure computed 50 averages for each of 121 starting points over 10
116. dt 3 GNaxh xmx x3 ENa v GK n 44 GK mx n m EK v GL EL v 1 C volt Sodium activation ni snfeminf v s 1 minf v tau m taum v second dm dt m inf m tau m 1 Sodium inactivation h inf hinf v 1 tau h tauh v second dh dt h inf h tau h 1 Potassium delay rectifier 3 2 Examples 37 Brian Documentation Release 1 4 1 n infsninf v 1 tau n taun v second dn dt n inf n tau n 1 gK GK n x4 siemens Potassium muscarinic alphan m A alphan mx v v12 alphan m 1 exp v12 alphan m v k alphan m hertz betan m A alphan mx v v12 alphan m 1 exp v12 alphan m v k alphan m hertz n minf alphan m alphan m betan m 1 taun m 1 alphan m betan m tadj second dn m dt n minf n m taun m 1 gK m GK m n m siemens Fluctuating synaptic conductances I rectify ge Ee v rectify gi Ei v amp dge dt 1 5 ge0 ge taue 1 5 sigmaex 2 taue 5 xi siemens dgi dt gi0 gi tauit t2 sigmaix 2 taui 5 xi siemens gtot GL rectify ge rectify gi gK gK_m siemens mmm neurons NeuronGroup N model eqs implicit True neurons v EL neurons m minf EL neurons h hinf EL neurons n ninf EL neurons n_m 0 M StateMonitor neurons v record True Mh StateMonitor neurons h record True run duration report text Collect spike thresholds and values of h threshold logh
117. dt gKinf gK tauK 1 IKLT dgK2 dt gK2 tauK2 1 Delayed rectifier gKinf 1 1 exp Va v ka 1 tauK ms tau ms gmax 1 ginh 1 Tow uniform lambda N rand N 5 2 uniform between 1 and 1 seed 31415 Get the same neurons every time neurons NeuronGroup N model eqs threshold v gt Vt reset v Vr gK2 1 neurons v Vr neurons gK 1 1 exp Va El ka neurons tauK 400 ms uniform N tauK spread alpha El Vt Vt EK 66 Chapter 3 Getting started Brian Documentation Release 1 4 1 neurons gmax alpha minx maxx minx rand N neurons tau 30 ms uniform N tau spread Store the value of state variables at rest print Calculate resting state run 2 second rest zeros neurons _S shape rest neurons _S Postsynaptic neurons noisy coincidence detectors eqs post dv dt n v tau cd 1 dn dt n tau n sigma 2 tau n x 5 xi 1 p postneurons NeuronGroup Nout model eqs_post threshold 1 reset 0 refractory refractory Random connections between pre and post synaptic neurons C Connection neurons postneurons v sparseness Nsynapses 1 N weight w0 STDP eqs stdp dApre dt Apre tau pre 1 Apost 1 To zh pre Apret a pre wt 0 b_prexw EES post Apost 0 wt Apretb_postx w rq Stdp STDP C eqs_stdp pre pre post post wmax Inf Record the evolution of synaptic weights MC C
118. duration report text Figure figure Raster plot subplot 211 Fig 6B i t zip i t for i t in spikes spikes if i 25 plot t leben 1i T50 k i t zip i t for i st in spikes spikes if i gt N amp i lt N 25 plot t array i i N 25 E i t zip i t for i t in spikes spikes if i 2 N amp i lt 2 N 25 plot t array i 2xN b ylim 0 75 xlabel Time s ylabel Trials Cross correlograms CC width 100 ms bin l1 ms spikes spikes spiketimes C_AB correlogram spikes 0 spikes N width width T duration for i in range 1 N C_AB correlogram spikes i spikes N i width width T duration C_AC correlogram spikes 0 spikes 2 N width width T duration for i in range 1 N C_AC correlogram spikes i spikes 2 N i width width T duration Shuffled auto correlogram SAC C 0 C_AB for i in range 0 N for j in range 0 N if i j C correlogram spikes i spikes j width width T duration lag arange len C 1len C 2 bin subplot 223 Fig 6C plot lag ms C bin N N 1 k ylim 0 1 1 max C AB binxN xlabel Lag ms ylabel Coincidences subplot 224 Fig 6D plot lag ms C_AB binxN k A vs B plot lag ms C AC bin N r A vs C ylim 0 1 1 max C_AB bin N xlabel Lag ms ylabel Coincidences show 62 Chapter 3 Getting started Brian Docu
119. eqs neuron dv dt Rm i v taum volt di dt i tau e amp Fg 150 Chapter 3 Getting started Brian Documentation Release 1 4 1 neuron NeuronGroup N model eqs_neuron taud 1 ms tauf 100 ms U 1 t aud 100 ms tauf 10 ms U 6 S Synapses input neuron model x 1 d d al we Wee pre u U u U xexp t lastupdate tauf x lt x 1 x exp t lastupdate taud it w ux x x 1 u uUr Ux 1 u f S i 3 one to one connection S w A SE Initialization of STP variables S x 1 S u U trace StateMonitor neuron v record 0 N 1 run 1000 ms subplot 211 plot trace times ms trace 0 title Vm subplot 212 plot trace times ms trace N 1 title Vm show mV mV Example STDP1 bis synapses Spike timing dependent plasticity Adapted from Song Miller and Abbott 2000 and Song and Abbott 2001 This simulation takes a long time Original time 278 s with DelayConnection 478 s New time 416 s from brian import x from time import time N 1000 taum 10 ms taupre 20 ms taupost taupre Ee 0 mV vt 54 mV vr 60 mV dApre 01 dApost dApre taupre taupost 1 05 3 2 Examples 151 Brian Documentation Release 1 4 1 dApost gmax dApre gmax eqs neurons dv dt ge Ee vr El v taum volt the synaptic current is linearized dge dt ge taue 1 FE in
120. eqs prepare This is automatically called by the NeuronGroup initialiser 4 15 File management A few functions are provided to read files with common formats The function xead neuron dat reads a Neuron dat text file and returns a vector of times and a vector of values This is the format used by the Neuron simulator when saving the time varying value of a variable from the GUI For example t v read neuron dat myfile dat The function read_atf reads an Axon atf text file and returns a vector of times and a vector of values This is a format used to store data recorded with Axon amplifiers Note that metadata stored in the file are not extracted Binary abf files are currently not supported See also Input output 4 15 File management 219 Brian Documentation Release 1 4 1 4 16 Managing simulation runs and data Often you want to run a simulation multiple times with different parameters to generate data for a plot There are many different ways to manage this and Brian has a few tools to make it easier 4 16 1 Saving data by hand The simplest strategy is to run your simulation and then save the data with a unique filename using either pickle writing text or binary data to a file with Python or with Numpy and Scipy 4 16 2 Structured data formats Another option is to use a more structured file type for example you could use the high performance HDF5 scientific data file format with PyTables
121. experimental codegen2 GPUSymbolMemoryManager usefloat False Manages symbol memory on the GPU Stores an attribute device and host which are dicts with keys the symbol names and values pycuda gpuarray GPUArray and numpy ndarray respectively Add symbols with add symbols which will allocate memory add symbols items Adds a collection of symbols Each item in items is of the form symname hostarr devname where symname is the sym bol name hostarr is the numpy ndarray containing the data and devname is the name the array pointer should have on the device Allocates memory on the device and copies data to the GPU copy to device symname Copy the memory in the numpy ndarray for symname to the allocated device memory If symname True do this for all symbols You can also pass a list for symname copy to host symname As for copy to device but copies memory from device to host generate code Generates declarations for array pointer names on the device and kernels to copy device pointers to the array pointers General form is device dtypestr name global void set array namej dtypestr _ name name _ name Stores the kernel function names in attribute symbol upload funcnames dict with keys being sym bol names Returns a string with declarations and kernels combined names The list of symbol names managed class brian experimental codegen2 GPUCode name cod
122. factor determining the time constant of the second filterbank order ERB 4 ERBrate 21 4 10g10 4 37 cf 1000 1 ERBwidth 24 7 x 4 37xcf 1000 1 ERBspace mean diff ERBrate the filter coefficients are updated every update_interval here in samples update_interval 1 bank of passive gammachirp filters As the control path uses the same passive filterbank than the signal path but shifted in frequency this filterbank is used by both pathway pGc LogGammachirp sound cf b b1 c cl fpl cf cl ERBwidth bl order ERB centre frequency of the signal path Control Path the first filterbank in the control path consists of gammachirp filters value of the shift in ERB frequencies of the control path with respect to the signal path lct ERB 1 5 n ch shift round lct ERB ERBspace value of the shift in channels index of the channel of the control path taken from pGc indchl control minimum maximum 1 arange 1 nbr cf 1 n ch shift nbr cf astype int 1 fpl control fpl indchl control the control path bank pass filter uses the channels of pGc indexed by indchl control pGc control RestructureFilterbank pGc indexmapping indchl control the second filterbank in the control path consists of fixed asymmetric compensation filters frat control 1 08 fr2 control frat control fpl control asym comp control AsymmetricCompensation pGco control fr2 control b b2
123. filename normalise False samplewidthz2 Save the sound as a WAV If the normalise keyword is set to True the amplitude of the sound will be normalised to 1 The sam plewidth keyword can be 1 or 2 to save the data as 8 or 16 bit samples 8 21 Brian hears 311 Brian Documentation Release 1 4 1 play normalise False sleep False Plays the sound normalised to avoid clipping if required If sleep True then the function will wait until the sound has finished playing before returning Properties duration The length of the sound in seconds nsamples The number of samples in the sound nchannels The number of channels in the sound times An array of times in seconds corresponding to each sample left The left channel for a stereo sound right The right channel for a stereo sound channel 7 Returns the nth channel of the sound Generating sounds All sound generating methods can be used with durations arguments in samples int or units e g 500 ms One can also set the number of channels by setting the keyword argument nchannels to the desired value Notice that for noise the channels will be generated independantly static tone args kwds Returns a pure tone at frequency for duration using the default samplerate or the given one The frequency and phase parameters can be single values in which case multiple channels can be speci fied with the nchannels argument or they can be sequences lists t
124. frequen cies phase is the unwrapped phase of spectrum brian hears savesound sound filename normalise False samplewidth 2 Save the sound as a WAV If the normalise keyword is set to True the amplitude of the sound will be normalised to 1 The samplewidth keyword can be 1 or 2 to save the data as 8 or 16 bit samples brian hears loadsound filename Load the file given by filename and returns a Sound object Sound file can be either a wav or a aif file brian hears play sounds normalise False sleep False Plays the sound normalised to avoid clipping if required If sleep True then the function will wait until the sound has finished playing before returning brian hears whitenoise args kwds Returns a white noise If the samplerate is not specified the global default value will be used brian hears powerlawnoise args kwds Returns a power law noise for the given duration Spectral density per unit of bandwidth scales as 1 f alpha Sample usage noise powerlawnoise 200 ms 1 samplerate 44100 Hz Arguments duration Duration of the desired output alpha Power law exponent samplerate Desired output samplerate brian hears brownnoise args kwds Returns brown noise i e powerlawnoise with alpha 2 brian hears pinknoise args kwds Returns pink noise i e powerlawnoise with alpha 1 brian hears irns args kwds Returns an IRN_S noise The iterated ripple noise is obtained trough a
125. group NeuronGroup N model dv dt v0 v tau W Connection group group v weight w group v rand N 10 mV S SpikeMonitor group run 300 ms raster plot S show Example rate model misc A rate model from brian import x N 50000 tau 20 ms I 10 Hz eqs rrt volt threshold 10 mV dv dt I v tau Hz note the unit here this is the output rate rrt group NeuronGroup N eqs threshold PoissonThreshold S PopulationRateMonitor group bin 1 ms run 100 ms plot S rate show Example realtime_plotting misc Realtime plotting example reset 0 mV These lines are necessary for interactive plotting when launching from the Eclipse IDE they may not be necessary in every environment 160 Chapter 3 Getting started Brian Documentation Release 1 4 1 import matplotlib matplotlib use WXAgg You may need to experiment try WXAgg GTKAgg QTAgg TkAgg from brian import x Set up the standard CUBA example N 4000 eqs dv dt getgi v 49 mV 20 ms volt dge dt ge 5 ms volt dgi dt gi 10 ms volt pan P NeuronGroup N eqs threshold 50 mV reset 60 mV P v 60 x mV 10 mV x rand len P Pe P subgroup 3200 Pi P subgroup 800 Ce Connection Pe P ge weight 1 62 mV sparseness 0 02 Ci Connection Pi P gi weight 9 mV sparseness 0 0
126. groups case this parameter can only have one value i e every group will have the same value the first of the list 8 19 Model fitting toolbox 309 Brian Documentation Release 1 4 1 bound strategy 1 In the case of a bounded problem there are two ways to handle the new generated points which fall outside the boundaries note for different groups case this parameter can only have one value i e every group will have the same value the first of the list bound_strategy 1 With this strategy every point outside the domain is repaired i e it is pro jected to its nearset possible value repairea In other words components that are infeasible in x are set to the closest boundary value in 2 epaireq The fitness function on the repaired search points is evaluated and a penalty which depends on the distance to the repaired solution is added f fitness Z f Erepairea t Lrepairea The repaired solution is disregarded afterwards bound_strategy 2 With this strategy any infeasible solution x is resampled until it become feasi ble It should be used only if the optimal solution is not close to the infeasible domain See p 28 of lt http www Iri fr hansen cmatutorial pdf gt for more details gamma gamma is the weight y in the previously introduced penalty function note for different groups case this parameter can only have one value i e every group will have the same value the first of the list 8 20 E
127. hrtfset fb hrtfset filterbank Repeat swapped channels num indices Now we apply cochlear filtering logically this comes before the HRTF filtering but since convolution is commutative it is more efficient to do the cochlear filtering afterwards cfmin cfmax cfN 150 Hz 5x kHz 40 cf erbspace cfmin cfmax cfN We repeat each of the HRTFSet filterbank channels cfN times so that for each location we will apply each possible cochlear frequency gfb Gammatone Repeat hrtfset_fb cfN tile cf hrtfset fb nchannels Half wave rectification and compression cochlea FunctionFilterbank gfb lambda x 15 clip x 0 Inf 1 0 3 0 Leaky integrate and fire neuron model eqs dV dt I V 1 ms 0 1 xi 0 5 ms 5 1 ds ud Fay G FilterbankGroup cochlea I qs reset 0 threshold 1 refractory 5 ms The coincidence detector cd neurons cd NeuronGroup num_indices cfN eqs reset 0 threshold 1 clock G clock Each CD neuron receives precisely two inputs one from the left ear and one from the right for each location and each cochlear frequency C Connection G cd V for i in xrange num indices cfN C i i 0 5 from right ear C i num indices cfN i 0 5 from left ear We want to just count the number of CD spikes counter SpikeCounter cd Run the simulation giving a report on how long it will take as we run run sound duration report stderr We take the
128. import loadtxt ms Equations from brian library modelfitting import af name main__ List of machines IP addresses machines bobs machine university com jims machine university com equations Equations dV dt RxI V tau 1 L3 B s tau second EP input loadtxt current txt spikes loadtxt spikes txt results modelfitting model equations reset 0 threshold 1 data spikes input input dt 1 ms popsize 1000 maxiter 3 delta 4 ms unit type CPU machines machines R 1 0e9 9 0e9 tau 10 ms 40xms refractory 0 ms 10xms print table results Example modelfitting modelfitting Model fitting example Fit an integrate and fire model to an in vitro electrophysiological recording during one second from brian import loadtxt ms Equations from brian library modelfitting import Xf name main 134 Chapter 3 Getting started Brian Documentation Release 1 4 1 equations Equations dV dt R I V tau 1 EaI Eu tau second p input loadtxt current txt spikes loadtxt spikes txt results modelfitting model equations reset 0 threshold 1 data spikes input input dt 1lx ms popsize 1000 maxiter 3 delta 4 ms R 1 0e9 9 0e9 tau 10 ms 40xms refractory 0 ms 10 ms print_table results 3 2 14 synapses Example delayed_stdp sy
129. in brian experimental codegen2 370 PythonForBlock class in brian experimental codegen2 367 PythonIfBlock class in brian experimental codegen2 368 PythonLanguage class in brian experimental codegen2 376 Q quantity 259 reinit default clock in module brian 263 remote control 302 RemoteControlClient example usage 159 RemoteControlClient class in brian 303 RemoteControlServer example usage 174 RemoteControlServer class in brian 302 Repeat example usage 49 83 109 Repeat class in brian hears 318 repeat brian hears Sound method 313 reporting progress 304 reset 266 variable 266 Reset class in brian 266 resized brian hears Sound method 313 Index 397 Brian Documentation Release 1 4 1 resolution_requires_loop brian experimental codegen2 ArrayIndex method 382 resolution requires loopO brian experimental codegen2 SliceIndex method 381 resolution requires loopO brian experimental codegen2 Symbol method 379 brian experimental codegen2 ArrayIndex method 382 resolve run in module brian 288 run all tests in module brian 335 RuntimeSymbol class in brian experimental codegen2 380 S samplerate brian hears Filterbank attribute 332 save brian experimental codegen2 Symbol method 380 save brian hears Sound method 311 savesound in module brian hears 315 resolve brian experimental codegen2 DenseMatrixS
130. in the group will be the number of channels in the filterbank TODO add reference to interleave serial channel stuff here filterbank The Filterbank object to be used by the group In fact any Bufferable object can be used targetvar The target variable to put the filterbank output into One additional keyword is available beyond that of NeuronGroup buffersize 32 The size of the buffered segments to fetch each time The efficiency depends on this in an unpredictable way larger values mean more time spent in optimised code but are worse for the cache In many cases the default value is a good tradeoff Values can be given as a number of samples or a length of time in seconds Note that if you specify your own Clock it should have 1 dt samplerate 8 21 6 Functions brian hears erbspace args kwds Returns the centre frequencies on an ERB scale low high Lower and upper frequencies N Number of channels earQ 9 26449 minBW 24 7 0rder 1 Default Glasberg and Moore parameters brian hears asymmetric compensation coeffs samplerate fr filt b filt a b c pO pl p2 p3 p4 This function is used to generated the coefficient of the asymmetric compensation filter used for the gammachirp implementation 8 21 7 Plotting brian hears log frequency xaxis labels ax None freqs None Sets tick positions for log scale frequency x axis at sensible locations Also uses scalar representation rather than exponential i e 100 rather than 10 2
131. initial burst sigma self chaingroup V q Vr rand len self chaingroup q Vt q Vr def run self Network run self self params duration def plot self raster plot ylabel 2 Layer title Synfire chain raster plot color 1 0 0 markersize 3 3 2 Examples 29 Brian Documentation Release 1 4 1 showgrouplines True spacebetweengroups 0 2 grouplinecol 0 5 0 5 self mon def estimate params mon time est Quick and dirty algorithm for the moment for a more decent algorithm use leastsq algorithm from scipy optimize minpack to fit const Gaussian http www scipy org doc api_docs SciPy optimize minpack html leastsq i times zip mon spikes times array times times times abs times time est lt 15 ms if len times return 0 0 ms better time est times mean times times abs times time est lt 5 ms if len times 0 return 0 0 ms return len times times std def single sfc net DefaultNetwork default params net run net plot def state space grid neuron multiply verbose True amin 0 amax 100 sigmamin 0 x ms sigmamax 3 ms params default_params params num_layers 1 params neurons per layer params neurons per layer neuron multiply net DefaultNetwork params i 0 uncomment these 2 lines for TeX labels import pylab pylab rc_params update text usetex True if verbose pr
132. input currents to neurons from brian import x N 5 duration 100 ms Vr 60 mV Vt 50 mV tau 10 ms Rmin 1 Mohm Rmax 10 Mohm freq 50 x Hz k 10 nA dV dt V Vr R I tau volt G NeuronGroup N qs reset V Vr threshold V Vt G R linspace Rmin Rmax N t linspace 0 second duration int duration defaultclock dt I clip k sin 2 pi freq t 0 Inf G I TimedArray I M MultiStateMonitor G record True run duration subplot 211 M I plot ylabel I amp subplot 212 M V plot ylabel V volt 166 Chapter 3 Getting started Brian Documentation Release 1 4 1 show Example topographic_map misc Topographic map an example of complicated connections Two layers of neurons The first layer is connected randomly to the second one in a topographical way The second layer has random lateral connections from brian import N 100 tau 10 ms tau_e 2 x ms AMPA synapse eqs LOD dv dt I v tau volt dI dt I tau e volt py rates zeros N Hz rates N 2 10 N 2 10 ones 20 30 Hz layerl PoissonGroup N rates rates layer2 NeuronGroup N model eqs threshold 10 mV reset 0 mV topomap lambda i j exp abs i j 1 3 mV feedforward Connection layerl layer2 sparseness 5 weight topomap Zfeedforward 2 3 1 mV lateralmap lambda i j exp abs i j
133. into the following directories brian The main package documented above with the following additional directories deprecated For code that is no longer up to date but that we keep for backwards compatibility experimental Package for storing experimental code that can be used but whose syntax and functionality may change library Modules where specific models are defined e g neuron and synaptic models tests Package for storing tests composed of 11 7 Repository structure 385 Brian Documentation Release 1 4 1 testcorrectness Package for tests of mathematical correctness of algorithms etc testinterface Package for tests of individual Brian modules Module names are the names of the module being tested prepended by test unused Old stuff utils Modules that are not Brian specific for example circular py defines circular arrays used for storing spiking events dev The main development folder for works in progress debugging stuff tools etc Consists of benchmarking Code for benchmarking performance against other languages and simulators BEPs The Brian Enhancement Proposals debugging Dumping ground for files used for debugging a problem troubleshooting Used for debugging problems from the brian support mailing list ideas For ideas for new features incomplete implementations etc This is where new things go before going into the main Brian package or the experimental package logo The Brian logo in va
134. ionMat rix for details on connection matrix types This class implements a sparse matrix with a variable number of nonzero entries Row access and column access are provided but are not as fast as for SparseConnectionMatrix The matrix should be initialised with a scipy sparse matrix The get row and get col methods return 5parseConnectionVector objects In addition to the usual slicing operations supported M val is supported where val must be a scalar or an array of length nnz Implementation details The values are stored in an array alldata of length nnzmax maximum number of nonzero entries This is a dynamic array see http en wikipedia org wiki Dynamic array You can set the resizing constant with the argument dynamic array const Normally the default value 2 is fine but if memory is a worry it could be made smaller Rows and column point in to this data array and the list row j consists of an array of column indices for each row with coli containing arrays of row indices for each column Similarly rowdataind and coldataind consist of arrays of pointers to the indices in the alldata array 8 7 2 Construction matrix types class brian ConstructionMatrix Base class for construction matrices 278 Chapter 8 Reference Brian Documentation Release 1 4 1 A construction matrix is used to initialise and build connection matrices A ConstructionMatrix class has to implement a method connection_matrix args
135. is the amount of time elapsed and complete is the fraction of the run completed See function how many spikes to see where these messages come from pid elapsed complete message queue get nowait controller update process pid to id pid elapsed complete except QueueEmpty break controller update if stoprunningsim 0 print Terminated simulation processes break controller destroy He Hec SHS SH SHS def plot_result weight numspikes plot weight numspikes color 0 0 0 5 axis tight draw this forces matplotlib to redraw Note that how_many_spikes only takes one argument which is a tuple of its actual arguments The reason for this is that Pool imap_unordered can only pass a single argument to the function its applied to but that argument can be a tuple def how many spikes excitatory weight message queue reinit default clock clear True ore eqs dv dt getgi v 49 mV 20 ms volt dge dt ge 5 ms volt dgi dt gi 10 ms volt r P NeuronGroup 4000 eqs threshold 50 mV reset 60 mV P v 60 mV 10 mV x rand len P Pe P subgroup 3200 Pi P subgroup 800 Ce Connection Pe P ge Ci Connection Pi P gi Ce connect random Pe P 0 02 weight excitatory weight Ci connect random Pi P 0 02 weight 9 mV 88 Chapter 3 Getting started Brian Documentation Release 1 4 1 if
136. is the only code generation version of a Brian class which is not GPU enabled at present 11 5 5 Extending code generation To extend code generation you will probably need to add new Symbo1 classes Read the documentation for this class to start and the documentation for the most important symbols SliceIndex ArraySymbol ArrayIndex NeuronGroupStateVariableSymbol See also Code Item particularly the process described in CodeItem generate 362 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 11 5 6 Inheritance diagrams The overall structure of the classes in the code generation package are included below for reference Languages languages Language languages CLanguage languages PythonLanguage management GPULanguage 11 5 Code generation 363 Brian Documentation Release 1 4 1 Code objects codeobject Code codeobject PythonCode codeobject CCode management GPUCode Code items codeitems Codeltem ras statements Statement blocks Block m statements MathematicalStatement statements CodeStatement blocks ControlBlock y statements CDefineFromArray blocks IfBlock blocks ForBlock blocks PythonifBlock blocks CIfBlock blocks PythonForBlock blocks CForBlock Equations ex
137. is to write a list of the differential equations that define it For the moment we ll just give the simplest possible example a single differential equation You write it in the following form dx dt f x unit where x is the name of the variable f x can be any valid Python expression and unit is the physical units of the variable x In our case we will write dV dt V El tau volt to define the variable V with units volt To complete the specification of the model we also define a threshold and reset value and create a group of 40 neurons with this model G NeuronGroup N 40 model dV dt V El tau volt threshold Vt reset Vr 3 1 Tutorials 13 Brian Documentation Release 1 4 1 The statement creates a new object G which is an instance of the Brian class NeuronGroup initialised with the values in the line above and 40 neurons In Python you can call a function or initialise a class using keyword arguments as well as ordered arguments so if I defined a function f x y I could call itas f 1 2 or as f y 2 x 1 and get the same effect See the Python tutorial for more information on this For the moment we leave the neurons in this group unconnected to each other each evolves separately from the others Simulation Finally we run the simulation for 1 second of simulated time By default the simulator uses a timestep dt 0 1 ms run l second And that s it To see some
138. it doesn t give it a name only a pointer and the kernel functions use a named array Calls GPUSymbolMemoryManager generate code initialise memory Copies allocated memory pointers to named global memory pointer variables so that kernels can use them The kernel names to do this are in the GPUSymbolMemoryManager symbol upload funcnames dict keys are symbol names and the allocated pointers are in the GPUSymbolMemoryManager device dict make combined kernel names Not used at present Will be used to combine multiple kernels with the same vectorisation index for efficiency prepare Compiles code and initialises memory Performs the following steps 11 5 Code generation 373 Brian Documentation Release 1 4 1 1 GPUKernel prepare is called for each kernel converting the partial code into a complete kernel and adds symbols to the GPUSymbolMemoryManager which allocates space on the GPU and copies data to it from the CPU 2 generate_code is called combining individual kernels into one source file and adding mem ory management kernels and declarations 3 compile is called which JIT compiles the code using pycuda 4 initialise_memory is called which allocates memory run name Runs the named kernel Calls GPUKernel run Note that all symbols are copied to and from the GPU before and after the kernel run although this is only for the development phase and will change later class brian
139. last parameter is the inverse of the sampling frequency I and Vraw must be 1D Numpy arrays with the same length The Lp_compensate function returns the compensated trace Vcomp and the best parameters params which is a 2D Numpy array where each column contains the parameters R tau Vr Re taue Columns correspond to consecutive slices of the current and the voltage the compensation is performed independently on each slice The duration of the slices can be specified with the slice_duration keyword argument Also the p parameter can also be specified as a keyword argument 5 5 Electrophysiology trace analysis The electrophysiology library also contains methods to analyze intracellular recordings To import the electrophysiol ogy library from brian library electrophysiology import x There is a series of example scripts in the examples electrophysiology folder Currently most methods are related to the analysis of spike shape 230 Chapter 5 The library Brian Documentation Release 1 4 1 5 5 1 Miscellaneous You can low pass filter a trace as follows v lp lowpass v tau where tau is the time constant cut off frequency 1 2 pi tau and v is the trace a vector of values By default tau is in units of the timestep Alternatively one can specify the timestep v lp lowpass v tau dt 0 1 ms 5 5 2 Spike analysis Detecting spikes The following function returns the time indexes of spike peaks in a trace v peaks sp
140. list attribute contents which is a sequence of items and implements iter to return iter contents CodeStatement Defines a fixed string which is not language invariant and a fixed set of dependencies and resolved The convert to method simply returns the fixed string Does not define an__iter__ method because the default values for dependencies and resolved are overwritten convert to language symbols namespace Returns a string representation of the code for this item in the given language From the user point of view you should call generate but in developing new CodeItem derived classes you need to implement this The default behaviour is simply to concatenate the strings returned by the subitems generate name language symbols namespace None Returns a Code object The method resolves the symbols using resolve converts to a string with convert to and then converts that to a Code object with Language code object subdependencies subresolved codeobject class brian experimental codegen2 Code name code str namespace pre_code None post_code None language None The basic Code object used for all Python C GPU code generation The Code object has the following attributes name The name of the code should be unique This matters particularly for GPU code which uses the name attribute for the kernel function names code_str A representation of the code in string form namespace A dictionary o
141. ll run 100 ms plot Mv times ms Mv 0 mV 158 Chapter 3 Getting started Brian Documentation Release 1 4 1 plot Mw times ms Mw 0 mV show Example phase locking misc Phase locking of IF neurons to a periodic input from brian import x tau 20 ms N 100 b 1 2 constant current mean the modulation varies f 10 Hz eqs etr dv dt vt axsin 2 pixf t b tau 1 CER ME rrt neurons NeuronGroup N model eqs threshold 1 reset 0 neurons v rand N neurons a linspace 05 0 75 N S SpikeMonitor neurons trace StateMonitor neurons v record 50 run 1000 ms subplot 211 raster plot S subplot 212 plot trace times ms trace 50 show Example remotecontrolclient misc Example of using RemoteControlServer and RemoteControlClient to control a simulation as it runs in Brian Run the script remotecontrolserver py before running this from brian import x import time client RemoteControlClient time sleep 1 subplot 121 plot client evaluate M times M values client execute G I 1 1 time sleep 1 subplot 122 plot client evaluate M times M values 3 2 Examples 159 Brian Documentation Release 1 4 1 client stop show Example mirollo strogatz misc Mirollo Strogatz network from brian import x tau 10 ms vO 11 mV N 20 w 1 mV
142. lo Hog ge randn len P 1 5 4 10 nS gi randn len P 12 20 10 nS Record the number of spikes and a few traces trace StateMonitor P v record 1 10 100 3 2 Examples 175 Brian Documentation Release 1 4 1 run l second plot trace 1 plot trace 10 plot trace 100 show Example stim2d misc Example of a 2D stimulus see the complete description at the Brian Cookbook from brian import x import scipy ndimage as im all bar StimulusArrayGroup def bar width height thickness angle Kor An array of given dimensions with a bar of given thickness and angle EFF stimulus zeros width height stimulus int height 2 thickness 2 int height 2 thickness 2 1 stimulus im rotate stimulus angle reshape False return stimulus class StimulusArrayGroup PoissonGroup KW A group of neurons which fire with a given stimulus at a given rate The argument stimulus should be a 2D array with values between 0 and 1 The point in the stimulus array at position y x will correspond to the neuron with index i y widthtx This neuron will fire Poisson spikes at rate xstimulus y x Hz The stimulus will start at time onset for auration Kr def init self stimulus rate onset duration height width stimulus shape stim stimulus ravel rate self stimulus stim def stimfunc t if ons
143. mV ylabel w nA show Example Diesmann et al 1999 longer frompapers Implementation of synfire chain from Diesmann et al 1999 Dan Goodman Dec 2007 import brian no units from brian import x import time from brian library IF import from brian library synapses import def minimal example Neuron model parameters Vr 70 mV Vt 55 mV taum 10 ms taupsp 0 325 ms weight 4 86 mV Neuron model equations Equations dV dt V Vr x 1 taum so wolt dx dt x y 1 taupsp veut dy dt y 1 taupsp 25 27 mV ms 39 24 mV msx x0 5 xxi volt rer Neuron groups P NeuronGroup N 1000 model equations threshold Vt reset Vr refractory 1 ms P NeuronGroup N 1000 model dV dx dy init 0 volt 0 volt 0 volt threshold Vt reset Vr refractory 1 ms Pinput PulsePacket t 50 ms n 85 sigma l ms The network structure 3 2 Examples Brian Documentation Release 1 4 1 Pgp P subgroup 100 for i in range 10 C Connection P P y for i in range 9 C connect full Pgp i Pgp i 1 weight Cinput Connection Pinput P y Cinput connect full Pinput Pgp 0 weight Record the spikes Mgp SpikeMonitor p record True for p in Pgp Minput SpikeMonitor Pinput record True monitors Minput Mgp Setup the network and run it P V Vr rand len P Vt Vr run 100 ms
144. mapminmax It is None by default no scaling and mapminmax by default for the CMAES algo rithm algorithm CMAES The optimization algorithm It can be PSO GA or CMAI Ey m optparams Optimization parameters See method Euler Integration scheme used on the CPU and GPU Euler default RK or exponential_Euler See also Numerical integration machines A list of machine names to use in parallel See Clusters Return values Return an Opt imizationResult object with the following attributes best_pos Minimizing position found by the algorithm For array like fitness functions it is a single vector if there is one group or a list of vectors For keyword like fitness functions it is a dictionary where keys are parameter names and values are numeric values If there are several groups it is a list of dictionaries best_fit The value of the fitness function for the best positions It is a single value if there is one group or it is a list if there are several groups info A dictionary containing various information about the optimization Also the following syntax is possible with an OptimizationResult instance or The key is either an optimizing parameter name for keyword like fitness functions or a dimension index for array like fitness func tions or key itis the best key parameter found single value or the list of the best parameters key found for all groups or i where i is a group index Thi
145. mapped to a neural place code using delay lines each neuron receives input from both ears with different delays Romain Brette from brian import x defaultclock dt 02 ms dt defaultclock dt Sound sound TimedArray 10 randn 50000 white noise Ears and sound motion around the head constant angular speed sound speed 300 metre second interaural distance 20 cm big head max delay interaural distance sound speed print Maximum interaural delay max delay angular speed 2 pi x radian second 1 turn second tau ear 1 x ms Sigma ear 1 3 2 Examples 185 Brian Documentation Release 1 4 1 rrr eqs ears dx dt sound t delay x tau_ear sigma_ear 2 tau_ear 5 xi 1 delay distance sin theta second distance second distance to the centre of the head in time units dtheta dt angular speed radian EES ears NeuronGroup 2 model eqs_ears threshold 1 reset 0 refractory 2 5 ms ears distance 5 max delay 5 max delay traces StateMonitor ears x record True Coincidence detectors N 300 tau 1 ms sigma 1 eqs_neurons dv dt v tautsigmas 2 tau 5 xi 1 pp por neurons NeuronGroup N model eqs neurons threshold 1 reset 0 synapses Connection ears neurons v structure dense delay True max delay 1 1 synapses connect_full ears neurons weight 5 synapses delay 0 linspa
146. meaning that the capacitance neutralization circuit is always set at the maximum value The quality of the clamp is limited by the electrode or series resistance which can be compen sated in a similar way as bridge compensation in current clamp recordings Series resistance compensation consists in adding a current dependent voltage offset to the voltage command Because of the feedback that compensation needs to be slightly delayed with a low pass circuit The following example defines a voltage clamp amplifier with half compensated series resistance and compensation delay 1 ms amp voltage clamp Re 20 Mohm Rs 10 Mohm tau_u 1 ms The t au_u keyword is optional and defaults to 1 ms Acquisition board An acquisition board samples a recording and sends a command e g injected current at regular times It is defined as a NeuronGroup Use board AcquisitionBoard P neuron V V I I clock where P neuron group possibly containing amplifier and electrode V potential variable name I current variable name clock acquisition clock The recording variable is then stored in board record and a command is sent with the instruction board command I Discontinuous current clamp The discontinuous current clamp DCC consists in alternatively injecting current and measuring the potential in order to measure the potential when the voltage across the electrode has vanished The sampling clock is mainly determined by the elec
147. model as in the functional threshold example can be defined as follows group NeuronGroup 100 model eqs reset 0 mV threshold VariableThreshold state v threshold state w Empirical threshold For Hodgkin Huxley models one needs to determine the threshold empirically Here the threshold should really be understood rather as the onset of the spikes used to propagate the spikes to the other neurons since there is no explicit reset There is a Threshold subclass for this purpose group NeuronGroup 100 model eqs threshold EmpiricalThreshold threshold 20 mV refractory 3x ms Spikes are triggered when the membrane potential reaches the value 20 mV but only if it has not spiked in the last 3 ms otherwise there would be spikes every time step during the action potential The st ate keyword may be used to specify the state variable which should be checked for the threshold condition Poisson threshold It is possible to generate spikes with a given probability rather than when a threshold condition is met by using the class PoissonThreshold as in the following example group NeuronGroup 100 model x Hz threshold PoissonThreshold state x x linspace 0 Hz 10 Hz 100 Here spikes are generated as Poisson processes with rates given by the variable x the state keyword is optional default first variable defined Note that x can change over time inhomogeneous Poisson processes The units of variabl
148. ms The electrode should be compensated for capacitance capacitance neutralization but not resistance bridge compensation The best choice for the input current is a series of independent random values and the last ksize steps of v should be null i e the injection should stop before the end Here it was assumed that the recording was done at the soma if it is done in a thin process such as a dendrite or axon the function electrode kernel dendrite should be used instead The full kernel can also be obtained from a step current injection K full kernel from step v i ksize Ke electrode kernel soma K start tail where i is a constant value in this case note that this is not the best choice for real recordings Once the electrode kernel has been found any recording can be compensated as follows vcomp AEC compensate v i ke where v is the raw voltage recording i is the injected current and ke is the electrode kernel 5 4 2 Lp compensation The Lp compensation is an other electrode compensation method It is based on linear model fitting of an electrode and a neuron in response to an injected current The fitness function is the Lp error between the full model response and the raw trace with p 2 to minimize the bias due to the nonlinear voltage excursions of action potentials You can use it like this Vcomp params Lp compensate I Vraw lxms where I is the injected current Vraw is the raw voltage trace and the
149. net run beta 250 ms Return the voltage trace return self monitor times self monitor 0 if name main cond model TimeWarpModel True curr model TimeWarpModel False N cond model N E e bees esses sess eee se tees seeds eee eee eee sees e sessed ead dates dees eee ess te Reproduce Fig 2 from G tig and Sompolinsky 2009 E e eee sees eee sees sede seeded see eese eee esses eees sete ead eases dees ge ees eee beta 2 0 timesl vl cond model run beta 1 0 times2 v2 cond model run beta beta maxtime 250 beta subplot 4 1 1 neurons times zip cond model unwarped spiketimes 34 Chapter 3 Getting started Brian Documentation Release 1 4 1 plot array times ms neurons g axis 0 maxtime 0 N xticks yticks title Time warp invariant voltage traces conductance based subplot 4 1 2 plot timesl ms vl g axis 0 maxtime 1 5 1 5 xticks yticks subplot 4 1 3 plot array times beta ms neurons b axis 0 maxtime 0 N xticks yticks 1 500 subplot 4 1 4 plot times2 ms v2 b plot timesl ms beta vl g axis 0 maxtime 1 5 1 5 xlabel Time ms xticks 0 250 500 yticks 1 1 show d PETESTSTSSHSTSHRHESTREARRHHTRRT HHRHRHRHRHTRHERRHRRHHHTHARHTHAHRHHRHHRHRHURHHHATRHUHHAHHRTAH HTHRTEHETTATTU Reproduce Fig 3 C from G tig and Sompolinsky
150. neuron was producing only one spike In this part we alter the model so that some more spikes will be generated What we ll do is alter the resting potential E1 so that it is above threshold this will ensure that some spikes are generated The first few lines remain the same from brian import x tau 20 msecond membrane time constant Vt 50 mvolt spike threshold Vr 60 x mvolt reset value But we change the resting potential to 49 mV just above the spike threshold El 49 mvolt resting potential same as the reset And then continue as before G NeuronGroup N 40 model dV dt V El tau volt threshold Vt reset Vr M SpikeMonitor G run l second print M nspikes Running this program gives the output 840 That s because every neuron starts at the same initial value and proceeds deterministically so that each neuron fires at exactly the same time in total 21 times during the 1s of the run In the next part we ll introduce a random element into the behaviour of the network 10 Chapter 3 Getting started Brian Documentation Release 1 4 1 Exercises 1 Try varying the parameters and seeing how the number of spikes generated varies 2 Solve the differential equation by hand and compute a formula for the number of spikes generated Compare this with the program output and thereby partially verify it Hint each neuron starts at above the threshold and so fires a spik
151. nspikes 4000 second raster plot M show Example I F curve misc Input Frequency curve of a neuron cortical RS type Network 1000 unconnected integrate and fire neurons Brette Gerstner with an input parameter I The input is set differently for each neuron Spikes are sent to a neuron group with the same size and variable n which has the role of a spike counter from brian import x from brian library IF import x N 1000 qs Brette Gerstner Current I amp print eqs group NeuronGroup N model eqs threshold 20 mV reset AdaptiveReset group vm 70 mV group I linspace 0 nA 1 nA N counter NeuronGroup N model n 1 C IdentityConnection group counter n i N 8 10 trace StateMonitor group vm record i duration 5 second run duration subplot 211 plot group I nA counter n duration xlabel I nA ylabel Firing rate Hz subplot 212 plot trace times ms trace i mV xlabel Time ms ylabel Vm mV show Example I F_curve2 misc Input Frequency curve of a IF model Network 1000 unconnected integrate and fire neurons leaky IF with an input parameter vO The input is set differently for each neuron Spikes are sent to a spike counter counts the spikes emitted by each neuron from brian import x N 1000 tau 10 ms eqs dv dt v0 v tau volt vO volt FX group NeuronGroup
152. package inside Brian and are subject to change without notice The most likely changes are ones of syntax and naming although functionality may also be subject to change 10 1 Code generation Brian has support for automatic generation of C code detailed in Compiled code We also have experimental support for C code generation more widely implementing the algorithms described in Goodman 2010 This support can be activated using the usecodegen usenewpropagate and usecstdp global preferences see Preferences Note that not all code will run without problems using code generation yet but in most cases it will and speed improvements can be very substantial especially for STDP 10 1 1 References Goodman DFM 2010 Code Generation A Strategy for Neural Network Simulators Neuroinformatics 8 no 3 9 doi 10 1007 s12021 010 9082 x pdf 10 2 GPU CUDA Brian has some experimental support for doing numerical integration only using GPUs using the PyCUDA package Note that only numerical integration is done on the GPU which means that variables that can be altered on the CPU via synapses or user operations need to be copied to and from the GPU each time step as well as variables that are used for thresholding and reset operations This creates a memory bandwidth bottleneck which means that for the moment the GPU code is only useful for complicated neuron models such as Hodgkin Huxley type neurons although in this case it can le
153. performed to extract an index value as sometimes an index will be repeated or skipped However this form of clock can be used for backwards compatibility with versions of Brian before the new integer based clock was introduced and for more flexibility than the new version allows for Note also that the equality condition for this clock uses an epsilon of 1e 8 rather than 1e 14 See Clock for more details on this For full backwards compatibility with older versions of Brian use NaiveClock class brian NaiveClock args kwds Provided for backwards compatibility with older versions of Brian Does not perform any approximate equality tests for clocks meaning that clock processing sequence is undpredictable Typically users should use Clock or FloatClock class brian RegularClock args kwds Deprecated Now the same as Clock The old Clock class is now FloatClock 8 3 2 The default clock brian defaultclock The default clock object Note that this is only the default clock object if you haven t redefined it with the define default clock function or the makedefaultclock True option of a Clock ob ject A safe way to get hold of the default clock is to use the functions get default clock ereinit default clock 262 Chapter 8 Reference Brian Documentation Release 1 4 1 However it is suitable for short scripts e g defaultclock dt 1 ms brian define_default_clock kwds Create a new default clo
154. possible not introducing namespace clashes symbols starting with are reserved etc The way the process works is we start with the statement V V 1 and a Symbol object with name V specifically a NeuronGroupStateVariableSymbol The statement V V 1 depends on V with both a Read and Write dependency We therefore have to resolve the symbol V To do this we call the method resolve on V In the case of Python this gives us V arr V neuron index arr V neuron index V 1 It adds arr V to the namespace and creates a dependency on neuron index The reason that V V 1 is translated to arr V neuron index V 1 is that on the left hand side we have a write variable and on the right hand side we have a read variable In Python when vectorising we have no choice but to give the underlying array with its slice when writing to an array However at this point the code generation frame work doesn t know what neuron index will be so it could be for example an array of indices In this case suppose we did V V it would be more efficient to compute V arr V neuron index and then com pute V V than to compute arr V neuron index arr V neuron index and in the case where neuron index slice None itis no slower so we always do this In the case of C the first resolution step gives us double amp V arr V neuron index V ytl For the second resolution step we need to resolve _neuron_index which is a
155. possible to ask Brian to simulate differential equations in an event driven fashion for one dimensional linear equations using the keyword event driven A typical example is pre and postsynaptic traces in STDP model w 1 dApre dt Apre taupre 1 event driven dApost dt Apost taupost 1 event driven Here Brian updates the value of Apre for a given synapse only when this synapse receives a spike whether it is presynaptic or postsynaptic More precisely the variables are updated every time either the pre or post code is called for the synapse so that the values are always up to date when these codes are executed Automatic event driven updates are only possible for one dimensional linear equations These equations must also be independent of the other ones that is a differential equation that is not event driven cannot depend on an event driven equation since the values are not continuously updated In other cases the user can write event driven code explicitly in the update codes see below Pre and post codes The pre post code is executed at each synapse receiving a presynaptic spike For example pre v Ww adds the value of synaptic variable w to postsynaptic variable v As for the model equations the _post _pre suffix indicates a postsynaptic presynaptic variable and variables not found in the synaptic variables are considered postsynaptic by default Internally the execution of the code is v
156. relative to the maximum weight wmax see below The interactions keyword determines how pairs of pre post synaptic spikes interact a11 if contributions from all pairs are added nearest for only nearest neighbour inter actions nearest pre if only the nearest presynaptic spike and all postsynaptic spikes are taken into account and nearest post for the symmetrical situation The weight update can be additive i e w w wmax f s or multiplicative w w w f s for depression usually s 0 and w w wmax w f s for potentiation usually s gt 0 It can also be mixed multiplicative for depression additive for potentiation Delays By default transmission delays are assumed to be axonal i e synapses are located on the soma if the delay of the connection C is d then presynaptic spikes act after a delay d while postsynaptic spikes act immediately This behaviour can be overriden with the keywords delay_pre and delay_post in both classes STDP and Exponential STDP 4 4 Spike timing dependent plasticity 199 Brian Documentation Release 1 4 1 4 5 Short term plasticity Brian implements the short term plasticity model described in Markram et al 1998 Differential signaling via the same axon of neocortical pyramidal neurons PNAS 95 9 5323 8 Synaptic dynamics is described by two variables x and u which follows the following differential equations dx dt 1 x taud depression du dt U u tauf facilitation where taud tauf a
157. representations of gammachirp functions as the impulse response The impulse responses which need to have the same length for every channel have a duration of 12 times the biggest time constant The length of the impulse response is therefore 12 xmax time constant sampling rate The envelope is a gaussian function Gabor filter The impulse responses are normalized with respect to the transmitted power i e the rms of the filter taps is 1 Initialisation parameters source Source sound or filterbank f List or array of the sweep starting frequencies instantaneous f c t time constant Determines the duration of the envelope and consequently the length of the impluse re sponse c 1 The glide slope or sweep rate given ins Hz second The time dependent instantaneous frequency is f cx t and is therefore going upward when c gt 0 and downward when c 0 c can either be a scalar and will be the same for every channel or an array with the same length as f phase 0 Phase shift of the carrier 8 21 Brian hears 323 Brian Documentation Release 1 4 1 Has attributes length_impulse_response Number of sample in the impulse responses impulse_response Array of shape nchannels length_impulse_response with each row being an impulse response for the corresponding channel class brian hears IIRFilterbank source nchannels passband stopband gpass gstop btype ftype Filterbank of IIR filters The filters can be low high
158. returned read The string that should be used when this symbol is read by default just the symbol name resolution requires loop Should return True if the resolution of this symbol will require a loop The resolve function uses this to optimise the symbol resolution order resolve read write vectorisable item namespace Creates a modified item in which the symbol has been resolved For example if we started from the expression x 1 and we wanted to produce the following C code for int i 0 i lt n i double amp x arr x i x 1 11 5 Code generation 379 Brian Documentation Release 1 4 1 we would need to take the expression x 1 and embed it inside a loop Function arguments read Whether or not we read the value of the symbol This is computed by analysing the dependencies by the main resolve function write Whether or not we write a value to the symbol vectorisable Whether or not the expression is vectorisable In Python we can only vectorise one multi valued index so if there are two or more only the innermost loop will be vectorised item The code item which needs to be resolved namespace The namespace to put data in The default implementation first calls update namespace then creates a new Block consisting of the value returned by load the item and the value returned by save Finally this symbol s name is added to the resolved set for this block sav
159. self input return self gain input This is the class for the updater object class GainController object def init self target target rms time constant self target target self target rms target rms self time constant time constant def reinit self self sumsquare 0 self numsamples 0 def call self input T input shape 0 self target samplerate self sumsquare sum input 2 self numsamples input size rms sqrt self sumsquare self numsamples g self target gain g_tgt self target_rms rms 320 Chapter 8 Reference Brian Documentation Release 1 4 1 tau self time_constant self target gain g_tgt exp T tau g g_tgt And an example of using this with an input source a target RMS of 0 2 and a time constant of 50 ms updating every 10 ms gain_fb GainFilterbank source updater GainController gain fb 0 2 50 ms control ControlFilterbank gain fb source gain fb updater 10 ms class brian hears CombinedFilterbank source Filterbank that encapsulates a chain of filterbanks internally This class should mostly be used by people writing extensions to Brian hears rather than by users directly The purpose is to take an existing chain of filterbanks and wrap them up so they appear to the user as a single filterbank which can be used exactly as any other filterbank In order to do this derive from this class and in your initialisation follow this pattern class Rect
160. shift produces threshold variability but also spikes with variable shapes unavoidable in a single compartment model The script demonstrates that the spike threshold is proportional to the logarithm of h from brian import x from scipy import stats from brian library electrophysiology import x defaultclock dt 0 05 ms duration 500 ms N 1000 we simulate 1000 neurons to have more threshold statistics rectify lambda x clip x 0 inf siemens Biophysical parameters Passive parameters area pix 105 umetre 2 C 1 uF GL 0 0452 msiemens EL 80 mV Active fixed parameters celsius 36 temp 23 q10 22 3 Sodium channel parameters ENa 50 mV GNa 51 6 msiemens vTraub Na 63 mV Traub convention vshift 20xmV Inactivation shift 62 mV instead of 42 mV g activation A alpham 0 32 ms mV open V A betam 0 28 ms mV close V v12 alpham 13 mV v1 2 for act v12 betam 40 mV v1 2 for act k_alpham 4 mV act slope k_betam 5 mvV fact slope peces inactivation A alphah 0 128 ms inact recov V A_betah 4 ms inact V v12 alphah 17 mV vl1 2 for inact v12 betah 40 mV v1 2 for inact k alphah 18 mV inact tau slope k betah 5 mV inact tau slope Potassium channel parameters EK 90 mV f delay rectifier GK 10 msiemens vTraub K 63 mV A alphan 0 032 ms mV open V 36 Chapter 3 Getting started Brian Documentation Release 1 4 1 A_b
161. source neurons with indices in spikes fired do propagate The method called by the Network update step typically just propagates the spikes obtained by calling the get spikes method of the source NeuronGroup class brian DelayConnection source target state 0 modulationzNone structure sparse weight None sparseness None delay None max_delay 5 0 msecond kwds Connection which implements heterogeneous postsynaptic delays Initialised as for a Connect ion but with the additional keyword max delay Specifies the maximum delay time for any neuron Note the smaller you make this the less memory will be used Overrides the following attribute of Connection delay A matrix of delays This array can be changed during a run but at no point should it be greater than max delay In addition the methods connect connect random connect full and connect one to one have a new keyword delay forsetting the initial values of the delays where delay can be one of A float all delays will be set to this value A pair min max delays will be uniform between these two values eA function of no arguments will be called for each nonzero entry in the weight matrix eA function of two argument i j will be called for each nonzero entry in the weight matrix eA matrix of an appropriate type e g ndarray or lil matrix Finally there is a method set delays source target delay Where delay must be of one of the
162. sparse vector with zeros where sv has zeros the potentially nonzero elements of dv where sv has no entry will be simply ignored It is for this reason that itis a SparseConnectionVector and not a general SparseVector because these semantics make sense for rows and columns of connection matrices but not in general Implementation details The underlying numpy array contains the values the attribute n is the length of the sparse vector and indis an array of the indices of the nonzero elements 8 8 Plasticity 8 8 1 Spike timing dependent plasticity STDP class brian STDP C eqs pre post wmin 0 wmax inf level 0 clock None delay prezNone de lay post None Spike timing dependent plasticity Initialised with arguments C Connection object to apply STDP to eqs Differential equations with units 8 8 Plasticity 279 Brian Documentation Release 1 4 1 pre Python code for presynaptic spikes use the reserved symbol w to refer to the synaptic weight post Python code for postsynaptic spikes use the reserved symbol w to refer to the synaptic weight wmin Minimum weight default 0 weights are restricted to be within this value and wmax wmax Maximum weight default unlimited weights are restricted to be within wmin and this value delay pre Presynaptic delay delay post Postsynaptic delay backward propagating spike The STDP object works by specifying a set of differential equations associated to each synapse eqs
163. stereo sound with channels LR then you can get an output with channels LLLRRR or LRLRLR by writing respectively fb Repeat sound 3 fb Tile sound 3 To combine multiple filterbanks into one you can either join them in series or interleave them as follows 240 Chapter 5 The library Brian Documentation Release 1 4 1 fb Join sourcel source2 fD Interleave sourcel source2 For a more general but more complicated approach see RestructureFilterbank Two of the most important generic filterbanks upon which many of the others are based are LinearFilterbank and FIRFilterbank The former is a generic digital filter for FIR and IIR filters The latter is specifically for FIR filters These can be implemented with the former but the implementation is optimised using FFTs with the latter which can often be hundreds of times faster particularly for long impulse responses IR filter banks can be designed using IIRFilterbank which is based on the syntax of the iirdesign scipy function You can change the input source to a Filterbank by modifying its source attribute e g to change the input sound of a filterbank fb you might do fb source newsound Note that the new source should have the same number of channels You can implement control paths using the output of one filter chain path to modify the parameters of another filter chain path using Cont rolFilterbank see reference documentation for more details For
164. symbol like arr V for symbol V and resolve itself either by doing nothing in Python as the variable is already vectorised or by introducing a loop in C or by setting the index variable as the kernel thread for GPU For more details see the section on resolution below make integration step euler rk2 exp euler Numerical integration schemes each in tegration scheme such as euler converts a set of differential equations into a sequence of MathematicalStatement objects comprising an integration step CodeGenStateUpdater CodeGenThreshold CodeGenReset CodeGenConnection Brian objects using code generation 11 5 2 Resolution process Example We start with a worked example Consider the statement V V 1 Here V is a NeuronGroup state variable We wish to transform this into code that can be executed In the case of Python the output would look like neuron index slice None MV arr V neuron index arr V neuron index V 1 The symbol arr V would be added directly to the namespace In the case of C it would look like 11 5 Code generation 359 Brian Documentation Release 1 4 1 for int _neuron_index 0 _neuron_index lt _len__arr_V _neuron_index double amp V arr V neuron index V V 1 Here the symbols arr V and len arr V would be added to the namespace The reason for these complicated names is to do with making the code as generic as
165. symbol of type SliceIndex telling us that neuron index varies over all neurons Note that we could also have _neuron_index being an ArrayIndex for examples spikes and then this could be used for a reset operation we would iterate only over those indices of neurons which had spiked Here though we iterate over all neurons In Python calling the resolve method of neuron index gives us neuron index slice None V arr V neuron index arr V neuron index V 1 and in C for int neuron index 0 neuron index len arr V neuron index t double amp V arr V neuron index V V 1 In both cases the neuron index symbol is resolved and the process is complete Note that we have actually mixed two stages here the stage of generating a structured representation of the code using CodeItem objects and the stage of generating code strings using CodeItem convert to In fact the converting of for example Vto arr V neuron index only happens at the second stage 360 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 resolve The first stage acting on the structured representation of nested CodeItem objects is resolved using the function resolve Thiscalls Symbol resolve foreach of the symbols in turn The resolution order is determined by an optimal efficiency algorithm see the reference documentation for resolve for the full algorithm description Symbol resolve
166. the sub groups myconnection connect_full group1 0 20 group2 10 40 weight 5 nS The second one is used to set uniform weights for random pairs of neurons in the sub groups myconnection connect_random group1 0 20 group2 10 40 sparseness 0 02 weight 5xnS Here the third argument 0 02 is the probability that a synaptic connection exists between two neurons The number of presynaptic neurons can be made constant by setting the keyword ixed True probability number of neurons in groupl1 Finally the method connect one to one connects neuron i from the first group to neuron i from the second group myconnection connect one to one groupl group2 weight 3 nS Both groups must have the same number of neurons If you are connecting the whole groups you can omit the first two arguments e g myconnection connect full weight 5 nS connects groupl1 to group2 with weights 5 nS Building connections with connectivity functions There is a simple and efficient way to build heterogeneous connections by passing functions instead of constants to the methods connect full and connect random The function must return the synaptic weight for a given pair of neuron i j For example 196 Chapter 4 User manual Brian Documentation Release 1 4 1 myconnection connect_full group1 group2 weight lambda i j 1 cos i j 2 nS where i j indexes neurons in group1 group2 This is the same as doing by hand
167. the variables of an Equations object are reorderered so that the first one is most likely to be the membrane potential using Equations get Vm The first variable is with decreasing priority ev m vm Vm the first defined variable 4 14 4 Numerical integration The currently available integration methods are Exact integration when the equations are linear Euler integration explicit first order Runge Kutta integration explicit second order Exponential Euler integration implicit first order The method is selected when a NeuronGroup is initialized If the equations are linear exact integration is au tomatically selected Otherwise Euler integration is selected by default unless the keyword implicit True is passed which selects the exponential Euler method A second order method can be selected using the keyword order 2 explicit Runge Kutta method midpoint estimation It is possible to override this behaviour with the method keyword when initialising a NeuronGroup Possible values are linear nonlinear Euler RK exponential Euler Exact integration If the differential equations are linear then the update phase X t gt X t dt can be calculated exactly with a matrix product First the equations are examined to determine whether they are linear with the method islinear and the function is affine this is currently done using dynamic typing Second the matrix M and the vector B such
168. there are no file concurrency issues and then in the data analysis phase the data generated separately by each process is merged together Methods get key Return dictionary with keys the session names and values the values stored in that session for the given key get_merged key Return a single list of the merged lists or tuples if each value for every session is a list or tuple get_matching match Returns a dictionary with keys the keys matching match and values get key If match is a string a matching key has to start with that string If match is a function a key matches if match key get merged matching match Like get merged key but across all keys that match get flat matching match Returns a straight list of every value session key for all sessions and all keys matching match iteritems Returnsall key value pairs for each Shelf file as an iterator useful for large files with too much data to be loaded into memory itervalues Return all values for each Shelf file as an iterator items values Asforiteritems and itervalues but returns a list rather than an iterator itemcount Returns the total number of items across all the Shelf files keys A list of all the keys across all sessions session Returns a randomly named session Shelf multiple processes can write to these without worrying about concurrency issues computer session Returns a consistently named Shelf specific to that us
169. third neuron This third neuron has two different state variables called Va and Vb The first two neurons will be connected to the third neuron but a spike arriving at the third neuron will be treated differently according to whether it came from the first or second neuron which you can consider as meaning that the first two neurons have different types of synapses on to the third neuron The program starts as follows from brian import x tau_a 1 ms tau b 10 ms Vt 10 mV Vr 0 mV Differential equations This time we will have multiple differential equations We will use the Equations object although you could equally pass the multi line string defining the differential equations directly when initialising the NeuronGroup object see the next part of the tutorial for an example of this 3 1 Tutorials 23 Brian Documentation Release 1 4 1 eqs Equations dVa dt Va tau a volt dVb dt Vb tau b volt re So far we have defined a model neuron with two state variables Va and Vb which both decay exponentially towards 0 but with different time constants tau a and tau b This is just so that you can see the difference between them more clearly in the plot later on SpikeGeneratorGroup Now we introduce the SpikeGeneratorGroup class This is a group of neurons without a model which just produces spikes at the times that you specify You create a group like this by writing G
170. this as None which defaults to host localhost port 2719 To allow remote control use portnumber authkey The authentication key to allow access change it from brian if you are allowing access from outside otherwise you allow others to run arbitrary code on your machine clock The clock specifying how often to poll for incoming commands 302 Chapter 8 Reference Brian Documentation Release 1 4 1 global_ns local_ns level Namespaces in which incoming commands will be executed or evaluated if you leave them blank it will be the local and global namespace of the frame from which this function was called if level 1 or from a higher level if you specify a different level here Once this object has been created use a Remot eCont rolClient to issue commands Example usage Main simulation code includes a line like this server RemoteControlServer In an Python shell you can do something like this client RemoteControlClient spikes client evaluate M spikes i t zip spikes plot t ty i client execute stop class brian RemoteControlClient server None authkey brian Used to remotely control via IP a running Brian script Initialisation arguments server The IP server details a pair host port If you want to allow control only on the one machine for example by an Python shell leave this as None which defaults to host localhost port 2719 To
171. time of last update of all synapses synapse gt last update This only exists if there are dynamic synaptic variables Internal attributes source The source neuron group target The target neuron group _S The state matrix a 2D dynamical array with values of synaptic variables At run time it is transformed into a static 2D array with compress presynaptic The dynamic array of presynaptic neuron indexes for all synapses synapse gt i postsynaptic The array of postsynaptic neuron indexes for all synapses synapse gt j synapses pre A list of dynamic arrays giving the set of synapse indexes for each presynaptic neuron i i gt synapses synapses_post A list of dynamic arrays giving the set of synapse indexes for each postsynaptic neuron j j gt synapses queues List of SpikeQueues for pre and postsynaptic spikes codes The compiled codes to be executed on pre and postsynaptic spikes namespaces The namespaces for the pre and postsynaptic codes class brian SynapticEquations expr level 0 kwds Equations for the Synapses class The only difference with Equations is that differential equations can be marked for an event driven implementation e g dx dt x tau 1 event driven class brian synapses synapticvariable SynapticVariable data synapses name A vector of synaptic variables that is returned by Synapses __get att r__ and that can be subscripted with 2 or 3 arguments Example usages whe
172. to compute the histogram bin_edges A ID array of the bin edges used to compute the histogram In addition if M isa StateHistogramMonitor object you write M i for the histogram of neuron i 8 12 Plotting Most plotting should be done with the PyLab commands all of which are loaded when you import Brian See http matplotlib sourceforge net matplotlib pylab html for help on PyLab Brian currently defines just two plotting functions of its own raster plot andhist plot brian raster plot monitors additionalplotoptions Raster plot of a SpikeMonitor Usage 296 Chapter 8 Reference Brian Documentation Release 1 4 1 raster_plot monitor options Plots the spike times of the monitor on the x axis and the neuron number on the y axis raster plot monitor0 monitorl options Plots the spike times for all the monitors given with y axis defined by placing a spike from neuron n of m in monitor i at position i n m raster plot options Guesses the monitors to plot automagically Options Any of PyLab options for the plot command can be given as well as showplot False setto True to run pylab s show function newfigure False set to True to create a new figure with pylab s figure function xlabel label for the x axis ylabel label for the y axis title title for the plot showgrouplines False set to True to show a line between each monitor grouplinecol colour for group lines spacebetweengroup
173. trains Only spikes are considered for the fitness Several target spike trains can be specified in order to fit independently several data sets In this case the modelfitting function returns as many parameters sets as there are target spike trains The model is defined as any spiking neuron model in Brian by giving the equations as mathematical equations and the reset and threshold values The free parameters of the model that shall be fitted by the library are also specified The data is specified by the input a vector containing the time varying injected current the timestep of the input and the data as a list of spike times 5 6 1 How it works Fitting a spiking neuron model to electrophysiological data is performed by maximizing a fitness function measuring the adequacy of the model to the data This function is defined as the gamma factor which is based on the number of coincidences between the model spikes and the experimentally recorded spikes defined as the number of spikes in the experimental train such that there is at least one spike in the model train within plus or minus delta where delta is the size of the temporal window typically a few milliseconds For more details on the gamma factor see Jolivet et al 2008 A benchmark test for a quantitative assessment of simple neuron models J Neurosci Methods available in PDF here The optimization procedure is performed by an optimization algorithm The optimization toolb
174. trains use a CoincidenceCounter object C CoincidenceCounter source group data data delta delta data is a list of pairs neuron index spike time and delta is the time window in second To get the number of coincidences for each neuron of the group use coincidences C coincidences The gamma precision factor can be obtained with gamma C gamma 4 7 5 Recording population rates The population rate can be monitored with a PopulationRateMonitor object M PopulationRateMonitor group After the simulation M times contains the list of recording times and M rate is the list of rate values where the rate is meant in the spatial sense average rate over the whole group at some given time The bin size is set with the bin keyword in seconds M PopulationRateMonitor group bin 1 ms 206 Chapter 4 User manual Brian Documentation Release 1 4 1 Here the averages are calculated over 1 ms time windows Alternatively one can use the snmooth_rate method to smooth the rates rates M smooth_rate width l ms filter gaussian The rates are convolved with a linear filter which is either a Gaussian function gaussian default or a box function flat 4 7 6 Van Rossum Metric The Van Rossum metric can be computed by monitoring a group with a VanRossumMet ric object M VanRossumMetric G tau 4 ms imshow M distance 4 8 Inputs Some specific types of neuron groups are available to provid
175. u v tau volt u 3 v volt W V pk Details For more details see More on equations in the user manual For information on integration methods and the StateUpdater class see Integration 8 4 2 The NeuronGroup object class brian NeuronGroup args kwds Group of neurons Initialised with arguments N The number of neurons in the group model An object defining the neuron model It can be an Equations object a string defining an Equations object a StateUpdater object or a list or tuple of Equations and strings threshold None A Threshold object a function a scalar quantity or a string If threshold isa function with one argument it will be converted to a SimpleFunThreshold otherwise it will be a FunThreshold If threshold is a scalar then a constant single valued threshold with that value will be used In this case the variable to apply the threshold to will be guessed If there is only one variable or if you have a variable named one of V Vm v or vm it will be used If threshold is a string then the appropriate threshold type will be chosen for example you could do threshold V gt 10 mvV The string must be a one line string reset None A Reset object a function a scalar quantity or a string If it s a function it will be converted to a FunReset object If it s a scalar then a constant single valued reset with that value will be used In this case the variable to apply the reset to will be guessed
176. usage is similar to that of a Python list String equations String equations can be of any of the following forms l dx dt f unit differential equation 2 x f unit equation 3 x y alias 4 x unit parameter ons object or by adding 8 4 Neuron models and groups 263 Brian Documentation Release 1 4 1 Here each of x and y can be any valid Python variable name f can be any valid Python expression and unit should be the unit of the corresponding x You can also include multi line expressions by appending a N character at the end of each line which is continued on the next line following the Python standard or comments by including a symbol These forms mean Differential equation A differential equation with variable x which has physical units unit The variable x will become one of the state variables of the model Equation n equation defining the meaning of x can be used for building systems of complicated differential equations Alias The variable x becomes equivalent to the variable y useful for connecting two separate systems of equa tions together Parameter The variable x will have physical units unit and will be one of the state variables of the model but will not evolve dynamically instead it should be set by the user Noise String equations can also use the reserved term xi for a Gaussian white noise with mean 0 and variance 1 Example usage eqs Equations dv dt
177. use the following instructions board switch_on board command 5 nA run 200 ms board command 0 nA run 150 ms board switch_off During the simulation the variable board record stores the compensated potential 5 4 Electrophysiology electrode compensation The electrophysiology library also contains methods to compensate for the electrode voltage in single electrode current clamp recordings To import the electrophysiology library from brian library electrophysiology import x There is a series of example scripts in the examples electrophysiology folder 5 4 1 Active Electrode Compensation AEC The electrophysiology library includes the Active Electrode Compensation AEC technique described in Brette et al 2008 High resolution intracellular recordings using a real time computational model of the electrode Neuron 5 4 Electrophysiology electrode compensation 229 Brian Documentation Release 1 4 1 59 3 379 9 Given a digital current clamp recording of the uncompensated potential v vector of values and injected current i the following instructions calculate the full kernel of the system and the electrode kernel K full kernel v i ksize Ke electrode kernel soma K start tail ksize is the size of the full kernel number of sampling steps typical size is about 15 ms and start tail is the size of the electrode kernel start point of the tail of the full kernel typical size if about 4
178. useful is the C one or the Java one The C one can be downloaded here Having downloaded and installed Eclipse you should download and install the PyDev plugin from their web site The best way to do this is directly from within the Eclipse IDE Follow the instructions on the PyDev manual page 6 Chapter 2 Installation Brian Documentation Release 1 4 1 2 2 3 Installing Python IPython is an interactive shell for Python It has features for SciPy and PyLab built in so it is a good choice for scientific work Download from their page If you are using Windows you will also need to download PyReadline from the same page 2 2 4 C compilers The default for Brian is to use the gcc compiler which will be installed already on most unix or linux distributions If you are using Windows you can install cygwin make sure to include the gcc package Alternatively some but not all versions of Microsoft Visual C should be compatible but this is untested so far See the documentation for the SciPy Weave package for more information on this Mac users should have XCode installed so as to have access to gcc and hence take advantage of brian compiled code See also the section on Compiled code 2 3 Testing You can test whether Brian has installed properly by running Python and typing the following two lines from brian import x brian sample run A sample network should run and produce a raster plot 2 4 Optimisations After
179. values Note this function may change The following function returns the average spike triggered voltage shape spike shape v onsets None before 100 after 100 If onsets is unspecified it is calculated with the spike onsets function Note that you can align spikes on other times for example peaks The arguments before and after specify the number of time steps before and after the triger times Note this should not be specific to spikes it s a stimulus triggered average 232 Chapter 5 The library Brian Documentation Release 1 4 1 Spike mask It is often useful to discard spikes from the trace to analyse it The following function returns an array of booleans which are True in spikes spike_mask v spikes None T None The starting point of each spike time bin is given by the spikes variable default onsets and T is the duration of each spike in time bins This function can then be used to select the subthreshold trace or the spikes v_subthreshold v spike_mask v T 100 J v Spikes v spike mask v T 100 5 6 Model fitting The modelfitting library is used for fitting a neuron model to data The library provides a single function model fitting which accepts the model and the data as arguments and returns the model parameters that fit best the data The model is a spiking neuron model whereas the data consists of both an input time varying signal for example an injected current and a set of spike
180. variables It seems that this method set eq order is already called by check units and therefore it is probably not necessary to call it here This method computes the dependency graph of static equations on other static variables which must have no cycle otherwise an error is raised From that graph an update list is built and put in eq names Then for each variable static or differential the list of dependent static variables is built and sorted in update order The result is put in the dependencies dictionary This is a necessary step to calculate the RHS of any equation it gives the ordered list of static variables to calculate first before calculating the RHS Inserting static variables into differential equations The value of static variables are then replaced by their string value RHS in all differential equations substitute eq The previous step ordering ensures that the result if correct and does not depend on static variables anymore To avoid namespace conflicts all identifiers in the namespace of a static variable is augmented by a prefix name _ e g x y for identifier y in equation x 2 y Then namespaces are merged It might not be optimal to do it in this way because some of calculations will be done several times in an update step It might be better to keep the static variables separate Recompiling functions Functions are then recompiled so that differential equations are now independe
181. vector of the running sum of squares and update it for each buffered segment as it is computed At the end of the processing we divide the sum of squares by the number of samples and take the square root The Filterbank process method allows us to pass an optional function f output running of two arguments In this case process will first call running f output 0 for the first buffered segment output It will then call running f output running for each subsequent segment In other words it will accumulate the output of passing the output of each call to the subsequent call To compute the vector of RMS values then we simply do def sum_of_squares input running return running sum input 2 axis 0 rms sqrt fb process sum of squares nsamples If the computation you wish to perform is more complicated than can be achieved with the process method you can derive a class from Filterbank see that class reference documentation for more details on this 5 7 6 Buffering interface The Sound OnlineSound and Filterbank classes and all classes derived from them all implement the same buffering mechanism The purpose of this is to allow for efficient processing of multiple channels in buffers Rather than precomputing the application of filters to all channels which for large numbers of channels or long sounds would not fit in memory we process small chunks at a time The entire design of these classes is
182. want to be able to reinitialise see below At it s simplest spiketimes could be a list of lists where spiketimes 0 contains the firing times for neuron 0 spiketimes 1 for neuron 1 etc But any iterable object can be passed so spiketimes 0 could be a generator for example Each spike time container should be sorted in time If the containers are numpy arrays units will not be checked times should be in seconds clock A clock if omitted the default clock will be used period Optionally makes the spikes recur periodically with the given period Note that iterator objects cannot be used as the spikelist with a period as they cannot be reinitialised Note that if two or more spike times fall within the same dt spikes will stack up and come out one per dt until the stack is exhausted A warning will be generated if this happens Also note that if you pass a generator then reinitialising the group will not have the expected effect because a generator object cannot be reinitialised Instead you should pass a callable object which returns a generator this will be called each time the object is reinitialised by calling the reinit method Sample usage spiketimes l msecond 2 msecond P MultipleSpikeGeneratorGroup spiketimes 8 7 Connections The best way to understand the concept of a Connection in Brian is to work through Tutorial 2 Connections 8 7 Connections 273 Brian Documentation Release 1 4 1 cla
183. with two arrays the first one being the neuron indices and the second one times WARNING units are not checked in this case the time array should be in seconds clock An optional clock to update with omit to use the default clock period Optionally makes the spikes recur periodically with the given period Note that iterator objects cannot be used as the spikelist with a period as they cannot be reinitialised gather False Set to True if you want to gather spike events that fall in the same timestep Deprecated since Brian 1 3 1 sort True Set to False if your spike events are already sorted Has an attribute spiketimes This can be used to reset the list of spike times however the values of N clock and period cannot be changed Sample usages The simplest usage would be a list of pairs i t spiketimes 0 1 ms 1 2x ms SpikeGeneratorGroup N spiketimes A more complicated example would be to pass a generator import random def nextspike nexttime random uniform 0Q ms 10 ms while True yield random randint 0 9 nexttime nexttime nexttim random uniform 0 ms 10 ms P SpikeGeneratorGroup 10 nextspike This would give a neuron group P with 10 neurons where a random one of the neurons fires at an average rate of one every 5ms Please note that as of 1 3 1 this behavior is preserved but will run slower than initializing with arrays or lists Notes Note that if a neuron fires more than on
184. x 1 samplerate I zeros len f dtype bool for cf in vowel I I abs f lt cf width amp abs f gt cf width I v 1 0 x ifft y return Sound x real vl generate vowel ramp v2 generate vowel ar ramp v3 generate vowel oo ramp 114 Chapter 3 Getting started Brian Documentation Release 1 4 1 v4 generate vowel er ramp for s in vl v2 v3 v4 S play normalise True sleep True sl Sound vl v2 s1 play normalise True sleep True s2 Sound v3 v4 f s2 play normalise True sleep True vl save mono_sound wav sl save stereo sound wav subplot 211 plot vl times v1 subplot 212 vl spectrogram show Example simple anf hears Example of a simple auditory nerve fibre model with Brian hears from brian import x from brian hears import soundl tone 1 kHz 1 second sound2 whitenoise 1 second sound soundl sound2 sound sound ramp cf erbspace 20 Hz 20 kHz 3000 cochlea Gammatone sound cf Half wave rectification and compression x 1 3 ihe FunctionFilterbank cochlea lambda x 3 clip x 0 Inf 1 0 3 0 Leaky integrate and fire model with noise and refractoriness eqs vee dv dt I v 1xms 0 2 xi 2 1xms x 5 1 p S X rrt anf FilterbankGroup ihc I qs reset 0 threshold 1 refractory 5x ms M SpikeMonitor anf
185. ymbokefpynapseIndex method 370 brian experimental codegen2 SliceIndex method 382 resolve analysis 189 259 semi exact numerical integration 216 resolve brian experimental codegen2 SparseMatrixS ymbolediysiapese Index method 370 resolve brian experimental codegen2 Symbol method 379 resolve in module brian experimental codegen2 377 resolve_c brian experimental codegen2 ArrayIndex method 382 resolve_c brian experimental codegen2 SliceIndex method 382 resolve gpu brian experimental codegen2 ArrayIndex method 383 resolve gpu brian experimental codegen2 SliceIndex method 382 resolve python brian experimental codegen2 ArrayIndex method 383 resolve python brian experimental codegen2 SliceIndex method 382 rest brian NeuronGroup method 265 RestructureFilterbank example usage 49 83 109 120 RestructureFilterbank class in brian hears 317 right brian hears Sound attribute 312 rk2 in module brian experimental codegen2 375 run example usage 26 31 33 35 39 41 43 45 46 49 50 53 54 56 57 60 63 65 66 68 69 72 74 77 79 82 84 91 93 95 99 102 106 109 115 125 128 130 132 135 144 147 174 176 187 run brian experimental codegen2 CCode method 370 run brian experimental codegen2 Code method 370 run brian experimental codegen2 GPUCode method 375 run brian experimental codegen2 GPU Kernel method 372 run
186. you can access the group of pre post synaptic variables as stdp pre_group stdp post_group These latter attributes can be passed to a Stat eMonitor to record their activity for example However note that in the case of STDP acting on a connection with heterogeneous delays the recent values of these variables are automatically monitored and these can be accesses as follows stdp G pre monitors A pre stdp G post monitors A post Technical details The equations are split into two groups pre and post Two groups are created to carry these variables and to update them these are implemented as NeuronGroup objects As well as propagating spikes from the source and target of C via C spikes are also propagated to the respective groups created At spike propagation time the weight values are updated 280 Chapter 8 Reference Brian Documentation Release 1 4 1 class brian ExponentialSTDP C taup taum Ap Am interactions all wmin 0 wmax None up date additive delay_pre None delay_post None clock None Exponential STDP Initialised with the following arguments taup taum Ap Am Synaptic weight change relative to the maximum weight wmax f s Apxexp s taup if s gt 0 f s Am exp s taum if s lt 0 interactions all contributions from all pre post pairs are added nearest only nearest neighbour pairs are considered e nearest pre nearest presynaptic spike all postsynapti
187. you could do class ABFilterbank DoNothingFilterbank def init self source a AFilterbank source b BFilterbank a DoNothingFilterbank init self b However a more general way of writing compound filterbanks is to use CombinedFilterbank class brian hears ControlFilterbank source inputs targets updater max interval None Filterbank that can be used for controlling behaviour at runtime Typically this class is used to implement a control path in an auditory model modifying some filterbank param eters based on the output of other filterbanks or the same ones The controller has a set of input filterbanks whose output values are used to modify a set of output filterbanks The update is done by a user specified function or class which is passed these output values The controller should be inserted as the last bank in a chain Initialisation arguments source The source filterbank the values from this are used unmodified as the output of this filterbank inputs Either a single filterbank or sequence of filterbanks which are used as inputs to the updater targets The filterbank or sequence of filterbanks that are modified by the updater 8 21 Brian hears 319 Brian Documentation Release 1 4 1 updater The function or class which does the updating see below max interval If specified ensures that the updater is called at least as often as this interval but it may be called more often Can be specified
188. 0 Example with short term plasticity with event driven updates defined by differential equations from brian import x tau e 3 ms taum 10 ms A SE 250 pA Rm 100 Mohm N 10 148 Chapter 3 Getting started Brian Documentation Release 1 4 1 rra eqs dx dt rate 1 rate Hz d i input NeuronGroup N model eqs threshold 1 reset 0 input rate linspace 5 Hz 30 Hz N eqs neuron dv dt Rmxi v taum volt di dt i tau e amp rg neuron NeuronGroup N model eqs neuron taud 1 ms tauf 100 ms U 1 t aud 100 ms tauf 10 ms U 6 S Synapses input neuron model w 1 dx dt 1 x taud 1 event driven du dt U u tauf 1 event driven TI pre ict w u x x 1 u ut Ux 1 u S i j one to one connection S w A_SE Initialization of STP variables S x 1 S u U trace StateMonitor neuron v record 0 N 1 run 1000 ms subplot 211 plot trace times ms trace 0 mV title Vm subplot 212 plot trace times ms trace N 1 mV title Vm show Example poisson synapses synapses This example shows how to efficiently simulate neurons with a large number of Poisson inputs targetting arbi trarily complex synapses The approach is very similiar to what the PoissonInput class does internally but PoissonInput cannot be combined with the Synapses class You could also just use many PoissonGroup objec
189. 0 self level2 prev exp deca val self levell prev levell the value is stored for the next iteration self level2 prev level2 the overall intensity is computed between the two filterbank outputs level total lev_weight level_ref levell level_ref level_pwrl1 1 lev_weight level_ref level2 level_ref level_pwr2 then it is converted in dB level dB 20 10g10 maximum level total level min RMStoSPL the frequency factor is calculated frat fratO fratl level dB the centre frequency of the asymmetric compensation filters are updated fr2 fpl frat coeffs asymmetric compensation coeffs samplerate fr2 self target filt b self target filt a b2 c2 p0 pl p2 p3 p4 self target filt_b self target filt_a coeffs Signal Path the signal path consists of the passive gammachirp filterbank pGc previously defined followed by a asymmetric compensation filterbank frl fplx frato varyingfilter signal path AsymmetricCompensation pGc frl b b2 c c2 updater CompensensationFilterUpdater varyingfilter_signal_path 122 Chapter 3 Getting started Brian Documentation Release 1 4 1 the controler which takes the two filterbanks of the control path as inputs fand the varying filter of the signal path as target is instantiated control ControlFilterbank varyingfilter signal path pGc control asym comp control varyingfilter signal path updater update interval
190. 00 3 2 Examples 143 Brian Documentation Release 1 4 1 taum 10 ms tau pre 20 x ms tau_post tau_pre Ee 0 mV vt 54 mV vr 60 mV El 74 x mV 5 ms dA pre 01 dA post dA pre tau pre tau post 1 05 dA post gmax dA pre gmax eqs neurons dv dt gex Ee vr El v taum volt the synaptic current is linearized dge dt ge taue 1 py input PoissonGroup N rates F neurons NeuronGroup l model eqgs neurons threshold vt reset vr S Synapses input neurons model w l1 A presi A poste Iet pre ge w A_pre A_prexexp lastupdate t tau_pre dA_pre A_post A_post exp lastupdate t tau_post w clip wtA_post 0 gmax post A pre A prexexp lastupdate t tau pre A post A postx exp lastupdate t tau post dA post w clip w A pre 0 gmax neurons v vr S True S w rand gmax rate PopulationRateMonitor neurons M StateMonitor S w record 0 1 monitors synapses number 0 and 1 start_time time run 10 second report text print Simulation time time start time figure subplot 311 plot rate times second rate smooth rate 100 ms subplot 312 plot S w gmax subplot 313 hist S w gmax 20 figure plot M times M 0 gmax plot M times M 1 gmax show 144 Chapter 3 Getting started Brian Documentation Release 1 4 1
191. 022 eee ee Experimental features 10 1 10 2 10 3 10 4 10 5 Code generatlon suce aces End Sh we ORR Bed A Om dE Bae T Se wae OEVEQE CE e E alee A GPU CUDA i e Boer y UR de Sack Big ee domu See eee Se oa dus bee oue deus Multilinear stateaipdater ss oe 24522455 484 0o Heh be Ue babe Baas Realtime Connection Monitor se 2 2 4 4 2 eee eG Soe eee OX Re Sp we X REOR eS Automatic Model Documentation 3 4 soll 4 be b o PRA SUE EX duy S Developer s guide Til 11 2 11 3 11 4 11 5 11 6 11 7 Guidelines 2 2 uos opos t a nube m kd MUR EG ihi dede Die Ee Red deed oe n simulation principles ooo xo mo E ko vox m dex RR roe eo Ro CR e UR Po Se E Main code SIEUCDUfe lt lt is tue andere ntt ao Be indie Bae R Lee artt tiras io dt cb Equations so ocu Sexo pop uem Ros w Gee bens ee eee ee dels m RR e dC o Ee RR BOR E ud Code generation 23 os Ec Ro Eos UE abe a bw ee SIR e os wee wes Brian package Structure sx oso m ERR SE E OX A OR NUR A ee Re ee Ere Rus Repository sucii oes See Yee Eg SOS de ALD the amp e OR ae WE e x MS es 257 259 259 259 261 263 269 270 273 279 282 285 290 296 298 299 300 302 302 304 305 310 311 334 335 337 337 339 339 339 340 341 341 Python Module Index 387 Index 389 CHAPTER ONE INTRODUCTION Brian is a clock driven simulator for spiking neural networks written in the Python programming language The simulator is written almost entirely in Python
192. 0ms at a timestep of 0 1ms and took 201s to run on the same processor as above Brian Documentation Release 1 4 1 4 Chapter 1 Introduction CHAPTER TWO INSTALLATION If you already have a copy of Python 2 5 2 7 try the Quick installation below otherwise take a look at Manual installation 2 1 Quick installation 2 1 1 easy_install pip The easiest way to install the most recent version of Brian if you already have a version of Python 2 5 2 7 including the easy install script is to simply run the following in a shell easy install brian This will download and install Brian and all its required packages NumPy SciPy etc Similarly you can use the pip utility pip install brian Note that there are some optimisations you can make after installation see the section below on Optimisations 2 1 2 Debian Ubuntu packages If you use a Debian based Linux distribution in addition to Debian itself this includes for example Ubuntu or Linux Mint you can install Brian directly from your favourite package manager e g Synaptic or the Ubuntu Software Centre thanks to the packages provided by the NeuroDebian team The package is called python brian the documentation and tutorials can be found in python brian doc To install these packages from the command line use sudo apt get install python brian python brian doc Note that in contrast to the procedure described above for easy install pip you will not necessari
193. 1 388 Python Module Index A ACF in module brian 300 ACVF in module brian 300 add kernel brian experimental codegen2 GPUManager method 373 add symbols brian experimental codegen2 GPUManager method 373 INDEX atf file Axon 302 atlevel brian hears Sound method 314 atmaxlevel brian hears Sound method 314 auditory modelling 236 autocorrelogram in module brian 300 add symbols brian experimental codegen2 GPUSymboIMeRfUryMana method 374 aer file Spikes 301 AERSpikeMonitor example usage 168 AERSpikeMonitor class in brian 294 aiff sound 239 alias equations 192 analysis numpy 189 259 scipy 189 259 apply brian hears HRTF method 329 applying equations 218 ApproximateGammatone example usage 113 115 ApproximateGammatone class in brian hears 322 arcsinh example usage 108 118 arctan example usage 40 array quantity 260 units 260 ArrayIndex class in brian experimental codegen2 382 ArraySymbol class in brian experimental codegen2 380 asymmetric compensation coeffs in module brian hears 328 AsymmetricCompensation example usage 120 AsymmetricCompensation class in brian hears 325 er atf file 502 B BaseSound class in brian hears 333 Block class in brian experimental codegen2 367 brian module 1 brian experimental model_documentation module 341 brownnoise brian hears Sound static method 312 br
194. 1 ms rather than 10 ms but we have set it up through the connection strengths that an incoming spike from neuron 0 of G1 causes a large increase of 6 mV to Va whereas a spike from neuron 1 of G1 causes a smaller increase of 3 mV to Vb The value for Va then jumps at times 1 ms and 4 ms when we defined neuron 0 of G1 to fire and decays almost back to rest in between The value for Vb jumps at times 2 ms and 3 ms and because the times are closer together and the time constant is longer they add together In the next part of this tutorial we ll see how to use this system to do something useful 3 1 Tutorials 25 Brian Documentation Release 1 4 1 Exercises 1 Try playing with the parameters t au_a tau Db and the connection strengths C1 0 0 and C2 0 1 Try changing the list of spike times 2 In this part of the tutorial the states Va and Vb are independent of one another Try rewriting the differential equations so that they re not independent and play around with that 3 Write a network with inhibitory and excitatory neurons Hint you only need one connection 4 Write a network with inhibitory and excitatory neurons whose actions have different time constants for example excitatory neurons have a slower effect than inhibitory ones Solutions 3 Simple write C i j 3 mV to make the connection from neuron i to neuron j inhibitory 4 See the next part of this tutorial 3 2 Examples These examples c
195. 2 M SpikeMonitor P trace RecentStateMonitor P v record range 5 duration 200 ms ion subplot 211 raster plot M refresh 10 ms showlast 200 ms redraw False subplot 212 trace plot refresh 10 ms showlast 200 ms run l second ioff switch interactive mode off show and wait for user to close the window before shutting down Example spike_triggered_average misc Example of the use of the function spike_triggered_average A white noise is filtered by a gaussian filter low pass filter which output is used to generate spikes poission process Those spikes are used in conjunction with the input signal to retrieve the filter function from brian import x from brian hears import from numpy random import randn from numpy linalg import norm from matplotlib import pyplot dt 0 1 ms defaultclock dt dt stimulus duration 15000 ms stimulus randn int stimulus_duration dt filter n 200 filt exp linspace 0 5 n n n 5 2 2 n 3 filt filt norm filt 1000 filtered_stimulus convolve stimulus filt neuron PoissonGroup 1 lambda t filtered_stimulus int t dt 3 2 Examples 161 Brian Documentation Release 1 4 1 spikes SpikeMonitor neuron run stimulus_duration report text spikes spikes 0 resulting spikes max_interval 20 ms window duration of the spike triggered average onset 10 ms sta time_axis s
196. 2000 5 number of stimulus durations durations are multiplexed sigma 0 1 More less noise best_duration 500 ms Read group index for each neuron f open groups str int best_duration ms txt group_number array int x for x in f read split nneurons max group_number 1 one postsynaptic neuron per group f close Calculate group size count zeros nneurons number of presynaptic neurons for each postsynaptic neuron for i in range len group number if group number i 1 count group number i 1 Presynaptic neurons ginh_max 5 Nx 5 number of neurons per row N Nx Nx number of neurons rest_time l second initial time eqs dv dt El v gmax gK gmax2xgK2 ginh x EK v tau volt dgK dt gKinf gK tauK 1 4 IKLT dgK2 dt gK2 tauK2 1 Delayed rectifier gKinf 1 1 exp Va v ka 1 ginh ginh max t rest time amp t lt rest_timetduration 1 tauk i ms tau ms gmax 1 duration second rrr 68 Chapter 3 Getting started Brian Documentation Release 1 4 1 uniform lambda N rand N 5 2 uniform between 1 and 1 seed 31418 Get the same neurons every time _tauk 400 mst tuniform N tauK_spread alpha El Vt Vt EK _gmax alpha minx maxx minx rand N _tau 30 mst tuniform N tau_spread neurons NeuronGroup N Ndur model eqgs threshold v Vt reset v Vr gK2 1 neurons v Vr neurons gK 1 1 exp Va El ka
197. 2009 but for random spike trains and not in a speech recognition task d PETETSET DSTSSHTAHH HHSAHTHSEHHRHRHAHTRHTTHRHTHURTHTHT HTHRHHAHHHTAHATHHHHAETHHASHTETHTHEHSTHTHSHETTHE betas arange 0 2 3 1 0 1 betas array 1 0 2 0 cond_results curr_results for beta in betas print Testing warp factor 1f beta cond results append cond model run beta curr_results append curr_model run beta figure colors mpl cm gist earth betas betas 0 betas 1 betas 0 lookup dict zip betas colors for beta cond result curr result in zip betas cond results curr results times cond v cond cond result times curr v curr curr result subplot 1 2 1 plot times cond ms beta v cond color lookup beta axis 0 250 1 5 1 5 subplot 1 2 2 plot times curr ms beta v curr color lookup beta axis 0 250 1 5 1 5 subplot 1 2 1 title conductance based subplot 1 2 2 title current based show 3 2 Examples 35 Brian Documentation Release 1 4 1 Example Plakiewicz_Brette_2010 frompapers Spike threshold variability in single compartment model Figure 7 from Platkiewicz J Brette R 2010 A Threshold Equation for Action Potential Initiation PLoS Comput Biol 6 7 e1000850 doi 10 137 1 journal pcbi 1000850 The original HH model is from Traub and Miles 1991 modified by Destexhe et al 2001 and we shift Na inactivation to 62 mV This
198. 23 imshow C w reshape N N interpolation nearest title Synaptic connections subplot 224 plot R times ms R smooth_rate 2 ms filter flat title Firing rate show Example nonlinear synapses synapses NMDA synapses from brian import x import time a 1 10 ms b 1 10 ms c 1 10 ms input NeuronGroup 2 model dv dt 1 10xms 1 threshold 1 reset 0 neurons NeuronGroup 1 model dv dt gtot v 10 ms 1 atoe z Amem S Synapses input neurons model dg dt axg b xx 1 g 1 dx dt c x 1 w 1 synaptic weight rrt pre xt w NMDA synapses neurons gtot S g S True S w 1 10 input v 0 0 5 M StateMonitor S g record True Mn StateMonitor neurons v record 0 run 100 ms subplot 211 plot M times ms M 0 plot M times ms M 1 subplot 212 plot Mn times ms Mn 0 show Example licklider synapses Spike based adaptation of Licklider s model of pitch processing autocorrelation with delay lines with phase locking Romain Brette 3 2 Examples 153 Brian Documentation Release 1 4 1 from brian import x defaultclock dt 02 ms Ear and sound max delay 20 x ms 50 Hz tau ear 1 ms sigma_ear 1 eqs ear dx dt sound x tau_ear sigma_ears 2 tau_ear 5 xi 1 sound 5 sin 2 pixfrequency t 3 1 nonlinear distorsion Ssound 5 Sin 4 pixfrequency t 5 sin 6 pixfre
199. 316 decibel 316 default clock 261 262 defaultclock in module brian 262 define_default_clock in module brian 263 delay brian DelayConnection attribute 276 DelayConnection class in brian 276 DenseConnectionMatrix class in brian 277 DenseConnection Vector class in brian 279 DenseConstructionMatrix class in brian 279 DenseMatrixSymbols class in brian experimental codegen2 370 DenseMatrixSymbols SynapseIndex class in brian experimental codegen2 370 DenseMatrixSymbols TargetIndex class in brian experimental codegen2 370 DenseMatrixSymbols Value class in brian experimental codegen2 370 dependencies brian experimental codegen2 ArraySymbol method 380 direct control spikes 272 document connections brian experimental model documentation Docum method 341 document group brian experimental model_documentation DocumentW1 method 341 document groups brian experimental model documentation DocumentW method 342 document network brian experimental model documentation Document method 342 document network in module brian experimental model documentation 343 document operation brian experimental model documentation Documen method 342 document operations brian experimental model documentation Docume method 342 document sim brian experimental model documentation DocumentWirit method 342 DocumentWriter class in brian experimental model_documentation
200. 341 DoNothingFilterbank class in brian hears 319 DRNL class in brian hears 325 dt brian Clock attribute 261 duration brian hears Filterbank attribute 332 duration brian hears Sound attribute 312 DynamicConnectionMatrix class in brian 278 DynamicConstructionMatrix class in brian 279 E efficient code 247 vectorisation 247 empirical dependencies brian experimental codegen2 DenseMatrixSymbdiscEhrdtIad8x method 370 dependencies X brian experimental codegen2 Symbol method 379 Dependency class in brian experimental codegen2 371 derived classes extending brian 251 338 multiple files 251 338 differential equations 192 differential equations compilation 218 freezing 218 non autonomous 218 stochastic 217 time dependent 218 DimensionMismatchError 259 dimensions inconsistent 259 units 259 EmpiricalThreshold example usage 174 EmpiricalThreshold class in brian 268 end brian Clock attribute 261 equal subtask brian ProgressReporter method 304 equation 192 equations 192 Equations example usage 43 45 91 93 95 97 99 133 134 141 156 171 172 174 equations 215 263 alias 192 applying 218 combining 215 compilation 218 differential 192 equation 192 external variables 215 fixed points 219 Index 391 Brian Documentation Release 1 4 1 freezing 218 linear 216 membrane potential 216 model 263 namespaces 215 neuron 263 non
201. 49 83 109 111 115 123 get samplerate 128 IdentityConnection 40 72 155 180 IIRFilterbank 117 IRCAM LISTEN 49 83 109 120 LinearFilterbank 108 118 LinearGammachirp 111 linked var 56 60 178 184 load aer 168 log 35 62 74 79 84 108 118 120 153 187 LogGammachirp 120 124 LowPass 115 123 MembraneEquation 167 177 MiddleEar 125 126 128 mixture process 163 184 MultiStateMonitor 166 184 Network 27 125 128 network operation 46 60 74 77 79 144 165 173 181 NeuronGroup 26 31 35 39 41 43 45 46 49 50 53 54 56 57 60 63 65 66 68 69 72 74 TT 79 82 84 91 93 95 99 102 106 109 130 132 135 144 147 160 162 164 167 169 174 177 182 184 187 Parameters 27 play 114 124 PoissonGroup 46 99 130 131 135 136 139 142 144 151 157 158 161 162 165 167 168 176 177 180 PoissonInput 43 PoissonThreshold 160 186 PopulationRateMonitor 39 54 98 102 130 131 141 143 151 152 160 165 172 173 181 183 PopulationSpikeCounter 141 156 162 172 PulsePacket 45 140 183 raster plot 31 39 45 56 60 79 82 84 97 102 106 115 131 136 137 140 152 154 156 159 160 162 164 167 170 173 176 178 185 187 RecentStateMonitor 99 160 174 Refractoriness 170 reinit 63 reinit default clock 43 54 128 168 RemoteControlClient 159 RemoteControlServer 174 Repeat 49 83 109 392
202. 50 49 Vr 11 mV reset 60 49 we 60x0 27 10 excitatory weight wi 20 4 5 10 inhibitory weight duration 1000 ms mmm Equations eqs PT d dv dt getgi v449 mV 20xms volt dge dt ge 5 ms volt dgi dt gi 10 xms volt ES This is a linear system so each update corresponds to multiplying the state matrix by a 3 3 update matrix mmm Update matrix A array exp dt taum 0 0 taue taum taue exp dt taum exp dt taue exp dt taue 0 taui taum taui exp dt taum exp dt taui 0 exp dt taui T mmm State variables P NeuronGroup 4000 model eqs threshold 50 mV reset 60 mV mmm S zeros 3 N mmm Initialisation P v 60x xmVt10x xmVx xrand len P mmm S 0 rand N Vt Vr Vr Potential uniform between reset and threshold mmm Connectivity matrices Pe P subgroup 3200 excitatory group Pi P subgroup 800 inhibitory group Ce Connection Pe P ge weight 1 62smV sparseness p Ci Connection Pi P gi weight 9 mV sparseness p nmm We target We weight 348 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 for _ in range Ne k scirandom binomial N p 1 0 target sample xrange N k target sort We target append target We_weight append 1 62 mV k Wi_target Wi_weight for _ in range Ni k scirandom binomial N p 1 0 target sample xrange
203. 55 mV El 65 mV vmean 65 mV taum 5 ms taue 3 ms taui 10 ms eqs Equations dv dt dge dt dgi dt m input parameters p 15 ne 4000 ni 1000 lambdac 40 Hz lambdae lambdai 1 Hz Synapse parameters we 5 mV taum taue wi vmean El lambdaexne NeuronGroup definition ge gi v El taum volt ge taue volt gi taui volt taum taue taum xwextaue lambdaexnixtaui group NeuronGroup N 2 model eqs reset El threshold theta refractory 5x ms group v El group ge group gi 0 independent E I Poisson inputs pl PoissonInput group 0 N ne rate lambdae weight we state ge p2 PoissonInput group 0 N ni rate lambdai weight wi state gi independent E I Poisson p3 PoissonInput group 1 p4 PoissonInput group 1 p5 PoissonInput group 1 run the simulation reinit_default_clock M SpikeMonitor group SM StateMonitor group run 1 second plot trace and spikes for i in 0 1 spikes M spiketimes val SM values i subplot 2 1 1i 1 plot SM times val plot tile spikes 2 vstack val array spikes 10000 inputs 4 synchronous E events N ne rate lambdae p 1 0 ne lambdac weight we state ge N ni rate lambdai weight wi state gi N 1 rate lambdac weight p we state ge v record True i 940003 1 dtype int
204. 60 12 17 xexp vu 60 14 25 ms ms mm KLT channel low threshold K eqs klt mmm iklt gkltbar w 4 z EK v amp dw dt q10 winf w wtau 1 dz dt ql0 zinf z wtau 1 winf 1 1 exp vu 48 6 0 25 1 zint ass l 95 L exp Grd Tle 7 20 d wtau 100 6 exp vut60 6 16 exp vut60 45 1 5 xms ms ztau 1000 exp vut60 20 exp vu 60 8 50 ms ms mmm Ka channel transient K eqs ka mnm ika gkabarxaxx4xbxc EK v amp da dt q10 ainf a atau 1 42 Chapter 3 Getting started Brian Documentation Release 1 4 1 db dt ql0 binf b btau 1 dc dt q10 cinf c ctau 1 ainf L 1 exp vu 31 6 0 25 i 1 binf 1l 1 exp vu 66 7 0 5 1 cinf 1 1 exp vu 66 7 0 5 t 1 atau 100 7 exp vu 60 14 29 xexp vu 60 24 0 1 ms btau 1000 14 exp vut60 27 29xexp vu 60 24 1 ms ctau 90 1 exp 66 vu 17 10 ms ms Leak eqs leak ileak gl El v amp h current for octopus cells eqs hcno ihcno gbarno hl frac h2 l frac Eh v amp dhl dt hinfno h1 taul 1 dh2 dt hinfno h2 tau2 1 hinfno 1 1 exp vu 66 7 1 taul bet1 qt 0 008 1l alpl ms ms tauz bet2 qt 0 0029 1l alp2 ms ms alpl exp le 3 3 vut50 9
205. 648e4 8 315 273 16 celsius J bet1 exp le 3 3 0 3 vut50 9 648e4 8 315 273 16 celsius 1 alp2 exp le 3x3x vut84 9 648e4 8 315 273 16 celsius 1 bet2 exp le 3 3 0 6 vut84 9 648e4 8 315 273 16 celsius 1 eqs dv dt ileakt tinat ikhtt iklt ikat tihtihcno I C volt vu v mV 1 unitless v I amp qs eqs leak eqs ka eqs na eqs_ih eqs klt eqs_kht eqs_hcno neuron NeuronGroup 1 eqs implicit True neuron v El run 50 ms Go to rest M StateMonitor neuron v record 0 neuron I Ipulse run 100 ms report text plot M times ms M 0 mV show Example Rossant et al 2011bis frompapers Distributed synchrony example Fig 14 from ms ms Rossant C Leijon S Magnusson AK Brette R 2011 Sensitivity of noisy neurons to coincident inputs Journal of Neuroscience 31 47 3 2 Examples 43 Brian Documentation Release 1 4 1 5000 independent E I Poisson inputs are injected into a leaky integrate and fire neuron Synchronous events following an independent Poisson process at 40 Hz are considered where 15 E Poisson spikes are randomly shifted to be synchronous at those events The output firing rate is then significantly higher showing that the spike timing of less than 1 of the excitatory synapses have an important impact on the postsynaptic firing from brian import x neuron parameters theta
206. Benchmark 1 random network of integrate and fire neurons with exponential synaptic conductances Clock driven implementation with Euler integration no spike time interpolation R Brette Dec 2007 Brian is a simulator for spiking neural networks written in Python developed by R Brette and D Goodman http brian di ens fr from brian import x import time Time constants taum 20 msecond taue 5 msecond taui 10 msecond Reversal potentials Ee 0 60 mvolt Ei 80 60 mvolt start_time time time eqs Equations dv dt v gex Ee v gi Ei v x 1 taum volt dge dt gex 1 taue 1 dgi dt gi t 1 taui 1 EEE NB 1 conductances are in units of the leak conductance NB 2 multiplication is faster than division P NeuronGroup 4000 model eqs threshold 10 mvolt reset 0 mvolt refractory 5 msecond order 1 compile True P subgroup 3200 P subgroup 800 we 6 10 excitatory synaptic weight voltage wi 67 10 inhibitory synaptic weight hg Fg H 0 og Ce Connection Pe P ge weight we sparseness 0 02 Ci Connection Pi P gi weight wi sparseness 0 02 Initialization P v randn len P 5 5 mvolt P ge randn len P 1 5 4 P gi randn len P 12 20 Record the number of spikes Me PopulationSpikeCounter Pe Mi PopulationSpikeCounter Pi print Network construct
207. Brian Documentation Release 1 4 1 Romain Brette Dan Goodman May 02 2013 CONTENTS 1 Introduction 1 2 Installation 5 2 4 Quick wistallavone lt p lt 2 penso a m mma me RE BO ee ee be oe Y eee oo Re A 3 2 2 Manual installation gt gt oss ooo mk rpne xx o EORR we ee RR os 6 2 3 WESUMS secsi okak uem bium e Hb dede Swe fk A BRS Bee amp eR RAUM Bede Soe i 7 24 Optimusations 4 20044 254 45502 22 bead OR M ADR eee OR RO ee we OR Ros 7 3 Getting started 9 3 1 tortals eb BREESE SSS See Pe he ete Bhs a RS SDR ESL tede 9 ee EXMP ES RC rrr 26 4 User manual 189 4d UNS 24 268046 ba caw beeon Phe et Robo se RS OR S ak rom de Ee s PEA s 189 42 Models and neuron groups o 4 ss sg ooo o o gk eR RR Roe b m Ee e a 191 43 Connections s ssa eset Bow eGR eA RARE EAA eee ee RUE ee S 196 4 4 Spike timing dependent plasticity s soe eo osora Re Re ee 198 45 Short term plasticity sj sese ban 9s pep ba be ee ee So OB bad Ee ge y Se e A 200 4 6 JSynapses os etc Gb RR Ae X eed SR eH OX GE UE BEA ESS ES RES ae Ba 200 4 7 Recording 4 boc eee BO ee 303 Be ee S BOR eee E oe Bape Eos BUR oe 204 48 J puts 4g 424 4 eue Sd Se Bde ee he quee aed d ge ge ire m Pere 1 Bee 4 207 49 User dehned operations ss scan bse RR RO eS HS ee ee SE SH E 210 4 10 Analysis and plotting gt 64 5024 5 224 SRA ASO Ruhm m wee eed oe RR UR 210 4 01 Realtime control s 2o Shwe ea ee Bee ur he ERE RR Gk ECL ACE ey Se E 212 4 12 CloCKS zu SU
208. Ds corresponding to n angles equally spaced between azim max and azim max are used The default diameter is that which gives the maximum ITD as 650 microseconds The ITDs are computed with the formula diameter sin azim speed of sound in air In this case the generated HRTFSet will have coordinates of az im and itd itd Instead of specifying the keywords above just give the ITDs directly In this case the generated HRTFSet will have coordinates of itd only fractional itds False Set this to True to allow ITDs with a fractional multiple of the timestep 1 samplerate Note that the filters used to do this are not perfect and so this will introduce a small amount of numerical error and so shouldn t be used unless this level of timing precision is required See FractionalDelay for more details To get the HRTFSet the simplest thing to do is just hrtfset HeadlessDatabase 13 1load subject The generated ITDs can be returned using the itd attribute of the HeadlessDatabase object If fractional itds False then Note that the delays induced in the left and right channels are not sym metric as making them so wastes half the samplerate if the delay to the left channel is itd 2 and the delay to the right channel is itd 2 Instead for each channel either the left channel delay is O and the right channel delay is itd if itd 0 or the left channel delay is itd and the right channel delay is 0 if itd gt 0 If fractional itds True then del
209. E ERROR eee eR A Ee ee hae ARE cR E a 212 4 13 Simulan Control 53m d Re pute t RS ER ake ERS BAe RRS eli 213 44 More on equations cc esea o enm o m hoe o m Rok kom m cR E ndm m Rd P UE RR Ros 215 4 15 Filemanagement ues oeei die ia EB eg Rr OX Res eem RC ERE RARE e Ae s 219 4 16 Managing simulation runsand dat o opp RUERG S ER I BR 220 5 Thelibrary 223 oJ Library models atn or RRA Se oe iod eae os e des oe od 223 23 2 Random processeS uso gk dede ee ded e e SRR dede mex EROS db edm s 226 35 9 JElectrophysiology models es os oo ero mew R9 ye p eal Gea RW 227 5 44 Electrophysiology electrode comppensatioh so sosoca Re 229 5 5 Electrophysiology trace analysis ees 230 5 6 Modelfitt ng 212 go emo Ex y eoe Be PAA Remi SOROR ROG Rb R ECEDESRUM a eene 233 Df Brian hears iced oe o oe nes tomo x X EROS EUR ER ee Ee Re ee ge A es 236 6 Advanced concepts 247 10 11 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 How to write efficient Briancode i p e socos p ee Compiled code ole Ge hb Ro bee AA 9 Eo boh dos ER he wae Ok Eee doe bt d Projects with multiple files or functions ee ee eee Connection miatflC6S s a A ge ee Re o3 RD ee ee ER ee Rd a Re ws Parameters lt lt 24 64 44 34 42 be PORA E EUR Stee eae ee P RuDORAELE RIEN b NU eS Ss Extending Brian Reference 8 1 8 2 8 3 8 20 8 21 8 22 8 23 SeiPy NumPy and PyLab a cca a a ee UR HO Ee a ee Units system eds ea dthaedo w
210. F v weight 3 mV MS SpikeMonitor PG True Mv StateMonitor IF v record True rates StateMonitor PG rate record True run 100 ms subplot 211 plot rates times ms rates 0 Hz subplot 212 plot Mv times ms Mv 0 mV show 3 2 Examples 177 Brian Documentation Release 1 4 1 Example cable misc Dendrite with 100 compartments from brian import x from brian compartments import x from brian library ionic currents import x length 1 nseg 100 dx length nseg Cm 1 uF cm 2 gl 0 02 x msiemens cm x 2 diam 1 um area pi diam dx El 0 x mV Ri 100 ohm cm ra Ri 4 pi diam x 2 Imm print Time constant Cm gl print Space constant 5 diam gl Ri 5 segments for i in range nseg segments i MembraneEquation Cm area segments 0 Current I nA cable Compartments segments for i in range nseg 1 cable connect i i 1 ra x dx neuron NeuronGroup 1 model cable Zneuron vm 0 10 xmV neuron I 0 05 nA trace for i in range 10 trace append StateMonitor neuron wm str 10 x i run 200 ms for i in range 10 plot trace i times ms show trace i 0 mV Example reliability misc leak current gl area record True Reliability of spike timing See e g Mainen amp Sejnowski 1995 for experimental r
211. Group NE NI model eqs neurons threshold vt reset el refractory 5 ms Pe neurons subgroup NE Pi neurons subgroup NI dOTHERTRHESTHESSHATAHHRHTHHETTHSRAHHARTSTAEHTRHEHTEHAHTAHTS Connecting the network SESTSITEITRTRHTSRSHSSAITUTHSEHTESSTHTRHEHTATRTRHUHRHUHTTTYT con e Connection Pe neurons g ampa weight 0 3 sparseness epsilon con ie Connection Pi Pe g gaba weight 1e 10 sparseness epsilon con ii Connection Pi Pi g gaba weight 3 sparseness epsilon doSEHESHAEHSSSAESSATHASAHSTEHSESEHAESTEHAESTEHATEE Setting up monitors OSTHTESAEHTSESEEHESEHHAESHEHTHATHREHAEHHAHATEHSEHTH Y sm SpikeMonitor Pe d OTHTERTHRSSATESSHEH HTOTHHTARATESATTRESETAEATRHEHTTAHRTDAHTE Run without plasticity dOTHTSRT HETHISHHTAHATHHTHHEEHRHAHHTSHARHTRHAHTRHHTRHAHRTEHT S run 1 second do etetedeeteteetet t ataeta a dad ta tate ta teeta tte Inhibitory Plasticity dToSPRSEHRRRH HRTSABSARSUHSATRETSATSARHSRATHTRAATTRSRHTATT Y alpha 3 Hz tau stdp 2 Target rate parameter gmax 100 Maximum inhibitory weight eqs stdp inhib dA pre dt A pre tau stdp 1 dA post dt A post tau stdp 1 TEF stdp ie STDP con ie eqs eqs_stdp_inhib pre A_pre 1 w A_post alpha eta post A_post 1 wt A_prexeta wmax gmax d oSTHTESTEHTEESTHEHEADHHATEHRHHTESHEAHRHHHTTRSESTHA Run with plasticity doSTEHTEHAHSHEHUHHSSTESTH HTHTHAESAETTHTEHASHESHTEE run simtime 1 second report text
212. Inf volt N 200 200 neurons to get more statistics only one is shown duration 1 second Biophysical parameters ENa 60 mV EL 70 xmV vT 2 55x xmV Vi 63 xmV tauh 5 ms tau 5 ms ka 5 mV ki 6 mV a ka ki taul 5 ms mu 15 mV sigma 6 mV sqrt taulI taul tau Theoretical prediction for the slope threshold relationship approximation a l tepsilon thresh lambda slope a Vi slope xtauh log 1 Vi vT a slope tauh pee Exact calculation of the slope threshold relationship thresh ex lambda s optimize fsolve lambda th a s tauh exp Vi th s tauh th 1 a a s tauh Vi eqs n dv dt EL v mu sigma I tau volt dtheta dt vT axrectify v Vi theta tauh volt dI dt I tauI 2 tauI x x 5xxi 1 4 Ornstein Uhlenbeck nm neurons NeuronGroup N eqs threshold v gt theta reset v EL refractory 5 ms neurons v EL neurons theta vT neurons I 0 S SpikeMonitor neurons M StateMonitor neurons v record True Mt StateMonitor neurons theta record 0 run duration report text Linear regression gives depolarization slope before spikes tx M times M times 0 amp M timesci 5 tauh slope threshold v array M _values for i t in S spikes ind M times lt t amp M times t tauh mx v i ind S _ _ _ _ linregress tx len mx mx slope append s threshold append mx 1 Figure M insert spikes S displays spikes on the trace s
213. M SpikeMonitor P This reporter function is called every second and it sends a message to the server process updating the status of the current run def reporter elapsed complete message queue put os getpid elapsed complete run 4000 ms report reporter report period 1 second return excitatory_weight M nspikes name main numprocesses None number of processes to use set to None to have one per CPU We have to use a Queue from the Manager to send messages from client processes to the server process manager multiprocessing Manager message queue manager Queue pool multiprocessing Pool processes numprocesses This generator function repeatedly generates random sets of parameters to pass to the how many spikes function def args while True weight rand 3 5 mV yield weight message_queue imap_unordered returns an AsyncResult object which returns results as and when they are ready we pass this results object which is returned immediately to the sim_mainloop function which monitors this updates the GUI and plots the results as they come in results pool imap unordered how many spikes args ion this puts matplotlib into interactive mode to plot as we go sim mainloop pool results message queue Example taskfarm multiprocessing Uses the run_tasks function to run a task on multiple CPUs and save the results to a Dat aManager o
214. M23inh x y x flatten y flatten barrels23inh dict i j layer23inh subgroup N23inh for i in xrange barrelarraysize for j in for i in range barrelarraysize for j in range barrelarraysize barrels23inh i j x xti barrels23inh i jl y y j print Building synapses please wait Feedforward connections feedforward Synapses layer4 layer23exc model w volt A pre 1 A post 1 pre gect w A pre A prexexp lastupdate t taup 4Ap A post A postxexp lastupdate t taud w clip w A post 0 EPSC post A pre A prexexp lastupdate t taup A post A post exp lastupdate t taud Ad w clip w A pre 0 EPSC for i in range barrelarraysize for j in range barrelarraysize feedforward barrels4 i j barrels23 i j 5 feedforward w barrels4 i j barrels23 i j EPSC 5 Excitatory lateral connections recurrent_exc Synapses layer23exc layer23 model w volt pre get w recurrent exc layer23exc layer23exc 15 exp 5 layer23exc x i layer23exc x j 4 x2 layer recurrent exc w layer23exc layer23exc EPSC 3 recurrent exc layer23exc layer23inh 15 exp 5 layer23exc x i layer23inh x j 4 2 layer recurrent exc w layer23exc layer23inh EPSC Inhibitory lateral connections recurrent inh Synapses layer23inh layer23exc model w volt pre gict w recurrent inh exp 5 layer23inh x i layer23exc x j 2 x2 layer23inh y i
215. Matrix and DynamicConnectionMatrix For customised run time modifications to sparse and dense connection matrices you have two options You can modify the data structures directly using the information in the reference pages linked to in the paragraph above or you can use the methods defined in the Connect ionMatrix class which work for dense sparse and dynamic matrix structures and do not depend on implementation specific details These methods provide element row and column access The row and column access methods use either DenseConnectionVector or SparseConnectionVector objects The dense connection vector is just a 1D numpy array of length the size of the row column The sparse connection vector is slightly more complicated but not much see its documentation for details The idea is that in most cases both dense and sparse connection vectors can be operated on without having to know how they work so for example if v is a ConnectionVector then 2 v is of the same type So fora ConnectionMatrix W this should work whatever the structure of W W set row i 2 W get_row i Or equivalently W i 2 W i The syntax W i W i and W i j is supported for integers i and j for respectively row column and element access 6 5 Parameters Brian includes a simple tool for keeping track of parameters If you only need something simple then a dict or an empty class could be used The point of the parameters class is that allows yo
216. N O Inf SAC 0 mean PSTH PSTHnoself N N 1 SAC 1 mean PSTH i PSTH i for i in range 1 p SAC hstack SAC 1 SAC 1 return arange len SAC len SAC 2 bin SAC halfwidth x Fr Returns half width of function given by x in bin numbers This is used to calculate the precision left panel Ko M n max x argmax x return find x n lt M 2 0 n find x n lt M 2 1 reproducibility SNR Fr Calculates the precision timescale and reliability strength for a given signal to noise ratio Wr sys stdout write SNR str SNR n sys stdout flush we use this instead of print because of multiprocessing reinit_default_clock important because we do multiple simulations The common noisy input N 5000 number of neurons simultaneously simulated duration 30 second duration of one simulation 200 seconds in the paper tau_noise 5 ms input NeuronGroup 1 model dx dt x tau_noise 2 tau_noise 5 xi 1 The noisy neurons receiving the same input tau 10 ms sigma 5 input amplitude Z sigmaxsqrt tau_noiset tau tau_noisex SNR 2 1 normalizing factor eqs neurons dx dt 2Z SNR I u x tau 1 du dt u tau_noise 2 tau_noise 5 xi l E vu FGE neurons NeuronGroup N model eqs_neurons threshold 1 reset 0 refractory 5 ms neurons x rand N random initial conditions neurons I linked var input x rate PopulationR
217. N k target sort Wi target append target Wi weight append 9 mV k nmm Spike monitor M SpikeMonitor P will contain a list of i t where neuron i spiked at time t n nmm spike monitor Empty list of spikes mmm State monitor trace StateMonitor P v record 0 record only neuron 0 nmm trace Will contain v t for each t for neuron 0 mmm Simulation run duration nmm tl time t 0 ms while t lt duration STATE UPDATES S dot A S Threshold all spikes S 0 Vt nonzero 0 List of neurons that meet threshold condition PROPAGATION OF SPIKES Excitatory neurons spikes S 0 Ne gt Vt nonzero 0 In Brian we actually use bisection to speed it up for i in spikes S 1 We_target i We_weight i Inhibitory neurons spikes S 0 Ne N gt Vt nonzero 0 for i in spikes 2 Wi_target i Wi_weight i Reset neurons after spiking S 0 all spikes Vr Reset membrane potential 11 2 Simulation principles 349 Brian Documentation Release 1 4 1 Spike monitor Spike monitor i t for i in all spikes State monitor trace append S 0 0 tt dt t2 time print Simulated in t2 tl s print len spike_monitor spikes non Plot subplot 211 raster_plot M subplot 212 plot trace times ms trace 0 mV show Here we cheat a little non from brian import raster_plot class M pass M spik
218. N model eqs threshold 10 mV reset 0 mV refractory 5 ms 3 2 Examples 155 Brian Documentation Release 1 4 1 group v 0 mV group v0O linspace 0 mV 20 mV N counter SpikeCounter group duration 5 second run duration plot group v0O mV counter count duration show Example noisy_ring misc Integrate and fire neurons with noise from brian import x tau 10 ms sigma 5 N 100 J 1 eqs wwe dv dt mu tautsigma taux 5 xi 1 mmm group NeuronGroup N model eqs threshold 1 reset 0 C Connection group group v for i in range N C i i 1 N J C connect_full group group weight J for i in range N C i i 0 S SpikeMonitor group trace StateMonitor group v record True run 500 x ms i t S spikes 1 subplot 211 raster_plot S subplot 212 plot trace times ms trace 0 show Example COBA misc This is a Brian script implementing a benchmark described in the following review paper Simulation of networks of spiking neurons A review of tools and strategies 2007 Brette Rudolph Carnevale Hines Beeman Bower Diesmann Goodman Harris Zirpe Natschlager Pecevski Ermentrout Djurfeldt Lansner Rochel Vibert Alvarez Muller Davison El Boustani and Destexhe Journal of Computational Neuroscience 23 3 349 98 156 Chapter 3 Getting started Brian Documentation Release 1 4 1
219. Python also includes an object for storing data in a dictionary like database object with the shelve module Brian includes a simple modification of Python s shelves to make it easy to generate data in parallel on a single machine or across several machines The problem with Python shelves and HDFS is that they cannot be accessed by several processes on a single machine concurrently if two processes attempt to write to the file at the same time it gets corrupted In addition if you want to run simulations on two computers at once and merge them you have to write a separate program to merge the databases produced With the Dat aManager class you generate a directory containing multiple files and the data can be distributed amongst these files To merge the results generated on two different computers just copy the contents of one directory into the other The way it works is that to write data to a DataManager you first generate a session object which is essentially a Python shelf object and then write data to that However when you want to read data it will look in all the files in the directory and return merged data from them Typically a session file will have the form username computername so that merging directories across multiple computers users is straightforward no name conflicts You can also create a locking session This object can be used in multiple processes concurrently without danger of losing data 4 16 3 Multiple r
220. R amp current_name I defines the same equation as eqs Equations dvm dt I 200 pF volt I V0 vm R amp ELO The keyword current name is optional if there is no ambiguity i e if there is only one variable or only one variable with amp units As for standard equations Cur rent objects can be initialised with a multiline string several equations By default the convention for the current direction is the one for injected current For the ionic current convention use the TonicCurrent class eqs MembraneEquation 200 pF IonicCurrent I vm V0 R amp 223 Brian Documentation Release 1 4 1 5 1 2 Compartmental modelling Compartmental neuron models can be created by merging several MembraneEquation objects with the compartments module If soma and dendrite are two compartments defined as MembraneEquation ob jects then a neuron with those 2 compartments can be created as follows neuron_eqs Compartments soma soma dendrite dendrite neuron_eqs connect soma dendrite Ra neuron NeuronGroup 1 model neuron eqs The Compartments object is initialised with a dictionary of MembraneEquation objects The returned object neuron eqs is also a MembraneEquation object where the name of each compartment has been appended to variable names with a leading underscore For example neuron vm soma refers to variable vm of the somatic compartment The conn
221. The noise term is independent between neurons Thus one cannot use this method to analyse the response to frozen noise where all neurons receive the same input noise One would need to use an external variable representing the input updated by a user defined operation The noise term is independent between equations This can however be solved by the following trick dx dt x tauc sigmax u taux x 5 volt dy dt y tautsigmay u tau 5 volt u xi secondxx 5 Important notice It is not possible to modulate the noise term with a variable e g v xi tau 5 One reason is that with multi plicative noise there is an ambiguity between the Ito and the Stratonovich interpretation Unfortunately this limitation also applies to parameters i e sigma xi taux 5 is not possible if sigma is a parameter as in the following ex ample 4 14 More on equations 217 Brian Documentation Release 1 4 1 eqs Equations dx dt x tau sigmaxxi taux x 5 volt sigma volt group NeuronGroup 1 eqs threshold x vt However the problem can usually be solved by some rewriting eqs Equations dy dt y tau xi taux x 5 1 x Sigmaxy volt sigma volt group NeuronGroup 1 eqs threshold x vt 4 14 6 Non autonomous equations The time variable t can be directly inserted into an equation string It is replaced at run time by the current value of the time variable for the relevant neuron group
222. W Gerstner Inhibitory Plasticity Balances Excitation and Inhibition in Sensory Pathways and Memory Networks Science November 10 2011 from brian import x do STSEPPSTSSSSASHTTRHSATRSSSATTSSASTSAATSTAZHSETTEHTHTY Defining network model parameters dOoSTSEHRTSTERAHBRA RHEHATRTSTSATRATEASTSHTTERTAHAHT NE 8000 Number of excitatory cells NI NE 4 Number of inhibitory cells w l nS Basic weight unit tau ampa 5 0 ms Glutamatergic synaptic time constant tau_gaba 10 0 ms GABAergic synaptic time constant epsilon 0 02 Sparseness of synaptic connections eta le 2 Learning rate tau_stdp 20 ms STDP time constant simtime 10 second Simulation time ttteteetetaettaeatae tad tad tat tet ttt tat tat tt tte tt Neuron model d OTHTSTSHESTSESTHETHHSHEHSEHTSHEHA3STSETOHTHEHTHTHHTHHSRAHHTS gl 10 0 nsiemens Leak conductance el 60 mV Resting potential er 80 mV Inhibitory reversal potential vt 50 mV Spiking threshold 3 2 Examples 31 Brian Documeniation Release 1 4 1 memc 200 0 pfarad Membrane capacitance bgcurrent 200 pA External current eqs neurons dv dt gl v el g ampa w v g gabax v er xw bgcurrent memc volt dg ampa dt g ampa tau ampa 1 dg gaba dt g gaba tau gaba 1 rg E eHH HHH HP HEHEHE PE EAA Ea EEE a ER PE Initialize neuron group dPoOSESTEES ERESASSASAAHTHATTESHATTEEHAHATEEATESTTEHEATET neurons Neuron
223. a 2 tau 5 xi 1 I 0 5 3 p B 1 B od p l cre input NeuronGroup 1 eqs_input neurons NeuronGroup N eqs threshold 1 reset 0 neurons p linspace 0 1 N neurons v rand N neurons B linked var input B M StateMonitor input B record 0 S SpikeMonitor neurons run 1000 ms subplot 211 The input plot M times ms M 0 subplot 212 raster_plot S plot 0 1000 250 250 7 show Example Brette Gerstner 2005 frompapers Adaptive exponential integrate and fire model http www scholarpedia org article Adaptive exponential integrate and fire model Introduced in Brette R and Gerstner W 2005 Adaptive Exponential Integrate and Fire Model as an Effective De scription of Neuronal Activity J Neurophysiol 94 3637 3642 from brian import x Parameters C 281 pF gL 30 nS aum C gL 70 6 mV VT 50 4 mV DeltaT 2 x mV Vcut VT 5 DeltaT 1 ct Pick an electrophysiological behaviour tauw a b Vr 144 ms 4 nS 0 0805 nA 70 6 mV Regular spiking as in the paper Ztauw a b Vr 20 ms 4 nS 0 5 nA VT45 mV Bursting tauw a b Vr 144 ms 2 C 144 xms 0 nA 70 64mV Fast spiking eqs hey dvm dt gL EL vm gL DeltaT exp vm VT DeltaT I w C volt dw dt a vm EL w tauw amp 3 2 Examples 57 Brian Documentation Release 1 4 1 amp mnm neuron NeuronGroup 1 model eqs thr
224. a class from SpikeGeneratorGroup as follows class EquallySpacedSpikeGroup SpikeGeneratorGroup def init self N t spikes 0 i dt for i in range N SpikeGeneratorGroup init self spikes You would use these objects in the following ways obj1 equally spaced spike group 100 10x ms obj2 EquallySpacedSpikeGroup 100 10 ms For simple examples like the one above there s no particular benefit to using derived classes but using derived classes allows you to add methods to your derived class for example which might be useful For more experienced Python programmers or those who are thinking about making their code into an extension for Brian this is probably the preferred approach Finally it may be useful to note that there is a protocol for one object to contain other objects That is suppose you want to have an object that can be treated as a simple NeuronGroup by the person using it but actually instantiates several objects perhaps internal Connection objects These objects need to be added to the Network object in order for them to be run with the simulation but the user shouldn t need to have to know about them To this end for any object added to a Net work if it has an attribute contained objects then any objects in that container will also be added to the network 338 Chapter 9 Typical Tasks CHAPTER TEN EXPERIMENTAL FEATURES The following features are located in the experimental
225. ad to very substantial speed improvements class brian experimental cuda GPUNeuronGroup N model threshold None reset NoReset init None refractory 0 0 second level 0 clock None order 1 implicit False unit_checking True max_delay 0 0 second compile False freeze False method None precisionz double maxblocksize 512 forcesync False page locked_mem True gpu_to_cpu_vars None cpu to gpu vars None Neuron group which performs numerical integration on the GPU 339 Brian Documentation Release 1 4 1 Initialised with arguments as for NeuronGroup and additionally precision double The GPU scalar precision to use older models can only use precision float maxblocksize 512 If GPU compilation fails reduce this value forcesync False Whether or not to force copying of state variables to and from the GPU each time step This is slow so it is better to specify precisely which variables should be copied to and from us ing gpu to cpu vars and cpu_to_gpu_vars pagelocked mem True Whether to store state variables in pagelocked memory on the CPU which makes copying data to from the GPU twice as fast cpu to gpu vars None gpu to cpu vars None Which variables should be copied each time step from the CPU to the GPU before state update and from the GPU to the CPU after state update The point of the copying of variables to and from the GPU is that the GPU maintains a separate memory from the CPU and
226. afterwards cfmin cfmax cfN 150 Hz 5 x kHz 40 cf erbspace cfmin cfmax cfN We repeat each of the HRTFSet filterbank channels cfN times so that for each location we will apply each possible cochlear frequency 3 2 Examples 83 Brian Documentation Release 1 4 1 gfb Gammatone Repeat hrtfset_fb cfN tile cf hrtfset fb nchannels Half wave rectification and compression cochlea FunctionFilterbank gfb lambda x 15 clip x 0 Inf 1 0 3 0 Leaky integrate and fire neuron model eqs dV dt I V 1xms 0 1 xi 0 5 ms x 5 1 Eos vere G FilterbankGroup cochlea I qs reset 0 threshold 1 refractory 5x ms The coincidence detector cd neurons cd NeuronGroup num indices cfN qs reset 0 threshold 1 clock G clock Each CD neuron receives precisely two inputs one from the left ear and one from the right for each location and each cochlear frequency C Connection G cd V for i in xrange num indices cfN C i i 0 5 from right ear C i num indices cfN i 0 5 from left ear We want to just count the number of CD spikes counter SpikeCounter cd Run the simulation giving a report on how long it will take as we run run sound duration report stderr We take the array of counts and reshape them into a 2D array which we sum across frequencies to get the spike count of each location specific assembly count counter count count sh
227. ains cf gains product freqs 1 gains tones Sound gen tone freq levels 0 for freq _ in cf gains F out test TanCarneySignal MiddleEar tones gain np array g for g in cf gains cf for cf in cf gains update interval 1 process reshaped Fout F out test T reshape len freqgs 1 len gains 1 rms np sqrt np mean reshaped Fout start end T np mean reshaped Fout start end axis 2 T T 2 axis 2 get the best gain for each CF using simple linear interpolation gain dict freqs 0 1 reference gain for idx freq in enumerate freqs 1 gain dict freqg interpld rms idx gains ref rms now do the real test tones at different levels for different CFs tones Sound gen tone freq level for freq level in cf level 3 2 Examples 127 Brian Documentation Release 1 4 1 F_out TanCarneySignal MiddleEar tones gain np array gain_dict cf for cf _ in cf_level cf for cf in cf level update interval 1 process reshaped Fout F out T reshape len fregs len levels 1 rms np sqrt np mean reshaped Fout start end T np mean reshaped Fout start end axis 2 T T 2 axis 2 This should more or less reproduce Fig 7 plt plot levels rms T plt legend 0f Hz cf for cf in freqs 0 plt xlim 20 100 plt ylim 1e 6 1 plt yscale log plt xlabel input signal SPL dB plt yla
228. al for i in range 8 synapses inh i 4 i 1 8 winh synapses_inh i 4 i 8 winh synapses_inh i 4 i 1 spikes SpikeCounter neurons S 8 winh run duration nspikes spikes count x sum nspikes exp gamma 1j print Angle deg arctan imag x real x degree polar concatenate gamma gamma 0 2 pi concatenate nspikes nspikes 0 duration show Example Rothman Manis 2003 frompapers Cochlear neuron model of Rothman amp Manis Rothman JS Manis PB 2003 The roles potassium currents play in regulating the electrical activity of ventral cochlear nucleus neurons J Neurophysiol 89 3097 113 All model types differ only by the maximal conductances Adapted from their Neuron implementation by Romain Brette from brian import x defaultclock dt 0 025 ms for better precision FUP Simulation parameters choose current amplitude and neuron type from typeic typelt typel2 type 21 type2 type2o vFrX neuron type typelc Ipulse 250 pA C 12 pF Eh 43 mV EK 70 mV 77 mV in mod file El 65 mV ENa 50 mV nf 0 85 proportion of n vs p kinetics zss 0 5 steady state inactivation of glt celsius 22 temperature q10 2 3 xx celsius 22 10 hcno current octopus cell frac 0 0 3 2 Examples 41 Brian Documeniation Release 1 4 1 qt 4 5 celsius 33 10 Maximal conduc
229. al features Brian Documentation Release 1 4 1 subs k G MultiLinearNeuronGroup eqs subs G v 1 G w 0 M StateMonitor G v record True run 1 second for i in range len G plot M times M i show 10 4 Realtime Connection Monitor You can visual weight matrices in realtime using the PyGame package with the following class class brian experimental realtime_monitor RealtimeConnectionMonitor C size None scal ing fast wmin None wmax None clock None cmap lt matplotlib colors LinearSeg instance at Oxa5b366c Realtime monitoring of weight matrix Short docs C Connection to monitor size Dimensions width height of output window leave as None to use C W shape scaling If output window dimensions are different to connection matrix scaling is used options are fast for no interpolation or smooth for slower smooth interpolation wmin wmax Minimum and maximum weight matrix values if left to None then the min max of the weight matrix at each moment is used and this scaling can change over time clock Leave to None for an update every 100ms cmap Colour map to use black and white by default Get other values from matplotlib cm x Note that this class uses PyGame and due to a limitation with pygame there can be only one window using it Other options are being considered 10 5 Automatic Model Documentation class brian experimental model_documentatio
230. alf wave rectify inputs FunctionFilterbank source lambda x clip x 0 Inf The syntax lambda x clip x 0 Inf defines a function object that takes a single argument x and returns clip x 0 Inf The numpy function clip x low high returns the values of x clipped between low and high so if x lt low it returns low if x gt high it returns high otherwise it returns x The symbol Inf means infinity i e no clipping of positive values Technical details Note that functions should operate on arrays in particular on 2D buffered segments which are arrays of shape bufsize nchannels Typically most standard functions from numpy will work element wise If you want a filterbank that changes the shape of the input e g changes the number of channels set the nchannels keyword argument to the number of output channels class brian hears SumFilterbank source weights None Sum filterbanks together with given weight vectors For example to take the sum of two filterbanks SumFilterbank fbl fb2 To take the difference SumFilterbank fbl fb2 1 1 class brian hears DoNothingFilterbank source Filterbank that does nothing to its input Useful for removing a set of filters without having to rewrite your code Can also be used for simply writing compound derived classes For example if you want a compound Filterbank that does AFilterbank and then BFilterbank but you want to encapsulate that into a single class
231. all offsets corresponding to delays This assumes that delays will not change during the simulation If they do between two runs for example then this method can be called Offsets Offsets are used to solve the problem of inserting multiple synaptic events with the same delay This is difficult to vectorise If there are n synaptic events with the same delay these events are given an offset between 0 and n 1 corresponding to their relative position in the data structure They can be either precalculated faster or determined at run time saves memory Note that if they are determined at run time then it is possible to also vectorise over presynaptic spikes 8 10 Network The Network object stores simulation objects and runs simulations Usage is described in detail below For simple scripts you don t even need to use the Net work object itself just directly use the magic functions run and reinit described below class brian Network args kwds Contains simulation objects and runs simulations Initialised as Network with any collection of objects that should be added to the Network You can also pass lists of objects lists of lists of objects etc Objects that need to passed to the Net work object are NeuronGroup and anything derived from it such as PoissonGroup Connection and anything derived from it Any monitor such as SpikeMonitor or StateMonitor Any network operation defined with the netwo
232. and also appears as a state variable of the neuron group 4 14 7 Freezing External variables can be frozen by passing the keyword freeze True default False at initialization of a NeuronGroup object Then when the string defining the equations are compiled into Python functions method compile functions the external variables are replaced by their float values units are discarded This can result in a significant speed up TODO more on the implementation 4 14 8 Compilation State updates can be compiled into Python code objects by passing the keyword compile True at initialization of aa NeuronGroup Note that this is different from the method compile functions which compiles the equation for every variable into a Python function not the whole state update process When the compile keyword is set the method orward euler code orexponential euler code is called It generates a string containing the Python code for the update of all state variables one time step then compiles it into Python code object That compiled object is then called at every time step All external variables are frozen in the process regardless of the value of the freeze keyword This results in a significant speed up although the exponential Euler code is not quite optimised yet Note that only Python code is generated thus a C compiler is not required 4 14 9 Working with equations Equations object can also be used outside simulation
233. ang Buszaki model J Neurosci 1996 Oct 15 16 20 6402 13 Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model Wang XJ Buzsaki G 3 2 Examples 45 Brian Documentation Release 1 4 1 Note that implicit integration exponential Euler cannot be used and therefore simulation is rather slow from brian import x defaultclock dt 0 01 ms Cm 1 uF cm 2 Tapp 2 uA gL 0 1 msiemens EL 65 mV Na 55 mV K 90 mV Na 35 msiemens K 9xmsiemens QQ few eqs dv dt gNaxmx x3xhx v ENa gK n x4x v EK gL v EL kIapp Cm volt m alpham alpham betam 1 alpham 0 1 mV v 35xmV exp 0 1 mVx v 35 mV 1 ms Hz betam 4xexp vt 60xmV 18xmV ms Hz dh dt 5 x alphah 1 h betah h 1 alphah 0 07 exp v 58 mV 20xmV ms Hz betah 1 exp 0 1 mVx vt 28 mV 1 ms Hz dn dt 5 x alphan x 1 n betan n 1 alphan 0 01 mVx v 34xmV exp 0 1 mVx v 34 mV 1 ms Hz betan 0 125xexp v 44xmV 80xmV ms Hz rrt neuron NeuronGroup 1 eqs neuron v 70 mV neuron h 1 M StateMonitor neuron v record 0 run 100 ms report text plot M times ms M 0 mV show Example Kremer_et_al_ 2011 frompapers Late Emergence of the Whisker Direction Selectivity Map in the Rat Barrel Cortex Kremer Y Leger JF Goodman DF Brette R Bourdieu L 2011 J Neurosci 31 29 10689 700 Development of direction maps wit
234. ank object that can be used to apply the HRTF as part of a chain of filterbanks You can get the number of samples in the impulse response with 1en hrtf class brian hears HRTFSet data samplerate coordinates A collection of HRTFs typically for a single individual Normally this object is created automatically by an HRTFDatabase Attributes hrtf Alist of HRTF objects for each index num indices The number of HRTF locations You can also use 1en hrtfset num samples The sample length of each HRTF fir serial fir interleaved The impulse responses in a format suitable for using with FIRFilterbank in serial LLLLL RRRRR or interleaved LRLRLR Methods subset condition Generates the subset of the set of HRTFs whose coordinates satisfy the condition This should be one of a boolean array of length the number of HRTFs in the set with values of True False to indicate if the corresponding HRTF should be included or not an integer array with the indices of the HRTFs to keep or a function whose argument names are names of the parameters of the coordinate system e g condition lambda azim azim lt pi 2 8 21 Brian hears 329 Brian Documentation Release 1 4 1 filterbank source interleaved False kwds Returns an FIRFilterbank object which applies all of the HRTFs in the set If interleaved False then the channels are arranged in the order LLLL RRRR otherwise they are arranged in the order LRLRLR
235. antity object with some additional information name and string representation You can define new units which will be used when generating string representations of quantities simply by doing an arithmetical operation with only units for example Nm newton metre Note that operations with units are slower than operations with Quantity objects so for efficiency if you do not need the extra information that a Unit object carries around write 1 second in preference to second 260 Chapter 8 Reference Brian Documentation Release 1 4 1 8 3 Clocks Many Brian objects store a clock object always passed in the initialiser with the keyword clock If no clock is specified the program uses the global default clock When Brian is initially imported this is the object defaultclock and it has a default time step of 0 1ms In a simple script you can override this by writing for example defaultclock dt 1 ms However there are other ways to access or redefine the default clock see functions below You may wish to use multiple clocks in your program In this case for each object which requires one you have to pass a copy of its Clock object The network run function automatically handles objects with different clocks updating them all at the appropriate time according to their time steps value of dt Multiple clocks can be useful for example for defining a simulation that runs with a very small dt but with some
236. ape num indices cfN count sum count axis 1 count array count dtype float amax count Our guess of the location is the index of the strongest firing assembly index guess argmax count Now we plot the output using the coordinates of the HRTFSet coords hrtfset coordinates azim elev coords azim coords elev scatter azim elev 100 count plot azim index elev index r ms 15 mew 2 plot azim index guess elev index guess xg ms 15 mew 2 xlabel Azimuth deg ylabel Elevation deg xlim 5 350 ylim 50 95 show Example Fig7B Licklider frompapers computing with neural synchrony hearing Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 12B Spike based adaptation of Licklider s model of pitch processing autocorrelation with delay lines from brian import x defaultclock dt 02 ms Ear and sound max delay 20 ms 50 Hz tau ear 1 x ms 84 Chapter 3 Getting started Brian Documentation Release 1 4 1 sigma ear 1 eqs ear dx dt sound x tau_ear sigma_ears 2 tau_ear 5 xi 1 sound 5 sin 2 xpixfrequencyxt 3 1 nonlinear distorsion Ssound 5 Sin 4 pixfrequency t 5 sin 6 pixfrequency t 1 missing fundamental frequency 200 200 t Hz Hz Hz increasing pitch CEF receptors NeuronGroup 2 model eqs_ear threshold
237. ariable tau is changed in the string to taum e Equation dv dt v tau volt tau None The name of the variable tau is changed in the string to a unique identifier Explicit namespace e Equation dv dt v tau volt tau 2 ms The namespace is explicitly given tau 2 ms In this case Brian does not try to build a namespace magically so the namespace must be exhaustive Units need not be passed Implicit namespace e Equation dv dt v tau volt The namespace is built from the globals and locals in the caller s frame For each identifier in the string the name is looked up in 1 locals of caller 2 globals of caller 3 globals of equations py module typically units Identifiers can be any Python object for example functions Issues e Special variables xi and t are not taken into account at this stage i e they are integrated in the namespace if present This should probably be fixed and a warning should be raised A warning is raised for t at the preparation stage see below f identifiers are not found then no error is raised This is to allow equations to be built in several pieces which is useful in particular for library objects If an identifier is found whose name is the same as the name of a variable then no error is raised here and it is included in the namespace This is difficult to avoid in the case when equations are built in several pieces e g the conflict appears only when the
238. ariable name for threshold or reset is not given e g threshold 10 mV The method looks for one these names v V vm Vm If one is present it is the membrane potential variable If none or more than one is present no variable is found If it is found the corresponding variable is swapped with the first variable in the diffeq names list note not in the diffeq names nonzero list Otherwise nothing happens This way the first variable in the list is the membrane potential Possibly a warning could be issued if it is not found The problem it might issue warnings too often A better way would be to issue warnings only when threshold and reset are used ambiguously i e no Vm found and more than 1 variable Cleaning the namespace Then variables and t are removed from the namespace if present N B xi does not appear to be removed and warnings are issued using log warn method clean namespace Compiling functions This is done by the compile functions method Python functions are created from the string definition of equations For each equation differential equation the list of identifiers is obtained from the string definition then only those referring to variables are kept A Python lambda function of these remaining identifiers is then compiled using eval and put in the function dictionary Compiled functions are used for checking units obtaining the list of arguments this could be done independently
239. array of counts and reshape them into a 2D array which we sum 110 Chapter 3 Getting started Brian Documentation Release 1 4 1 across frequencies to get the spike count of each location specific assembly count counter count count shape num_indices cfN count sum count axis 1 count array count dtype float amax count Our guess of the location is the index of the strongest firing assembly index_guess argmax count Now we plot the output using the coordinates of the HRTFSet coords hrtfset coordinates azim elev coords azim coords elev scatter azim elev 100 count plot azim index elev index r ms 15 mew 2 plot azim index_guess elev index guess xg ms 15 mew 2 xlabel Azimuth deg ylabel Elevation deg xlim 5 350 ylim 50 95 show Example online computation hears Example of online computation using process Plots the RMS value of each channel output by a gammatone filterbank from brian import x from brian hears import soundl tone 1 kHz 1 second sound2 whitenoise 1 second sound soundl sound2 sound sound ramp sound level 60 dB cf erbspace 20 Hz 20 kHz 3000 fb Gammatone sound cf def sum_of_squares input running return running sum input 2 axis 0 rms sqrt fb process sum_of_squares sound nsamples Sound rms sqrt mean soundx 2 axhline sound rms l
240. arseness 0 02 Ci Connection Pi P gi weight 9 mV sparseness 0 02 M SpikeMonitor P run l second raster_plot M show Example van_rossum_metric misc Example of how to use the van Rossum metric The VanRossumMetric function which is defined as a monitor and therefore works online computes the metric between every neuron in a given population The present example show the concept of phase locking N neurons are driven by sinusoidal inputs with different amplitude Use output VanRossumMetric source tau 4 ms source is a NeuronGroup of N neurons tau is the time constant of the kernel used in the metric output is a monitor with attribute distance which is the distance matrix between the neurons in source from brian import from time import time tau 20 ms 170 Chapter 3 Getting started Brian Documentation Release 1 4 1 N 100 b 1 2 constant current mean the modulation varies f 10 Hz delta 2 ms eqss dv dt vtaxsin 2 pixf t b tau 1 ar rrt neurons NeuronGroup N model eqs threshold 1 reset 0 neurons v rand N neurons a linspace 05 0 75 N S SpikeMonitor neurons trace StateMonitor neurons v record 50 van rossum metric VanRossumMetric neurons tau 4 ms run 1000xms raster plot S title Raster plot figure title Distance matrix between spike trains imshow van rossum metric distance colorbar show Example curren
241. at changing the value of x in p2 will not change the value of x in p1 this is a copy operation 6 6 Precalculated tables One way to speed up simulations is to use precalculated tables for complicated functions The Tabulate class defines a table of values of the given function at regularly sampled points The TabulateInterp class defines a table with linear interpolation which is much more precise Both work with scalar and vector arguments class brian Tabulate f xmin xmax n An object to tabulate a numerical function Sample use g Tabulate f 0 1 1000 y g 5 v g 1 3 v g array 1 3 Arguments of g must lie in xmin xmax n IndexError is raised is arguments are above xmax but not always when they are below xmin it can give weird results class brian TabulateInterp f xmin xmax n An object to tabulate a numerical function with linear interpolation Sample use 6 6 Precalculated tables 253 Brian Documentation Release 1 4 1 g TabulateInterp f 0 1 1000 y g 5 v g 1 3 v g array 1 3 Arguments of g must lie in xmin xmax n IndexError is raised is arguments are above xmax but not always when they are below xmin it can give weird results 6 7 Preferences 6 7 1 Functions Setting and getting global preferences is done with the following functions brian set global preferences kwds Set global preferences for Brian Usage set global preferences
242. at due to internal implementation details passing a full matrix rather than a sparse one may slow down your code because zeros will be propagated as well as nonzero values WARNING No unit checking is done at the moment For a more efficient low level method see connect from sparse Additionally you can directly access the matrix of weights by writing 274 Chapter 8 Reference Brian Documentation Release 1 4 1 C Connection P Q print C i j C i j Where here i is the source neuron and j is the target neuron Note if C i jJ should be zero it is more efficient not to write C i j 0 if you write this then when neuron i fires all the targets will have the value 0 added to them rather than just the nonzero ones WARNING No unit checking is currently done if you use this method Take care to set the right units Connection matrix structures Brian currently features three types of connection matrix structures each of which is suited for different situa tions Brian has two stages of connection matrix The first is the construction stage used for building a weight matrix This stage is optimised for the construction of matrices with lots of features but would be slow for runtime behaviour Consequently the second stage is the connection stage used when Brian is being run The connection stage is optimised for run time behaviour but many features which are useful for construction are absent e g the ability to ad
243. atch file For example with Eclipse right click on the Brian project then Team gt Create Patch gt Save in filesystem then Next gt Project Send your patch as an attachment to the developers mailing list and make sure the subject of your message starts with PATCH Then describe your patch in your message From that point your patch will either be directly included in the svn or more likely will be first discussed in the mailing list New modules New Brian modules typically start in the dev ideas folder then go to brian experimental when they starting looking like modules They move to the main folder when they are stable especially the user syntax 11 2 Simulation principles The following paper outlines the principles of Brian simulation Goodman D and Brette R 2008 Brian a simulator for spiking neural networks in Python Front Neuroinform doi 10 3389 neuro 11 005 2008 This one describes the simulation algorithms which are based on vectorisation Brette R and Goodman DF Vectorised algorithms for spiking neural network simulation Neural Computation in press 11 2 1 Sample script Below we present a Brian script and a translation into pure Python to illustrate the basic principles of Brian simula tions Original Brian script A script in Brian 346 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 vier Very short example program EEF from brian import from time import t
244. ate 1 state 0 Threshold mechanism where one state variable is compared to another Initialised as VariableThreshold threshold state 1 state 0 with arguments threshold state The state holding the lower bound for spiking state The state that is checked If x is the value of state variable threshold state on neuron i and y is the value of state variable state on neuron i then neuron i will fire if y x Typically using this class is more time efficient than writing a custom thresholding operation Compilation Note that if the global variable useweave is set to True then this function will use a C accelerated version class brian EmpiricalThreshold args kwds Empirical threshold e g for Hodgkin Huxley models In empirical models such as the Hodgkin Huxley method after a spike neurons are not instantaneously reset but reset themselves as part of the dynamical equations defining their behaviour This class can be used to model that It is a simple threshold mechanism that checks e g V gt Vt but it only does so for neurons that 268 Chapter 8 Reference Brian Documentation Release 1 4 1 haven t recently fired giving the dynamical equations time to reset the values naturally It should be used in conjunction with the NoReset object Initialised as EmpiricalThreshold threshold l1 mV refractory l ms state 0 clock with arguments threshold The lower bound for the state variable to
245. ateMonitor neurons PSTH run duration t SAC autocor rate rate N T 30 ms timescale float halfwidth SAC mean rate rate 2 xdefaultclock dt precision strength sum SAC mean rate rate 2 float defaultclock dt mean rate rate reliability return timescale strength i name_ _ main__ pool multiprocessing Pool multiprocessing cpu count 1 all cores but one SNRdB linspace 10 15 20 100 points in the paper SNR 10 SNRdB 10 3 2 Examples 59 Brian Documentation Release 1 4 1 results pool map reproducibility SNR launches multiple processes timescale strength zip results Figure subplot 211 plot SNRdB timescale 1000 xlabel SNR dB ylabel Precision ms subplot 212 plot SNRdB strength 100 xlabel SNR dB ylabel Reliability show Example Fig5D_reproducibility frompapers computing with neural synchrony coincidence detec tion and synchrony Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 5D left Caption Fig 5D Responses of a noisy integrate and fire model in repeated trials Protocol neuron receives input signal noise both O U processes signal is identical in all trials frozen noise The total variance is held fixed Signal to noise ratio is 3 in this simulation from brian import x The common noisy input tau noise 5 ms
246. ated version which uses the scipy Weave package if the user has a suitable compiler on their system This version is much more efficient but the code is rather dense and difficult to understand 11 4 Equations An Equation is a set of single lines in a string 1 dx dt f unit differential equation 2 x f unit equation 3 x y alias 4 x unit parameter The equations may be defined on multiple lines with the character Comments using may also be included Two special variables are defined t time and xi white noise Ultimately it should be possible using Sympy to define equations implicitly e g tau dv dt v unit although it makes unit specification ambiguous An equation can be seen as a set of functions or code and a namespace to evaluate them A key part of object construction is the construction of the namespace after parsing 354 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 11 4 1 Namespace construction The namespaces are stored in eq _ namespace Each equation string has a specific namespace Proposition for a simplification there could be just one namespace per Equation object rather than per string Possible conflicts would be dealt with when equations are added with prefix as when inserting static variables see below Variable substitution These are simply string substitutions e Equation dv dt v tau volt tau taum The name of the v
247. ation consisting of two strings for the left respectively the right hand side of an equation lhs and rhs and a Brian Unit unit into a LaTeX expression aligning on the equality sign for amsmath s align environment static latex_equation eq_string Helper function to convert the right hand side of an equation string eq string to a LaTeX expression not a full equation in LaTeX terms using sympy static latex equations eqs Convert Brian equations either a possibly multi line string or an Equation object eqs into a LaTeX equation using amsmath s align environment 342 Chapter 10 Experimental features Brian Documentation Release 1 4 1 brian experimental model_documentation document_network net None output text kwargs Convenience method for documenting a network without having to construct a Document Writer object first If no network net is given a MagicNetwork is automatically created and documented The output argument should be either text the default or latex Any further keyword arguments are passed on to the respective DocumentWriter brian experimental model documentation labels from namespace namespace Creates a labels dictionary that can be handed over to the document network from a given namespace Would typically be called like this net document network labels labels from namespace locals This allows doc ument network to use the variable names used in the Python code as
248. ator will destroy the signature of the original function and replace it with the signature args x kwds Other decorators will do the same thing and this decorator critically needs to know the signature of the function it is acting on so it is important that it is the first decorator to act on a function It cannot be used in combination with another decorator that also needs to know the signature of the function Typically you shouldn t need to use any details about the following two classes and their implementations are subject to change in future releases of Brian class brian Quantity value A number with an associated physical dimension In most cases it is not necessary to create a Quant ity object by hand instead use the constant unit names second kilogram etc The details of how Quant ity objects work is subject to change in future releases of Brian as we plan to reimplement it in a more efficient manner more tightly integrated with numpy The following can be safely used Quantity this name will not change and the usage isinstance x Quantity should be safe The standard unit objects second kilogram etc documented in the main documentation will not be subject to change as they are based on SI standardisation Scalar arithmetic will work with future implementations class brian Unit value A physical unit Normally you do not need to worry about the implementation of units They are derived from the Qu
249. ay 0xms The maximum delay in second of synaptic events At run time the structure is resized to the maximum delay in delays and thus the max delay should only be specified if delays can change during the simulation in which case offsets should not be precomputed maxevents INITIAL MAXSPIKESPER DT The initial size of the queue for each timestep Note that the data structure automatically grows to the required size and therefore this option is generally not useful precompute offsets True A flag to precompute offsets By default offsets an internal array de rived from delays used to insert events in the data structure see below are precomputed for all neurons 284 Chapter 8 Reference Brian Documentation Release 1 4 1 the first time the object is run This usually results in a speed up but takes memory which is why it can be disabled Data structure A spike queue is implemented as a 2D array X that is circular in the time direction rows and dynamic in the events direction columns The row index corresponding to the current timestep is currentime Each element contains the target synapse index The class is implemented as a SoikeMonitor so that the propagate method is called at each timestep of the monitored group Methods next Advances by one timestep peek Returns the all the synaptic events corresponding to the current time as an array of synapse indexes precompute_offsets Precompute
250. ays in the left and right channels will be symmetric around a global offset of delay offset 8 21 9 Base classes Useful for understanding more about the internals class brian hears Bufferable Base class for Brian hears classes Defines a buffering interface of two methods buffer init Initialise the buffer should set the time pointer to zero and do any other initialisation that the object needs buffer fetch start end Fetch the next samples start end from the buffer Value returned should be an array of shape end start nchannels Can throw an IndexError exception if it is outside the possible range In addition bufferable objects should define attributes nchannels The number of channels in the buffer samplerate The sample rate in Hz By default the class will define a default buffering mechanism which can easily be extended To extend the default buffering mechanism simply implement the method buffer fetch next samples Returns the next samples from the buffer 8 21 Brian hears 331 Brian Documentation Release 1 4 1 The default methods for bu fer init and buffer fetch will define a buffer cache which will get larger if it needs to to accommodate a buffer fetch start end where end start is larger than the current cache If the filterbank has a minimum buffer size attribute the internal cache will always have at least this size and the buffer fetch next samples method will always get called with
251. bandstop or bandpass and be of type Elliptic Butterworth Chebyshev etc The passband and stopband can be scalars for low or high pass or pairs of parameters for stopband and passband yielding similar filters for every channel They can also be arrays of shape 1 nchannels for low and high pass or 2 nchannels for stopband and passband yielding different filters along channels This class uses the scipy iirdesign function to generate filter coefficients for every channel See the documentation for scipy signal iirdesign for more details Initialisation parameters samplerate The sample rate in Hz nchannels The number of channels in the bank passband stopband The edges of the pass and stop bands in Hz For lowpass and highpass filters in the case of similar filters for each channel they are scalars and passband lt stopband for low pass or stopband gt passband for a highpass For a bandpass or bandstop filter in the case of similar fil ters for each channel make passband and stopband a list with two elements e g for a bandpass have passband 200 Hz 500 Hz and stopband 100 Hz 600 Hz passband and stopbandcan also be arrays of shape 1 nchannels forlow and high pass or 2 nchannels for stopband and passband yielding different filters along channels gpass The maximum loss in the passband in dB Can be a scalar or an array of length nchannels gstop The minimum attenuation in the stopband in dB Can be a scalar or an array of len
252. bank mon T aspect auto show Example time varying filter2 hears This example implements a band pass filter whose center frequency is modulated by a sinusoid function This modula tor is implemented as a Funct ionFilterbank One state variable here time must be kept it is therefore imple mented with a class The bandpass filter coefficients update is an example of how to use a Cont rolFilterbank The bandpass filter is a basic biquadratic filter for which the Q factor and the center frequency must be given The input is a white noise from brian import x from brian hears import samplerate 20 kHz SoundDuration 300 ms sound whitenoise SoundDuration samplerate ramp number of frequency channel here it must be one as a spectrogram of the foutput is plotted nchannels 1 fc init 5000 Hz initial center frequency of the band pass filter Q 5 quality factor of the band pass filter update_interval 1 the filter coefficients are updated every sample mean center freq 4 kHz mean frequency around which the CF will oscillate amplitude 1500 Hz famplitude of the oscillation frequency 10 Hz frequency of the oscillation this class is used in a FunctionFilterbank via its __call__ It outputs the 118 Chapter 3 Getting started Brian Documentation Release 1 4 1 center frequency of the band pass filter Its output is thus later passed as input to the controler class CenterFrequen
253. based on the idea of buffer ing as defined by the base class Buf ferable see section Options Each class has two methods buffer_init to initialise the buffer and buffer_fetch start end to fetch the portion of the buffer from samples with indices from start to end not including end as standard for Python The buffer_fetch start end method should return a 2D array of shape end start nchannels with the buffered values From the user point of view all you need to do having set up a chain of Sound and Filterbank objects is to call buffer_fetch start end repeatedly If the output of a Filterbank is being plugged into a FilterbankGroup object everything is handled automatically For cases where the number of channels is small or the length of the input source is short you can use the Filterbank fetch duration method to auto matically handle the initialisation and repeated application of buffer_fetch To extend Filterbank it is often sufficient just to implement the bu fer apply input method See the documentation for Filterbank for more details 5 7 7 Library Brian hears comes with a package of predefined filter classes to be used as basic blocks by the user All of them are implemented as filterbanks First a series of standard filters widely used in audio processing are available 5 7 Brian hears 243 Brian Documentation Release 1 4 1 Class Descripition Example IIRFilterbankBank of low high
254. bel rms of AC component of Fout plt show Example tan carney simple test hears tan carney 2003 Fig 1 and 3 spking output without spiking refractory period should reproduce the output of the AN3 test tone m and ANS3 test click m scripts available in the code accompanying the paper Tan amp Carney 2003 This matlab code is available from http www urmc rochester edu labs Carney Lab publications auditory models cfm Tan Q and L H Carney A Phenomenological Model for the Responses of Auditory nerve Fibers II Nonlinear Tuning with a Frequency Glide The Journal of the Acoustical Society of America 114 2003 2007 import numpy as np import matplotlib pyplot as plt from brian stdunits import kHz Hz ms from brian network import Network from brian monitor import StateMonitor SpikeMonitor from brian globalprefs import set global preferences set global preferences useweave True from brian hears import Sound get samplerate set default samplerate tone click silence dB TanCarney MiddleEar ZhangSynapse from brian clock import reinit default clock set default samplerate 50 kHz sample length 1 get samplerate None cf 1000 x Hz print Testing click response duration 25 ms levels 40 60 80 100 120 a click of two samples tones Sound Sound sequence click sample_length 2 peak levelxdB silence duration duration sample length for level in levels
255. bilistic synapses Seems to work from brian import x N 20 tau 5 ms input PoissonGroup 2 rates 20 Hz neurons NeuronGroup N model dv dt v tau 1 S Synapses input neurons model w 1 p 1 transmission probability 3 2 Examples 139 Brian Documentation Release 1 4 1 pre vt w rand lt p Transmission probabilities S True S w 0 5 S p 0 linspace 0 1 N transmission probability between 0 and 1 S p 1 linspace 0 1 N 1 reverse order for the second input M StateMonitor neurons v record True run 500 ms for i in range N plot M times ms M i i k show Example Diesmann et al 1999 synapses Synfire chains M Diesmann et al 1999 Stable propagation of synchronous spiking in cortical neural networks Nature 402 529 533 from brian import x Neuron model parameters Vr 70 mV Vt 55 mV taum 10 ms taupsp 0 325 ms weight 4 86 mV Neuron model C0 eqs dV dt V Vr x 1 taum volt dx dt x y x 1 taupsp volt dy dt y 1 taupsp 25 27 mV ms N 39 24 mV ms 0 5 xi volt Pik Fe Neuron groups P NeuronGroup N 1000 model eqs threshold Vt reset Vr refractory 1 ms Pinput PulsePacket t 50 ms n 85 sigma 1 ms The network structure Pgp P subgroup 100 for i in range 10 C Synapses P P model w volt pre yt w for i in range 9 C Pgp i Pgp i 1 True C w Pg
256. bject from brian import x from brian tools datamanager import x from brian tools taskfarm import x def find rate k report if Eg eqs dV dt k V 10 ms 1 E on d G NeuronGroup 1000 qs reset 0 threshold 1 M SpikeCounter G run 30 second report report return k mean M count 30 i name main N 20 dataman DataManager taskfarmexample if dataman itemcount lt N M N dataman itemcount run_tasks dataman find rate rand M 19 1 X Y zip dataman values 3 2 Examples 89 Brian Documentation Release 1 4 1 plot X Y Ta xlabel k ylabel Firing rate Hz show 3 2 7 interface Example interface interface Interface example Install cherrypy for this example Then run the script and go to http localhost 8080 on your web browser You can use cherrypy to write html interfaces to your code from brian import x import cherrypy import os path The server is defined here class MyInterface object Qcherrypy expose def index self redirect to the html page we wrote return meta HTTP EQUIV Refresh content 0 URL index html gt Qcherrypy expose def runscript self we 1 62 wi 9 xxkwd f runscript is the script name we and wi are the names of form fields we float we wi float wi From minimalexample reinit_default_clock Pau eqs dv dt getgi v 49 mV 20 ms volt dge dt
257. ble of a group with the value from the array corresponding to the current simulation time 298 Chapter 8 Reference Brian Documentation Release 1 4 1 Initialisation arguments group The NeuronGroup to which the variable belongs var The name or index of the state variable in the group arr The array of values used to set the variable in the group Can be an array or a TimedArray If it is an array you should specify the times or clock arguments or leave them blank to use the default clock times Times corresponding to the array values see TimedArray for more details clock The clock for the NetworkOperation If none is specified use the group s clock If arr is not a TimedArray then this clock will be used to initialise it too start dt Can specify these instead of a clock see TimedArray for details when The standard NetworkOperation when keyword although note that the default value is start brian set group var by array args kwds Sets NeuronGroup values with a TimedArray Creates a TimedArraySetter see that class for details 8 13 2 Linked variables brian linked var source var 0 funcz None when start clockz None Used for linking one NeuronGroup variable to another Sample usage G NeuronGroup H NeuronGroup G V linked var H W In this scenario the variable V in group G will always be updated with the values from variable W in group H The groups G and H must
258. by a red Each location has a corresponding assembly of neurons whose summed firing rates give the sizes of the blue circles in the plot The most 3 2 Examples 109 Brian Documentation Release 1 4 1 strongly responding assembly is indicated by the green x which is the estimate of the location by the model Reference Goodman DFM Brette R 2010 Spike timing based computation in sound localization PLoS Comput Biol 6 11 from brian import from brian hears import Download the IRCAM database and replace this filename with the location you downloaded it to hrtfdb IRCAM LISTEN r F V HRTFNIRCAM subject 1002 hrtfset hrtfdb load subject subject This gives the number of spatial locations in the set of HRTFs num indices hrtfset num indices Choose a random location for the sound to come from index randint hrtfset num indices A sound to test the model with sound Sound whitenoise 500xms This is the specific HRTF for the chosen location hrtf hrtfset hrtf index We apply the chosen HRTF to the sound the output has 2 channels hrtf fb hrtf filterbank sound We swap these channels equivalent to swapping the channels in the subsequent filters but simpler to do it with the inputs swapped channels RestructureFilterbank hrtf fb indexmapping 1 0 Now we apply all of the possible pairs of HRTFs in the set to these swapped channels which means repeating them num indices times first
259. c spikes e pearest post nearest postsynaptic spike all presynaptic spikes wmin 0 minimum synaptic weight wmax maximum synaptic weight update additive modifications are additive independent of synaptic weight or hard bounds multiplicative modifications are multiplicative proportional to w or soft bounds e mixed depression is multiplicative potentiation is additive See documentation for STDP for more details 8 8 2 Short term plasticity STP class brian STP C taud tauf U Short term synaptic plasticity following the Tsodyks Markram model Implements the short term plasticity model described in Markram et al 1998 Differential signaling via the same axon of neocortical pyramidal neurons PNAS Synaptic dynamics is described by two variables x and u which follow the following differential equations dx dt 1 x taud depression du dt U u tauf facilitation where taud tauf are time constants and U is a parameter in 0 1 Each presynaptic spike triggers modifications of the variables u lt u U 1 u x xx 1 u Synaptic weights are modulated by the product ux in 0 1 before update Reference Markram et al 1998 Differential signaling via the same axon of neocortical pyramidal neurons PNAS 8 8 Plasticity 281 Brian Documentation Release 1 4 1 8 9 Synapses The Synapses class was introduced in Brian version 1 4 and can be used to define everything arou
260. cascade of gain and delay filtering For more details see Yost 1996 or chapter 15 in Hartman Sound Signal Sensation brian hears irno args kwds Returns an IRN_O noise The iterated ripple noise is obtained many attenuated and delayed version of the original broadband noise For more details see Yost 1996 or chapter 15 in Hartman Sound Signal Sensation 8 21 Brian hears 315 Brian Documentation Release 1 4 1 brian hears tone args kwds Returns a pure tone at frequency for duration using the default samplerate or the given one The frequency and phase parameters can be single values in which case multiple channels can be specified with the nchannels argument or they can be sequences lists tuples arrays in which case there is one frequency or phase for each channel brian hears click args kwds Returns a click of the given duration If peak is not specified the amplitude will be 1 otherwise peak refers to the peak dB SPL of the click according to the formula 28e 6 10 peak 20 brian hears clicks args kwds Returns a series of n clicks see click separated by interval brian hears harmoniccomplex args kwds Returns a harmonic complex composed of pure tones at integer multiples of the fundamental frequency 0 The amplitude and phase keywords can be set to either a single value or an array of values In the former case the value is set for all harmonics and harmonics up to the sampling fre
261. ce I injected current efull False if True return a dict with the following keys correlation spikes coefficients after onsets peaks prediction after onsets spike before spike onset spike after 8 21 Brian hears See Also User guide for Brian hears brian hears set default samplerate samplerate Sets the default samplerate for Brian hears objects by default 44 1 kHz 8 21 1 Sounds cass brian hears Sound Class for working with sounds including loading saving manipulating and playing For an overview see Sounds Initialisation The following arguments are used to initialise a sound object data Can be a filename an array a function or a sequence list or tuple If its a filename the sound file WAV or AIFF will be loaded If its an array it should have shape nsamples nchannels Ifitsa function it should be a function f t If its a sequence the items in the sequence can be filenames functions arrays or Sound objects The output will be a multi channel sound with channels the corresponding sound for each element of the sequence samplerate None The samplerate if necessary will use the default for an array or function or the sam plerate of the data for a filename duration None The duration of the sound if initialising with a function Loading saving and playing static Load filename Load the file given by filename and returns a Sound object Sound file can be either a wav or a aif file save
262. ce 0 x ms 1 1 max delay N synapses delay 1 linspace 0 ms 1 1 max delay N 1 Spikes SpikeMonitor neurons run 1000 ms raster plot spikes show Example filterbank audition An auditory filterbank implemented with Poisson neurons The input sound has a missing fundamental only harmonics 2 and 3 from brian import x defaultclock dt 01 ms N 1500 tau 1 x ms Decay time constant of filters 2x tau freq linspace 100 Hz 2000 Hz N characteristic frequencies f stimulus 500 Hz stimulus frequency gain 500 Hz eqs Fg dv dt a w v I tau Hz dw dt v w tau Hz 4 e g linearized potassium channel with conductance a ar I gainx sin A pi f stimulusxt sin 6 pi f stimulus t Hz TEP neurones NeuronGroup N model eqs threshold PoissonThreshold neurones a 2 pi freq tau 2 spikes SpikeMonitor neurones counter SpikeCounter neurones run 100 ms 186 Chapter 3 Getting started max_delay Brian Documentation Release 1 4 1 subplot 121 CF array freq i for i _ in spikes spikes timings array t for _ t in spikes spikes plot timings ms CF xlabel Time ms ylabel Characteristic frequency Hz subplot 122 plot counter count 300 ms freq xlabel Firing rate Hz show Example licklider audition Spike based adaptation of Licklider s model of pit
263. ce to look for names in the namespace Usually 0 for user code Standard functions for expressions rand A uniform random number between 0 and 1 randn A Gaussian random number with mean 0 and standard deviation 1 For example these could be used to implement an adaptive model with random reset noise with the following string E l mV V Vrc rand x 5 mV class brian VariableReset resetvaluestate 1 state 0 Resets specified state variable to the value of another state variable Initialised with arguments resetvaluestate The state variable which contains the value to reset to state The name or number of the state variable to reset This will reset all of the neurons that have just spiked The given state variable of the neuron group will be set to the value of the state variable resetvaluestate class brian Refractoriness args kwds Holds the state variable at the reset value for a fixed time after a spike Initialised with arguments 266 Chapter 8 Reference Brian Documentation Release 1 4 1 resetvalue The value to reset and hold to period The length of time to hold at the reset value If using variable refractoriness this is the maximum period state The name or number of the state variable to reset and hold class brian SimpleCustomRefractoriness args kwds Holds the state variable at the custom reset value for a fixed time after a spike Initialised as SimpleCustomR
264. ch processing autocorrelation with delay lines with phase locking Romain Brette from brian import x defaultclock dt 02 ms Ear and sound max delay 20 ms 50 Hz tau ear 1 x ms sigma ear 1 eqs ear dx dt sound x tau ear sigma earx 2 tau ear x 5xxi 1 sound 5 sin 2 xpixfrequencyxt 3 1 nonlinear distorsion Sound 5 sin 4 pixfrequency t 5 sin 6 pixfrequency t 1 missing fundamental frequency 200 200 t Hz Hz Hz increasing pitch EEF receptors NeuronGroup 2 model eqs_ear threshold 1 reset 0 refractory 2 ms traces StateMonitor receptors x record True sound StateMonitor receptors sound record 0 Coincidence detectors min freq 50 Hz max freq 1000 Hz N 300 tau 1 ms sigma 1 eqs neurons dv dt v tautsigmas 2 tau 5 xi 1 pug pr neurons NeuronGroup N model eqs neurons threshold 1 reset 0 synapses Connection receptors neurons v structure dense max delay 1 1 max delay delay T synapses connect full receptors neurons weight 5 synapses delay 1 1 exp linspace log min freq Hz log max freq Hz N spikes SpikeMonitor neurons run 500 ms raster plot spikes ylabel Frequency yticks 0 99 199 299 array 1 synapses delay todense 1 0 99 199 299 dtype int show 3 2 Examples 187 Brian Documentation Release 1 4 1 188 Chapter 3 Getti
265. chedule_groups_resets_connections method before running the network for the first time As the name suggests the reset operations are done before connections and the appropriately named network operations are called relative to this rearrangement You can also define your own update schedule with the set update schedule method see that method s API documentation for details This might be useful for example if you have a sequence of network operations which need to be run in a given order brian network operation args kwds Decorator to make a function into a NetworkOperation A NetworkOperation is a callable class which is called every time step by the Network run method Sometimes it is useful to just define a function which is to be run every update step This decorator can be used to turn a function into a NetworkOperat ion to be added to a Network object Example usages Operation doesn t need a clock Qnetwork operation def f Automagically detect clock Qnetwork operation def f clock Specify a clock Qnetwork operation specifiedclock def f clock 8 10 Network 287 Brian Documentation Release 1 4 1 Specify when the network operation is run default is end Qnetwork operation when start def f Then add to a network as follows net Network f class brian NetworkOperation function None clock None when end Callable class for operations that should be called ev
266. cifying modelfitting refractory 10 ms 10xms popsize Size ofthe population number of particles per target train used by the optimization algorithm maxiter Number of iterations in the optimization algorithm 8 19 Model fitting toolbox 305 Brian Documentation Release 1 4 1 optparams Optimization algorithm parameters It is a dictionary keys are parameter names values are parameter values or lists of parameters one value per group This argument is specific to the optimization algorithm used See PSO GA CMAES delta 4xms The precision factor delta a scalar value in second slices 1 The number of time slices to use overlap 0 ms When using several time slices the overlap between consecutive slices in seconds initial_values A dictionary containing the initial values for the state variables cpu The number of CPUs to use in parallel It is set to the number of CPUs in the machine by default gpu The number of GPUs to use in parallel It is set to the number of GPUs in the machine by default precision GPU only a string set to either float or double to specify whether to use single or double precision on the GPU If it is not specified it will use the best precision available returninfo False Boolean indicating whether the modelfitting function should return technical informa tion about the optimization scaling None Specify the scaling used for the parameters during the optimization It can be None or
267. ck Uses the keywords of the Clock initialiser Sample usage define default clock dt 1 ms brian reinit default clock t 0 0 second Reinitialise the default clock to zero or a specified time brian get default clock Returns the default clock object 8 4 Neuron models and groups 8 4 1 The Equations object class brian Equations expr level 0 kwds Container that stores equations from which models can be created Initialised as Equations expr level 0 keywords with arguments expr An expression which can each be a string representing equations an Equations objects or a list of strings and Equations objects See below for details of the string format level Indicates how many levels back in the stack the namespace for string equations is found so that e g level 0 looks in the namespace of the function where the Equations object was created 1evel 1 would look in the namespace of the function that called the function where the created etc Normally you can just leave this out Equations object was keywords Any sequence of keyword pairs key value where the string key in the string equations will be replaced with value which can be either a string value or None in the latter case a unique name will be generated automatically but it won t be pretty Systems of equations can be defined by passing lists of Equat ions toanew Equati Equations objects together the
268. ck dt 0 1 ms monclock Clock dt 0 3 ms inputclock Clock dt 100 ms simple leaky I amp F model with external current Iext as a parameter tau 10 ms eqs dV dt V Iext tau volt Iext volt wr A single leaky I amp F neuron with simclock as its clock G NeuronGroup 1 model eqs reset 0 mV threshold 10 mV clock simclock G V 5 x mV This function will be run in sync with inputclock i e every 100 ms Qnetwork operation clock inputclock def update Iext G Iext rand len G 20 mV V is monitored in sync with monclock MV StateMonitor G V record 0 clock monclock run and plot run 1000 ms plot MV times ms MV 0 mV show You should see 10 different regions sometimes Iext will be above threshold in which case you will see regular spiking at different rates and sometimes it will be below threshold in which case you ll see exponential decay to that value Example using classes misc Example of using derived classes in Brian Using a class derived from one of Brian s classes can be a useful way of organising code in complicated simulations A class such as a NeuronGroup can itself create further NeuronGroup Connection and NetworkOperation objects In order to have these objects included in the simulation the derived class has to include them in its contained objects list this tells Brian to add these to the Network when the derived class object is added to the ne
269. cked object should be put in a particular frame Standard usage If A is a tracked class derived from InstanceTracker then the following wouldn t work 334 Chapter 8 Reference Brian Documentation Release 1 4 1 def f x A x return x objs f print get_instances A 0 0 Instead you write def f x A x magic_register x return x objs f print get_instances A 0 0 Definition Call as magic_register level 1 The can be any sequence of tracked objects or containers of tracked objects and each tracked object will have its instance id the execution frame in which it was created set to that of its parent or to its parent at the given level This is equivalent to calling x set_instance_id level level For each object x passed to magic_register See Also Projects with multiple files or functions Describes difficulties and solutions for using magic functions on projects with multiple files or functions 8 23 Tests brian run all tests 8 23 Tests 335 Brian Documentation Release 1 4 1 336 Chapter 8 Reference CHAPTER NINE TYPICAL TASKS TODO typical things you want to achieve in running your simulation and how to go about doing them 9 1 Projects with multiple files or functions Brian works with the minimal hassle if the whole of your code is in a single Python module py file This is fine when learning Brian or for quick proje
270. clip wtApost 0 inf Apret dApre This creates two sets of delay variables one for each pathway They can be accessed by first indexing with the pathway number The following statement for example sets the delay of the synapse between the first neurons of the source and target groups in the second pathway S delay 1 0 0 23 ms 4 6 6 Monitoring synaptic variables A StateMonitor object can be used to monitor synaptic variables For example the following statement creates a monitor for variable w for the synapses 0 and 1 M StateMonitor S w record 0 1 Note that these are synapse indexes not neuron indexes These can be obtained with the synapse index method s S synapse index i j where i and j may be integers arrays or slices A third index can also be given The recorded traces can then be accessed in the usual way for example plot M times M 0 4 7 Recording The activity of the network can be recorded by defining monitors 4 7 1 Recording spikes To record the spikes from a given group define a SpikeMonitor object M SpikeMonitor group At the end of the simulation the spike times are stored in the variable spikes as a list of pairs i t where neuron i fired at time t For example the following code extracts the list of spike times for neuron 3 Spikes3 t for i t in M spikes if i 3 but this operation can be done directly as follows spikes3 M 3 The total number of spikes i
271. clock is clock2 with t 10 ms etc The update method simply runs each operation in the current clock s update schedule See below for details on the update schedule Update schedules 286 Chapter 8 Reference Brian Documentation Release 1 4 1 An update schedule is the sequence of operations that are called foreach update step The standard update schedule is Network operations with when start Network operations with when before groups Call update method for each NeuronGroup this typically performs an integration time step for the differential equations defining the neuron model Network operations with when after groups Network operations with when middle Network operations with when before connections eCall do propagate method for each Connect ion this typically adds a value to the target state variable of each neuron that a neuron that has fired is connected to See Tutorial 2 Connections for a more detailed explanation of this Network operations with when after connections Network operations with when before resets Call reset method for each NeuronGroup typically resets a given state variable to a given reset value for each neuron that fired in this update step Network operations with when after resets Network operations with when end There is one predefined alternative schedule which you can choose by calling the update_s
272. connection matrix Brian s system for connection matrices can be slightly confusing The way it works is roughly as follows There are two types of connection matrix data structures Const ruct ionMat rix and Connect ionMatrix The con struction matrix types are used for building connectivity and are optimised for insertion and deletion of elements but access is slow The connection matrix types are used when the simulation is running and are optimised for fast access but not for adding removing or modifying elements When a Connect ion object is created it is given a construction matrix data type and when the network is run this matrix is converted to its corresponding connection matrix type As well as this construction connection matrix type distinction there is also the distinction between dense sparse dynamic matrices each of which have their own construction and connection versions The dense matrix structure is very simple both the construction and connection types are basically just 2D numpy arrays The sparse and dynamic matrix structures are very different for construction and connection Both the sparse and dynamic construction matrices are essentially just the scipy lil matrix sparse matrix type however we add some slight improvements to scipy s matrix data type to make it more efficient for our case The sparse and dynamic connection matrix structures are documented in more detail in the reference pages for SparseConnection
273. ct gammatone implementation Slaney M 1993 An Efficient Implementation of the Patterson Holdsworth Auditory Filter Bank Apple Computer Technical Report 35 The code is based on Slaney s Matlab implementation Initialised with arguments 8 21 Brian hears 321 Brian Documentation Release 1 4 1 source Source of the filterbank cf List or array of center frequencies b 1 019 parameter which determines the bandwidth of the filters and reciprocally the duration of its impulse response In particular the bandwidth b ERB cf where ERB cf is the equivalent bandwidth at fre quency cf The default value of b to a best fit Patterson et al 1992 b can either be a scalar and will be the same for every channel or an array of the same length as cf erb order 1 ear Q 9 26449 min bw 24 7 Parameters used to compute the ERB bandwidth ERB cf ear Q erb erder ip py rb erder 1 erb order Their default values are the ones rec ommended in Glasberg and Moore 1990 cascade None Specify or 2 to use a cascade of or 2 order 8 or 4 filters instead of 4 2nd order filters Note that this is more efficient but may induce numerical stability issues class brian hears ApproximateGammatone source cf bandwidth order 4 Bank of approximate gammatone filters implemented as a cascade of order IIR gammatone filters The filter is derived from the sampled version of the complex analog gammatone impulse response g t 1 1 Aet w
274. ct substitutions consists of pairs word rep where each word word appearing in expr is replaced by rep Here a word means anything matching the regexp bword b 11 5 Code generation 371 Brian Documentation Release 1 4 1 brian experimental codegen2 flattened_docstring docstr numtabs 0 spacespertab 4 split False Returns a docstring with the indentation removed according to the Python standard split True returns the output as a list of lines Changing numtabs adds a custom indentation afterwards brian experimental codegen2 indent_string s numtabs 1 spacespertab 4 split False Indents a given string or list of lines split True returns the output as a list of lines brian experimental codegen2 get_identifiers expr Return all the identifiers in a given string expr that is everything that matches a programming language variable like expression which is here implemented as the regexp b A Za z_ A Za z0 9_ b brian experimental codegen2 strip_empty_lines s Removes all empty lines from the multi line string s class brian experimental codegen2 GPUKernel name code namespace mem_man maxblock size 512 scalar double force_sync True Generates final kernel source code and used to launch kernels Used in conjunction with GPUManager Each kernel is prepared with prepare which generates source code and adds symbols to the GPUSymbo1MemoryManager The GPUManager compiles the code and sets th
275. ction stimcentre stimcentre stimspeed stimnorm defaultclock dt if sum stimcentre stimzonecentre 2 gt stimradius2 new direction for i j b in barrels4 iteritems whiskerpos array i j l dtype float 0 5 isactive abs dot whiskerpos stimcentre stimnorm lt 5 if barrels4active i j isactive barrels4active i j isactive b rate float isactive tuning layer4 selectivity barrelindices i j direction new direction run 5 xsecond report text figure Preferred direction selectivity array mean array feedforward i todens selectivity arctan2 selectivity imag selectivity real exp layer4 selectivity 1j for i in range 2 pi 180 pi 48 Chapter 3 Getting started Brian Documentation Release 1 4 1 I zeros barrelarraysize M23exc barrelarraysize M23exc ix arr around layer23exc x M23exc dtype int ay iy array I iy ix imshow I hsv colorbar for i in range 1 barrelarraysizetl plot ixmax ix barrelarraysize i max ix barrelarraysize 0 max iy k plot 0 max ix i max iy barrelarraysize i max iy barrelarraysize k around layer23exc y M23exc dtype int selectivity figure hist selectivity show Example Goodman Brette 2010 frompapers Sound localization with HRTFs Goodman DF and R Brette 2010 Spike timing based computation in sound localization PLoS Comp Biol 6 11 e1000993 d
276. cts but for larger more realistic projects with the source code separated into multiple files there are some small issues you need to be aware of These issues essentially revolve around the use of the magic functions run etc The way these functions work is to look for objects of the required type that have been instantiated created in the same execution frame as the run function In a small script that is normally just any objects that have been defined in that script However if you define objects in a different module or in a function then the magic functions won t be able to find them There are three main approaches then to splitting code over multiple files or functions 9 1 1 Use the Network object explicitly The magic run function works by creating a Network object automatically and then running that network Instead of doing this automatically you can create your own Net work object Rather than writing something like groupl group2 3 C Connection groupl group2 run 1 second You do this groupl group2 C Connection groupl group2 net Network groupl group2 C net run 1 second In other words you explicitly say which objects are in your network Note that any NeuronGroup Connection Monitor or function decorated with network operation should be included in the Network See the documentation for Network for more details This is the preferred solution for almost all case
277. cyGenerator object def init self self t 0 second def call self input update of the center frequency fc mean center freq tamplitude sin 2 pi frequencyxsself t fupdate of the state variable self t self t 1l samplerate return fc center_frequency CenterFrequencyGenerator fc generator FunctionFilterbank sound center frequency the updater of the controller generates new filter coefficient of the band pass filter based on the center frequency it receives from the fc generator its input class CoeffController object def init self target self BW 2 arcsinh 1 2 Q 1 44269 self target target def call self input fc input 1 the control variables are taken as the last of the buffer w0 2 pixfc array samplerate alpha sin w0 sinh log 2 2 self BW xw0 sin w0 self target filt b 0 0 sin w0 2 self target filt b 1 0 0 self target filt b 2 0 sin w0 2 self target filt a 0 0 l alpha self target filt a 1 0 2 cos w0 self target filt a 2 0 1 alpha In the present example the time varying filter is a LinearFilterbank therefore we must initialise the filter coefficients the one used for the first buffer computation w0 2 pixfc_init samplerate BW 2 arcsinh 1 2 Q 1 44269 alpha sin w0 sinh log 2 2 BW w0 sin w0 filt_b zeros nchannels 3 1 filt_a zeros nchannels 3 1 filt_b
278. d Sounds can be played using the play function or Sound play method play sound sound play Sequences of sounds can be played as play soundl sound2 sound3 5 7 Brian hears 239 Brian Documentation Release 1 4 1 The number of channels in a sound can be found using the nchannels attribute and individual channels can be extracted using the Sound channel method or using the left and right attributes in the case of stereo sounds print sound nchannels print amax abs sound left sound channel 0 As an example of using this the following swaps the channels in a stereo sound sound Sound test_stereo wav swappedsound Sound sound right sound left swappedsound play The level of the sound can be computed and changed with the sound level attribute Levels are returned in dB which is a special unit in Brian hears For example 10 dB 10 will raise an error because 10 does not have units of dB The multiplicative gain of a value in dB can be computed with the function gain level All dB values are measured as RMS dB SPL assuming that the values of the sound object are measured in Pascals Some examples sound whitenoise 100 ms print sound level sound level 60 dB sound level 10 dB sound gain 10 dB 5 7 2 Filter chains The standard way to set up a model based on filterbanks is to start with a sound and then construct a chain of filterbanks that modify it for example a
279. d save method or by initialising with a filename sound loadsound test wav sound Sound test aif sound save test wav Various standard types of sounds can also be constructed e g pure tones white noise clicks and silence sound tone 1l kHz 1 second sound whitenoise l second sound click 1 ms sound silence 1l second You can pass a function of time or an array to initialise a sound Equivalent to Sound tone sound Sound lambda t sin 50 Hz 2x pixt duration 1 second Equivalent to Sound whitenoise sound Sound randn int 1l second 44 1 kHz samplerate 44 1 kHz Multiple channel sounds can be passed as a list or tuple of filenames arrays or Sound objects sound Sound left wav right wav sound Sound randn 44100 randn 44100 samplerate 44 1 kHz sound Sound Sound tone 1 kHz 1 second Sound tone 2 kHz 1 second A multi channel sound is also a numpy array of shape nsamples nchannels and can be initialised as this or converted to a standard numpy array sound Sound randn 44100 2 samplerate 44 1 kHz arr array sound Sounds can be added and multiplied sound Sound tone l1 kHz 1 second 0 1 Sound whitenoise l1 second For more details on combining and operating on sounds including shifting them in time repeating them resampling them ramping them finding and setting intensities plotting spectrograms etc see Soun
280. d duration ms 0 360 xlabel Time ms ylabel Azimuth title Left ear subplot 122 imshow img right origin lower left aspect auto extent 0 sound duration ms 0 360 xlabel Time ms ylabel Azimuth title Right ear show Example dcgc hears Implementation example of the compressive gammachirp auditory filter as described in Irino T and Patterson R A compressive gammachirp auditory filter for both physiological and psychophysical data JASA 2001 A class called DCGC implementing this model is available in the library 120 Chapter 3 Getting started Brian Documentation Release 1 4 1 Technical implementation details and notation can be found in Irino T and Patterson R A Dynamic Compressive Gammachirp Auditory Filterbank IEEE Trans Audio Speech Lang Processing from brian import from brian hears import x simulation duration 50 ms samplerate 50xkHz level 50 dB level of the input sound in rms dB SPL sound whitenoise simulation duration samplerate ramp sound sound atlevel level nbr cf 50 number of centre frequencies center frequencies with a spacing following an ERB scale cf erbspace 100 Hz 1000 Hz nbr cf cl 2 96 glide slope of the first filterbank bl 1 81 factor determining the time constant of the first filterbank c2 2 2 glide slope of the second filterbank b2 2 17
281. d or remove synapses Conversion between construction and connection stages is done by the compress method of Connection which is called automatically when it is used for the first time The structures are dense A dense matrix Allows runtime modification of all values If connectivity is close to being dense this is probably the most efficient but in most cases it is less efficient In addition a dense connection matrix will often do the wrong thing if using STDP Because a synapse will be considered to exist but with weight 0 STDP will be able to create new synapses where there were previously none Memory requirements are 8NM bytes where N M are the dimensions A double float value uses 8 bytes sparse A sparse matrix See SparseConnectionMatrix for details on implementation This class fea tures very fast row access and slower column access if the column access True keyword is specified making it suitable for learning algorithms such as STDP which require this Memory requirements are 12 bytes per nonzero entry for row access only or 20 bytes per nonzero entry if column access is specified Synapses cannot be created or deleted at runtime with this class although weights can be set to zero dynamic A sparse matrix which allows runtime insertion and removal of synapses See DynamicConnectionMatrix for implementation details This class features row and column access The row access is slower than for sparse so this class should o
282. d the threshold G V Vr Vt Vr x rand len G Now we run run 500 ms And finally we plot the results Just for fun we do a rather more complicated plot than we ve been doing so far with three subplots The upper one is the raster plot of the whole network and the lower two are the values of V on the left and ge and gi on the right for the neuron we recorded from See the PyLab documentation for an explanation of the plotting functions but note that the raster_plot keyword newfigure False instructs the Brian function raster plot not to create a new figure so that it can be placed as a subplot of a larger figure subplot 211 raster plot M title The CUBA network newfigure False subplot 223 lot MV times ms MV 0 mV label Time ms label V mvV ubplot 224 lot Mge times ms Mge 0 mV lot Mgi times ms Mgi 0 mV label Time ms ylabel ge and gi mV legend ge gi upper right show WO U u wU 22 Chapter 3 Getting started Brian Documentation Release 1 4 1 The CUBA network Neron numer r LS d 100 700 b i a Er Time ms Tutorial 2a The concept of a Connection The network In this first part we ll build a network consisting of three neurons The first two neurons will be under direct control and have no equations defining them they ll just produce spikes which will feed into the
283. d variable An example is nonlinear synapses e g NMDA neurons NeuronGroup 1 model dv dt gtot v 10 ms 1 gtot l1 S Synapses input neurons model dg dt a xgtb x 1 g 1 dx dt c x 1 w 1 synaptic weight vee pre xt w neurons gtot S g Here each synapse has a conductance g with nonlinear dynamics The neuron s total conductance is gtot The link between the two is specified by the last statement What happens during the simulation is that at each time step presynaptic conductances are summed for each neuron and the result is copied to the variable gt ot Another example is gap junctions neurons NeuronGroup N model dv dt v0 vtIgap tau 1 igap 3 1 S Synapses neurons model w 1 gap junction conductance Igap w v pre v post 1 neurons Igap S Igap Here Igap is the total gap junction current received by the postsynaptic neuron 4 6 2 Creating synapses Creating a Synapses instance does not create synapses it only specifies their dynamics The following command creates a synapse between neuron i in the source group and j in the target group S i j True It is possible to create several synapses for a given pair of neurons S i j 3 This is useful for example if one wants to have multiple synapses with different delays Multiple synapses can be created in a single statement S True S 1 True S Pe Pi True 202 Chapter 4 User manual B
284. d with Brian Half wave rectification and compression x 1 3 ihe FunctionFilterbank fb lambda x 3 clip x 0 Inf 1 0 3 0 Leaky integrate and fire model with noise and refractoriness eqs CET dv dt I v 1 ms 0 2 xix 2 l ms 5 1 Tor I ETI anf FilterbankGroup ihc I eqs reset 0 threshold 1 refractory 5 ms This model would give output something like this 5 7 Brian hears 237 Brian Documentation Release 1 4 1 Neuron number Time ms The human cochlea applies the equivalent of 3000 auditory filters which causes a technical problem for modellers which this package is designed to address At a typical sample rate the output of 3000 filters would saturate the computer s RAM in a few seconds To deal with this we use online computation that is we only ever keep in memory the output of the filters for a relatively short duration say the most recent 20ms do our modelling with these values and then discard them Although this requires that some models be rewritten for online rather than offline computation it allows us to easily handle models with very large numbers of channels 3000 or 6000 for human monaural or binaural processing is straightforward and even much larger banks of filters can be used for example around 30 000 in Goodman DFM Brette R 2010 Spike timing based computation in sound localization PLoS Comput Biol 6 11 e1000993 doi 10 1371 journal pcbi
285. de the interval bound_min bound_max during the optimization The complete list of arguments can be found in the reference section of the modelfitting function The best parameters and the corresponding best fitness values found by the optimization procedure are returned in the OptimizationResult object result 5 6 3 Important note for Windows users The model fitting library uses the Python multiprocessing package to distribute fitting across processors in a single computer or across multiple computers However there is a limitation of the Windows version of multiprocessing which you can read about here The end result is that a script like this from brian library modelfitting import results modelfitting will crash going into an endless loop and creating hundreds of Python processes that have to be shut down by hand Instead you have to do this 234 Chapter 5 The library Brian Documentation Release 1 4 1 from brian library modelfitting import af name__ __ main__ results modelfitting 5 6 4 Clusters The model fitting package can be used with a cluster of computers connected over IP Every computer must have Brian and Playdoh installed and they must run the Playdoh server see the Playdoh documentation Then you can launch the modelfitting function with the machines keyword which is the list of the IP addresses of the machines to use in parallel for the fitting procedure You must also spec
286. ds to measure spike thresholds but they do not always give very good results perhaps the trace should be preliminary filtered onsets2 spike onsets dv2 v vc None onsets3 spike onsets dv3 v vc None The first one finds the maximum of the second derivative d2v dt2 the second one finds the maximum of d3v dt3 These are global maxima in each interspike interval it could be that looking for the last local maximum gives better results The following function returns the depolarization slope preceding each spike as an array slopes slope threshold v onsets None T None In this function spike onset indexes are passed through the onset keyword The depolarization slope is calculated by linear regression over the T time bins preceding each spike The result is in units of the time bin In a similar way the following function returns the average membrane potential preceding each spike as an array vm threshold v onsets None T None Spike shape The following function returns the average spike duration defined as the time from onset to reset next voltage mini mum duration spike duration v The onsets can be passed to save computation time with the onsets keyword With the option ull True the function returns the mean time from onset to peak the mean time from onset down to same value note that this may not be meaningful for some neurons mean time from onset to next minimum and standard deviations for these 3
287. e The St ateMonitor class of monitors record state variables each time step to a list Construction of Network When the user calls the function run a MagicNetwork object is created and the Network run method is called MagicNetwork gathers using the magic module a list of all appropriate objects and runs them to gether Alternatively the user can specify their own list of objects using a Network object Each time an object is added to a Network either via the initialiser or the Network add method it checks to see if it has an attribute contained objects and if so it adds all the objects in that to the network too This allows for example the STDP object to contained NeuronGroup and Connection objects which the user doesn t see but are used to implement the STDP functionality The Network run method calls the Connection compress method on every Connect ion object to convert construction matrices to connection matrices It also builds an update schedule see below The magic module The magic module is used for tracking instances of objects A class that derives from the magic InstanceTracker class can be tracked in this way including NeuronGroup Connection NetworkOperation and Clock The find instances function can be used to search for instances Note that find instances will only return instances which were instantiated in the same execution frame as the find instances calling frame or if the Level keyword is us
288. e read write vectorisable Called by resolve can be overridden to perform more complicated saving code By default returns an empty Block supported Returns True if the language specified at initialisation is supported By default checks if the language name is in the class attribute supported languages list however can be overridden supported languages update namespace read write vectorisable namespace Called by resolve can be overridden to modify the namespace e g adding data write The string that should be used when this symbol is written by default just the symbol name class brian experimental codegen2 RuntimeSymbol name language This Symbol is guaranteed by the context to be inserted into the namespace at runtime and can be used without modification to the name for example t or dt supported Returns True class brian experimental codegen2 ArraySymbol arr name language index None ar ray_name None This symbol is used to specify a value taken from an array Schematically name arr index arr numpy array The numpy array which the values will be taken from name language The name of the symbol and language index The index name by default _index_ name array name The name of the array by default _arr_ name Introduces a read dependency on index and array_name dependencies Read dependency on index load args kwds Method generated by 1anguage i
289. e based IAF eqs Equations dv dt El v tau m gex Ee v gix Ei v c_m volt dge dt gex 1 tau_exc uS dgi dt gis l tau inh ws mS n cells 12500 Total number of cells n exc int 0 8 n cells 4 1 ratio for exc inh size 1 Size of the network 3 2 Examples 99 Brian Documentation Release 1 4 1 simtime 1000 ms Simulation time sim_step x ms Display snapshots every sim_step ms epsilon 0 02 Probability density s_lat 0 2 Spread of the lateral connections g_exc 4 nS Excitatory conductance g_inh 64 x nS Inhibitory conductance g_ext 200 nS External drive velocity 0 3 mm ms velocity xt_rat 100 x Hz Rate of the external source max distance size x mm numpy sqrt 2 Since this is a torus max delay max distance velocity Needed for the connectors Generate the images with the letters B R I A N To do that we create a png image and read it as a matrix pylab figure pylab text 0 125 0 4 B R IA TN size 80 pylab setp gca xticks yticks pylab savefig BRIAN png brian letters imread BRIAN png os remove BRIAN png brian letters numpy flipud mean brian letters 2 T pylab close We create the cells and generate random positons in 0 size x 0 size all cells NeuronGroup n cells model eqs threshold Vt reset Vr refractory tau ref all cells posit
290. e differential equations The first connection has the target state Va and the second has the target state Vb C1 Connection Gl G2 Va C2 Connection Gl G2 Vb So far this only declares our intention to connect neurons in group G1 to neurons in group G2 because the connection matrix is initially all zeros Now with connection C1 we connect neuron 0 in group G1 to neuron 0 in group G2 with weight 3 mV This means that when neuron 0 in group G1 fires the state variable Va of the neuron in group G2 will be increased by 6 mV Then we use connection C2 to connection neuron in group G1 to neuron 0 in group G2 this time with weight 3 mV 24 Chapter 3 Getting started Brian Documentation Release 1 4 1 C1 0 0 6 mV C2 1 0 3 mV The net effect of this is that when neuron 0 of G1 fires Va for the neuron in G2 will increase 6 mV and when neuron 1 of G1 fires Vb for the neuron in G2 will increase 3 mV Now we set up monitors to record the activity of the network run it and plot it Ma StateMonitor G2 Va record True Mb StateMonitor G2 Vb record True run 10 ms plot Ma times Ma 0 plot Mb times Mb 0 show 0 005 0 007 0 001 DOR OO 10007 0004 0 006 70008 0010 The two plots show the state variables Va and Vb for the single neuron in group G2 Va is shown in blue and Vb in green According to the differential equations Va decays much faster than Vb time constant
291. e ee Me d SORS UE ee dew Pw EUER e HAE CloOCKS 24 scs nb be eee ae ee S BOR ne e ee o RO aoe a ee NOR Pee oe ek Neuron models and groups i 45 224 424554 2484 6449446542 6454 24555 Integration i a 4k a eo Boh oe ee eS o mdp de Sh hhh ndp ee ew de Se Standard Groups 4 ow Ga x bad eee meon Yo RU Rex ORO pod Row Re Re es Y nre MP C Plasticity 6 i sei see Pade ede hoe ee ee ade Ghee T SyDapSeS c osse Ble bake Bedok e Gs bot Gee h Si REX m ach Gabe Sk egw el eS ts ely a NetWork TT hil MEN E PLC x beri we Ae Rees he See ae we Pe TIT lap PC TT Variableupdatilig 4 o Sx udo epe pep Eu Eee db MEE SS Pe SEB EE S d xS Analysis s o5oxesok 6 X SOEUR see we mo EAR oe E ROBORIS DNUEME RO Bondop in E BOR Vers Inp t oUtpub 020b oe bep deret x x dite a qus BS d dp de dits i e qt a arcis Tun Remis gU eun MP T TT Remote control cs cea torrer eee eee E ER doe PRE RO SCR GROSS Rok doe E beh PropresSTepOTBg s eh Sotho eo ed R ECKE AR ee SU hob RE Rh Rude cR eR eed Rede E Modelfit ngtoolbox i vas be Bee BAR ERA REED AD Re ro m Xe A SOROR OR E Ro d Electrode compensation soras ac Ue RR RS RES AG Eee PERG Ba eS RR RR e Brian heads 20478 Soke n eG Ge Sud Ret Rey eR a ee o a a fem SORTE Rede Magie qj Brian o9 deos ee o ure REESE BANS EASES om boe deo eco TOSS Lose Re E OE EO eee e Ae UR NUR RC WIE RO ee E ae RACES RT ELS IE ee Typical Tasks 9 1 Projects with multiple files or functions 0 0 200000
292. e excitatory ones and even the double excitatory spike after the inhibitory one can t cancel it out In the next part of this tutorial we set up our first serious network with 4000 neurons excitatory and inhibitory Exercises 1 Try changing the parameters and spike times to get a feel for how it works 2 Try an equivalent implementation with the equation taum dV dt V ge gi 3 Verify that the differential equation has been solved correctly Solutions Solution for 2 20 Chapter 3 Getting started Brian Documentation Release 1 4 1 Simply use the line C2 1 0 3 mV to get the same effect Solution for 3 First set up the situation we described at the top for which we already know the solution of the differential equations by changing the spike times as follows spiketimes 0 0 ms Now we compute what the values ought to be as follows t Mv times Vpredicted exp t taum exp t taue tauex 3 mV taum taue Now we can compute the difference between the predicted and actual values Vdiff abs Vpredicted Mv 0 This should be zero print max Vdiff Sure enough it s as close as you can expect on a computer When I run this it gives me the value 1 3 aV which is 1 3 104 18 volts i e effectively zero given the finite precision of the calculations involved Tutorial 2c The CUBA network In this part of the tutorial we set up our first serious network that actually does somethin
293. e final code Symbols will be things like a NeuronGroup state variable or a synaptic weight value The output of this process is a new more complicated structured representation including things like loops if necessary Next we convert this structured representation into a code string Finally this code string is JIT compiled into an executable object Using numerical integration generation You can use Brian s equations format to generate C C code for a numerical integration step for example rra eqs dv dt getgi v 49 mV 20 ms volt dge dt ge 5 ms volt dgi dt gi 10 ms volt rrt code vars params make c integrator egs method euler dt 0 1 ms print code has output double temp v 50 0 ge 50 0 gi 50 0 v 2 45 double temp ge 200 0 ge double temp gi 100 0xgi v temp v 0 0001 ge temp gex0 0001 gi temp gix0 0001 See the documentation for the function make c integrator Using the code generation package The basic way to use the code generation module is as follows 1 Create a Block of Statement objects which you want to execute You can use statements from codestring to do this 2 Create a dictionary of Symbo1 objects corresponding to the symbols in the block above 358 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 3 Call CodeItem generate with the specified language and symbols to give you a Code object
294. e gpu func attribute and the kernel can then be called via run The initialisation method extracts variable gpu vector index from the namespace and stores it as at tribute index and_gpu_vector_sliceas the pair start end prepare Generates kernel source code and adds symbols to memory manager We extract the number of GPU indices from the namespace num gpu indices We loop through the namespace and for each value determine it to be either an array or a single value If it is an array then we place it in the GPUSymbolMemoryManager otherwise we add it to the list of arguments provided to the function call This allows scalar variables like t to be transmitted to the kernel function in its arguments We then generate a kernel of the following Python template form __global__ void name funcargs t int vector index blockIdx x blockDim x threadIdx x if vector_index lt start vector_index gt end return code_str We also compute the block size and grid size using the user provided maximum block size prepare gpu func Calls the pycuda GPU function prepare method for low overhead function calls 372 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 run Calls the function on the GPU extracting the scalar variables in the argument list from the namespace class brian experimental codegen2 GPUManager force_sync True usefloat False This object con
295. e immediately Solution Solving the differential equation gives V El Vr El exp t tau Setting V Vt at time t gives t tau log Vr El Vt E If the simulator runs for time T and fires a spike immediately at the beginning of the run it will then generate n spikes where n T t 1 If you have m neurons all doing the same thing you get nm spikes This calculation with the parameters above gives t 48 0 ms n 21 nm 840 As predicted Tutorial 1g Recording membrane potentials In the previous part of this tutorial we plotted a raster plot of the firing times of the network In this tutorial we introduce a way to record the value of the membrane potential for a neuron during the simulation and plot it We continue as before from brian import x tau 20 msecond membrane time constant Vt 50 mvolt spike threshold Vr 60 x mvolt reset value El 49 x mvolt resting potential same as the reset psp 0 5 mvolt postsynaptic potential size G NeuronGroup N 40 model dV dt V El tau volt threshold Vt reset Vr C Connection G G C connect_random sparseness 0 1 weight psp This time we won t record the spikes Recording states Now we introduce a second type of monitor the StateMonitor The first argument is the group to monitor and the second is the state variable to monitor The keyword record can be an integer list or the value True If it is an
296. e inputs to a network 4 8 1 Poisson inputs Poisson spike trains can be generated as follows group PoissonGroup 100 rates 10 Hz Here 100 neurons are defined which emit spikes independently according to Poisson processes with rates 10 Hz To have different rates across the group initialise with an array of rates group PoissonGroup 100 rates linspace 0 Hz 10 Hz 100 Inhomogeneous Poisson processes can be defined by passing a function of time that returns the rates group PoissonGroup 100 rates lambda t 1 cos t 10 Hz or r0 linspace 0 Hz 10 Hz 100 group PoissonGroup 100 rates lambda t 1 cos t r0 There is another class for Poisson inputs PoissonInput which updates the state variable of a NeuronGroup dynamically without storing in memory all the Poisson events It can be used like this input PoissonInput group N N rate rate weight w state I In this case the variable I represents the sum of N independent Poisson spike inputs with rate rate where each individual synaptic event increases the variable I by w Several PoissonInput objects can be created for a given NeuronGroup in which case all the independent inputs are linearly superimposed Other features of the PoissonInput class include the following see the reference e record the individual Poisson events record True keyword having identical Poisson events for all neurons instead of having independent copies for every neuron fre
297. e is calculated as the average first minimum after a spike with the following function reset reset potential v peaks None full False The time indexes of spike peaks can be given this may save some computation time With the ull True option the standard deviation is also returned Spike threshold There are 3 ways to measure the spike threshold The first derivative method uses a threshold criterion on the first derivative dv dt to identify spike onsets onsets spike onsets v criterion None vc None 5 5 Electrophysiology trace analysis 231 Brian Documentation Release 1 4 1 where criterion is the derivative criterion and vc is the voltage criterion to detect spikes Note that the criterion is in units of voltage per time step First the algorithm detects spike peaks Then for each spike we look for the last local maximum of dv dt before the spike which should be the inflexion point of the spike Then we identify the last time before the inflexion point when dv dt is smaller than the criterion The function returns the time indexes of the onsets not their values which are v onsets The derivative criterion may be automatically determined using the following function criterion find onset criterion v guess 0 1 vc None where guess is an optional initial guess for the optimization method The algorithm is simple find the criterion that minimizes the variability of onsets There are two other metho
298. e ordered in time 208 Chapter 4 User manual Brian Documentation Release 1 4 1 Gaussian spike packets There is a subclass of SpikeGeneratorGroup for generating spikes with a Gaussian distribution input PulsePacket t 10 ms n 10 Sigma 3 ms Here 10 spikes are produced with spike times distributed according a Gaussian distribution with mean 10 ms and standard deviation 3 ms 4 8 4 Direct input Inputs may also be defined by accessing directly the state variables of a neuron group The standard way to do this is to insert parameters in the equations rrt eqs dv dt I v tau volt I volt group NeuronGroup 100 model eqs reset 0 mV threshold 15 mvV group I linspace O mV 20 mV 100 Here the value of the parameter I for each neuron is provided at initialisation time evenly distributed between 0 mV and 20 mV Time varying inputs It is possible to change the value of I every timestep by using a user defined operation see next section Alternatively you can use a TimedArray to specify the values the variable will have at each time interval for example EEH eqs dv dt I v tau volt I volte px group NeuronGroup 1 model eqs reset 0 mV threshold 15 mV group I TimedArray linspace 0 mV 20 mV 100 dt 10 ms Here I will have value 0 mV for t between 0 and 10 ms 0 2 mV between 10 ms and 20 ms and so on A more intuitive syntax is I TimedArray
299. e spike in a given interval dt additional spikes will be discarded A warning will be issued if this is detected 272 Chapter 8 Reference Brian Documentation Release 1 4 1 Also if you want to use a SpikeGeneratorGroup with many spikes and or neurons please use an initialization with arrays Also note that if you pass a generator then reinitialising the group will not have the expected effect because a generator object cannot be reinitialised Instead you should pass a callable object which returns a generator In the example above that would be done by calling P SpikeGeneratorGroup 10 nextspike Whenever P is reinitialised it will call next spike to create the required spike container class brian MultipleSpikeGeneratorGroup spiketimes clock None period None Emits spikes at given times Warning This function has been deprecated after Brian 1 3 1 and will be removed in a future release Use SpikeGeneratorGroup instead To convert spiketimes forMultipleSpikeGeneratorGroup into a form suitable for SoikeGeneratorGroup do N len spiketimes spiketimes i t for i in xrange N for t in spiketimes i Initialised as MultipleSpikeGeneratorGroup spiketimes clock period with arguments spiketimes a list of spike time containers one for each neuron in the group although note that elements of spiketimes can also be callable objects which return spike time containers if you
300. e str namespace pre code None post codezNone language None Code object for GPU For the user works as the same as any other Code object Behind the scenes source code is passed to the GPUManager gpu man from the GPULanguage object via GPUManager add kernel Compila tion is handled by GPUManager prepare and running code by GPUManager run 374 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 compile Simply calls GPUManager prepare run Simply runs the kernel via GPUManager run class brian experimental codegen2 GPULanguage scalar double gpu_man None force sync True Language object for GPU Has an attribute gpu man the GPUManager object responsible for allocating copying memory etc One is created if you do not specify one CodeObjectClass alias of GPUCode integration class brian experimental codegen2 EquationsContainer eqs Utility class for defining numerical integration scheme Initialise with a set of equations eqs You can now iterate over this object in two ways firstly over all the differential equations for var expr in eqscontainer yield f expr Or over just the differential equations with nonzero expressions i e not including dx dt 0 for parameters for var expr in eqscontainer nonzero yield f expr Here var is the name of the symbol and expr is a string the right hand side of the differential equation dvar dt expr Also has attr
301. e x must be Hertz 4 2 Models and neuron groups 195 Brian Documentation Release 1 4 1 4 3 Connections 4 3 1 Building connections First one must define which neuron groups are connected and which state variable receives the spikes The following instruction myconnection Connection groupl group2 ge defines a connection from group group1 to group2 acting on variable ge When neurons from group group1 spike the variable ge of the target neurons in group group2 are incremented When the connection object is ini tialised the list of connections is empty It can be created in several ways First explicitly myconnection 2 5 3 nS This instruction connects neuron 2 from group1 to neuron 5 from group2 with synaptic weight 3 nS Units should match the units of the variable defined at initialisation time ge The matrix of synaptic weights can be defined directly with the method Connection connect W rand len groupl len group2 nS myconnection connect groupl group2 W Here a matrix with random elements is used to define the synaptic weights from group1 to group2 It is possible to build the matrix by block by using subgroups e g W rand 20 30 nS myconnection connect group1 0 20 group2 10 40 W W There are several handy functions available to set the synaptic weights connect full connect random and connect one to one The first one is used to set uniform weights for all pairs of neurons in
302. ear filtering See Preferences and Compiled code for more details 8 21 Brian hears 333 Brian Documentation Release 1 4 1 8 21 11 Class diagram ReymmatricCompensation 8 22 Magic in Brian brian magic_return f Decorator to ensure that the returned object from a function is recognised by magic functions Usage example magic_return def f return PulsePacket 50 ms 100 10 ms Explanation Normally code like the following wouldn t work def f return PulsePacket 50 ms 100 10 ms pp f M SpikeMonitor pp run 100 ms raster_plot show The reason is that the magic function run only recognises objects created in the same execution frame that itis run from The magic return decorator corrects this it registers the return value of a function with the magic module The following code will work as expected Qmagic return def f return PulsePacket 50 ms 100 10 ms pp f M SpikeMonitor pp run 100 ms raster_plot show Technical details The magic return function uses magic_register with the default Level 1 on just the object returned by a function See details for magic register brian magic register args kwds Declare that a magically tra
303. ect method adds a coupling current between the two named compartments with the given resistance Ra 5 1 3 Integrate and Fire models A few standard Integrate and Fire models are implemented in the IF library module from brian library IF import x All these functions return Equat ions objects more precisely MembraneEquation objects e Leaky integrate and fire model dvm dt El vm tau volt eqs leaky_IF tau 10 ms El 70 mV Perfect integrator dvm dt Im tau volt eqs perfect IF tau 10 ms e Quadratic integrate and fire model C dvm dt a vm EL vm VT volt eqs quadratic IF C 200 pF a 10 nS mV EL 70 mV VT 50 mV e Exponential integrate and fire model C dvm dt gL EL vm gL DeltaTx exp vm VT DeltaT volt eqs exp IF C 200x pF gL 10 nS EL 70xmV VT 55 mV DeltaT 3 mV In general it is possible to define a neuron group with different parameter values for each neuron by passing strings at initialisation For example the following code defines leaky integrate and fire models with heterogeneous resting potential values eqs leaky_IF tau 10 ms El V0 Equations VO volt group NeuronGroup 100 model eqs reset 0 mV threshold 15 mvV 5 1 4 Two dimensional IF models Integrate and fire models with two variables can display a very rich set of electrophysiological behaviours In Brian two such models have been implemented Izhikevich
304. ection with heterogeneous delays specify this to set the maximum allowed delay smaller values use less memory The default is 5ms modulation The state variable name from the source group that scales the synaptic weights for short term synaptic plasticity structure Data structure sparse default dense or dynamic See below for more information on structures weight If specified the connection matrix will be initialised with values specified by weight which can be any of the values allowed in the methods connect below sparseness If weight is specified and sparseness is not a full connection is assumed otherwise ran dom connectivity with this level of sparseness is assumed Methods connect random P Q p weight 1 fixed False seed None Connects each neuron in P to each neuron in Q with independent probability p and weight weight this is the amount that gets added to the target state variable If ixed is True then the number of presynaptic neurons per neuron is constant If seed is given it is used as the seed to the random number generators for exactly repeatable results connect full P Q weight 1 Connect every neuron in P to every neuron in Q with the given weight connect one to one P Q If P and Q have the same number of neurons then neuron i in P will be connected to neuron i in Q with weight 1 connect P Q W Youcan specify a matrix of weights directly can be in any format recognised by NumPy Note th
305. ectorized simultaneously executed for all synapses receiving presynaptic spikes during the current timestep Therefore the code should be understood as acting on arrays rather than single values Any sort of code can be executed For example the following code defines stochastic synapses with a synaptic weight w and transmission probability p S Synapses input neurons model w 1 p H JN pre 2 v t w rand p The code means that w is added to v with probability p note that internally rand is transformed to a instruction that outputs an array of random numbers The code may also include multiple lines As mentioned above it is possible to write event driven update code for the synaptic variables For this two special variables are provided t is the current time when the code is executed and 1astupdate is the last time when the synapse was updated either through pre or post code An example is short term plasticity in fact this could be done automatically with the use of the event driven keyword mentioned above 4 6 Synapses 201 Brian Documentation Release 1 4 1 S Synapses input neuron model x 1 ud Wes ee pre u U u U exp t lastupdate tauf x 1 x 1 exp t lastupdate taud it 2w ux Xx x 1 u ut Ux 1 u t Lumped variables In many cases the postsynaptic neuron has a variable that represents a sum of variables over all its synapses This is called a lumpe
306. ed but there is a dynamic sparse matrix structure It is less computationally efficient but allows runtime adding and deleting of synaptic connections Use the structure dynamic keyword For more details see the reference documentation for Connect ion 4 3 4 Modulation The synaptic weights can be modulated by a state variable of the presynaptic neurons with the keyword modulation myconnection Connection groupl group2 ge modulation u When a spike is produced by a presynaptic neuron group1 the variable ge of each postsynaptic neuron group2 is incremented by the synaptic weight multiplied by the value of the variable u of the presynaptic neuron This is useful to implement short term plasticity 4 3 5 Direct connection In some cases it is useful to connect a group directly to another one in a one to one fashion The most efficient way to implement it is with the class Tdent it yConnection myconnection IdentityConnection groupl group2 ge weight 1 nS With this structure the synaptic weights are homogeneous it is not possible to define them independently When neuron i from group spikes the variable ge of neuron i from group2 is increased by 1 nS A typical application is when defining inputs to a network 4 3 6 Simple connections If your connection just connects one group to another in a simple way you can initialise the weights and delays at the time you initialise the Connection object by using
307. ed one of the frames higher up in the call stack The idea is that you may have modular code with objects defined in different places but that you don t want to use all objects that exist at all in the network This system causes a bit of trouble but seems unavoidable See the user manual section Projects with multiple files or functions for details on getting around this 11 3 3 Details of network running Update schedules An update schedule gives the sequence of operations to be carried out each time step of the simulation Typically this is state update and threshold propagation reset although an option is available for switching propagation and reset around Network operations can be weaved in anywhere amongst these basic steps See the reference documentation for the Network object for more details Simulation proceeds by choosing the clock with the lowest current time selecting all objects which have that clock as their clock and performing the update schedule on those objects before applying the Clock tick method to increment the clock time by dt 11 3 Main code structure 353 Brian Documentation Release 1 4 1 Network operations A NetworkOperation object is called as if it were a function i e the___cal1___ method is called with no argu ments The network_operation decorator exists to convert a function into a suitable NetworkOperation object This technique is used for the internal functioning of many of Brian
308. ed to connect these neurons Firstly we declare that there is a connection from neurons in G to neurons in G For the moment this is just something that is necessary to do the reason for doing it this way will become clear in the next tutorial C Connection G G Now the interesting part we make these neurons be randomly connected with probability 0 1 and weight psp Each neuron i in G will be connected to each neuron j in G with probability 0 1 The weight of the connection is the amount that is added to the membrane potential of the target neuron when the source neuron fires a spike C connect random sparseness 0 1 weight psp These two previous lines could be done in one line C Connection G G sparseness 0 1 weight psp Now we continue as before M SpikeMonitor G G V Vr rand 40 x Vt Vr 3 1 Tutorials 15 Brian Documentation Release 1 4 1 run l second print M nspikes You can see that the number of spikes has jumped from around 800 850 to around 1000 1200 In the next part of the tutorial we ll look at a way to plot the output of the network Exercise Try varying the parameter psp and see what happens How large can you make the number of spikes output by the network Why Solution The logically maximum number of firings is 400 000 40 1000 0 1 the number of neurons in the network the time it runs for the integration step size you cannot have more than one spike per s
309. efractoriness resetfunc period 5 ms state 0 with arguments resetfun The custom reset function reset fun P spikes forP aNeuronGroup and spikes a list of neurons that fired spikes period The length of time to hold at the reset value state The name or number of the state variable to reset and hold it is your responsibility to check that this corresponds to the custom reset function The assumption is that reset fun P spikes will reset the state variable st ate on the group P for the spikes with indices spikes The values assigned by the custom reset function are stored by this object and they are clamped at these values for period This object does not introduce refractoriness for more than the one specified variable st ate or for spike indices other than those in the variable spikes passed to the custom reset function class brian CustomRefractoriness args kwds Holds the state variable at the custom reset value for a fixed time after a spike Initialised as CustomRefractoriness resetfunc period 5x ms refracfunc resetfunc with arguments resetfunc The custom reset function reset func P spikes forPaNeuronGroup and spikes a list of neurons that fired spikes refracfunc The custom refractoriness function refracfunc P indices for P a NeuronGroup and indices a list of neurons that are in their refractory periods In some cases you can choose not to specify this and it will use the reset function peri
310. el IF with adaptive threshold eqs dv dt getgitEl v taum volt dge dt ge taue volt dgi dt gi taui volt dvt dt Vt vt tauvt volt adaptation x tol EE rrt Tuning curve tuning lambda theta clip cos theta 0 Inf Fmax Layer 4 layer4 PoissonGroup N4 Nbarrels barrels4 dict i j layer4 subgroup N4 for i in xrange barrelarraysize for j in xrange barre barrels4active dict ij False for ij in barrels4 barrelindices dict ij slice b origin b _origint len b for ij b in barrels4 iteritems layer4 selectivity zeros len layer4 for i j inds in barrelindices iteritems 3 2 Examples 145 Brian Documentation Release 1 4 1 layer4 selectivity inds linspace 0 2 pi N4 Layer 2 3 layer23 NeuronGroup Nbarrels N23exct N23inh model eqs threshold v gt vt reset v EL vtt vt_inc refr layer23 v El1 layer23 vt Vt Layer 2 3 excitatory layer23exc layer23 subgroup Nbarrels N23exc x y meshgrid arange M23exc 1 M23exc arange M23exc 1 M23exc x y x flatten y flatten barrels23 dict i j layer23exc subgroup N23exc for i in xrange barrelarraysize for j in xrai for i in range barrelarraysize for j in range barrelarraysize barrels23 i j x x i barrels23 i j y y j Layer 2 3 inhibitory layer23inh layer23 subgroup Nbarrels N23inh x y meshgrid arange M23inh 1 M23inh arange M23inh 1
311. en randomly assign the neuron numbers to them times gauss t sigma for i in range n times sort neuron range n shuffle neuron return zip neuron times returns a list of pairs i t Gl SpikeGeneratorGroup 1000 pulse packet 50 ms 1000 5 ms M1 SpikeMonitor G1 PRM1 PopulationRateMonitor Gl bin 1 ms ll G2 M2 ll PulsePacket 50 ms 1000 5 ms SpikeMonitor G2 3 2 Examples 183 Brian Documentation Release 1 4 1 PRM2 PopulationRateMonitor G2 bin 1 ms run 100 ms subplot 221 raster plot M1 subplot 223 plot PRM1 rate subplot 222 raster plot M2 subplot 224 plot PRM2 rate show Example correlated inputs2 misc An example with correlated spike trains From Brette R 2007 Generation of correlated spike trains from brian import x N 100 Qm Su nu linspace 1 Hz 10 Hz N P c dot nu reshape N 1 nu reshape 1 N mean nu 2 tauc 5 ms spikes mixture process nu P tauc 1 second input SpikeGeneratorGroup N spikes S SpikeMonitor input run 1000 ms raster plot S show Example linked var misc Example showing 1inked var connecting two different NeuronGroup variables Here we show something like a simplified haircell and auditory nerve fibre model where the hair cells and ANFs are implemented as two separate NeuronGroup objects The hair cells filter their inputs via a differential equa
312. ens envelope A ramping function if not specified uses sin pixt 2 2 The function should be a function of one variable t ranging from 0 to 1 and should increase from f 0 0 to f 0 1 The reverse is applied for the offset ramp inplace Whether to apply ramping to current sound or return a new array ramped args kwds Returns a ramped version of the sound see Sound ramp Plotting spectrogram low None high None log_power True other None kwds Plots a spectrogram of the sound Arguments low None high None If these are left unspecified it shows the full spectrogram otherwise it shows only between low and high in Hz log_power True If True the colour represents the log of the power xkwds Are passed to Pylab s specgram command 314 Chapter 8 Reference Brian Documentation Release 1 4 1 Returns the values returned by pylab s specgram namely pxx freqs bins im where pxx is a 2D array of powers freqs is the corresponding frequencies bins are the time bins and im is the image axis spectrum args kwds Returns the spectrum of the sound and optionally plots it Arguments low high If these are left unspecified it shows the full spectrum otherwise it shows only between low and high in Hz log power True If True it returns the log of the power display False Whether to plot the output Returns Z freqs phase where Z is a 1D array of powers freqs is the corresponding
313. entation Release 1 4 1 HRTF Set has a set of coordinates which can be accessed via the coordinates attribute e g print hrtfset coordinates azim print hrtfset coordinates elev You can also generated filterbanks associated either to an HRTF or an entire HRTFSet Here is an example of doing this with the IRCAM database and applying this filterbank to some white noise and plotting the response as an image Load database hrtfdb IRCAM_LISTEN r D HRTF IRCAM hrtfset hrtfdb load_subject 1002 Select only the horizontal plane hrtfset hrtfset subset lambda elev elev 0 Set up a filterbank sound whitenoise 10 ms fb hrtfset filterbank sound Extract the filtered response and plot img fb process T img_left img img shape 0 2 img_right img img shape 0 2 subplot 121 imshow img_left origin lower left aspect auto extent 0 sound duration ms 0 360 xlabel Time ms ylabel Azimuth title Left ear subplot 122 imshow img right origin lower left aspect auto extent 0 sound duration ms 0 360 xlabel Time ms ylabel Azimuth title Right ear show This generates the following output Left ear Right ear 350 0 2 4 6 8 10 0 2 4 6 8 10 Time ms Time ms For more details see the reference documentation for HRTF HRTFSet HRTFDatabase IRCAM LISTEN and HeadlessDa
314. enter frequencies linear 10 x 0 0674 1 016 1log10 center_frequencies bandwidth linear 10 x 0 037 0 785x1log10 center_frequencies order_linear 3 gammatone ApproximateGammatone sound center frequencies linear bandwidth linear order order linear linear gain g 10 4 2 0 48 10g10 center frequencies func gain lambda x g x gain FunctionFilterbank gammatone func gain low pass filter cascade of 4 second order lowpass butterworth filters cutoff frequencies linear center frequencies linear order lowpass linear 2 lp 1 LowPass gain cutoff frequencies linear lowpass linear Cascade gain lp 1l 4 Nonlinear Pathway bandpass filter third order gammatone filters center frequencies nonlinear center frequencies bandwidth nonlinear 10 0 031 0 774 10g10 center frequencies order nonlinear 3 bandpass nonlinearl ApproximateGammatone sound center frequencies nonlinear bandwidth nonlinear order order nonlinear compression linear at low level compress at high level a 10 1 402 0 819 log10 center frequencies linear gain 116 Chapter 3 Getting started Brian Documentation Release 1 4 1 b 10 1 619 0 818 10g10 center frequencies v 2 compression exponent func compression lambda x sign x minimum a abs x b abs x v compression FunctionFilterbank bandpass_nonlinearl func_compression
315. er update_interval 4 the filter coefficients are updated every 4 samples parameters of the Ornstein Uhlenbeck process s_i 1200 Hz tau i 100 ms mu_i fc_init tau_i sigma i sqrt 2 s_i sqrt tau i deltaT defaultclock dt this function is used in a FunctionFilterbank It outputs a noise term that will be later used by the controler to update the center frequency noise lambda x mu_ixdeltaT sigma_ixrandn 1 sqrt deltaT noise generator FunctionFilterbank sound noise this class will take as input the output of the noise generator and as target the bandpass filter center frequency class CoeffController object def init self target self target target self deltaT 1 samplerate self BW 2 arcsinh 1 2 Q 1 44269 self fc fc init 108 Chapter 3 Getting started Brian Documentation Release 1 4 1 def call self input the control variables are taken as the last of the buffer noise term input 1 fupdate the center frequency by updateing the OU process self fc self fc self fc tau i self deltaT noise term w0 2 pixself fc samplerate update the coefficient of the biquadratic filterbank alpha sin w0 sinh log 2 2x self BWxw0 sin w0 self target filt b 0 0 sin w0 2 self target filt_b 1 0 0 self target filt b 2 0 sin w0 2 self target filt a 0 0 l alpha self target filt_a 1 0 2xcos w0 self target filt a 2
316. er and computer only one process can write to it without worrying about concurrency issues locking session locking computer session Returns a LockingSession object a limited proxy to the underlying Shelf which acquires and releases a lock before and after every operation making it safe for concurrent access session filenames A list of all the shelf filenames for all sessions make unique key Generates a unique key for inserting an element into a session without overwriting data uses uuid4 Attributes basepath The base path for data files computer name A hopefully unique identifier for the user and computer consists of the username and the computer network name computer session filename The filename of the computer specific session file This file should only be accessed by one process at a time there s no way to protect against concurrent write accesses causing it to be corrupted 8 15 2 Spikes management The following function describes how to load Address Event Representation files AER files See also the AERSpikeMonitor for saving spikes in that format and SpikeGeneratorGroup for reusing them in a sim ulation 8 15 Input output 301 Brian Documentation Release 1 4 1 brian load_aer filename check_sorted False reinit_time False Loads Address Event Representation AER data files for use in Brian Files contain spikes as a binary repre sentation of an address i e neuron identifier a
317. erential equations 218 equations 218 frozen equations in module brian experimental codegen2 371 FunctionFilterbank example usage 49 83 108 109 115 118 123 FunctionFilterbank class in brian hears 318 FunReset class in brian 267 FunThreshold class in brian 269 G GA class in brian library modelfitting 308 gain example usage 115 186 Gammatone Index 393 Brian Documentation Release 1 4 1 example usage 49 83 109 111 115 123 hodgkin huxley Gammatone class in brian hears 321 threshold 268 gaussian noise 264 HRTF 244 generate brian experimental codegen2 CodelItem database 244 method 369 IRCAM 244 generate brian PulsePacket method 271 HRTF class in brian hears 329 generate code brian experimental codegen2 GPUManageHRTFDatabase class in brian hears 330 method 373 HRTFSet class in brian hears 329 generate code brian experimental codegen2 GPUSymbolMemory Manager method 374 generation IdentityConnection code 358 example usage 40 72 155 180 get_default_clock in module brian 263 IdentityConnection class in brian 277 get_duration brian Clock method 262 IfBlock class in brian experimental codegen2 368 get global preference in module brian 254 IIRFilterbank get identifiers in module example usage 117 brian experimental codegen2 372 IIRFilterbank class in brian hears 324 get neuron group symbols in module indent_stri
318. ery update step Typically you should just use the network operation decorator but if you can t for whatever reason use this Note current implementation only works for functions not any callable object Initialisation NetworkOperation function clock If your function takes an argument the clock will be passed as that argument The magic functions run and reinit work by searching for objects which could be added to a network constructing a network with all these objects and working with that They are suitable for simple scripts only If you have problems where objects are unexpectedly not being added to the network the best thing to do would probably be to just use an explicit Net work object as above rather than trying to tweak your program to make the magic functions work However details are available in the brian magic py source code brian run duration threads 1 report None report period 10 0 second Run a network created from any suitable objects that can be found Arguments duration the length of time to run the network for report How to report progress the default None doesn t report the progress Some standard values for report text stdout Prints progress to the standard output stderr Prints progress to the standard error output stderr graphical tkinter Uses the Tkinter module to show a graphical progress bar this may interfere with any other GUI code you have Alternatively you can
319. es spike_monitor subplot 211 raster_plot M subplot 212 plot arange len trace dt ms array trace mV show 11 3 Main code structure 11 3 1 Overview Brian features can be broadly categorised into construction of the network and running the network Constructing the network The following objects need to be specified by the user explicitly or implicitly NeuronGroup Connection Monitors Network After that the network needs to be prepared Preparation of the network involves initialising objects data structures appropriately in particular compressing the Connection matrices Connection matrices are initially stored as in stances of a ConstructionMatrix class sparse dense etc and then later compressed into an instance of a ConnectionMatrix class Two levels are necessary because at construction time all matrices have to be editable 350 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 whereas at runtime for efficiency reasons some matrix types are read only or partially read only Data structures appropriate to the construction of a matrix particularly sparse matrices are not the most efficient for runtime access Constructing the NeuronGroup object is a rather complicated operation involving the construction of many subsi didary objects The most complicated aspect is the creation manipulation and analysis of an Equat ions object Running the network The network i
320. eshold Vcut reset vm Vr wt b freeze True neuron vm EL trace StateMonitor neuron vm record 0 Spikes SpikeMonitor neuron run 20 ms neuron I 1 x nA run 100 ms neuron I 0 x nA run 20 ms We draw nicer spikes vm trace 0 for _ t in spikes spikes i int t defaultclock dt vm i 20 mV plot trace times ms vm mV show 3 2 2 frompapers computing with neural synchrony coincidence detection and synchrony Example Fig5E precision reliability frompapers computing with neural synchrony coincidence detection and synchrony Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 5E very long simulation Caption Fig 5E Precision and reliability of spike timing as a function of SNR Simulations are run in parallel on all cores but one from brian import x import multiprocessing def autocor PSTH N None T 20 ms bin None rrr Autocorrelogram of PSTH to calculate a shuffled autocorrelogram N number of spike trains T temporal window bin PSTH bin The baseline is not subtracted Returns times SAC Kor if bin is None bin defaultclock dt n len PSTH p int T bin 58 Chapter 3 Getting started Brian Documentation Release 1 4 1 def def SAC zeros p if N is None SAC 0 mean PSTH PSTH else correction to exclude self coincidences PSTHnoself clip PSTH 1 binx
321. esults in vitro 18 Brette from brian import x The common noisy input N 25 tau input 5 ms input NeuronGroup 1 model dx dt x tau input 2 tau input xx 5x xi 1 178 Chapter 3 Getting started Brian Documentation Release 1 4 1 The noisy neurons receiving the same input tau 10 ms sigma 015 eqs neurons dx dt 0 9 5 I x tautsigma 2 tau 5 xi l d d p neurons NeuronGroup N model eqs neurons threshold 1 reset 0 refractory 5 ms rand N neurons I linked var input x input x is continuously fed into neurons I spikes SpikeMonitor neurons neurons Hox run 500 ms raster plot spikes show Example if misc A very simple example Brian script to show how to implement an integrate and fire model In this example we also drive the single integrate and fire neuron with regularly spaced spikes from the SoikeGeneratorGroup from brian import x tau 10 ms Vr 70 mV Vt 55 mV G NeuronGroup 1 model V volt threshold Vt reset Vr input SpikeGeneratorGroup 1 0 t ms for t in linspace 10 100 25 C Connection input G C 0 0 2 x mV M StateMonitor G V record True G V Vr run 100 ms plot M times ms M 0 mV show Example minimalexample misc Very short example program from brian import Wy eqs dv dt getgi v 49 mV 20 ms volt dge dt ge 5 ms vo
322. et t lt onset duration return stim else return 0 Hz PoissonGroup init self width x height stimfunc if name main import pylab subplot 121 stim bar 100 100 10 90 0 9 0 1 pylab imshow stim origin lower pylab gray G StimulusArrayGroup stim 50 Hz 100 ms 100 x ms M SpikeMonitor G run 300 ms subplot 122 176 Chapter 3 Getting started Brian Documentation Release 1 4 1 raster_plot M axis xmin 0 xmax 300 show Example leaky_if misc A very simple example Brian script to show how to implement a leaky integrate and fire model In this example we also drive the single leaky integrate and fire neuron with regularly spaced spikes from the SoikeGeneratorGroup from brian import x tau 10 ms Vr 70 mV Vt 55 mV G NeuronGroup 1 model dV dt V Vr tau volt threshold Vt reset Vr spikes 0 t second for t in linspace 10 ms 100 ms 25 input SpikeGeneratorGroup l spikes C Connection input G C 0 0 5 mV M StateMonitor G V record True G V Vr run 100 ms plot M times ms M 0 mV show Example poissongroup misc Poisson input to an IF model from brian import x PG PoissonGroup 1 lambda t 200 Hz 1 cos 2 pi t 50 Hz IF NeuronGroup 1 model dv dt v 10 ms volt reset 0 volt threshold 10 mV C Connection PG I
323. eta wmax gmax doSEHEHSH HHRHESAHSEH HHRHEHATHARHTESESHERHRHEHASDESTHSHE ES Run with plasticity g oSTHTESTEHTESTHSOHER HHTEA RHRHTHHAESAHHATREHHSTSESTSHEEA run simtime 1 second report text dOSESTESAEHSTEESHUHEHAEHHAHSHHREHSES EHTTERHTEHAHRHTEHTHA Make plots g OTEHTSSRHESRHSTISTRHETHRHAHEOHTEHATRHRH EHHRERHTSEHTHRHHATTHUHSETS 3 2 Examples 107 Brian Documentation Release 1 4 1 subplot 211 raster plot sm ms 1 title Before xlabel xlim 0 8 1le3 1 1e3 subplot 212 raster plot sm ms 1 title After xlim simtime 0 2 second 1e3 simtime 1e3 show 3 2 10 hears Example time varying filter1 hears This example implements a band pass filter whose center frequency is modulated by an Ornstein Uhlenbeck The white noise term used for this process is output by a FunctionFilterbank The bandpass filter coefficients update is an example of how to use a ControlFilterbank The bandpass filter is a basic biquadratic filter for which the Q factor and the center frequency must be given The input is a white noise from brian import x from brian hears import x samplerate 20 kHz SoundDuration 300 ms sound whitenoise SoundDuration samplerate ramp number of frequency channel here it must be one as a spectrogram of the foutput is plotted nchannels 1 fc init 5000 Hz initial center frequency of the band pass filter Q 5 quality factor of the band pass filt
324. etan 0 5 ms close V v12 alphan 15 mV v1 2 for act v12 betan 10 mV V1 2 for act k alphan 5 mV act slope k_betan 40 mV fact slope joe muscarinic GK m 0 5 msiemens A alphan m 1e 4 ms mV A betan m 1e 4 ms mV v12 alphan m 30 mV v12 betan m 30 mV k alphan m 9 mV k betan m 9 mV Input parameters Ee 0 mV Ei 75 xmV taue 2 728 ms taui 10 49 ms Ge0 0 0121 usiemens cm 2 Gi0 20 0573 usiemens cm 2 Sigmae 0 012 usiemens cm 2 Sigmai 0 0264x usiemens cm 2 tadj q10 celsius temp 10 ge0 Ge0 area gi0 Gi0 area sigmae Sigmae area sigmai Sigmai area Traubm lambda v v vTraub Na alpham lambda v A alpham Traubm v v12 alpham 1 exp v12 alpham Traubm v k alpham betam lambda v A betam Traubm v v12 betam 1 exp v12 betam Traubm v k betam minf lambda v alpham v alpham v betam v taum lambda v 1 alpham v betam v Shift lambda v Traubm v vshift alphah lambda v A alphahx exp v12 alphah Shift v k_alphah betah lambda v A betah 1 exp v12 betah Shift v k_betah hinf lambda v alphah v alphah v tbetah v tauh lambda v 1 alphah v betah v TraubK lambda v v vTraub K alphan lambda v A alphan TraubK v v12 alphan 1 exp v12 alphan TraubK v k_alphan betan lambda v A betan exp v12 betan TraubK v k betan ninf lambda v alphan v alphan v betan v taun lambda v 1 alphan v 4betan v tadj eqs n dv
325. etto True to indicate that the slice covers the whole range possible small optimisation for Python multiple values True 11 5 Code generation 381 Brian Documentation Release 1 4 1 resolution requires loop Returns True except for Python resolve args kwds Method generated by 1anguage invariant symbol method Languages and methods follow python resolve python gpu resolve gpu c resolve c resolve c read write vectorisable item namespace Returns item embedded in a C for loop resolve gpu read write vectorisable item namespace If not vectorisable retum resolve c If vectorisable we mark it by adding gpu vector index name and gpu vector slice start end to the names pace The GPU code will handle this later on resolve python read write vectorisable item namespace If vectorisable and a11 then we simply return item and add name slice None to the names pace If vectorisable and not a11 then we prepend the following statement to item name slice start end If not vectorisable then we add a for loop over xrange start end supported languages python c gpu class brian experimental codegen2 ArrayIndex name array name language ar ray lenz None index name None ar ray slice None Multi valued symbol giving an index that iterates through an array Schematically name array name array slice name language Symbol name and
326. euronGroup init method code is rather complicated and deals with many special cases The most complicated aspect of this is the definition of the state variables and the update procedure Typically the user simply gives a list of differential equations and Brian attempts to automatically extract the appropriate state variable definitions and creates a differential equation solver appropriate to them it needs some help in this at the moment e g specifying the order or type of the solver The main work in this is done by the magic state updater function which uses the Equations object see next section Once the state variables are defined various internal objects are created The state variables are stored in the _S attribute of a NeuronGroup This is an MxN matrix where M is the number of variables and N is the number of neurons The other major data structure generated is the LS attribute last spikes This is a SpikeContainer instance a circular array used to contain spikes See brian utils circular py Finally note that the construction of many of these objects requires a Clock object which can either be specified explicitly or is guessed by the guess cl1ock function which searches for clocks using the magic module see below EventClock objects are excluded from this guessing 11 3 Main code structure 351 Brian Documentation Release 1 4 1 The magic_state_updater function and the Equations object
327. euronGroup returns anew NeuronGroup that can be used in exactly the same way as its parent group At the moment the subgrouping mechanism can only be used to create contiguous groups of neurons so you can t have a subgroup consisting of neurons 0 100 and also 200 300 say We designate the first 3200 neurons as Ge and the second 800 as Gi these will be the excitatory and inhibitory neurons Ge G subgroup 3200 Excitatory neurons Gi G subgroup 800 Inhibitory neurons Now we define the connections As in the previous part of the tutorial ge is the excitatory current and gi is the inhibitory one Ce says that an excitatory neuron can synapse onto any neuron in G be it excitatory or inhibitory Similarly for inhibitory neurons We also randomly connect Ge and Gi to the whole of G with probability 0 02 and the weights given in the list of parameters at the top Ce Connection Ge G ge sparseness 0 02 weight we Ci Connection Gi G gi sparseness 0 02 weight wi Set up some monitors as usual The line record 0 in the Stat eMonitor declarations indicates that we only want to record the activity of neuron 0 This saves time and memory M SpikeMonitor G MV StateMonitor G V record 0 Mge StateMonitor G ge record 0 Mgi StateMonitor G gi record 0 And in order to start the network off in a somewhat more realistic state we initialise the membrane potentials uniformly randomly between the reset an
328. example for Euler integration the differential equations dx dt expr 11 5 Code generation 361 Brian Documentation Release 1 4 1 are separated by Equations into variable x with expression expr This then becomes Lemp x expr x temp x dt This can then be resolved by the code generation mechanisms described already Synaptic propagation TODO synaptic propagation including docstrings and code comments NOTE GPU functionality not included for synaptic propagation yet 11 5 4 GPU GPU code is handled by five classes GPULanguage derived from CLanguage Identifies the language as CUDA and stores a singleton GPUManager object which is used to manage the GPU GPUCode derived from Code Returned from the code generation process but mostly just acts as a proxy to GPUManager GPUKernel Handles the final stage of taking a partially generated kernel without the vectorisation over threads and computing the final kernel using vectorisation over threads Also adds data to the GPUSymbolMemoryManager GPUManager Manages the GPU generally Stores a set of kernels GPUKernel and manages memory via GPUSymbolMemoryManager Handles joining the memory management code and kernel code into a single source file and compiling it GPUSymbolMemoryManager Handles allocation of GPU memory for symbols For more details see the reference documentation for the classes in the order above Note that CodeGenConnect ion
329. example met re3 metrex 3 watt2 wattx watt etc You can optionally use short names for some units derived from volts amps farads siemens seconds hertz and me tres mV mA uA nA pA mF uF nF mS uS ms Hz kHz MHz cm cm2 cm3 mm mm2 mm3 um um2 um3 Since these names are so short there is a danger that they might clash with your own variables names so watch out for that 4 1 3 Arrays and units Versions of Brian before 1 0 had a system for allowing arrays to have units this has been removed for the 1 0 release because of stability problems as new releases of NumPy SciPy and PyLab came out it required changes to the units code Now all arrays used by Brian are standard NumPy arrays and have no units 4 1 4 Checking units Units are automatically checked when arithmetic operations are performed and when a neuron group is initialised the consistency of the differential equations is checked They can also be checked explictly when a user defined function is called by using the decorator check_units which can be used as follows check_units I amp R ohm wibble metre result volt def getvoltage I R x k return I R 190 Chapter 4 User manual Brian Documentation Release 1 4 1 Remarks not all arguments need to be checked keyword arguments may be checked the result can optionnally be checked no error is raised if the values are strings 4 1 5 Disabling units Unit checking can sl
330. examples of this in action see the following Example time varying filterl hears Example time varying filter2 hears Example dcgc hears 5 7 3 Connecting with Brian To create spiking neuron models based on filter chains you use the FilterbankGroup class This acts exactly like a standard Brian NeuronGroup except that you give a source filterbank and choose a state variable in the target equations for the output of the filterbank A simple auditory nerve fibre model would take the inner hair cell model from earlier and feed it into a noisy leaky integrate and fire model as follows Inner hair cell model as before cfmin cfmax cfN 20 Hz 20 kHz 3000 cf erbspace cfmin cfmax cfN sound Sound whitenoise 100 ms gfb Gammatone sound cf ihe FunctionFilterbank gfb lambda x 3xclip x 0 Inf 1 0 3 0 Leaky integrate and fire model with noise and refractoriness eqs dv dt I v 1 ms 0 2 xix 2 l ms 5 1 gp o odi Kw G FilterbankGroup ihc I eqs reset 0 threshold 1 refractory 5 ms Run and raster plot of the spikes M SpikeMonitor G run sound duration raster_plot M show And here s the output after 6 seconds of computation on a 2GHz laptop 5 7 Brian hears 241 Brian Documentation Release 1 4 1 Neuron number Time ms 5 7 4 Plotting Often you want to use log scaled axes for frequency in plots but the built in matplot
331. eze True keyword 4 8 Inputs 207 Brian Documentation Release 1 4 1 copying every Poisson input a specified number of times copies p keyword This is equivalent of specifying weight p w except that those copies can be randomly shifted jitter keyword or can be unreliable to model synapse unreliability reliability keyword The latter case corresponds to a Binomial synaptic weight 4 8 2 Correlated inputs Generation of correlated spike trains is partially implemented using algorithms from the the following paper Brette R 2009 Generation of correlated spike trains Neural Computation 21 1 188 215 Currently only the method with Cox processes or doubly stochastic processes first method in the paper is fully implemented Doubly stochastic processes To generate correlated spike trains with identical rates and homogeneous exponential correlations use the class HomogeneousCorrelatedSpikeTrains group HomogeneousCorrelatedSpikeTrains 100 r 10 Hz c 0 1 tauc 10 ms where r is the rate c is the total correlation strength and t auc is the correlation time constant The cross covariance functions are c r tauc exp s tauc To generate correlated spike trains with arbitrary rates r i and cross covariance functions c ij exp Isl tauc use the class CorrelatedSpikeTrains group CorrelatedSpikeTrains rates C tauc where rates is the vector of rates r 1 C is the correlation matrix which must be symmetrical a
332. f name value pairs in which the code will be executed code_compiled An optional value can be None consisting of some representation of the compiled form of the code pre_code post_code Two optional Code objects which can be in the same or different languages and can share partially or wholly the namespace They are called respectively before or after the current code object is executed language A Language object that stores some global settings and state for all code in that language Each language e g PythonCode extends some or all of the methods 11 5 Code generation 369 Brian Documentation Release 1 4 1 init Unsurprisingly used for initialising the object should call Code __init__ with all of its arguments compile Compiles the code if necessary If not necessary set the code_compiled value to any dummy value other than None run Runs the compiled code in the namespace It will usually not be necessary to override the call mechanism call xkwds Calls pre code kwds updates the namespace with kwds executes the code calls sel f run and then calls post code kwds compile run class brian experimental codegen2 PythonCode name code str namespace pre code None post code None language None compile run class brian experimental codegen2 CCode name code str namespace pre code None post code None language None run connection class brian expe
333. form x 10P0 810 cf where cf is the center frequency param cf lin p0 2 0 067 param cf lin m 71 016 param bw lin p0 20 037 param bw lin m 20 785 param cf nl p0 2 0 052 param cf nl m 1 016 param bw nl p0 2 0 031 param bw nl m 20 774 param a p0 1 402 param a m 20 819 param b p0 1 619 param b m 2 0 818 param c p0 param c_m 0 param g p0 param g_m 0 48 param lp lin cutoff p0 2 0 067 param lp lin cutoff m 1 016 param lp nl cutoff p0 2 0 052 param lp nl cutoff m 1 016 class brian hears DCGC source cf update intervalz1 paramz The compressive gammachirp auditory filter as described in Irino T and Patterson R A compressive gam machirp auditory filter for both physiological and psychophysical data JASA 2001 Technical implementation details and notation can be found in Irino T and Patterson R A Dynamic Compres sive Gammachirp Auditory Filterbank IEEE Trans Audio Speech Lang Processing The model consists of a control pathway and a signal pathway in parallel The control pathway consists of a bank of bandpass filters followed by a bank of highpass filters this chain yields a bank of gammachirp filters The signal pathway consist of a bank of fix bandpass filters followed by a bank of highpass filters with variable cutoff frequencies this chain yields a bank of gammachirp filters with a level dependent bandwidth The hig
334. functions is very similar to Matlab If you already know Matlab you could read this tutorial NumPy for Matlab users and this list of Matlab Python translations pdf version here A tutorial is also available on the web site of Pylab 3 1 2 Tutorial 1 Basic Concepts In this tutorial we introduce some of the basic concepts of a Brian simulation Importing the Brian module into Python Using quantities with units Defining a neuron model by its differential equation Creating a group of neurons Running a network Looking at the output of the network Modifying the state variables of the network directly Brian Documentation Release 1 4 1 Defining the network structure by connecting neurons Doing a raster plot of the output Plotting the membrane potential of an individual neuron The following Brian classes will be introduced NeuronGroup Connection SpikeMonitor StateMonitor We will build a Brian program that defines a randomly connected network of integrate and fire neurons and plot its output This tutorial assumes you know The very basics of Python the import keyword variables basic arithmetical expressions calling functions lists The simplest leaky integrate and fire neuron model The best place to start learning Python is the official tutorial http docs python org tut Tutorial contents Tutorial 1c Making some activity In the previous part of the tutorial we found that each
335. g amp current_clamp Re 80 Mohm Ce 10 pF bridge 78 Mohm capa_comp 8 pF The capacitance neutralization is a feedback circuit so that it becomes unstable if the feedback capacitance is larger than the actual capacitance of the electrode The bridge compensation is an input dependent voltage offset bridgexi cma and thus is always stable unless an additional feedback such as dynamic clamp is provided Note that the bridge and capacitance neutralization parameters can be variable names e g amp current_clamp Re 80 Mohm Ce 10 pF bridge Rbridge capa_comp 8 pF and then the bridge compensation can be changed dynamically during the simulation 5 3 Electrophysiology models 227 Brian Documentation Release 1 4 1 Voltage clamp amplifier The library includes a single electrode voltage clamp amplifier which clamps the potential at a given value and records the current going through the electrode The following command amp voltage clamp Re 20 Mohm defines a voltage clamp amplifier with an electrode modelled as a pure resistance The function returns an Equations object where the recording current is i rec the membrane potential is vm the electrode current entering the membrane is i inj and command voltage is v cmd note that i rec i inj These names can be overriden using the corresponding keywords For implementation reasons the amplifier always includes an elec trode Electrode capacitance is not included
336. g It implements the CUBA network Benchmark 2 from Simulation of networks of spiking neurons A review of tools and strategies 2006 Brette Rudolph Carnevale Hines Beeman Bower Diesmann Goodman Harris Zirpe Natschlager Pecevski Ermen trout Djurfeldt Lansner Rochel Vibert Alvarez Muller Davison El Boustani and Destexhe Journal of Computational Neuroscience This is a network of 4000 neurons of which 3200 excitatory and 800 inhibitory with exponential synaptic currents The neurons are randomly connected with probability 0 02 from brian import x taum 20 ms membrane time constant taue 5 ms excitatory synaptic time constant taui 10 x ms inhibitory synaptic time constant Vt 50 mV spike threshold Vr 60 mV reset value El 49 mV resting potential we 60 0 27 10 mV excitatory synaptic weight wi 20 4 5 10 mV inhibitory synaptic weight eqs Equations dV dt ge gi V El taum volt dge dt ge tau wollte dgi dt gi taui volt IGI So far this has been pretty similar to the previous part the only difference is we have a couple more parameters and we ve added a resting potential E1 into the equation for V Now we make lots of neurons 3 1 Tutorials 21 Brian Documentation Release 1 4 1 G NeuronGroup 4000 model eqs threshold Vt reset Vr Next we divide them into subgroups The subgroup method of aN
337. g the keyword timestep M StateMonitor group v record True timestep n Recording spike triggered state values You can record the value of a state variable at each spike using StateSpikeMonitor M StateSpikeMonitor group V The spikes attribute of M consists of a series of tuples i t V where V is the value at the time of the spike Recording multiple state variables You can either use multiple St at eMonitor objects or use the Mult iStateMonitor object M MultiStateMonitor group record True uni ses plot M V times M V 0 figure for name m in M iteritems plot m times m 0 label name 4 7 Recording 205 Brian Documentation Release 1 4 1 legend show Recording only recent values You can use the Recent StateMonitor object e g G NeuronGroup 1 dV dt xi 10 ms 0 5 1 MR RecentStateMonitor G V duration 5 ms run 7 ms MR plot show 4 7 3 Counting spikes To count the total number of spikes produced by a group use a PopulationSpikeCounter object M PopulationSpikeCounter group Then the number of spikes after the simulation is M nspikes If you need to count the spikes separately for each neuron use SpikeCounter object M SpikeCounter group Then M i is the number of spikes produced by neuron i 4 7 4 Counting coincidences To count the number of coincident spikes between the neurons of a group and given target spike
338. ge 35 62 74 79 84 108 118 120 example usage 125 126 128 153 187 MiddleBar class in brian hears 327 log frequency xaxis labels in module brian hears mixture process 328 example usage 163 184 log frequency yaxis labels in module brian hears model 266 328 equations 263 log level debug in module brian 255 neuron 263 log level error in module brian 255 modelfitting in module brian library modelfitting 305 log level info in module brian 255 modelling log level warn in module brian 255 auditory 236 LogGammachirp cochlea 240 Index 395 Brian Documentation Release 1 4 1 multi valued brian experimental codegen2 Symbol next brian SpikeQueue method 285 method 379 noise 264 MultiLinearNeuronGroup class in gaussian 264 brian experimental multilinearstateupdater white 264 340 xi 264 multiple clocks 261 non autonomous multiple files 250 337 differential equations 218 derived classes 251 338 equations 218 magic functions 250 337 NoReset class in brian 267 magic register 250 337 NoThreshold class in brian 269 magic return 250 337 nsamples brian hears Sound attribute 312 network 250 337 nspikes brian StateSpikeMonitor attribute 291 multiple values brian experimental codegen2 ArrayIndex numerical computation attribute 382 numpy 189 259 multiple values brian experimental codegen2 SliceIndex numerical integration attribute 381 equations 216 M
339. ge 5 ms volt dgi dt gi 10xms volt P NeuronGroup 4000 model eqs threshold 50 mV reset 60 mV P v 60 mV 10 mV x rand len P Pe P subgroup 3200 Pi P subgroup 800 Ce Connection Pe P ge Ci Connection Pi P gi Ce connect random Pe P 0 02 weight we mV Ci connect random Pi P 0 02 weight wi mV M SpikeMonitor P run 5 second clf raster plot M savefig image png Redirect to the html page we wrote return meta HTTP EQUIV Refresh content 0 URL results html gt Set the directory for static files current dir os path dirname os path abspath file conf tools staticdir on True tools staticdir dir current diry Start the server 90 Chapter 3 Getting started Brian Documentation Release 1 4 1 cherrypy quickstart MyInterface config conf 3 2 8 electrophysiology Example bridge electrophysiology Bridge experiment current clamp from brian import x from brian library electrophysiology import x defaultclock dt 01 ms flog level debug taum 20 ms gl 20 nS Cm taum gl Re 50 Mohm Ce 0 5 ms Re N 10 eqs Equations dvm dt gl vm i_inj Cm fRboridge ohm CC farad I amp pay volt lectrode 6 Re Ce qs eqst current_clamp vm v_el i_inj i_cmd i_cmd I Re 4 Re Ce Ce bridge Rbridge
340. generation 383 Brian Documentation Release 1 4 1 threshold class brian experimental codegen2 CodeGenThreshold group inputcode language level 0 11 6 Brian package structure List of modules with descriptions of contents Root package base Shared base classes for some Brian clases At the moment just the Object Container class used to imple ment the contained objects protocol clock The Clock object guess clock function and other clock manipulation functions compartments A class used in compartmental modelling see user documentation connection Everything to do with connections including the Connection and DelayConnection classes but also construction connection matrices and connection vector code One of the longest and most technical parts of Brian correlatedspikes A toolfor producing correlated spike trains directcontrol Classes for producing groups which fire spikes at user specified times equations Everything to do with the Equations class globalprefs Global preferences for Brian a few routines for getting and setting group A base class for NeuronGroup which creates an S attribute from an Equations object with the ap propriate dynamical variables and allows these variables to be accessed by e g grp V by overriding the getattr and setattr methods inspection Utility functions for inspecting namespaces checking consistency of equations some code manipula tion etc log Brian s
341. getitem and setitem methods are implemented by default and automatically select the appropriate methods from the above in the cases where the item to be got or set is of the form i j or i j class brian DenseConnectionMatrix val kwds Dense connection matrix See documentation for ConnectionMatrix for details on connection matrix types This matrix implements a dense connection matrix It is just a numpy array The get_row and get_col methods return DenseConnectionVector objects class brian SparseConnectionMatrix val column access True use minimal indices False kwds Sparse connection matrix See documentation for Connect ionMat rix for details on connection matrix types 8 7 Connections 277 Brian Documentation Release 1 4 1 This class implements a sparse matrix with a fixed number of nonzero entries Row access is very fast and if the column_access keyword is True then column access is also supported but is not as fast as row access If the use_minimal_indices keyword is True then the neuron and synapse indices will use the smallest possible integer type 16 bits for neuron indices if the number of neurons is less than 2 16 otherwise 32 bits Otherwise it will use the word size for the CPU architecture 32 or 64 bits The matrix should be initialised with a scipy sparse matrix The get_row and get col methods return 5parseConnectionVector objects In addition to the usual slicing o
342. ght w0 STDP eqs stdp dApre dt Apre tau pre 1 Apost 1 wr zur pre Apret a pre wt 0 EEL post Apost 0 w Apretb_post w Ct T stdp STDP syn eqs_stdp pre pre post post wmax Inf MC ConnectionMonitor syn store True clock EventClock dt record_period network_operation EventClock dt IP_period def intrinsic_plasticity synaptic scaling Increases weights of all synapses syn W alldatat syn W alldataxIP_rate IP_period Record the evolution of weights weights network_operation EventClock dt record_period def recordW Z syn W 0 copy weights append Z Il intensity 78 Chapter 3 Getting started Brian Documentation Release 1 4 1 print Started run duration report text Save data wsave t M todense for t M in MC values numpy save weights npy array zip wsave 1 3D array t i j numpy save spikesout npy array S2 spikes numpy save stimuli npy array stimuli Example Fig9B olfaction frompapers computing with neural synchrony olfaction Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 9B Caption Fig 9B Top Fluctuating concentration of three odors A blue B red C black Middle spiking responses of olfactory receptors Bottom Responses of postsynaptic neurons from the assembly selective to A blue and to B red Stimuli are
343. gth nchannels btype One of low high bandpass or bandstop ftype The type of IIR filter to design ellip elliptic butter Butterworth cheby1l Chebyshev I cheby2 Chebyshev ID bessel Bessel class brian hears Butterworth source nchannels order fc btype low Filterbank of low high bandstop or bandpass Butterworth filters The cut off frequencies or the band frequen cies can either be the same for each channel or different along channels Initialisation parameters samplerate Sample rate nchannels Number of filters in the bank order Order of the filters fc Cutoff parameter s in Hz For the case of a lowpass or highpass filterbank fc is either a scalar thus the same value for all of the channels or an array of length nchannels For the case of a bandpass or bandstop fc is either a pair of scalar defining the bandpass or bandstop thus the same values for all of the channels or an array of shape 2 nchannels to define a pair for every channel btype One of low high bandpass or bandstop class brian hears Cascade source filterbank n Cascade of n times a linear filterbank Initialised with arguments source Source of the new filterbank 324 Chapter 8 Reference Brian Documentation Release 1 4 1 filterbank Filterbank object to be put in cascade n Number of cascades class brian hears LowPass source
344. h pinwheels in the barrel cortex Whiskers are deflected with random moving bars N B network construction can be long In this version STDP is faster than in the paper so that the script runs in just a few minutes from brian import x Uncomment if you have a C compiler set global preferences useweave True usecodegen True usecodegenweave True usenewpropagate True use PARAMETERS Neuron numbers M4 M23exc M23inh 22 25 12 side of each barrel in neurons NA N23exc N23inh M4 2 M23exc 2 M23inh 2 neurons per barrel barrelarraysize 5 Choose 3 or 4 if memory error 46 Chapter 3 Getting started Brian Documentation Release 1 4 1 Nbarrels barrelarraysizex 2 Stimulation stim change time 5 ms Fmax 5 stim change time maximum firing rate in layer 4 5 spike stimulation Neuron parameters taum taue taui l10 ms 2 ms 25 ms El 2 70 xmV Vt vt inc tauvt 55 mV 2 xmV 50 ms adaptive threshold STDP taup taud 5 ms 25xms Ap Ad 05 04 EPSPs IPSPs EPSP IPSP l mV l mV EPSC EPSP taue taum taum taue taum IPSC IPSP taui taum taum taui taum Model IF with adaptive threshold eqs dv dt ge gi El v taum volt dge dt ge taue volt dgi dt gi taui volt dvt dt Vt vt tauvt volt adaptation x 1 wv s d Ir Tuning curve tuning lambda theta clip cos theta 0 Inf Fmax Layer 4 layer4 Poiss
345. h the dot notation i e group v is a vector with the values of variable v for all of the 100 neurons It is an array with units as defined in the equations here volt By default all state variables are initialised at value 0 It can be initialised by the user as in the following example group v linspace 0 mV 10 mvV 100 Here the values of v for all the neurons are evenly spaced between 0 mV and 10 mV linspace is a NumPy function The method group rest may also be used to set the resting point of the equations but convergence is not always guaranteed Important options refractory arefractory period default 0 ms to be used in combination with the reset value implicit default False if True then an implicit method is used This is useful for Hodgkin Huxley equations which are stiff 192 Chapter 4 User manual Brian Documentation Release 1 4 1 Subgroups Subgroups can be created with the slice operator subgroupl group 0 50 subgroup2 group 50 100 Then subgroup2 v i equals group v 50 i An alternative equivalent method is the following subgroupl group subgroup 50 subgroup2 group subgroup 50 The parent group keeps track of the allocated subgroups But note that the two methods are mutually exclusive e g in the following example subgroupl group 0 50 subgroup2 group subgroup 50 both subgroups are actually identical Subgroups are useful when creating connections or monitor
346. h the particle s personal best position influences its movement cg cg is the global best constant affecting how much the global best position influences each particle s movement See the wikipedia entry on PSO for more details note that they use c_1 and c_2 instead of cl and cg Reasonable values are 9 5 1 5 but experimentation with other values is a good idea class brian library modelfitting GA Standard genetic algorithm See the wikipedia entry on GA If more than one worker is used it works in an island topology i e as a coarse grained parallel genetic algorithms which assumes a population on each of the computer nodes and migration of individuals among the nodes Optimization parameters proportion parents 1 proportion out of 1 of the entire population taken as potential parents migration time interval 20 whenever more than one worker is used it is the number of iteration at which a migration happens note for different groups case this parameter can only have one value i e every group will have the same value the first of the list proportion migration 0 2 proportion out of 1 of the island population that will migrate to the next island the best one and also the worst that will be replaced by the best of the previous island note for different groups case this parameter can only have one value i e every group will have the same value the first of the list proportion xover 0 65 proporti
347. h units convert the arguments to unitless quantities as above 4 2 Models and neuron groups 4 2 1 Equations Equations objects are initialised with a string as follows eqs Equations dx dt y x tau a volt differential equation y 2 x volt equation Z X alias a volt second parameter BS 4 2 Models and neuron groups 191 Brian Documentation Release 1 4 1 It is possible to pass a string instead of an Equations object when initialising a neuron group In that case the string is implicitly converted to an Equations object There are 4 different types of equations Differential equations a differential equation also defining the variable as a state variable in neuron groups Equations a non differential equation which is useful for defining complicated models The variables are also accessible for reading in neuron groups which is useful for monitoring The graph of dependencies of all equations must have no cycle Aliases the two variables are equivalent This is implemented as an equation with write access in neuron groups Parameters these are constant variables but their values can differ from one neuron to the next They are implemented internally as differential equations with zero derivative Right hand sides must be valid Python expressions possibly including comments and multiline characters The units of all variables except aliases must be specified Note t
348. hat in first line the units volt are meant for x not dx dt The consistency of all units is checked with the method check units which is automatically called when initialising a neuron group through the method prepare When an Equations object is finalised through the method prepare automatically called the NeuronGroup initialiser the names of variables defined by non differential equations are replaced by their string values so that differential equations are self consistent In the process names of external variables are also modified to avoid conflicts by adding a prefix 4 2 2 Neuron groups The key idea for efficient simulations is to update synchronously the state variables of all identical neuron models A neuron group is defined by the model equations and optionally a threshold condition and a reset For example for 100 neurons eqs Equations dv dt v tau volt group NeuronGroup 100 model eqs reset 0 mV threshold 10 mvV The model keyword also accepts strings in that case it is converted to an Equations object e g group NeuronGroup 100 model dv dt v tau volt reset 0 mV threshold 10 mV The units of both the reset and threshold are checked for consistency with the equations The code above defines a group of 100 integrate and fire neurons with threshold 10 mV and reset 0 mV The second line defines an object named group which contains all the state variables which can be accessed wit
349. hat sets the source nchannels and samplerate from that of the source object For multiple sources the default implementation will check that each source has the same number of channels and samplerate and will raise an error if not There is a default buffer_init method that calls buffer_init onthe source or list of sources Example of deriving a class The following class takes N input channels and sums them to a single output channel class AccumulateFilterbank Filterbank def init self source Filterbank init self source self nchannels 1 def buffer_apply self input return reshape sum input axis 1 input shape 0 1 Note that the default Filterbank init willsetthe number of channels equal to the number of source channels but we want to change it to have a single output channel We use the bu fer apply method which automatically handles the efficient cacheing of the buffer for us The method receives the array input which has shape bufsize nchannels and sums over the channels axis 1 It s important to reshape the output so that it has shape bufsize outputnchannels so that it can be used as the input to subsequent filterbanks class brian hears BaseSound Base class for Sound and OnlineSound class brian hears OnlineSound 8 21 10 Options There are several relevant global options for Brian hears In particular activating scipy Weave support with the useweave True will give considerably faster lin
350. he average vector It equals 1 for spikes with constant phase and 0 for homogeneous phase distributions e Gamma precision factor gamma factor source target delta returns the gamma precision fac tor between source and target trains with precision delta These functions return NaN not a number when a spike train is empty 4 11 Realtime control A running Brian simulation can be controlled for example using an IPython shell This can work either on a single computer or over IP from another computer The process running the simulation calls something like server RemoteControlServer and the IPython shell calls client RemoteControlClient The shell can now execute and evaluate in the server process via spikes client evaluate M spikes i t zip spikes plot t i client stop Parameters can be changed as the simulation runs For more details see the reference documentation for RemoteControlServer and RemoteControlClient 4 12 Clocks Brian is a clock based simulator operations are done synchronously at each tick of a clock Many Brian objects store a clock object passed in the initialiser with the optional keyword clock For example to simulate a neuron group with time step dt 1 ms myclock Clock dt 1x ms group NeuronGroup 100 model dx dt 1xmV ms volt clock myclock If no clock is specified the program uses the global default clock When Brian is initially imported th
351. he first doesn t allow you to add or remove elements at runtime and is very optimised the second does allow you to and is less optimised Both are more optimised than scipy s sparse matrices which are used as the basis for the construction phase Connection objects can handle homogeneous delays all synapses with the same delay by pulling spikes from NeuronGroup s LS object with a delay Heterogeneous delays each synapse with a different delay are done by the DelayConnection object which stores a delayvec attribute alongside the W attribute The delay matrix is of the same type as the weight matrix and in the case of sparse matrices must have nonzero elements at the same places 352 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 The Connection object automatically turns itself into a DelayConnection object if heterogeneous delays are requested so that the user doesn t even need to know of the existence of DelayConnection The Connection object also provides methods for initialising the weight matrices either fully randomly etc See the user docs Construction of monitors The SpikeMonitor class of monitors derive from Connect ion Rather than propagating spikes to another group they store them in a list The work is done in the SpikeMonitor propagate method The StateMonitor class of monitors derive from NetworkOperation Network operations are called once every time step and execute arbitrary Python cod
352. he modelfitting function Arguments model reset threshold input input var dt initial values Same parameters as for the modelfitting function params The best parameters returned by the modelfitting function Returns spiketimes The spike times of the model with the given input and parameters brian library modelfitting predict model None reset None threshold None data None delta 4 0 msecond input None input var T dt None params Predicts the gamma factor of a fitted model with respect to the data with a different input current Arguments model reset threshold input_var dt Same parameters as for the modelfitting function input The input current that can be different from the current used for the fitting procedure data The experimental spike times to compute the gamma factor against They have been obtained with the current input params The best parameters returned by the model fitting function Returns gamma The gamma factor of the model spike trains against the data If there were several groups in the fitting procedure it is a vector containing the gamma factor for each group class brian library modelfitting PSO Particle Swarm Optimization algorithm See the wikipedia entry on PSO Optimization parameters omega The parameter omega is the inertial constant 8 19 Model fitting toolbox 307 Brian Documentation Release 1 4 1 cl c1 is the local best constant affecting how muc
353. hen The values can be start before_groups after_groups middle before_connections after_connections before_resets after_resets or end default end For example to call a func tion f at the beginning of every timestep network_operation when start def f do_something or to record the value of a state variable just before the resets M StateMonitor group x record True when before_resets 4 13 2 Basic simulation conirol The simulation is run simply as follows run 1000 ms where 1000 ms is the duration of the run It can be stopped during the simulation with the instruction st op and the network can be reinitialised with the instruction reinit The run function also has some options for reporting the progress of the simulation as it runs for example this will print out the elapsed time percentage of the simulation this is complete and an estimate of the remaining time every 10s run 100 second report text When the run function is called Brian looks for all relevant objects in the namespace groups connections monitors user operations and runs them In complex scripts the user might want to run only selected objects In that case there are two options The first is to create a Network object see next section The second is to use the forget function on objects you want to exclude from being used These can then be later added back using the recall funct
354. here y corresponds to order 7 defines the oscillation frequency cf and A defines the band width parameter The design is based on the Hohmann implementation as described in Hohmann V 2002 Frequency analysis and synthesis using a Gammatone filterbank Acta Acustica United with Acustica The code is based on the Matlab gammatone implementation from Meddis toolbox Initialised with arguments source Source of the filterbank cf List or array of center frequencies bandwidth List or array of filters bandwidth corresponding one for each cf order 4 The number of Ist order gammatone filters put in cascade and therefore the order the resulting gammatone filters class brian hears LogGammachirp source f b 1 019 c 1 ncascades 4 Bank of gammachirp filters with a logarithmic frequency sweep The approximated impulse response IR is defined as follows IR t t e 27 ERBUO cos 2 ft c In t where ERB 24 7 0 108 f Hz is the equivalent rectangular bandwidth of the filter centered at f The implementation is a cascade of 4 2nd order IIR gammatone filters followed by a cascade of ncascades 2nd order asymmetric compensation filters as introduced in Unoki et al 2001 Improvement of an IIR asymmetric compensation gammachirp filter Initialisation parameters source Source sound or filterbank f List or array of the sweep ending frequencies instantaneous f c t b 1 019 Parameters which determine the duration
355. honCode class brian experimental codegen2 CLanguage scalar double C language Has an attribute scalar double which gives the default type of scalar values used when dt ype is not specified This can be used for example on the GPU where double may not be available CodeObjectClass alias of CCode makeintegrator brian experimental codegen2 make c integrator args kwds Gives C C format code for the integration step of a differential equation eqs The equations can bean brian Equations object or a multiline string in Brian equations format method The integration method typically euler rk2 orexp euler although you can pass your own integration method see make integration step for details dt The value of the timestep dt in Brian units e g 0 1 ms values Optional dictionary of mappings variable gt value these values will be inserted into the generated code scalar By default itis double but if you want to use float as your scalar type set this to float timename The name of the time variable if used In Brian this is t but you can change it to T or time or whatever This can be used if you want users to specify time in Brian form t but the context in which this code will be used e g another simulator specifies time with a different variable name e g T timeunit The unit of the time variable scaled because Brian expects time to be in seconds Retur
356. hpass filters of the signal pathway are controlled by the output levels of the two stages of the control pathway Initialised with arguments source Source of the cochlear model cf List or array of center frequencies update interval Interval in samples controlling how often the band pass filter of the signal pathway is updated Smaller values are more accurate but give longer computation times param Dictionary used to overwrite the default parameters given in the original paper 326 Chapter 8 Reference Brian Documentation Release 1 4 1 The possible parameters to change and their default values see Irino T and Patterson R A Dynamic Com pressive Gammachirp Auditory Filterbank IEEE Trans Audio Speech Lang Processing are param b1 1 81 param cl 2 96 param b2 2 17 param c2 2 2 param decay_tcst 5 ms param lev weight 5 param level ref 50 param level pwrl 1 5 param level pwr2 5 param RMStoSPL 30 param frat0 2330 param frati1 005 param lct ERB 1 5 value of the shift in ERB frequencies param frat control 1 08 param order gc 4 param ERBrate 21 4x10g10 4 37 xcf 1000 1 cf is the center frequency param ERBwidth 24 7 x 4 37 cf 1000 1 class brian hears MiddleEar source gain 1 kwds Implements the middle ear model from Tan amp Carney 2003 linear filter with two p
357. ibutes names The symbol names for all the differential equations names_nonzero The symbol names for all the nonzero differential equations brian experimental codegen2 make_integration_step method eqs Return an integration step from a method and a set of equations The method should be a function method eqs which receives a EquationsContainer object as its argument and yields statements For example the euler integration step is defined as def euler eqs for var expr in eqs nonzero yield _temp_ var expr format var var expr expr for var expr in eqs nonzero yield var temp var dt format var var expr expr brian experimental codegen2 euler eqs Euler integration brian experimental codegen2 rk2 eqs 2nd order Runge Kutta integration brian experimental codegen2 exp_euler eqs Exponential Euler integration 11 5 Code generation 375 Brian Documentation Release 1 4 1 languages class brian experimental codegen2 Language name Base class for languages each should provide a name attribute and a method code object code object name code str namespace Return a Code object from a given name code string code str and namespace If the class has a class attribute CodeOb jectClass the default implementation returns CodeObjectClass name code str namespace language self class brian experimental codegen2 PythonLanguage Python language CodeObjectClass alias of Pyt
358. ielding one item at a time pools map tuple args result for pool in pools result x y for x in result for y in pool return result duration 50 ms samplerate 50 kHz set_default_samplerate samplerate CF 2200 freqs np arange 250 0 3501 50 levels 10 30 50 70 90 cf level product freqs levels tones Sound Sound sequence tone freq Hz duration atlevel level dB ramp when both duration 2 5 ms inplace False for freq level in cf level ihc TanCarney MiddleEar tones CF len cf level update interval 2 syn ZhangSynapse ihc CF S mon StateMonitor syn s record True clock syn clock net Network syn s mon 3 2 Examples 125 Brian Documentation Release 1 4 1 net run duration reshaped s_mon values reshape len freqs len levels 1 calculate the phase with respect to the stimulus pi np pi min freq max freq 1100 2900 freq subset fregs freqs min freq amp freqs lt max_freq reshaped subset reshaped freqs min freq amp fregsc max freq phases np zeros reshaped subset shape 0 len levels for f idx freq in enumerate freq subset period 1 0 freq for l idx in xrange len levels phase angles np arange reshaped subset shape 2 samplerate period period 2 pi temp phases np exp 1j phase angles gt reshaped subset f idx l id
359. iffential equations taum dV dt V ge gi taue dge dt ge taui dgi dt gi 18 Chapter 3 Getting started Brian Documentation Release 1 4 1 An excitatory neuron connects to state ge and an inhibitory neuron connects to state gi When an excitatory spike arrives ge instantaneously increases then decays exponentially Consequently V will initially but continuously rise and then fall Solving these equations if V 0 0 ge 0 g0 corresponding to an excitatory spike arriving at time 0 and gi 0 0 then gi 0 ge g0 exp t taue V exp t taum exp t taue taue gO taum taue We use a very short time constant for the excitatory currents a longer one for the inhibitory currents and an even longer one for the membrane potential from brian import x taum 20 ms taue 1 ms taui 10 ms Vt 10 mV Vr 0 mV eqs Equations dV dt V ge gi taum volt dge dt ge tau i volt dgi dt gi taui E volt F4 Connections As before we ll have a group of two neurons under direct control the first of which will be excitatory this time and the second will be inhibitory To demonstrate the effect we ll have two excitatory spikes reasonably close together followed by an inhibitory spike later on and then shortly after that two excitatory spikes close together spiketimes 0 1 ms 0 10 ms 1 40 ms 0 50 ms 0 55 ms Gl SpikeGeneratorGroup 2 sp
360. ifiedGammatone CombinedFilterbank def init self source cf CombinedFilterbank init self source source self get modified source At this point insert your chain of filterbanks acting on the modified source object gfb Gammatone source cf rectified FunctionFilterbank gfb lambda input clip input 0 Inf Finally set the output filterbank to be the last in your chain self set_output fb This combination of a Gammatone and a rectification via a FunctionFilterbank can now be used as a single filterbank for example x whitenoise 100 ms fb RectifiedGammatone x l kHz 1 5 kHz y fb process Details The reason for the get modified source callis that the source attribute of a filterbank can be changed after creation The modified source provides a buffer in fact a DoNothingFilterbank so that the input to the chain of filters defined by the derived class doesn t need to be changed 8 21 3 Filterbank library class brian hears Gammatone source cf bz 1 019 erb orderz1 ear Q 9 26449 min bwz24 7 Bank of gammatone filters They are implemented as cascades of four 2nd order IIR filters this 8th order digital filter corresponds to a 4th order gammatone filter The approximated impulse response IR is defined as follow IR t t exp 2x0ERB t cos 27 ft where ERB f 24 7 0 1087 Hz is the equivalent rectangular bandwidth of the filter centered at f It comes from Slaney s exa
361. ify the unit type keyword which is CPU or GPU to indicate whether you want to use CPUs or GPUs on these computers You can t mix CPUs and GPUs for the same optimization IP To connect several machines via IP pass a list of host names or IP addresses as strings to the machines keyword of the modelfitting function To specify a specific port use a tuple IP port instead of a string You can also specify a default port in the Playdoh user preferences see the Playdoh documentation Authentication You can specify an authentication string on all the computers running the Playdoh server to secure communications See the Playdoh documentation Example The following script launches a fitting procedure in parallel on two machines from brian import loadtxt ms Equations from brian library modelfitting import if name main List of machines IP addresses machines bobs machine university com jims machine university com equations Equations dV dt R I V tau 1 E Rr tau second PIA input loadtxt current txt spikes loadtxt spikes txt results modelfitting model equations reset 0 threshold 1 data spikes input input dt 1 ms popsize 1000 maxiter 3 5 6 Model fitting 235 Brian Documentation Release 1 4 1 delta 4 ms unit type CPU machines machines R 1 0e9 9 0e9 tau 10 ms 40xms refractory O ms 10 ms
362. ihc TanCarney MiddleEar tones cf len levels update interval 1 syn ZhangSynapse ihc cf 128 Chapter 3 Getting started Brian Documentation Release 1 4 1 s mon StateMonitor syn s record True clock syn clock R mon StateMonitor syn R record True clock syn clock spike mon SpikeMonitor syn net Network syn s mon R mon spike mon net run duration 1 5 for idx level in enumerate levels plt figure 1 plt subplot len levels 1 idx 1 plt plot s mon times ms s mon idx plt xlim 0 25 plt xlabel Time msec plt ylabel Sp sec plt text 15 np nanmax s mon idx 2 Peak SPL s SPL str level dB ymin ymax plt ylim if idx plt title Click responses plt figure 2 plt subplot len levels 1 idx 1 plt plot R mon times ms R mon idx plt xlabel Time msec plt xlabel Time msec plt text 15 np nanmax s mon idx 2 Peak SPL s SPL str level dB plt ylim ymin ymax if idx plt title Click responses with spikes and refractoriness plt plot spike mon spiketimes idx ms np ones len spike mon spiketimes idx np nanmax R mon idx rx print Testing tone response reinit default clock duration 60 ms levels 0 20 40 60 80 tones Sound Sound sequence tone cf duration atlevel level dB ramp when both duration 10 ms inplace False silence duration duration 2 for
363. ike peaks v vc 10 mV where vc is the voltage criterion we consider that there is a spike when v gt vc The algorithm works as follows First we identify positive crossings of the voltage criterion Then after each positive crossing we look for the first local maximum that is when the voltage first starts decreasing The last spike is treated differently because the peak may occur after the end of the recording in which case the last element is considered as the peak It is possible to omit the voltage criterion vc In this case it is guessed with the following rather complex function vc find spike criterion v The idea of this algorithm is to look at the trace in phase space v dv dt In this space spikes tend to circle around some area which contains no trajectory It appears that somewhere in the middle of these circles there is a voltage vc for which trajectories are either increasing dv gt 0 upstroke of a spike or decreasing dv 0 downstroke of a spike but never still dv 0 This means that a positive crossing of this voltage always leads to a spike We identify this voltage by looking for the largest interval of voltages v1 v2 for which there is no sign change of dv dt over two successive timesteps and we set vc v1 v2 2 the middle of this interval As this method is rather complex it is strongly advised to manually check whether it gives reasonable results Voltage reset The average voltage reset after a spik
364. ike this client RemoteControlClient spikes client evaluate M spikes i t zip spikes plot t i client execute stop 8 18 Progress reporting class brian utils progressreporting ProgressReporter report stderr period 10 0 first reportz 1 0 Standard text and graphical progress reports Initialised with arguments report Can be one of the following strings print text stdout Reports progress to standard console stderr Reports progress to error console graphical tkinter A simple graphical progress bar using Tkinter Alternatively it can be any output stream in which case text reports will be sent to it or a custom callback function report elapsed complete taking arguments elapsed the amount of time that has passed and complete the fraction of the computation finished period How often reports should be generated in seconds first report The time ofthe first report nothing will be done before this amount of time has elapsed Methods start Call at the beginning of a task to start timing it finish Call at the end of a task to finish timing it Note that with the Tkinter class if you do not call this it will stop the Python script from finishing stopping memory from being freed up update complete Call with the fraction of the task or subtask if subtask has been called completed between 0 and 1 subtask complete tasksize After calling subtask comp
365. ikeMonitor source filename record False delay 0 Records spikes to an AER file Initialised as FileSpikeMonitor source filename record False Does everything that a SpikeMonitor does except ONLY records the spikes to the named file in AER format during the simulation These spikes can then be reloaded via the 1o load aer function and used later into a SpikeGeneratorGroup It is about three times faster than the FileSpikeMonitor and creates smaller files On the other hand those files are not human readable because they are in binary format Has one additional method close Closes the file manually will happen automatically when the program ends class brian FileSpikeMonitor source filename record False delay 0 Records spikes to a file Initialised as FileSpikeMonitor source filename record False Does everything that a SpikeMonitor does except also records the spikes to the named file note that spikes are recorded as an ASCII file of lines each of the form i t Where i is the neuron that fired and t is the time in seconds Has one additional method close Closes the file manually will happen automatically when the program ends class brian ISIHistogramMonitor source bins delay 0 Records the interspike interval histograms of a group Initialised as ISIHistogramMonitor source bins source The source group to record from bins The lower bounds for each bin so that e g bins 0xms 10 ms
366. iketimes G2 NeuronGroup N 1 model eqs threshold Vt reset Vr Cl Connection Gl G2 ge C2 Connection Gl G2 gi The weights are the same when we increase ge the effect on V is excitatory and when we increase gi the effect on V is inhibitory C1 0 0 C2 1 0 3 mV 3 x mV We set up monitors and run as normal Mv StateMonitor G2 V record True Mge StateMonitor G2 ge record True Mgi StateMonitor G2 gi record True run 100 ms This time we do something a little bit different when plotting it We want a plot with two subplots the top one will show V and the bottom one will show both ge and gi We use the subplot command from pylab which mimics 3 1 Tutorials 19 Brian Documentation Release 1 4 1 the same command from Matlab figure subplot 211 plot Mv times Mv 0 subplot 212 plot Mge times Mge 0 plot Mgi times Mgi 0 show 0 00 0 02 0 04 0 06 0 08 0 10 0 00005 0 02 0 04 0 06 oge 0 10 The top figure shows the voltage trace and the bottom figure shows ge in blue and gi in green You can see that although the inhibitory and excitatory weights are the same the inhibitory current is much more powerful This is because the effect of ge or gi on V is related to the integral of the differential equation for those variables and gi decays much more slowly than ge Thus the size of the negative deflection at 40 ms is much bigger than th
367. ime N 10000 number of neurons Ne int N 0 8 excitatory neurons Ni N Ne inhibitory neurons p 80 N duration 1000 ms ra eqs dv dt ge gi v 49xmV 20xms volt dge dt ge 5 ms volt dgi dt gi 10 ms volt pg P NeuronGroup N model eqs threshold 50 mV reset 60 mV P v 60 mV 10 mV rand len P Pe P subgroup Ne Pi P subgroup Ni Ce Connection Pe P ge weight 1 62 mV sparseness p Ci Connection Pi P gi weight 9 mV sparseness p M SpikeMonitor P trace StateMonitor P v record 0 tl time run 1 second t2 time print Simulated in t2 t1 s print len M spikes spikes subplot 211 raster_plot M subplot 212 plot trace times ms trace 0 mvV show Equivalent in pure Python The script above translated into pure Python no Brian FEF A pure Python version of the CUBA example that reproduces basic Brian principles EEF from pylab import from time import time from random import sample from scipy import random as scirandom mmm Parameters nmi 11 2 Simulation principles 347 Brian Documentation Release 1 4 1 N 10000 number of neurons Ne int N 0 8 excitatory neurons Ni N Ne inhibitory neurons mV ms 1e 3 units dt 0 1 ms timestep taum 20 ms membrane time constant taue 5 ms taui 10 ms p 80 0 N connection probability 80 synapses per neuron Vt 1l mV threshold
368. in group G In our case this is an array of length 40 We set its values by generating an array of random numbers using Brian s rand function The syntax is rand size generates an array of length size consisting of uniformly distributed random numbers in the interval 0 1 14 Chapter 3 Getting started Brian Documentation Release 1 4 1 G V Vr rand 40 Vt Vr And now we run the simulation as before run l second print M nspikes But this time we get a varying number of spikes each time we run it roughly between 800 and 850 spikes In the next part of this tutorial we introduce a bit more interest into this network by connecting the neurons together Tutorial 1e Connecting neurons In the previous parts of this tutorial the neurons are still all unconnected We add in connections here The model we use is that when neuron i is connected to neuron j and neuron i fires a spike then the membrane potential of neuron j is instantaneously increased by a value psp We start as before from brian import x tau 20 msecond membrane time constant Vt 50 mvolt spike threshold Vr 60 x mvolt reset value El 49 x mvolt resting potential same as the reset Now we include a new parameter the PSP size psp 0 5 mvolt postsynaptic potential size And continue as before G NeuronGroup N 40 model dV dt V El tau volt threshold Vt reset Vr Connections We now proce
369. induce a spike refractory The time to wait after a spike before checking for spikes again state The name or number of the state variable to check clock If this object is being used for a NeuronGroup which doesn t use the default clock you need to specify its clock here class brian SimpleFunThreshold thresholdfun state 0 Threshold mechanism with a user specified function Initialised as FunThreshold thresholdfun state 0 with arguments thresholdfun A function with one argument the array of values for the specified state variable For effi ciency this is a numpy array and there is no unit checking state The name or number of the state variable to pass to the threshold function Sample usage FunThreshold lambda V V gt Vt state V class brian FunThreshold fhresholdfun Threshold mechanism with a user specified function Initialised as FunThreshold thresholdfun where thresholdfun is a function with one argument the 2d state value array where each row is an array of values for one state of length N for N the number of neurons in the group For efficiency data are numpy arrays and there is no unit checking Note if you only need to consider one state variable use the SimpleFunThreshold object instead class brian NoThreshold No thresholding mechanism Initialised as NoThreshold 8 5 Integration See Numerical integration for an overview 8 5 Integration 269 Brian Documenta
370. ing potential we 60 0 27 10 mV excitatory synaptic weight wi 20 4 5 10 mV inhibitory synaptic weight eqs Equations dV dt ge gi V El taum volt dge dt ge tau volt dgi dt gi taui volt prn G NeuronGroup 4000 model eqs threshold Vt reset Vr Ge G subgroup 3200 Excitatory neurons Gi G subgroup 800 Inhibitory neurons Ce Connection Ge G ge sparseness 0 2 weight we Ci Connection Gi G gi sparseness 0 2 weight wix10 Cii Connection Gi Gi gi sparseness 0 2 weight wi 3 2 Examples 97 Brian Documentation Release 1 4 1 E SpikeMonitor Ge Spi I Spike V St ge S gi S G V V r n 250 keMonitor G rae onitor Gi o ateMonitor G tateMonitor G tateMonitor G r Vt Vr O0 ms rye ge gi record 0 record 0 record 0 x rand len G subplot 211 raster_plot M raster plot E raster plot I subplot 223 title The CUBA network newfigure False plot MV times ms MV 0 mV xlabel Time ms ylabel V mV subplot 224 plot Mge times ms Mge 0 mV plot Mgi times ms Mgi 0 mV xlabel Time ms ylabel ge and gi mvV legend ge gi upper right show new Figure Example PeterDiehl twister Peter Diehl s entry for the 2012 Brian twister from brian import x AE ae i eqs dv dt
371. ing started Brian Documentation Release 1 4 1 neuronsA neurons N neuronsA tauK 400 ms neuronsA gmax 1 neuronsA theta 55 mV neuronsA duration linspace 100 ms 1 second N Neuron B duplicated to simulate multiple input durations simultaneously neuronsB neurons N neuronsB tauK 100 ms neuronsB gmax 1 5 neuronsB theta 54 mV neuronsB duration linspace 100 ms l second N Noisy coincidence detectors tau cd 5 ms tau n tau cd sigma 0 2 noise s d in units of the threshold eqs post dv dt n v tau cd 1 dn dt n tau n sigma 2 tau n x 5 xi 1 OF postneurons NeuronGroup N model eqs_post threshold 1 reset 0 CA IdentityConnection neuronsA postneurons v weight 0 5 CB IdentityConnection neuronsB postneurons v weight 0 5 spikes SpikeCounter postneurons M StateMonitor postneurons v record N 3 run rest time cl 1 second report text Figure subplot 121 Fig 1C example trace plot M times ms M N 3 k xlim 1350 1500 ylim 3 1 xlabel Time ms ylabel V subplot 122 Fig 1D duration tuning curve count spikes count Smooth the tuning curve window 200 rate zeros len count window for i in range 0 len count window rate i mean count i i window plot neuronsA duration window 2 window 2 ms 10 rate xlim 0 1000 ylim 0 0 5 xlabel Duration ms ylabel Spiking probability show FLO 7 KY
372. ing the state variables or spikes The best practice is to define groups as large as possible then divide them in subgroups if necessary Indeed the larger the groups are the faster the simulation runs For example for a network with a feedforward architecture one should first define one group holding all the neurons in the network then define the layers as subgroups of this big group Details For details see the reference documentation for NeuronGroup 4 2 3 Reset More complex resets can be defined The value of the reset keyword can be e a quantity 0xmV a string a function e a Reset object which can be used for resetting a specific state variable or for resetting a state variable to the value of another variable Reset as Python code The simplest way to customise the reset is to define it as a Python statement e g eqs ti dv dt v tau volt dw dt w tau volt EEE group NeuronGroup 100 model eqs reset Vv 0 mV wt 3 mV threshold 10 mv The string must be a valid Python statement possibly a multiline string It can contain variables from the neuron group units and any variable defined in the namespace e g tau as for equations Be aware that if a variable in the namespace has the same name as a neuron group variable then it masks the neuron variable The way it works is that the code is evaluated with each neuron variable v replaced by v spikes where spikes is the array of indexes of the ne
373. ing to the last For example suppose you had two sources each consisting of a stereo sound say source 0 was AB and source 1 was CD then indexmapping 1 0 3 2 would swap the left and right of each source but leave the order of the sources the same i e the output would be BADC class brian hears Join sources Filterbank that joins the channels of its inputs in series e g with two input sources with channels AB and CD respectively the output would have channels ABCD You can initialise with multiple sources separated by commas or by passing a list of sources class brian hears Interleave sources Filterbank that interleaves the channels of its inputs e g with two input sources with channels AB and CD respectively the output would have channels ACBD You can initialise with multiple sources separated by commas or by passing a list of sources class brian hears Repeat source numrepeat Filterbank that repeats each channel from its input e g with 3 repeats channels ABC would map to AAABB BCCC class brian hears Tile source numtile Filterbank that tiles the channels from its input e g with 3 tiles channels ABC would map to ABCABCABC 318 Chapter 8 Reference Brian Documentation Release 1 4 1 class brian hears FunctionFilterbank source func nchannels None params Filterbank that just applies a given function The function should take as many arguments as there are sources For example to h
374. input sound in rms dB SPL sound whitenoise 100 ms ramp generation of a white noise sound sound atlevel level set the sound to a certain dB level nbr center frequencies 50 number of frequency channels in the filterbank center frequencies with a spacing following an ERB scale center frequencies erbspace 100 Hz 1000 Hz nbr center frequencies f bandwidth of the filters different in each channel bw 10 0 037 0 785x1log10 center frequencies gammatone ApproximateGammatone sound center frequencies bw order 3 gt mon gammatone process figure imshow flipud gt mon T aspect auto show Example artificial_vowels hears This example implements the artificial vowels from Culling J F and Summerfield Q 1995a Perceptual segrega tion of concurrent speech sounds absence of across frequency grouping by common interaural delay J Acoust Soc Am 98 785 797 from brian import x from brian hears import duration 409 6x ms width 150 Hz 2 samplerate 10 kHz set default samplerate samplerate centres 225 Hz 625 Hz 975 Hz 1925x Hz vowels ee centres 0 centres 3 root centres 0 centres 2 er centres 1 centres 3 i 1 ar i centres 1 centres 2 sI 1 2h 1 def generate vowel vowel vowel vowels vowel x whitenoise duration y fft asarray x flatten f fftfreq len
375. int Completed start_time time time figure for ai in range grid 1 for sigmai in range grid 1 a int amin ai amax amin grid if a amax a amax sigma sigmamin sigmai sigmamax sigmamin grid params initial burst a params initial burst sigma a sigma net reinit params net run newa newsigma estimate params net mon 1 params initial burst t newa float newa float neuron multiply col float ai float grid float sigmai float grid 0 5 plot sigma ms newsigma ms a newa color col plot sigma ms a marker color col markersize 15 i 1 if verbose 30 Chapter 3 Getting started Brian Documentation Release 1 4 1 print str int 100 float i float grid 1 2 r if verbose print if verbose print Evaluation time time time start time seconds xlabel r Nsigma ms ylabel a title Synfire chain state space axis sigmamin ms sigmamax ms amin amax minimal example print Computing SFC with multiple layers single_sfc print Plotting SFC state space state_space 3 1 state_space 8 10 state_space 10 50 state_space 10 150 show Example Vogels_et_al_2011 frompapers Inhibitory synaptic plasticity in a recurrent network model F Zenke 2011 from the 2012 Brian twister Adapted from Vogels T P H Sprekeler F Zenke C Clopath and
376. integer i the monitor will record the state of the variable for neuron i If it s a list of integers it will record the states for each neuron in the list If it s set to True it will record for all the neurons in the group 3 1 Tutorials 11 Brian Documentation Release 1 4 1 M StateMonitor G V record 0 And then we continue as before G V Vr rand 40 Vt Vr But this time we run it for a shorter time so we can look at the output in more detail run 200 msecond Having run the simulation we plot the results using the plot command from PyLab which has the same syntax as the Matlab plot command i e plot xvals yvals The StateMonitor monitors the times at which it monitored a value in the array M times and the values in the array M 0 The notation M i means the array of values of the monitored state variable for neuron i In the following lines we scale the times so that they re measured in ms and the values so that they re measured in mV We also label the plot using PyLab s xlabel ylabel and title functions which again mimic the Matlab equivalents plot M times ms M 0 mV xlabel Time in ms ylabel Membrane potential in mV title Membrane potential for neuron 0 show Membrane potential for neuron 0 Zu ka 5 Memrane potential in mW in in T m D 50 100 150 200 Time hn ma You can clearly see the leaky integration exponential decay towa
377. iology Electrophysiology library with electrode and amplifier models IF Integrate and fire models leaky quadratic exponential ionic currents Ionic current models K Nat random_processes Currently only Ornstein Uhlenbeck synapses Synaptic models exponential alpha and biexponential models utils subpackage approximatecomparisons Some tools for doing approximate comparisons with floating point numbers be cause they are inexact autodiff Automatic differentiation routines for single valued functions circular and the ccircular subpackage The important SpikeContainer and related classes The C ver sion uses SWIG and is much faster but requires the user to compile themselves at the moment this will be addressed at some point in the future documentation Some utility functions related to documentation information theory Entropy and mutual information estimators Requires the ANN wrapper in scikits parallelpython A utility function for using the Parallel Python module parameters The Parameters class basically independent of Brian but potentially useful progressreporting A progress reporting framework which Network run can use to report how long it is taking to run with text or graphical options statistics Statistics of spike trains CV vector strength correlograms tabulate Tabulation of numerical functions precalculation 11 7 Repository structure The Brian source code repository is broken
378. ion Users of ipython may also want to make use of the clear function which removes all Brian objects and deletes their data This is useful because ipython keeps persistent references to these objects which stops memory from being freed 4 13 3 The Network class A Network object holds a collection of objets that can be run ie objects with class NeuronGroup Connection SpikeMonitor StateMonitor or subclasses or any user defined operation with the decorator network operation Thoses objects can then be simulated Example G NeuronGroup C Connection net Network G C net run 1 second You can also pass lists of objects The simulation can be controlled with the methods stop and reinit 214 Chapter 4 User manual Brian Documentation Release 1 4 1 4 13 4 The MagicNetwork object When run reinit and stop are called they act on the magic network the network consisting of all relevant objects such as groups connections monitors and user operations This magic network can be explicitly constructed using the MagicNetwork object G NeuronGroup C Connection net MagicNetwork net run 1 second 4 14 More on equations The Equations class is a central part of Brian since models are generally specified with an Equations object Here we explain advanced aspects of this class 4 14 1 External variables Equations may contain external variables When an Eq
379. ion size numpy random rand n cells 2 exc cells all cells 0 n exc inh cells all cells n exc n cells We initialize v values slightly above Vt to have initial spikes all cells v El l 1 numpy random rand n cells Vt El Now we create the source that will write the word BRIAN sources PoissonGroup 1 ext rate sources position array 0 5 0 5 Function to get the distance between one position and an array of positions This is needed to used the vectorized form of the connections in the brian Connection objects Note that the plane is wrapped to avoid any border effects def get_distance x y THE def TEE def def di abs x y min d numpy minimum dl1 size dl return numpy sqrt numpy sum min_d 2 1 Function returning the probabilities of connections as a functions of distances probas i j x y distance get distance x i y j return epsilon numpy exp distance 2 2 xs latx 2 Function returning linear delays as function of distances delays i j x y distance get_distance x i y j return 0 1 ms distance mm velocity Function assessing if a cell is located in a particular letter of the word BRIAN Return 0 if not and 1 if yes is in brzan ti j X y a b brian letters shape 100 Chapter 3 Getting started Brian Documentation Release 1 4 1 tmp x tmp y y jl l O a astype int y j l1 b ast
380. ion Release 1 4 1 method The integration method currently one of euler rk2 or exp_euler but you can define your own too See make integration step for details language The Language object Creates a Block from the equations and the method gets a set of Symbol objects from get neuron group symbols and defines the symbol neuron indexasaSliceIndex Then calls CodeItem generate to get the Code object Inserts t and dt into the namespace and_num_neurons and_num_gpu_indices incase they are needed symbols class brian experimental codegen2 Symbol name language Base class for all symbols Every symbol has attributes name and language which should be a string and Language object respectively The symbol class should define some or all of the methods below dependencies Returns the set of dependencies of this symbol can be overridden load read write vectorisable Called by resolve can be overridden to perform more complicated loading code By default returns an empty Block multi valued Should return True if this symbol is considered to have multiple values for example if you are iterating over an array like so for int i20 i lt n i double amp x arr i l Here the symbol x is single valued and depends on the symbol i which is multi valued and whose resolu tion required a loop By default returns False unless the class has an attribute multiple values in which case this is
381. ion time time time start time seconds print Simulation running start time time time run l second duration time time start time print Simulation time duration seconds print Me nspikes excitatory spikes print Mi nspikes inhibitory spikes 3 2 Examples 157 Brian Documentation Release 1 4 1 Example adaptive_threshold misc A model with adaptive threshold increases with each spike from brian import x EE eqs dv dt v 10 ms volt dvt dt 10 mV vt 15 ms volt CES reset v 0xmV vtt 3 mV tet IF NeuronGroup 1 model eqs reset reset threshold v vt IF rest PG PoissonGroup 1 500 Hz C Connection PG IF v weight 3 mV Mv StateMonitor IF v record True Mvt StateMonitor IF vt record True run 100 ms plot Mv times ms Mv 0 mV plot Mvt times ms Mvt 0 mV show Example adaptive misc An adaptive neuron model from brian import x PG PoissonGroup 1 500 Hz eqs dv dt w v 10xms volt the membrane equation dw dt w 30xms volt the adaptation current Pre The adaptation variable increases with each spike IF NeuronGroup 1 model eqs threshold 20 mV reset v O mv w 3 mV C Connection PG IF v weight 3 mV MS SpikeMonitor PG True Mv StateMonitor IF v record True Mw StateMonitor IF w record True
382. ire neurons with different delays for each target neuron with the delays forming a quadratic curve centred at neuron 50 The longest delay is 10ms and the network is run for 40ms At the end the delays are plotted above a colour plot of the membrane potential of each of the target neurons as a function of time demonstrating the delays from brian import x Starter neuron threshold is below 0 so it fires immediately reset is below threshold so it fires only once G NeuronGroup 1 model V 1 threshold 1 0 reset 2 0 100 LIF neurons no reset or threshold so they will not spike H NeuronGroup 100 model dV dt V 10xms volt C Connection with delays here the delays are specified as a function of i j giving the delay from neuron i to neuron j In this case there is only one presynaptic neuron so i will be O0 Connection G H weight 5 mV max delay 10 ms delay lambda i j 10 ms j 50 1 2 M StateMonitor H V record True run 40 ms subplot 211 These are the delays from neuron 0 to neuron i in ms plot C delay 0 i ms for i in range 100 ylabel Delay ms title Delays subplot 212 M values is an array of all the recorded values here transposed to make it fit with the plot above imshow M values T aspect auto extent 0 100 40 0 xlabel Neuron number ylabel Time ms title Potential show Example stopping misc Network
383. is is the object defaultclock and it has a default time step of 0 1 ms In a simple script you can override this by writing for example 212 Chapter 4 User manual Brian Documentation Release 1 4 1 defaultclock dt 1 ms You may wish to use multiple clocks in your program In this case for each object which requires one you have to pass a copy of its Clock object The network run function automatically handles objects with different clocks updating them all at the appropriate time according to their time steps value of dt Multiple clocks can be useful for example for defining a simulation that runs with a very small dt but with some computationally expensive operation running at a lower frequency In the following example the model is simulated with dt 0 01 ms and the variable x is recorded every ms simulation_clock Clock dt 0 01 ms record_clock Clock dt 1 ms group NeuronGroup 100 model dx dt x tau volt clock simulation clock M StateMonitor group x record True clock record clock The current time of a clock is stored in the attribute t simulation clock t and the timestep is stored in the attribute dt When using multiple clocks it can be important to specify the order in which they evaluated which you can using the order keyword of the C1ock object e g clock first Clock dt 1 ms order 0 clock second Clock dt 5 ms order 1 Every 5ms these two clocks will coincide and the order
384. it Feedforward connections feedforward Connection layer4 layer23exc ge for i in range barrelarraysize for j in range barrelarraysize feedforward connect_random barrels4 i j barrels23 i j sparseness 5 weight EPSC 5 stdp ExponentialSTDP feedforward taup taud Ap Ad wmax EPSC Excitatory lateral connections recurrent exc Connection layer23exc layer23 ge recurrent exc connect random layer23exc layer23exc weight EPSC 3 sparseness lambda i j 15 exp 5 layer23exc x i layer23exc x j recurrent exc connect random layer23exc layer23inh weight EPSC sparseness lambda i j 15 exp 5 layer23exc x i layer23inh x j Inhibitory lateral connections recurrent inh Connection layer23inh layer23exc gi recurrent inh connect random layer23inh layer23exc w sparseness lambda i j exp Stimulation stimspeed 1 stim change time speed at which the ll direction 0 0 stimzonecentre ones 2 barrelarraysize 2 stimcentre stimnorm zeros 2 zeros 2 stimradius ll stim_change_time stimspeed 1 5 stimradius2 stimradius 2 def new_direction global direction direction rand 2 pi stimnorm cos direction sin direction ight IPSC 5x layer23inh x i layer23exc x j 2 2 C bar of stimulation moves stimcentre stimzonecentre stimnorm stimradius Qnetwork operation def stimulation global dire
385. ite noise is filtered by a bank of butterworth bandpass filters and lowpass filters which are different for every channels The centre or cutoff frequency of the filters are linearly taken between 100kHz and 1000kHz and its bandwidth frequency increases linearly with frequency from brian import x from brian hears import x level 50 dB level of the input sound in rms dB SPL sound whitenoise 100 ms ramp sound sound atlevel level order 2 order of the filters example of a bank of bandpass filter test 4444 nchannels 50 center_frequencies linspace 100 Hz 1000 Hz nchannels bw linspace 50 Hz 300 Hz nchannels bandwidth of the filters arrays of shape 2 x nchannels defining the passband frequencies Hz fc vstack center frequencies bw 2 center_frequencies bw 2 filterbank Butterworth sound nchannels order fc bandpass filterbank mon filterbank process figure subplot 211 imshow flipud filterbank mon T aspect auto 112 Chapter 3 Getting started Brian Documentation Release 1 4 1 example of a bank of lowpass filter Hed t tet nchannels 50 cutoff frequencies linspace 200 Hz 1000 Hz nchannels filterbank Butterworth sound nchannels order cutoff frequencies low filterbank mon filterbank process subplot 212 imshow flipud filterbank mon T aspect auto show Example cochlear models hears
386. ity Network CUBA with short term synaptic plasticity for excitatory synapses Depressing at long timescales facilitat ing at short timescales from brian import from time import time rrt eqs dv dt ge gi v 49 xmV 20xms volt dge dt ge 5 ms volt dgi dt gi 10 ms volt pg P NeuronGroup 4000 model eqs threshold 50 mV reset 60 mV P v 60 x mV rand 4000 10 mV Pe P subgroup 3200 Pi P subgroup 800 Ce Connection Pe P ge weight 1 62 mV sparseness 02 Ci Connection Pi P gi weight 9 mV sparseness 02 stp STP Ce taud 200 ms tauf 20 ms U 2 M SpikeMonitor P rate PopulationRateMonitor P ll ll tl time run l second t2 time print Simulation time t2 t1 s print M nspikes spikes subplot 211 raster plot M subplot 212 plot rate times ms rate smooth rate 5 ms show Example STDP2 plasticity Spike timing dependent plasticity Adapted from Song Miller and Abbott 2000 Song and Abbott 2001 and van Rossum et al 2000 This simulation takes a long time 3 2 Examples 131 Brian Documentation Release 1 4 1 from brian import from time import time 1000 taum 10 ms tau pre 20 ms cau post tau pre Ee 0 mV vt 54 x mV vr 60 mV El 74 mV taue 5 ms gmax 0 01 F 15 x Hz dA_pre 01 dA_post dA_pre tau_pre tau_post
387. ive the algorithm can count several coincidences for a single model spike 8 11 Monitors 295 Brian Documentation Release 1 4 1 onset A scalar value in seconds giving the start of the counting no coincidences are counted before onset Has three attributes coincidences The number of coincidences for each neuron of the NeuronGroup coincidences i is the number of coincidences for neuron 1 model length The number of spikes for each neuron model length i is the spike count for neuron i target_length The number of spikes in the target spike train associated to each neuron class brian StateHistogramMonitor group varname range period 1 0 msecond nbins 20 Records the histogram of a state variable from a NeuronGroup Initialise as StateHistogramMonitor P varname range period 1 ms nbins 20 Where P The group to be recorded from varname The state variable name or number to be recorded range The minimum and maximum values for the state variable A 2 tuple of floats period When to record nbins Number of bins for the histogram The StateHistogramMonitor object has the following properties mean The mean value of the state variable for every neuron in the group var The unbiased estimate of the variances as in mean std The square root of var as in mean hist A 2D array of the histogram values of all the neurons each row is a single neuron s histogram bins A 1D array of the bin centers used
388. k model F Zenke 2011 Adapted from Vogels T P H Sprekeler F Zenke C Clopath and W Gerstner Inhibitory Plasticity Balances Excitation and Inhibition in Sensory Pathways and Memory Networks Science November 10 2011 Se CH SHE CH SHS HSS HS WFESTEISSTSTISSRHSAHSHAHTRHHTRATAHSASTSATTRHTATESHSATR from brian import do STPPPSTSTTRTSATESSSSAEHTSATSSESASTASSTSTEESTAHASS Defining network model parameters do STSPPSTSHASTTEHSTSEASATSSSATTSSETESATESS UESTTSHATE NE 8000 Number of excitatory cells NI NE 4 Number of inhibitory cells w 1l nS Basic weight unit tau ampa 5 0 ms Glutamatergic synaptic time constant tau gaba 10 0 ms GABAergic synaptic time constant epsilon 0 02 Sparseness of synaptic connections eta le 2 Learning rate tau stdp 20 ms STDP time constant simtime 10 second Simulation time tttteteetetaettaea tad tat tad tat tt tat dt tat tat ttt tae A Neuron model d OHTSTSHESTSHESTHTAHHHTHA2TSAHTSEA HTHHESEHA4TTHUHT d d 4 gl 10 0 nsiemens Leak conductance el 60 mV Resting potential er 80 mV Inhibitory reversal potential vt 50 mV Spiking threshold memc 200 0 pfarad Membrane capacitance bgcurrent 200 pA External current eqs neurons 106 Chapter 3 Getting started Brian Documentation Release 1 4 1 dv dt glx v el g ampaxw v g gabax v er xw bgcurrent memc volt dg ampa dt g ampa tau a
389. ke triggered average reverse correlation spikes is an array containing spike times stimulus is an array con taining the stimulus max interval second is the duration of the averaging window dt second is the sampling period onset second before which the spikes are discarded Note it will be at least as long as max interval display default False display the number of spikes processed out of the total number output the spike triggered average and the corresponding time axis 8 15 Input output 8 15 1 General data management class brian tools datamanager DataManager name datapath DataManager is a simple class for managing data produced by multiple runs of a simulation carried out in separate processes or machines Each process is assigned a unique ID and Python Shelf object to write its data to Each shelf is a dictionary whose keys must be strings The DataManager can collate information across multiple shelves using the get key method which returns a dictionary with keys the unique session names and values the value written in that session typically only the values will be of interest If each value is a tuple or list then you can use the get_merged key to get a concatenated list If the data type is more complicated you 300 Chapter 8 Reference Brian Documentation Release 1 4 1 can use the get key method and merge by hand The idea is each process generates files with names that do not interfere with each other so that
390. kes draw spikes for a nicer display Figure subplot 221 Fig 1A top 3 2 Examples 65 Brian Documentation Release 1 4 1 plot M times tmin ms M plotted neuron mV k xlim 0 tmax tmin ms ylabel V mV subplot 223 Fig 1A bottom plot Mg times tmin ms Mg plotted_neuron k xlim 0 tmax tmin ms xlabel Time ms ylabel g gmax subplot 122 Fig 1B times array t neurons duration i second rest time for i t in spikes spikes duration array neurons duration i second for i in spikes spikes plot duration ms times ms k xlabel Duration ms ylabel Latency ms show Example Fig4 duration stdp frompapers computing with neural synchrony duration selectivity Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 4D STDP in the duration model very long simulation default 5000 stimuli Caption Fig 4D Temporal evolution of the synaptic weights of the neuron corresponding to the blue curves in Fig 4C The script runs the simulation with STDP for a long time then displays the evolution of synaptic weights for one neuron from brian import x from pylab import cm from numpy random import seed from brian experimental connectionmonitor import x import numpy from params import Rebound neurons eqs P dv dt El v gmax gK gmax2 gK2 ginh EK v tau volt dgK
391. language array name The name ofthe array we iterate through array len The length of the array int or string by default has value 1en array name index name The name of the index into the array by default has value index array name array slice Apair start end giving a slice of the array if left the whole array will be used Dependencies are collected from those arguments that are used item array name array len array slice multiple values True resolution requires loop Returns True except for Python resolve args kwds Method generated by 1anguage invariant symbol method Languages and methods follow python resolve python c resolve c 382 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 resolve_c read write vectorisable item namespace Returns a C for loop of the form for int index name start index_name lt end index_name t const int name array name index name If defined start end array_slice otherwise start end 0 array len resolve_gpu read write vectorisable item namespace If not vectorisable use resolve c If vectorisable we set the following in the namespace _gpu_vector_index index_name _gpu_vector_slice start end Where start and end are as in resolve_c This marks that we want to vectorise over this index and the GPU code will handle this later Finally we prepend the item with const int name
392. le below the NeuronGroup object is only added to the network if certain conditions hold net Network if some condition x net NeuronGroup What happens when you run For an overview see the Concepts chapter of the main documentation When you run the network the first thing that happens is that it checks if it has been prepared and calls the prepare method if not This just does various housekeeping tasks and optimisations to make the simulation run faster Also an update schedule is built at this point see below Now the update method is repeatedly called until every clock has run for the given length of time After each call of the update method the clock is advanced by one tick and if multiple clocks are being used the next clock is determined this is the clock whose value of t is minimal amongst all the clocks For example if you had two clocks in operation say clock1 with dt 3 ms and clock2 with dt 5 ms then this will happen l update for c1ock1 tick clock1 to t 3 ms next clock is clock2 with t O ms 2 update for clock2 tick clock2 to t 5 ms next clock is clock1 with t 3 ms 3 update for clock1 tick clock1 to t 6 ms next clock is clock2 with t 5 ms 4 update for clock2 tick clock2 to t 10x ms next clock is clock1 with t 6 ms 5 update for clock1 tick clock1 to t 9xms next clock is clock1 with t 9 ms 6 update for clock1 tick clock1 to t 12 ms next
393. lease 1 4 1 eqs MembraneEquation C 200 pF Current I gl El vm gex Ee vm amp eqs alpha_synapse input ge_in tau 10 ms unit siemens output ge where alpha conductances have been inserted in the membrane equation One can directly insert synaptic currents with the functions exp_current alpha_current and biexp_current eqs MembraneEquation C 200 pF Current I gl El vm amp alpha current input ge tau 10 ms the units is amp by default or synaptic conductances with the functions exp_conductance alpha_conductance and biexp_conductance eqs MembraneEquation C 200 pF Current I gl El vm amp N alpha_conductance input ge E 0 mV tau 10 ms where E is the reversal potential 5 1 6 lonic currents A few standard ionic currents have implemented in the module ionic_currents from brian library ionic currents import x When the current name is not specified a unique name is generated automatically Models can be constructed by adding currents to a MembraneEquation e Leak current g1 El vm current leak current gl 10 nS E1 70 mV current_name I Hodgkin Huxley K current current K_current_HH gmax EK current_name IK Hodgkin Huxley Na current current Na current HH gmax ENa current name INa 5 2 Random processes To import the random processes library from brian libra
394. lectrode compensation The L p electrode compensation method is implemented along with a spike detection method and a quality test Rossant et al 2012 brian library electrophysiology Lp_compensate I Vraw dt slice_duration 1 0 second p 1 0 criterion None full False do compensation True initial_params Perform the L p electrode compensation technique on a recorded membrane potential I injected current 1D vector Vraw raw uncompensated voltage trace 1D vector same length as I edt sampling period inverse of the sampling frequency in second eslice_duration 1 second duration of each time slice where the fit is performed independently ep 1 0 parameter of the Lp error p should be less than 2 Experimenting with this parameter is recom mended Use p 1 at first especially with difficult recordings Use p 0 5 with good recordings less noise or with biophysical model simulations without noise criterion a custom error function used in the optimization If None it is the Lp error Otherwise it should be a function of the form lambda raw model error where raw and model are the raw and linear model membrane potential traces For instance the function for the Lp error is lambda raw model sum abs raw model self p It can also be a function of the form lambda raw model electrode error in the case when one needs the electrode response to compute the error efull False if False return a tuple
395. lements a cochleagram based on a gammatone filterbank followed by halfwave rectification cube root compression and 10 Hz low pass filtering from brian import x from brian hears import 3 2 Examples 123 Brian Documentation Release 1 4 1 soundl tone 1l kHz 1 second sound2 whitenoise 1 second sound soundl sound2 sound sound ramp cf erbspace 20 Hz 20 kHz 3000 gammatone Gammatone sound cf cochlea FunctionFilterbank gammatone lambda x clip x 0 Inf 1 0 3 0 lowpass LowPass cochlea 10 Hz output lowpass process imshow output T origin lower left aspect auto vmin 0 show Example sounds hears Example of basic use and manipulation of sounds with Brian hears from brian import x from brian hears import soundl tone 1 kHz 1 second sound2 whitenoise 1 second sound soundl1 sound2 sound sound ramp Comment this line out if you don t have pygame installed sound play The first 20ms of the sound startsound sound 20 ms subplot 121 plot startsound times startsound subplot 122 sound spectrogram show Example log_gammachirp hears Example of the use of the class LogGammachirp available in the library It implements a filterbank of IIR gam machirp filters as Unoki et al 2001 Improvement of an IIR asymmetric compensation gammachirp filter In this example a white noise is filtered by a linea
396. lete tasksize subsequent calls to update will report progress be tween a fraction complete and complete tasksize of the total task complete represents the amount of the total task completed at the beginning of the task and tasksize the size of the subtask as a proportion of the whole task equal subtask tasknum numtasks If a task can be divided into numtasks equally sized subtasks you can use this method instead of subtask where tasknum is the number of the subtask about to start 304 Chapter 8 Reference Brian Documentation Release 1 4 1 Note that in Python 2 6 this can be used as a context manager and it will automatically call the start and finish methods at the beginning and end e g with ProgressReporter period 0 1 as progress for i in xrange 10 time sleep 1 progress update it 1 0 10 8 19 Model fitting toolbox The model fitting toolbox uses the package Playdoh you can see the documentation here brian library modelfitting modelfitting kwds Model fitting function Fits a spiking neuron model to electrophysiological data injected current and spikes See also the section Model fitting in the user manual Arguments model An Equations object containing the equations defining the model reset A reset value for the membrane potential or a string containing the reset equations threshold A threshold value for the membrane potential or a string containing the threshold equations
397. level in levels ihe TanCarney MiddleEar tones cf len levels update_interval 1 syn ZhangSynapse ihc cf s mon StateMonitor syn s record True clock syn clock R mon StateMonitor syn R record True clock syn clock spike mon SpikeMonitor syn net Network syn s mon R mon spike mon net run duration 1 5 for idx level in enumerate levels plt figure 3 plt subplot len levels 1 idx 1 plt plot s mon times ms s mon idx plt xlim 0 120 plt xlabel Time msec plt ylabel Sp sec plt text 1 25 duration ms np nanmax s mon idx 2 ymin ymax plt ylim if idx 0 plt title CF 0f Hz Response to Tone at CF cf s SPL str level dB plt figure 4 3 2 Examples 129 Brian Documentation Release 1 4 1 plt subplot len levels 1 idx 1 plt plot R mon times ms R mon idx plt xlabel Time msec plt xlabel Time msec plt text 1 25 duration ms np nanmax R mon idx 2 s SPL str level dB plt ylim ymin ymax if idx plt title CF 0f Hz Response to Tone at CF with spikes and refractoriness cf plt plot spike mon spiketimes idx ms np ones len spike mon spiketimes idx np nanmax R mon idx rx plt show 3 2 12 plasticity Example STDP1 plasticity Spike timing dependent plasticity Adapted from Song Miller and Abbott 2000 and Song and Abbott 2001 This simulation takes a
398. lib axis labelling for log scaled axes doesn t work well for frequencies We provided two functions log_frequency_xaxis_labels and log_frequency_yaxis_labels to automatically set useful axis labels For example cf erbspace 100 Hz 10 kHz semilogx cf response axis tight log frequency xaxis labels 5 7 5 Online computation Typically in auditory modelling we precompute the entire output of each channel of the filterbank offline compu tation and then work with that This is straightforward but puts a severe limit on the number of channels we can use or the length of time we can work with otherwise the RAM would be quickly exhausted Brian hears allows us to use a very large number of channels in filterbanks but at the cost of only storing the output of the filterbanks for a relatively short period of time online computation This requires a slight change in the way we use the output of the filterbanks but is actually not too difficult For example suppose we wanted to compute the vector of RMS values for each channel of the output of the filterbank Traditionally or if we just use the syntax output fb process 242 Chapter 5 The library Brian Documentation Release 1 4 1 in Brian hears we have an array output of shape nsamples nchannels We could compute the vector of RMS values as rms sqrt mean output 2 axis 0 To do the same thing with online computation we simply store a
399. linspace 0 mV 20 mV 100 dt 10 ms egs euer dv dt I t volt v tau volt EOD group NeuronGroup 1 model eqs reset 0 mV threshold 15 mV Note however that the more efficient exact linear differential equations solver won t be used in this case because I t could be any function so the previous mechanism is often preferable Additionally be aware that the call to I t does return a value without units as units cannot be stored in arrays therefore you have to explicitly multiply it with the respective unit Linked variables Another option is to link the variable of one group to the variables of another group using 1inked var for example 4 8 Inputs 209 Brian Documentation Release 1 4 1 G NeuronGroup H NeuronGroup G V linked var H W In this scenario the variable V in group G will always be updated with the values from variable W in group H The groups G and H must be the same size although subgroups can be used if they are not the same size 4 9 User defined operations In addition to neuron models the user can provide functions that are to be called every timestep during the simulation using the decorator network operation Qnetwork operation def myoperation do something every timestep The operation may be called at regular intervals by defining a clock myclock Clock dt 1x ms Qnetwork operation myclock def myoperation do something every ms
400. long time from brian import from time import time N 1000 taum 10 ms tau pre 20 ms Lau post tau pre Ee 0 mV vt 54 x mV vr 60 mV El 74 mV taue 5 ms F 15 x Hz gmax 01 dA_pre 01 dA post dA_pre tau pre tau post 1 05 eqs neurons dv dt gex Ee vr El v taum volt the synaptic current is linearized dge dt ge taue 1 rrt input PoissonGroup N rates F neurons NeuronGroup l model eqgs neurons threshold vt reset vr synapses Connection input neurons ge weight rand len input len neurons gmax neurons v vr stdp ExponentialSTDP synapses tau_pre tau_post dA_pre dA_post wmax gmax Explicit STDP rule eqs_stdp dA_pre dt A_pre tau_pre 1 dA post dt A post tau post 1 vee dA_post gmax dA pre gmax stdp STDP synapses eqs eqs_stdp pre A_pret t dA_pre wt A_post 130 Chapter 3 Getting started Brian Documentation Release 1 4 1 post A_post dA_post wt A_pre wmax gmax rate PopulationRateMonitor neurons start_time time run 100 second report text print Simulation time time start time subplot 311 plot rate times second rate smooth rate 100 ms subplot 312 plot synapses W todense gmax subplot 313 hist synapses W todense gmax 20 show Example short term plasticity2 plastic
401. ls The number of channels samplerate The sample rate duration The duration of the filterbank If it is not specified by the user it is computed by finding the maxi mum of its source durations If these are not specified a KeyError will be raised for example using OnlineSound as a source To process the output of a filterbank the following method can be used process func None duration None buffersize 32 Returns the output of the filterbank for the given duration func Ifa function is specified it should be a function of one or two arguments that will be called on each filtered buffered segment of shape buffersize nchannels inorder If the function has one argument the argument should be buffered segment If it has two arguments the second argument is the value returned by the previous application of the function or O for the first application In this case the method will return the final value returned by the function See example below duration None The length of time in seconds or number of samples to process If no func is specified the method will return an array of shape duration nchannels with the filtered outputs Note that in many cases this will be too large to fit in memory in which you will want to process the filtered outputs online by providing a function func see example below If no duration is specified the maximum duration of the inputs to the filterbank will be used or an error raised if
402. lt dgi dt gi 10 ms volt rrt P NeuronGroup 4000 model eqs threshold 50 mV reset 60 mV 3 2 Examples 179 Brian Documentation Release 1 4 1 P v 60 x mv 10 mV gt x rand len P Pe P subgroup 3200 Pi P subgroup 800 ll Ce Connection Pe P ge weight 1 62 mV sparseness 0 02 Ci Connection Pi P gi weight 9 mV sparseness 0 02 M SpikeMonitor P run l second 4 while len M i lt 1 i 4 21 print The firing rate of neuron i is firing rate M i Hz print The coefficient of variation neuron i is CV M i raster plot M show Example explF network misc A network of exponential IF models with synaptic conductances from brian import x from brian library IF import x from brian library synapses import import time C 200 pF taum 10 msecond gL C taum EL 70 mV VT 55 mV DeltaT 3 mV Synapse parameters ry m Ee 0 mvolt i 80 mvolt taue 5 msecond taui 10 msecond eqs exp_IF C gL EL VT DeltaT Two different ways of adding synaptic currents eqs Current Ie gex He vm amp dge dt ge taue siemens ET eqs exp conductance gi Ei taui from library synapses P NeuronGroup 4000 model eqs threshold 20 mvolt reset EL Pe P subgroup 3200 Pi P subgroup 800 we 1 5 nS excitatory s
403. lue or an array of values In the former case the value is set for all harmonics and harmonics up to the sampling frequency are generated In the latter each harmonic parameter is set separately and the number of harmonics generated corresponds to the length of the array static vowel args kwds Returns an artifically created spoken vowel sound following the source filter model of speech production with a given pitch 6a 629 The vowel can be specified by either providing vowel as a string a i or u or by setting formants to a sequence of formant frequencies The returned sound is normalized to a maximum amplitude of 1 The implementation is based on the MakeVowel function written by Richard O Duda part of the Auditory Toolbox for Matlab by Malcolm Slaney http cobweb ecn purdue edu malcolm interval 1998 010 Timing and sequencing static sequence sounds samplerate None Returns the sequence of sounds in the list sounds joined together repeat n Repeats the sound n times extended duration Returns the Sound with length extended by the given duration which can be the number of samples or a length of time in seconds shifted duration fractional False filter length22048 Returns the sound delayed by duration which can be the number of samples or a length of time in seconds Normally only integer numbers of samples will be used but if ractional True then the filtering method from http
404. ly get the most recent version of Brian this way On the other hand you do not have to take care of future updates yourself as the Brian package gets updated with the standard update process Additionally the Brian package already includes all the compiled C code mentioned in the Optimisations section Another way to install Brian which combines these advantages with up to date versions is to directly add the NeuroDebian repository to your software sources Brian Documentation Release 1 4 1 2 2 Manual installation Installing Brian requires the following components 1 Python version 2 5 2 7 NumPy and Scipy packages for Python an efficient scientific library PyLab package for Python a plotting library similar to Matlab see the detailed installation instructions SymPy package for Python a library for symbolic mathematics not mandatory yet for Brian nan A U N Brian itself don t forget to download the extras zip file which includes examples tutorials and a complete copy of the documentation Brian is also a Python package and can be installed as explained below Fortunately Python packages are very quick and easy to install so the whole process shouldn t take very long We also recommend using the following for writing programs in Python see details below 1 Eclipse IDE with PyDev 2 Python shell Finally if you want to use the optional automatic C code generation features of Brian you should ha
405. me The state variable name or number to be recorded record What to record The default value is False and the monitor will only record summary statistics for the variable You can choose record integer to record every value of the neuron with that number record list of integers to record every value of each of those neurons or record True to record every value of every neuron although beware that this may use a lot of memory when When the recording should be made in the network update possible values are any of the strings start before groups after groups before connections after connections before resets after resets end in order of when they are run timestep A recording will be made each timestep clock updates so timestep should be an integer clock A clock for the update schedule use this if you have specified a clock other than the default one in your network or to update at a lower frequency than the update cycle Note though that if the clock here is different from the main clock the when parameter will not be taken into account as network updates are done clock by clock Use the timestep parameter if you need recordings to be made at a precise point in the network update step The StateMonitor object has the following properties times The times at which recordings were made mean The mean value of the state variable for every neuron in the group not just the ones specified in the record keywo
406. mentation Release 1 4 1 Example FigiC frompapers computing with neural synchrony coincidence detection and syn chrony Timescale and strength from brian import x rc lines linewidth 2 rc font size 16 rc xtick labelsize 16 rc ytick labelsize 16 rc legend fontsize 16 rc axes labelsize 16 titlesize 16 w h rcParamsDefault figure figsize p r fontsize 16 SNR timescale strength loadtxt reproducibility txt SNR 10 10g SNR log 10 SNR SNR 1 timescale timescale 1 strength strength 1 figure figsize w l 5 hx 5 subplot 121 plot SNR timescale ms k plot SNR timescale ms r plot SNR 0 SNR 7 k xlabel SNR dB ylabel Precision ms subplot 122 plot SNR strength 100 k ylim 0 100 plot SNR strength 100 r xlabel SNR dB ylabel Reliability savefig FigC eps show Example Fig1F ROC frompapers computing with neural synchrony coincidence detection and synchrony Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 1F simulation takes about 10 mins Coincidence detection is seen as a signal detection problem that of detecting a given depolarization in a background of noise within one characteristic time constant The choice of the spike threshold implements a particular trade off between false alarms depolarizatio
407. meters and SpikeGeneratorGroup to generate spikes which fire at prespecified times class brian PoissonGroup N rates 0 0 hertz clockzNone A group that generates independent Poisson spike trains Initialised as PoissonGroup N rates clock with arguments N The number of neurons in the group rates A scalar array or function returning a scalar or array The array should have the same length as the number of neurons in the group The function should take one argument t the current simulation time clock The clock which the group will update with do not specify to use the default clock 270 Chapter 8 Reference Brian Documentation Release 1 4 1 class brian PoissonInput target N None rate None weight None state None jitter None relia bility None copies 1 record False freeze False Adds a Poisson input to a NeuronGroup Allows to efficiently simulate a large number of independent Poisson inputs to a NeuronGroup variable without simulating every synapse individually The synaptic events are generated randomly during the simulation and are not preloaded and stored in memory unless record True is used All the inputs must target the same variable have the same frequency and same synaptic weight You can use as many PoissonInput objects as you want even targetting a same NeuronGroup There is the possibility to consider time jitter in the presynaptic spikes and synaptic unreliability The inputs can also be reco
408. model and Brette Gerstner adaptive exponential integrate and fire model also included in the IF module The equations are obtained in the same way as for one dimensional models 224 Chapter 5 The library Brian Documentation Release 1 4 1 qs Izhikevich a 0 02 ms b 0 2 ms qs Brette_Gerstner C 281 pF gL 30 nS EL 70 6 mV VT 50 4 mV DeltaT 2 mV tauw 144 ms a 4x nS eqs aEIF C 281 pF gL 30 nS EL 70 6 mV VT 50 4xmV DeltaT 2 xmV tauw 144 ms a 4 nS equivalent and two state variables are defined vm membrane potential and w adaptation variable The equivalent equations for Izhikevich model are dvm dt 0 04 ms mV vm 2 5 ms vm 140 mV ms w volt dw dt a x b vm w volt second and for Brette Gerstner model C dvm dt gLx EL vm gL DeltaT exp vm VT DeltaT w volt dw dt a x vm EL w tauw amp To simulate these models one needs to specify a threshold value and a good choice is VI 4 DeltaT The reset is particular in these models since it is bidimensional vm gt Vr and w gt w b A specific reset class has been implemented for this purpose Adapt iveReset initialised with Vr and b Thus a typical construction of a group of such models 1s qs Brette Gerstner C 281 pF gL 30 nS EL 70 6 mV VT 50 4 mV DeltaT 2 mV tauw 144 ms a 4 xnS group NeuronGroup 100 model eqs threshold 43 mV reset AdaptiveReset Vr 70 6 mvolt b 20 0805 nA 5 1 5 Synapses
409. mpa 1 dg gaba dt g gaba tau gaba 1 rrt E THTSTESSTHRSSHEATRHHATTSHTSEHSHTRSOHTSAHRHHAHEHHHRHU TS Initialize neuron group dOSESTESERESASSHSATHATTE HATEAHAREEHTASTSTATEHTTTE Y neurons NeuronGroup NE NI model eqs neurons threshold vt reset el refractory 5 ms Pe neurons subgroup NE Pi neurons subgroup NI E THTSESHSHSHTRHATAHATSHHEEHSA AHTRTSTAUHTRHSHTTUHTAHTS Connecting the network d OTHTST HESTHTESTHTERHHRHHTHETATAHTRTRHTHHAHTRTTHTHUHTAHTHS con e Connection Pe neurons g ampa weight 0 3 sparseness epsilon con ie Connection Pi Pe g gaba weight 1e 10 sparseness epsilon con ii Connection Pi Pi g gaba weight 3 sparseness epsilon g OSTHTESAHTEESAHTHEAAHSHATTEHAHHATHSTEHAESESHTATEHTEHT T Y Setting up monitors oSEHETEHAHSASAHUHEHA HHHARHTHAHSEHHTSASESTHAEPSTEHTHE sm SpikeMonitor Pe d OTHTSS HESTHTESTHDHUTHTHTRHRHHEHTRTRHTHEHHRHHRHTRHUHRHATS Run without plasticity E eHe eee Hee HH HEHE PE aE Ea Ea ER EA a EE REE run 1 second doRTRSEHRTSTTRRAHRA HUHEHATRETASTSATSATEHS HTSHTSTTSHAHYT Inhibitory Plasticity dToSTSEEHREH ATRSSTHATRSSATATASTARASASASHTETSHATSTSHAT Y alpha 3 Hz tau_stdp 2 Target rate parameter gmax 100 Maximum inhibitory weight eqs stdp inhib dA pre dt A pre tau stdp 1 dA post dt A post tau stdp 1 ret stdp ie STDP con ie eqs eqs_stdp_inhib pre A_pre 1 w A_post alpha eta post A post t 1 w t A_prex
410. n 5 xsecond report text discard the first spikes wait for convergence S SpikeMonitor neurons run 5 second report text i t zip S spikes plot t tau tau i xlabel Spike phase ylabel Parameter a yticks 0 N 2 N 2 3 4 show Example Rossant et al 2011 frompapers Coincidence detection example Fig 4 from Rossant C Leijon S Magnusson AK Brette R 2011 Sensitivity of noisy neurons to coincident inputs Journal of Neuroscience 31 47 Two distant or coincident spikes are injected into a noisy balanced leaky integrate and fire neuron The PSTH of the neuron in response to these inputs is calculated along with the extra number of spikes in the two cases This number is higher for the coincident spikes showing the sensitivity of a noisy neuron to coincident inputs from brian import x import matplotlib patches as patches import matplotlib path as path def histo bins cc ax get the corners of the rectangles for the histogram left array bins 1 right array bins 1 bottom zeros len left 54 Chapter 3 Getting started Brian Documentation Release 1 4 1 ne thet vmea taum taue taun sigm top bottom cc we need a numrects x numsides x 2 numpy array for the path helper function to build a compound path XY array left left right right bottom top top bottom T get the Path object barpath path Path make_compound_
411. n eqs eqs_stdp pre A_pre dA_pre w A_post post A_post dA_post wt A_pre wmax gmax The STDP object acts on the Connection object myconnect ion Equations of the synaptic variables are given in a string argument eqs as for defining neuron models When a presynaptic postsynaptic spike is received the code pre post is executed where the special identifier w stands for the synaptic weight from the specified connection matrix Optionally an upper limit can be specified for the synaptic weights wmax The example above defines an exponential STDP rule with hard bounds and all to all pair interactions 4 4 1 Current limitations The differential equations must be linear Presynaptic and postsynaptic variables must not interact that is a variable cannot be modified by both presy naptic and postsynaptic spikes However synaptic weight modifications can depend on all variables STDP currently works only with homogeneous delays not heterogeneous ones Exponential STDP In many applications the STDP function is piecewise exponential In that case one can use the Exponent ialSTDP class stdp ExponentialSTDP synapses taup taum Ap Am wmax gmax interactions all update additive Here the synaptic weight modification function is f s Ap exp s taup if s gt 0 Amxexp s taum if s 0 where s is the time of the postsynaptic spike minus the time of the presynaptic spike The modification is generally
412. n DocumentWriter Base class for documenting a network Already takes care of assigning labels to objects if none are given document connections connections Document the connections of the network including SpikeMonitor etc as they are modeled as Connection objects 10 4 Realtime Connection Monitor 341 Brian Documentation Release 1 4 1 document_group group Document a single NeuronGroup group Will normally be called for every group by document_groups document groups groups Document all NeuronGroup groups Should normally call document group for every group document network net None labelszNone sim True groups True connections True opera tions True graph connections False Documents the network net if not network is given a MagicNetwork is automatically created and documented i e if you are running scripts without any explicit network you use run instead of net run you can simply call writerdocument_network document operation operation Document a single NetworkOperation operation Should normally be called by document operations for every operation document_operations operations Document all Net workOperation operations including StateMonitor etc as they are modeled as NetworkOperation objects Should normally call document operation for every operation document_sim network Document some general properties of the network e g the timestep used in the simula
413. n G2 C matrix i j depression factor What s going on here First of all C W refers to the Connect ionMat rix object which is a 2D NumPy array with some extra stuff we don t need the extra stuff so we convert it to a straight NumPy array asarray C W We also store a copy of this as the variable C mat rix so we don t need to do this every time step The other thing we do is to use the operator instead of the x operator The most important step of all though is to vectorise the entire operation You don t need to loop over i and j at all you can manipulate the array object with a single NumPy expression C Connection Gl G2 V structure dense C matrix asarray C W QGnetwork operation when end def depress_C C_matrix depression_factor This final version will probably be hundreds if not thousands of times faster than the original It s usually possible to work out a way using NumPy expressions only to do whatever you want in a vectorised way but in some very rare instances it might be necessary to have a loop In this case if this loop is slowing your code down you might want to try writing that loop in inline C using the SciPy Weave package See the documentation at that link for more details but as an example we could rewrite the code above using inline C as follows from scipy import weave C Connection Gl G2 V structure dense C_matrix asarray C W Qnetwork operation when
414. n brian 296 Statement class in brian experimental codegen2 377 statements from codestring in module brian experimental codegen2 378 StateMonitor example usage 35 41 43 45 50 56 57 65 72 79 82 84 91 93 95 97 102 125 128 132 135 139 142 143 147 150 153 155 159 162 164 167 170 171 173 174 177 179 181 182 185 187 StateMonitor class in brian 291 StateSpikeMonitor example usage 26 StateSpikeMonitor class in brian 291 STDP example usage 31 66 77 98 106 130 STDP class in brian 279 stereo sound 240 still running brian Clock method 262 stochastic differential equations 217 stop example usage 159 stop brian RemoteControlClient method 303 stop in module brian 289 STP example usage 131 132 STP class in brian 281 StringReset class in brian 266 StringThreshold class in brian 268 strip empty lines in brian experimental codegen2 372 subdependencies brian experimental codegen2 CodeItem attribute 369 subgroup brian NeuronGroup method 265 subresolved brian experimental codegen2 Codeltem at tribute 369 subset brian hears HRTFSet method 329 subtask brian ProgressReporter method 304 SumFilterbank class in brian hears 319 supported brian experimental codegen2 RuntimeSymbol method 380 supported brian experimental codegen2 Symbol method 380 supported languages brian experimental codegen2 ArrayIndex attribute 383 supp
415. n was due to noise and misses depolarization was not detected Caption Fig 1F Receiver operation characteristic ROC for one level of noise obtained by varying the threshold black curve The hit rate is the probability that the neuron fires within one integration time constant t when depo larized by Dv and the false alarm rate is the firing probability without depolarization The corresponding theoretical curve with sensitivity index d Dv sigma is shown in red from brian import x from scipy special import erf 3 2 Examples 63 Brian Documentation Release 1 4 1 def spike_probability x firing probability for unit variance and zero mean and threshold x return 5 l erf x sqrt 2 coincidence detector process with the same time constant as the membrane t regular intervales T is the spacing to calculate the false alarm rate has a different threshold between 0 and 3 tau_cd 5 ms membrane time constant cd for tau_n tau_cd input is an Ornstein Uhlenbeck T 3 tau n neurons are depolarized by wa Nspikes 10000 number of input spikes TO T Nspikes initial period without inputs N 500 number of neurons each neuron w 1 synaptic weight depolarization sigma 1 input noise s d sigmav sigma sqrt tau_n tau_n tau_cd noise print d 1 sigmav discriminability index Integrate and fire neurons eqs OF dv dt sigmaxn v tau_cd 1 dn dt n tau_n 2 tau_n 5 xi
416. napses Delayed STDP from brian import x import time N 1 taum 10 ms taupre 20 ms taupost taupre Ee 0 mV vt 54 x mV vr 74 x mV El 74 mV taue 5 ms F 20 x Hz dApre 1 dApost dApre taupre taupost 2 eqs neurons dv dt ge Ee vr El v taum volt the synaptic current is linearized dge dt ge taue 1 pad input PoissonGroup N rates F neurons NeuronGroup l model eqgs neurons threshold vt reset vr S Synapses input neurons model w l1 dApre dt Apre taupre 1 event driven dApost dt Apost taupost 1 event driven pre get w 3 2 Examples 135 Brian Documentation Release 1 4 1 w clip wtApost 0 inf Apret dApre post Apost dApost w clip wtApre 0 inf neurons v vr S True S w 10 S delay 1 0 0 3 ms delayed trace try 0 ms to see the difference M StateMonitor S w record 0 Mpre StateMonitor S Apre record 0 Mpost StateMonitor S Apost record 0 Mv StateMonitor neurons v record 0 run 10xsecond report text subplot 211 plot M times ms M 0 plot M times ms Mpre 0 r plot M times ms Mpost 0 k subplot 212 plot Mv times ms Mv 0 show Example probabilistic_synapses2 synapses Probabilistic synapses Katz model from brian import x from numpy random import binomial Nin 1000 Nout 25 input PoissonG
417. nd Reinitialises the clock time to zero or to your specified time Attributes t dt Current time and time step with units Advanced Attributes 8 3 Clocks 261 Brian Documentation Release 1 4 1 end The time at which the current simulation will end set by the Network run method Methods tick Advances the clock by one time step set_t t set_dt dt set_end end Set the various parameters get_duration The time until the current simulation ends set_duration duration Set the time until the current simulation ends still running Returns a boo1 to indicate whether the current simulation is still running For reasons of efficiency we recommend using the methods tick set duration and still running which bypass unit checking internally class brian EventClock args kwds Clock that is used for events Works the same as a Clock except that it is never guessed as a clock to use by NeuronGroup etc These clocks can be used to make multiple clock simulations without causing ambiguous clock problems class brian FloatClock args kwds Similar to a Clock except that it uses a float value of t rather than an integer based underlying value This means that over time the values of t can drift slightly off the grid and sometimes t dt will be slightly less than an integer value sometimes slightly more This can cause problems in cases where the computa tion int t dt is
418. nd a timestamp This function returns two arrays an array of addresses neuron indices and an array of spike times in second Note For index files that point to multiple ae dat files typically aeidx files it will return a list containing tuples addr time as for single files Usage ids times load_aer path to file aedat Keyword Arguments reinit time If True sets the first spike time to zero and all others relative to that one check_sorted If True checks if timestamps are sorted and sorts them if necessary Example use To use the spikes recorded in the AER file filename in a Brian NeuronGroup one should do addr timestamp load AER filename reinit time True G AERSpikeGeneratorGroup addr timestamps An example script can be found in examples misc spikes io py 8 15 3 Other external datatypes brian read neuron dat name Reads a Neuron vector file dat Returns vector of times vector s of values brian read atf name Reads an Axon ATF file atf Returns vector of times vector of values 8 16 Task farming 8 17 Remote control class brian RemoteControlServer server None authkey brian clockzNone global ns None lo cal ns None level 0 Allows remote control via IP of a running Brian script Initialisation arguments server The IP server details a pair host port If you want to allow control only on the one machine for example by an IPython shell leave
419. nd set up a monitor to record those spikes to the disk Maer AERSpikeMonitor g dummy aedat Now we can run run 100 ms This line executed automatically when the script ends but here we need to close the file because we re use it from within the same script Maer close clear all True reinit_default_clock Hee eee RH HHH HAHAH EEE LOADING HHH Hees sts aa sd tH test Now we can re load the spikes addr timestamps load aer dummy aedat Feed them to a SpikeGeneratorGroup group SpikeGeneratorGroup N addr timestamps The group can now be used as any other here we choose to monitor the spikes newM SpikeMonitor group record True run 100 ms And plot the result raster_plot newM show 168 Chapter 3 Getting started Brian Documentation Release 1 4 1 Example poisson misc This example demonstrates the PoissonGroup object Here we have used a custom function to generate different rates at different times This example also demonstrates a custom SpikeMonitor import brian_no_units uncomment to run faster from brian import x Rates rl arange 101 201 0 1 Hz r2 arange 1 101 0 1 Hz def myrates t if t lt 10 second return r1 else return r2 More compact myrates lambda t t l0 xsecond and rl or r2 Neuron group P PoissonGroup 100 myrates Calculation of rates ns zeros len P def ratemonitor spikes n
420. nd some user specified data spike trains target spikes This number is defined as the number of target spikes such that there is at least one model spike within delta where delta is the half width of the time window Initialised as cc CoincidenceCounter source data delta 4 ms with the following arguments source NeuronGroup object which neurons are being monitored data The list of spike times Several spike trains can be passed in the following way Define a single 1D array data which contains all the target spike times one after the other Now de fine an array spiketimes offset of integers so that neuron i should be linked to target train data spiketimes offset i data spiketimes_offset i 1 etc It is essential that each spike train with the spiketimes array should begin with a spike at a large neg ative time e g 1 second and end with a spike that is a long time after the duration of the run e g duration 1 second delta 4xms The half width of the time window for the coincidence counting algorithm spiketimes offset A 1D array spiketimes offset i is the index of the first spike of the target train associated to neuron i spikedelays A 1D array with spike delays for each neuron All spikes from the target train associated to neuron i are shifted by spikedelays i coincidence count algorithm If set to exclusive the algorithm cannot count more than one co incidence for each model spike If set to inclus
421. nd synaptic interactions It can replace the Connection class but is much more flexible in particular it allows to directly incorporate descriptions of synaptic plasticity See section Synapses in the user manual for instructions how to use the class class brian Synapses source target None model None pre None post None max_delay 0 0 second level 0 clock None code_namespace None unit_checking True method None freeze False implicit False orderz 1 Set of synapses between two neuron groups Initialised with arguments source The source NeuronGroup target None The target NeuronGroup By default target source model None The equations that defined the synaptic variables as an Equations object or a string The syntax is the same as fora NeuronGroup pre None The code executed when presynaptic spikes arrive at the synapses There can be multiple presy naptic codes passed as a list or tuple of strings post None The code executed when postsynaptic spikes arrive at the synapses max_delay 0 ms The maximum pre and postsynaptic delay This is only useful if the delays can change during the simulation level 0 See Equations for details clock None The clock for updating synaptic state variables according to model Currently this must be identical to both the source and target clocks compile False Whether or not to attempt to compile the differential equation solvers into Python code Typically for best performance b
422. nd tauc is the correlation time constant Note that distortions are introduced with strong correlations and short correlation time constants For short time constants the mixture method is more appropriate see the paper above The two classes HomogeneousCorrelatedSpikeTrains and CorrelatedSpikeTrains define neuron groups which can be directly used with Connect ion objects Mixture method The mixture method to generate correlated spike trains is only partially implemented and the interface may change in future releases Currently one can use the function mixture process to generate spike trains Spiketrains mixture process nu P tauc t where nu is the vector of rates of the source spike trains P is the mixture matrix entries between 0 and 1 t auc is the correlation time constant t is the duration It returns a list of neuron numberspike time which can be passed to SpikeGeneratorGroup This method is appropriate for short time constants and is explained in the paper mentioned above 4 8 3 Input spike trains A set of spike trains can be explicitly defined as list of pairs i t meaning neuron i fires at time t which used to initialise a SpikeGeneratorGroup spiketimes 0 l ms 1 2 ms input SpikeGeneratorGroup 5 spiketimes The neuron 0 fires at time 1 ms and neuron 1 fires at time 2 ms there are 5 neurons but 3 of them never spike One may also pass a generator instead of a list in that case the pairs should b
423. nding brian 251 338 control simulation 213 control path filtering 241 ControlBlock class in brian experimental codegen2 367 ControlFilterbank example usage 108 118 120 ControlFilterbank class in brian hears 319 convert to brian experimental codegen2 CodelItem method 369 convert to brian experimental codegen2 CodeStatement method 377 convert to brian experimental codegen2 ControlBlock method 367 convert to brian experimental codegen2 Expression method 371 convert to brian experimental codegen2 MathematicalStatement method 378 copy to device brian experimental codegen2 GPUManager method 373 copy to device brian experimental codegen2 GPUSymbolMemoryMana method 374 copy to host brian experimental codegen2 GPUManager method 373 copy to host brian experimental codegen2 GPUSymbolMemoryManage method 374 correlogram example usage 60 correlogram in module brian 299 cos example usage 40 108 118 Current example usage 155 167 177 180 CustomRefractoriness class in brian 267 CV 390 Index Brian Documentation Release 1 4 1 example usage 179 CVQ in module brian 299 D dat file Neuron 302 database HRTF 244 DataManager class in brian tools datamanager 300 dB 316 sound 240 dB_error class in brian hears 316 dB_type class in brian hears 316 DCGC class in brian hears 326 decascade brian hears LinearFilterbank method
424. ndows otherwise the machine crashes phase zeros M 200 trials print This will take approximately 2 minutes pool multiprocessing Pool uses all available processors b results pool map trial range trials for i in range trials phase i results i PLOTTING for b in range 0 M m mean phase b axis 1 st std phase b axis 1 sqrt trials errorbar range 0 135 m range 0 135 yerr st range 0 135 xerr None fmt ecolor None elinewidth None capsize 3 barsabove False lolims False uplims False xlolims False xuplims False title STDP Oscillations Simulation xlabel Spike Number ylabel Spike Phase deg xlim 0 135 ylim 140 280 show 3 2 Examples 53 Brian Documentation Release 1 4 1 Example Brette_2004 frompapers Phase locking in leaky integrate and fire model Fig 2A from Brette R 2004 Dynamics of one dimensional spiking neuron models J Math Biol 48 1 38 56 This shows the phase locking structure of a LIF driven by a sinusoidal current When the current crosses the threshold a lt 3 the model almost always phase locks in a measure theoretical sense from brian import x defaultclock dt 0 0l4ms for a more precise picture N 2000 tau 100 ms freq 1 tau eqs EF dv dt vtat 2x sin 2 pixt tau tau 1 a t pg neurons NeuronGroup N eqs threshold 1 reset 0 neurons a linspace 2 4 N ru
425. nf max times times Inf Color of each neuron between 0 and 1 color times tmin tmax le 10 tmin to avoid zero division Assign groups each responding neuron gets a group number group size delta t tmax tmin size of a group as a proportion of the timing range group number array color group size dtype int group number color Inf 1 Get the size of each group count zeros max group number 1 number of neurons in each group for i in range len group number if group number i 1 count group number i 1 selected group group number selected neuron Display the synchrony partition Fig 2A axes frameon False axis scaled xticks yticks i 0 for y in linspace 0 1 Nx for x in linspace 0 1 Nx if color i Inf if group number i selected group w 4 ec k edge color else w 1 ec k cir Circle x y radius fc cm jet color i linewidth w ec ec else cir Circle x y radius fc w it 1 gca add patch cir xlim 0 2 radius 1 2 radius ylim 0 2 radius 1 2 radius Remove groups with fewer than two neurons and recalculate group numbers for i in range len group_number if group_number i gt 0 if count group_number i gt 2 3 2 Examples 71 Brian Documentation Release 1 4 1 group number i sum count group number i 2 else group number i 1 Save assignment to groups f open groups str int duration ms txt
426. ng in module brian experimental codegen2 brian experimental codegen2 383 372 get_read_or_write_dependencies in module initialise memory brian experimental codegen2 GPUManager brian experimental codegen2 371 method 373 get_samplerate input example usage 128 poisson 270 get_spikes in module brian library modelfitting 307 pulse packet 271 get_trace_quality in module insert spikes brian StateMonitor method 292 brian library electrophysiology 311 integration go brian RemoteControlClient method 303 linear 270 GPUCode class in brian experimental codegen2 374 methods 269 GPUKernel class in brian experimental codegen2 372 interface GPULanguage class in brian experimental codegen2 buffering 243 975 Interleave class in brian hears 318 GPUManager class in brian experimental codegen2 intro brian experimental model documentation DocumentWriter 373 method 342 GPUNeuronGroup class in brian experimental cuda IRCAM 339 HRTF 244 GPUSymbolMemoryManager class in IRCAM LISTEN brian experimental codegen2 374 example usage 49 83 109 120 graph connections brian experimental model documentagig Aweunient Bi era ss in brian hears 330 method 342 irno in module brian hears 315 group irns in module brian hears 315 neuron 263 is dimensionless in module brian 259 poisson 270 ISIHistogramMonitor class in brian 294 H J harmoniccomplex brian hears Sound static method Join cla
427. ng started CHAPTER FOUR USER MANUAL The SciPy NumPy and PyLab packages are documented on the following web sites http www scipy org Getting Started http www scipy org Documentation http docs scipy org http matplotlib sourceforge net Brian itself is documented in the following sections 4 1 Units 4 1 1 Basics Brian has a system for physical quantities with units built in and most of the library functions require that variables have the right units This restriction is useful in catching hard to find errors based on using incorrect units and ensures that simulated models are physically meaningful For example running the following code causes an error gt gt gt from brian import gt gt gt c Clock t 0 Traceback most recent call last File lt pyshell 1 gt line 1 in lt module gt c Clock t 0 File C Documents and Settings goodman Mes documents Programming Python simulator Brian units py raise DimensionMismatchError Function f name variable k should have dimensi DimensionMismatchError Function init variable t should have dimensions of s dimensions were 1 You can see that Brian raises a DimensionMismatchError exception because the Clock object expects t to have units of time The correct thing to write is gt gt gt from brian import gt gt gt c Clock t 0 second Similarly attempting to do numerical operations with inconsistent
428. nitor input M StateMonitor input rate record 0 run 1000 ms subplot 211 raster plot S subplot 212 3 2 Examples 163 Brian Documentation Release 1 4 1 plot S2 times ms S2 smooth rate 5 ms plot M times ms M 0 Hz show Example after potential misc A model with depolarizing after potential from brian import x v0 20 5 mV eqs rrt dv dt v0 v 30xms volt the membrane equation dAP dt AP 3 ms volt the after potential vm vt tAP volt 4 total membrane potential CE IF NeuronGroup 1 model eqs threshold vm gt 20 mvV reset v 0xmV AP 10xmV Mv StateMonitor IF vm record True ll run 500 ms plot Mv times ms Mv 0 mV show Example ring misc A ring of integrate and fire neurons from brian import tau 10 ms v0 11 mV N 20 w 1 mV ring NeuronGroup N model dv dt v0 v tau volt threshold 10 mV reset 0 mV W Connection ring ring v for i in range N W i i 1 N w ring v rand N 10 mV S SpikeMonitor ring run 300 ms raster plot S show Example heterogeneous delays misc Script demonstrating use of a Connect ion with homogenenous delays 164 Chapter 3 Getting started Brian Documentation Release 1 4 1 The network consists of a starter neuron which fires a single spike at time t 0 connected to 100 leaky integrate and f
429. nly be used when insertion and removal of synapses is crucial Memory requirements are 24 bytes per nonzero entry However note that more memory than this may be required because memory is allocated using a dynamic array which grows by doubling its size when it runs out If you know the maximum number of nonzero entries you will have in advance specify the nnzmax keyword to set the initial size of the array Low level methods connect from sparse W delay None column access True Bypasses the usual Brian mechanisms for constructing and compressing matrices and allows you to directly set the weight and optionally delay matrices from scipy sparse matrix objects This can be more memory efficient because the default sparse matrix used for construction is Scipy sparse lil matrix which is very memory inefficient Arguments W The weight matrix delay Optional delay matrix if you are using heterogeneous delays column access True Setto False to save memory if you are not using STDP Warning This is a low level method that bypasses the usual checks on the data In particular make sure that if you pass a weight and delay matrix that they have the same structure 8 7 Connections 275 Brian Documentation Release 1 4 1 Advanced information The following methods are also defined and used internally if you are writing your own derived connection class you need to understand what these do propagate spikes Action to take when
430. ns a triple code vars params code The C C code to perform the update step string vars A list of variable names params A list of per neuron parameter names reset class brian experimental codegen2 CodeGenReset group inputcode language level 0 376 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 resolution brian experimental codegen2 resolve item symbols namespace None Resolves symbols in item in the optimal order The first stage of this algorithm is to construct a dependency graph on the symbols The optimal order is resolve loops as late as possible We actually construct the inverse of the resolution order which is the intuitive order i e if the first thing we do is loop over a variable then that variable is the last symbol we resolve We start by finding the set of symbols which have no dependencies The graph is acyclic so this always possible Then among those candidates if possible we choose loopless symbols first this corresponds to executing loops as late as possible With this symbol removed from the graph we repeat until all symbols are placed in order We then resolve in reverse order because we start with the inner loop and add code outwards At the begin ning of this stage vectorisable is set to True But after we encounter the first multi valued symbol we set vectorisable to False we can only vectorise one loop and it has to be the innermost one This vectori
431. nse array x T minimum buffer size None If specified gives a minimum size to the buffer By default for the FFT convolution based implementation of FIRFilterbank the minimum buffer size will be 3 ir length For maximum efficiency with FFTs buffer size cir length should be a power of 2 otherwise there will be some zero padding and bu fer size should be as large as possible class brian hears RestructureFilterbank source numrepeat l type serial numtile 1 in dexmapping None Filterbank used to restructure channels including repeating and interleaving Standard forms of usage Repeat mono source N times RestructureFilterbank source N For a stereo source N copies of the left channel followed by N copies of the right channel RestructureFilterbank source N For a stereo source N copies of the channels tiled as LRLRLR LR 8 21 Brian hears 317 Brian Documentation Release 1 4 1 RestructureFilterbank source numtile N For two stereo sources AB and CD join them together in serial to form the output channels in order ABCD RestructureFilterbank AB CD For two stereo sources AB and CD join them together interleaved to form the output channels in order ACBD RestructureFilterbank AB CD type interleave These arguments can also be combined together for example to AB and CD into output channels AABBCCD DAABBCCDDAABBCCDD RestructureFilterbank AB CD 2 serial 3
432. nt noisy extra in mo 25 1 pA Mean background input current so 92 xpA Std dev of the noisy background input current Each model neuron is described as a leaky integrate and fire with adaptation and current driven sy 102 Chapter 3 Getting started Brian Documentation Release 1 4 1 nun eqs dv dt v tau a C x Ie C m0 sO xi temp C mV dx dt x taua 4 dIe dt Ie tau pA mmm Custom refractory mechanisms are employed here to allow the membrane potential to be clamped to ti def myresetfunc P spikes P v spikes H reset voltage P x spikes 1 low pass filter of spikes adaptation mechanism SCR SimpleCustomRefractoriness myresetfunc tauarp state v The population of identical N model neuon is defined now P NeuronGroup N model eqs threshold theta reset SCR The interneuronal connectivity is defined now Ce Connection P P Ie weight J sparseness Cee delay delta Initialization of the state variables for each model neuron P v rand len P x 20 mV membrane potential P x rand len P gt 2 flow pass filter of spikes P Ie 0 pA excitatory synaptic input Definition of tools for plotting and visualization of single neuron and population quantities R PopulationRateMonitor P M SpikeMonitor P trace StateMonitor P v record 0 tracex StateMonitor P x record 0 print Simulation running long la
433. nt of static variables Checking free variables Finally the list of undefined identifiers is checked free variables and a warning is issued if any is found 11 4 4 Freezing Freezing is done by calling compile functions freeze True Each string expression is then frozen with opti miser freeze which replaces identifiers by their float value This step does not necessarily succeed in which case a warning not an error is issued 11 4 Equations 357 Brian Documentation Release 1 4 1 11 4 5 Adding Equation objects Adding equations consists simply in merging the lists dictionaries of variables namespaces strings units and func tions Conflicts raise an error This step must precede preparation of the object 11 5 Code generation Warning This section is a work in progress documenting the most recent code generation framework which is in the package brian experimental codegen2 11 5 1 Overview To generate code we start with a basic statement or set of statements we want to evaluate for all neurons or for all synapses and then apply various transformations to generate code that will do this We start from a structured language invariant representation of the set of basic statements We then resolve the unknown symbols in it This is done recursively the resolution of each symbol can add vectorised statements or loops to the current representation and add data to a namespace that will be associated to th
434. nvariant symbol method Languages and methods follow 380 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 python load_python gpu load c e load o load c read write vectorisable Uses CDefineFromArray load python read write vectorisable If read is false does nothing Otherwise returns a CodeStatement of the form name array name index supported languages python c gpu update_namespace read write vectorisable namespace Adds pair array_name arr to namespace write args kwds Method generated by 1anguage invariant symbol method Languages and methods follow python write python gpu write c c write c write c write python Returns array name index class brian experimental codegen2 NeuronGroupStateVariableSymbol group varname name language index None Symbol for a state variable Wraps ArraySymbol Arguments name language Symbol name and language group The NeuronGroup varname The state variable name in the group index An index name or use default of ArraySymbol class brian experimental codegen2 SliceIndex name start end language allz False Multi valued symbol that ranges over a slice Schematically name slice start end name language Symbol name and language start The initial value can be an integer or string end The final value not included can be an integer or string all S
435. o multiple files there are some small issues you need to be aware of These issues essentially revolve around the use of the magic functions run etc The way these functions work is to look for objects of the required type that have been instantiated created in the same execution frame as the run function In a small script that is normally just any objects that have been defined in that script However if you define objects in a different module or in a function then the magic functions won t be able to find them There are three main approaches then to splitting code over multiple files or functions 6 3 1 Use the Network object explicitly The magic run function works by creating a Network object automatically and then running that network Instead of doing this automatically you can create your own Network object Rather than writing something like groupl group2 Es C Connection groupl group2 run 1 second You do this groupl group2 C Connection groupl group2 net Network groupl group2 C net run 1 second In other words you explicitly say which objects are in your network Note that any NeuronGroup Connection Monitor or function decorated with network operation should be included in the Network See the documentation for Network for more details This is the preferred solution for almost all cases You may want to use either of the following two solutions if you think your
436. od The length of time to hold at the reset value class brian FunReset resetfun A reset with a user defined function Initialised as FunReset resetfun with argument resetfun A function f G spikes where Gis the NeuronGroup and spikes is an array of the indexes of the neurons to be reset class brian NoReset Absence of reset mechanism Initialised as 8 4 Neuron models and groups 267 Brian Documentation Release 1 4 1 NoReset 8 4 4 Thresholds A threshold mechanism checks which neurons have fired a spike class brian Threshold threshold 1 0 mvolt state 0 All neurons with a specified state variable above a fixed value fire a spike Initialised as Threshold threshold 1 mV state 0 with arguments threshold The value above which a neuron will fire state The state variable which is checked Compilation Note that if the global variable useweave is set to True then this function will use a C accelerated version which runs approximately 3x faster class brian StringThreshold expr level 0 A threshold specified by a string expression Initialised with arguments expr The expression used to test whether a neuron has fired a spike Should be a single statement that returns a value For example V gt 50 mV or V Vt level How many levels up in the calling sequence to look for names in the namespace Usually 0 for user code class brian VariableThreshold threshold_st
437. odor B Il I2 intensity intensity c2 old c2 run 2 second t O times ms Figure 9B subplot 311 odor fluctuations plot t t lt 2000 0 0 t lt 2000 b plot t t gt 2000 amp t lt 4000 O 1 t gt 2000 amp t 4000 r plot t t gt 4000 amp t lt 6000 2 O 1 t gt 4000 amp t 6000 r plot t t gt 6000 amp t lt 8000 O 0 t gt 6000 amp t lt 8000 b plot t t gt 6000 amp t lt 8000 O 1 t gt 6000 amp t lt 8000 k plot t t gt 8000 amp t lt 10000 O 1 t gt 8000 amp t lt 10000 r plot t t gt 8000 amp t lt 10000 O 0 t gt 8000 amp t lt 10000 b xlim 0 10000 xticks subplot 312 raster_plot S xlim 0 10000 ylim 2500 2600 100 random neurons xticks subplot 313 raster plot S2 ylim 100 300 xlim 0 10000 show Example params frompapers computing with neural synchrony olfaction Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Parameters for the olfactory model with STDP from brian import x N 5000 Coincidence detectors sigma 15 taud 8 ms Connections Nsynapses 50 w0 150 0 02 N STDP factor 0 05 3 2 Examples 81 Brian Documentation Release 1 4 1 a_pre 0 06 factor b post 1l factor tau pre 3 ms Intrinsic plasticity non specific weight increase IP_period 10 ms IP ra
438. of the impulse response b can either be a scalar and will be the same for every channel or an array with the same length as f c 1 The glide slope or sweep rate given in Hz second The trajectory of the instantaneous frequency towards f is an upchirp when c 0 and a downchirp when c gt 0 c can either be a scalar and will be the same for every channel or an array with the same length as f ncascades 4 Number of times the asymmetric compensation filter is put in cascade The default value comes from Unoki et al 2001 322 Chapter 8 Reference Brian Documentation Release 1 4 1 class brian hears LinearGammachirp source f time_constant c phase 0 Bank of gammachirp filters with linear frequency sweeps and gamma envelope as described in Wagner et al 2009 Auditory responses in the barn owl s nucleus laminaris to clicks impulse response and signal analysis of neurophonic potential J Neurophysiol The impulse response IR is defined as follow IR t t e cos 2 ft c 2t p where c corresponds to time_constant and to phase see definition of parameters Those filters are implemented as FIR filters using truncated time representations of gammachirp functions as the impulse response The impulse responses which need to have the same length for every channel have a duration of 15 times the biggest time constant The length of the impulse response is therefore 15xmax time constant sampling rate The impulse re
439. of the output of this network go to the next part of the tutorial Exercise The units system of Brian is useful for ensuring that everything is consistent and that you don t make hard to find mistakes in your code by using the wrong units Try changing the units of one of the parameters and see what happens Solution You should see an error message with a Python traceback telling you which functions were being called when the error happened ending in a line something like Brian units DimensionMismatchError The differential equations are not homogeneous dimensions were m 2 kg s 3 A 1 m 2 kg s 4 A 1 Tutorial 1d Introducing randomness In the previous part of the tutorial all the neurons start at the same values and proceed deterministically so they all spike at exactly the same times In this part we introduce some randomness by initialising all the membrane potentials to uniform random values between the reset and threshold values We start as before from brian import x tau 20 msecond membrane time constant Vt 50 mvolt spike threshold Vr 60 mvolt reset value El 49 x mvolt resting potential same as the reset G NeuronGroup N 40 model dV dt V El tau volt threshold Vt reset Vr M SpikeMonitor G But before we run the simulation we set the values of the membrane potentials directly The notation G V refers to the array of values for the variable V
440. oi 10 1371 journal pcbi 1000993 Simplified version of the ideal sound localisation model The sound is played at a particular spatial location indicated on the final plot by a red Each location has a corresponding assembly of neurons whose summed firing rates give the sizes of the blue circles in the plot The most strongly responding assembly is indicated by the green x which is the estimate of the location by the model from brian import x from brian hears import Download the IRCAM database http recherche ircam fr equipes salles listen download html and replace this filename with the location you downloaded it to hrtfdb IRCAM LISTEN r Z HRTFNIRCAM subject 1002 hrtfset hrtfdb load subject subject This gives the number of spatial locations in the set of HRTFs num indices hrtfset num indices Choose a random location for the sound to come from index randint num indices A sound to test the model with sound Sound whitenoise 500 ms This is the specific HRTF for the chosen location hrtf hrtfset hrtf index We apply the chosen HRTF to the sound the output has 2 channels hrtf fb hrtf filterbank sound We swap these channels equivalent to swapping the channels in the subsequent filters but simpler to do it with the inputs swapped channels RestructureFilterbank hrtf fb indexmapping 1 0 Now we apply all of the possible pairs of HRTFs in the set to these
441. ole pairs and one double zero The gain is normalized for the response of the analog filter at 1000Hz as in the model of Tan amp Carney their actual C code does however result in a slightly different normalization the difference in overall level is about 0 33dB to get exactly the same output as in their model set the gain parameter to 0 962512703689 Tan Q and L H Carney A Phenomenological Model for the Responses of Auditory nerve Fibers II Nonlinear Tuning with a Frequency Glide The Journal of the Acoustical Society of America 114 2003 2007 class brian hears TanCarney source cf update_interval 1 param None Class implementing the nonlinear auditory filterbank model as described in Tan G and Carney L A phe nomenological model for the responses of auditory nerve fibers II Nonlinear tuning with a frequency glide JASA 2003 The model consists of a control path and a signal path The control path controls both its own bandwidth via a feedback loop and also the bandwidth of the signal path Initialised with arguments source Source of the cochlear model cf List or array of center frequencies update interval Interval in samples controlling how often the band pass filter of the signal pathway is updated Smaller values are more accurate but increase the computation time param Dictionary used to overwrite the default parameters given in the original paper cass brian hears ZhangSynapse source CF n per
442. olt spike threshold Vr 60 mvolt reset value El 60 mvolt resting potential same as the reset G NeuronGroup N 40 model dV dt V El tau volt threshold Vt reset Vr Counting spikes Now we would like to have some idea of what this network is doing In Brian we use monitors to keep track of the behaviour of the network during the simulation The simplest monitor of all is the 5pikeMonitor which just records the spikes from a given NeuronGroup M SpikeMonitor G Results Now we run the simulation as before run l second And finally we print out how many spikes there were print M nspikes So what s going on Why are there 40 spikes Well the answer is that the initial value of the membrane potential for every neuron is 0 mV which is above the threshold potential of 50 mV and so there is an initial spike at t 0 and then it resets to 60 mV and stays there below the threshold potential In the next part of this tutorial we ll make sure there are some more spikes to see 3 1 3 Tutorial 2 Connections In this tutorial we will cover in more detail the concept of a Connection in Brian Tutorial contents Tutorial 2b Excitatory and inhibitory currents In this tutorial we use multiple connections to solve a real problem how to implement two types of synapses with excitatory and inhibitory currents with different time constants The scheme The scheme we implement is the following d
443. om brian import x Parameters degree 2 x pi 360 duration 500 ms R 2 5 cm radius of scorpion vr 50 meter second Rayleigh wave speed phi 144 degree angle of prey A 250 x Hz deltaI 7 ms inhibitory delay gamma 22 5 45 arange 8 degree leg angle delay R vr x 1 cos phi gamma wave delay Wave vector w t arange int duration defaultclock dt 1 defaultclock dt Dtot 0 w 0 for f in range 150 451 D exp 300 2 2 50 x 2 xi 2 pi rand w 100 D cos 2 x pi x f x t xi Dtot D w 01 w Dtot Rates from the wave def rates t return w array t defaultclock dt dtype int Leg mechanical receptors tau legs 1 ms sigma 01 eqs legs dv dt 1 rates t d v tau_legs sigmas 2 tau_legs 5 xi l d second mnm legs NeuronGroup 8 model eqgs legs threshold 1 reset 0 refractory 1 ms legs d delay Spikes legs SpikeCounter legs Command neurons tau 1 x ms 40 Chapter 3 Getting started Brian Documentation Release 1 4 1 taus 1 ms wex 7 winh 2 eqs neuron dv dt x v tau 1 dx dt y x taus 1 alpha currents dy dt y taus 1 rrt neurons NeuronGroup 8 model eqgs neuron threshold 1 reset 0 synapses ex IdentityConnection legs neurons y weight wex synapses inh Connection legs neurons y delay delt
444. ompiled C code can be used in several places in Brian to get speed improvements in cases where performance is the most important factor 6 2 1 Weave Weave is a SciPy module that allows the use of inlined C code Brian by default doesn t use any C optimisations for maximum compatibility across platforms but you can enable several optimised versions of Brian objects and functions by enabling weave compilation See Preferences for more information See also Vectorisation for some information on writing your own inlined C code using Weave 6 2 2 C objects For maximum compatibility Brian works with pure Python only However as well as the optional weave opti misations there are also objects can run with a pure C version for a considerable speedup For this to work you need a copy of the gcc compiler installed either on Linux Mac or through cygwin on Windows to build them During installation via easy_install pip or with python setup py install two objects are compiled automatically brian utils fastexp fastexp providing a fast approximate exponential function and brian utils ccircular ccircular a circular array data structure If the compilation fails a warning message will be displayed and the pure Python versions used instead In addition it is possible to compile a C version of a more recent datastructure underlying the Synapses object the SpikeQueue To compile this object follow these instructions In a command
445. omputed whenever another value changes computed network parameters total neurons neurons per layer num layers un v plus we also use the default model parameters model params DEFAULT NETWORK STRUCTURE Single input layer multiple chained layers class DefaultNetwork Network def init self p define groups chaingroup NeuronGroup N p total neurons xModel p inputgroup PulsePacket p initial burst t p neurons in input layer p initial burst sigma layer chaingroup subgroup p neurons per layer for i in range p num layers connections chainconnect Connection chaingroup chaingroup 2 for i in range p num layers 1 chainconnect connect full layer i layer i 1 p psp peak p we inputconnect Connection inputgroup chaingroup 2 inputconnect connect full inputgroup layer 0 p psp peak p we monitors chainmon SpikeMonitor g True for g in layer inputmon SpikeMonitor inputgroup True mon inputmon chainmon network Network init self chaingroup inputgroup chainconnect inputconnect mon add additional attributes to self self mon mon self inputgroup inputgroup self chaingroup chaingroup self layer layer self params p def prepare self Network prepare self self reinit def reinit self p None Network reinit self q self params if p is None p q self inputgroup generate p initial burst t p initial burst a p
446. on out of 1 of the entire population which will undergo a cross over proportion elite 0 05 proportion out of 1 of the entire population which will be kept for the next generation based on their best fitness The proportion of mutation is automatically set to 1 proportion xover proportion elite func selection stoch uniform This function define the way the parents are chosen it is the only one available It lays out a line in which each parent corresponds to a section of the line of length proportional to its scaled value The algorithm moves along the line in steps of equal size At each step the algorithm allocates a parent from the section it lands on The first step is a uniform random number less than the step size func xover intermediate func xover specifies the function that performs the crossover The following ones are avail able intermediate creates children by taking a random weighted average of the parents You can specify the weights by a single parameter ratio xover which is 0 5 by default The function creates the child from parent and parent2 using the following formula child parentl rand x Ratio x parent2 parentl discrete random creates a random binary vector and selects the genes where the vector is a 1 from the first parent and the gene where the vector is a 0 from the second parent and combines the genes to form the child 308 Chapter 8 Reference Brian Doc
447. on is averaged over trials 50 in Figure 4 though 10 trials should be fine for testing The trials run in parallel on all available processors 10 trials take about 2 minutes on a modern PC IMPORTS from brian import x import multiprocessing PARAMETERS 5000 10 taum 33x ms tau_pre 20 ms tau_post tau_pre Ee 0 mV vt 54xmV vr 70 xmV El 70 mV taue 5 ms f 20 Hz theta period 1 f Rm 200 Mohm a linspace 51 65 num M weights 001 ratio 1 50 dA_pre 01 dA post 01xratio trials 10 52 Chapter 3 Getting started Brian Documentation Release 1 4 1 SIMULATION LOOP def trial n n is the trial number LE reinit_default_clock clear True eqs neurons dv dt ge Ee vr 4Rm I El v taum volt dge dt ge taue 1 I amp nF inputs PoissonGroup N rates lambda t 5 5 cos 2 pixfxt 10 Hz neurons NeuronGroup M model eqs_neurons threshold vt reset vr neurons I axpA synapses Connection inputs neurons ge weight weights neurons v vr S SpikeMonitor neurons run 2 second stdp ExponentialSTDP synapses tau_pre tau_post dA_pre dA_post wmax 10 weights interactions all run 5 second phase zeros M 200 for b in range 0 M tmp_phase S b Stheta_period 360 theta_period phase b range 0 len tmp_phase tmp phase return phase gt name__ main This is very important on Wi
448. onGroup N4 Nbarrels barrels4 dict i j layer4 subgroup N4 for i in xrange barrelarraysize for j in xrange barre barrels4active dict ij False for ij in barrels4 barrelindices dict ij slice b origin b _origin len b for ij b in barrels4 iteritems layer4 selectivity zeros len layer4 for i j inds in barrelindices iteritems layer4 selectivity inds linspace 0 2 pi N4 Layer 2 3 layer23 NeuronGroup Nbarrels N23exc N23inh model eqs threshold v gt vt reset v El vtt vt_inc refr layer23 v El1 layer23 vt Vt Layer 2 3 excitatory layer23exc layer23 subgroup Nbarrels N23exc x y meshgrid arange M23exc 1 M23exc arange M23exc 1 M23exc x y x flatten y flatten barrels23 dict i j layer23exc subgroup N23exc for i in xrange barrelarraysize for j in xrai for i in range barrelarraysize for j in range barrelarraysize barrels23 i j x x i barrels23 i j l y vy j Layer 2 3 inhibitory layer23inh layer23 subgroup Nbarrels N23inh x y meshgrid arange M23inh 1 M23inh arange M23inh 1 M23inh x y x flatten y flatten barrels23inh dict i j layer23inh subgroup N23inh for i in xrange barrelarraysize for j in for i in range barrelarraysize for j in range barrelarraysize 3 2 Examples 47 Brian Documentation Release 1 4 1 barrels23inh i j x x i barrels23inh i jl y y j print Building synapses please wa
449. ond 1 lgi V E_i g_i second 1 dg e dt g e tau syn secondx 1 dg i dt g i tau syn secondx 1 rire else eqs dV dt V EL g L I syn I_syn 5 x g_e g_i second 1 3 2 Examples 33 Brian Documentation Release 1 4 1 dg e dt g e tau syn secondx 1 dg i dt g i tau syn secondx 1 Pag for simpler voltage traces no spiking neuron NeuronGroup 1 model eqs threshold None every input neuron fires once in a random interval self unwarped spiketimes i t 250 ms for i t in zip range 0 self N rand self N final spiketimes will be set in the run function self input SpikeGeneratorGroup self N e input self input subgroup N ex i input self input subgroup N inh conn Connection e input neuron g e weight 6 N ex tau syn i conn Connection i input neuron g i weight 5 6 N ex tau syn record membrane potential self monitor StateMonitor neuron varname V record True putting everything together self net Network neuron self input e conn i conn self monitor def run self beta 1 0 Ku y Run the network with the original spike train warped by a certain factor beta Beta gt 1 corresponds to an extended and beta 1 to a shrinked input spike train wu self net reinit warp spike train in time self input spiketimes i betaxt for i t in self unwarped spiketimes self
450. one HRTFDatabase for the IRCAM LISTEN public HRTF database For details on the database see the website The database object can be initialised with the following arguments basedir The directory where the database has been downloaded and extracted e g x D NHRTFNIRCAM Multiple directories in a list can be provided as well e g IRCAM and IRCAM New compensated False Whether to use the raw or compensated impulse responses samplerate None If specified you can resample the impulse responses to a different samplerate otherwise uses the default 44 1 kHz The coordinates are pairs azim elev where azim ranges from 0 to 345 degrees in steps of 15 degrees and elev ranges from 45 to 90 in steps of 15 degrees After loading the database the attribute subjects gives all the subjects number that were detected as installed Obtaining the database The database can be downloaded here Each subject archive should be extracted to a folder e g IRCAM with the names of the subject e g IRCAM IRC 1002 etc 330 Chapter 8 Reference Brian Documentation Release 1 4 1 class brian hears HeadlessDatabase n None azim_max 1 5707963267948966 diame ter 0 22308 metre itd None samplerate None frac tional itds False Database for creating HRTFSet with artificial interaural time differences Initialisation keywords n azim max diameter Specify the ITDs for two ears separated by distance diameter with no head IT
451. onnectionMonitor C store True clock print Learning Series of inhibitory pulses for i in range Npulses print pulse i 1 EventClock dt record_period duration 200 ms rand 300 ms random stimulus duration neurons ginh ginh_max run duration C W alldata C W alldatat tC W alldataxb_pre homeostasis synaptic scaling neurons ginh 0 run rest_time let neurons spike neurons _S rest f reset to save time Figure 4D neuron 0 wsave t M todense for t M in MC values W array zip wsave 1 weights W neuron Evolution of all synaptic weights for for i in range weights shape 1 this neuron plot arange len weights i record_period weights i k 3 2 Examples 67 Brian Documentation Release 1 4 1 xlim 0 weights shape 0 float record_period ylim 0 1 show Example Fig2C decoding synchrony frompapers computing with neural synchrony duration se lectivity Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 2C Decoding synchrony patterns Caption Fig 2C Activation of the postsynaptic assembly as a function of duration grey individual neurons black average The script Fig2A_synchrony_partition must be run first it produces a file from brian import x from numpy random import seed from params import x from pylab import cm Ndur
452. ons dvm dt gl vmti_inj Cm volt Rbridge ohm bridge resistance I amp command current ree eqs current clamp i cmd I Re Re Ce Ce setup NeuronGroup 1 model eqs ampli DCC setup v rec I 1 kHz soma StateMonitor setup vm record True recording StateMonitor setup v rec record True DCCrecording StateMonitor ampli record record True No compensation run 50 ms ampli command 5 nA run 100 ms ampli command 0 nA run 50 ms ampli set frequency 2 kHz ampli command 5 nA run 100 ms ampli command 0 nA run 50 ms plot recording times ms recording 0 mV b plot DCCrecording times ms DCCrecording 0 mV k plot soma times ms soma 0 mV r show Example threshold analysis electrophysiology Analysis of spike threshold Loads a current clamp voltage trace compensates remove electrode voltage and analyses the spikes from brian import x from brian library electrophysiology import x import numpy dt 1 ms Vraw numpy load trace npy Raw current clamp trace I numpy load current npy V _ Lp compensate I Vraw dt Electrode compensation Peaks spike criterion find spike criterion V print Spike detected when V exceeds float spike criterion mV mV peaks spike peaks V vc spike criterion vc is optional Onsets spike threshold onsets spike onsets V c
453. ons in an already defined group The subset has to be a continguous set of neurons They can be overlapping if defined with the slice notation or consecutive if defined with the subgroup method Subgroups can themselves be subgrouped Subgroups can be used in almost all situations exactly as if they were groups except that they cannot be passed to the Net work object 8 4 Neuron models and groups 265 Brian Documentation Release 1 4 1 Details TODO details of other methods and properties for people wanting to write extensions 8 4 3 Resets Reset objects are called each network update step to reset specified state variables of neurons that have fired class brian Reset resetvalue 0 0 volt state 0 Resets specified state variable to a fixed value Initialise as R Reset resetvalue 0 mvolt state 0 with arguments resetvalue The value to reset to state The name or number of the state variable to reset This will reset all of the neurons that have just spiked The given state variable of the neuron group will be set to value resetvalue class brian StringReset expr level 0 Reset defined by a string Initialised with arguments expr The string expression used to reset This can include multiple lines or statements separated by a semi colon For example V 70 mV or V 70xmV Vt 10 mvV Some standard functions are pro vided see below level How many levels up in the calling sequen
454. ontroller does not improve the settling time of the clamp but only the final voltage value Active Electrode Compensation The electrophysiology library includes the Active Electrode Compensation AEC technique described in Brette et al 2008 High resolution intracellular recordings using a real time computational model of the electrode Neuron 59 3 379 9 1 It can be applied offline or online using the models of experimental setup described above for dynamic clamp or voltage clamp recordings the electrode compensation must be done online An AEC board is initialized in the same way as an acquisition board board AEC neuron V 1I clock where clock is the acquisition clock The estimation phase typically looks like board start_injection run 2 second board start injection run 100 ms board estimate where white noise is injected for 2 seconds default amplitude 5 nA You can change the default amplitude and DC current as follows board start injection amp 5 nA DC 1 nA After estimation the kernel is stored in board Ke The following options can be passed to the function estimate ksize default 150 sampling steps kt ail default 50 sampling steps and dendritic default False use True is the recording is a thin process i e axon or dendrite Online compensation is then switched on with board switch_on and off with board switch_off For example to inject a 5 nA current pulse for 200 ms
455. ording StateMonitor setup ic record True soma StateMonitor setup vm record True run 200 ms figure plot recording times ms recording 0 nA k figure plot soma times ms soma 0 mV b show i rec ic 3 2 Examples 95 Brian Documentation Release 1 4 1 Example compensation ex2 spikes electrophysiology Example of spike detection method Requires binary files current npy and rawtrace npy Rossant et al A calibration free electrode compensation method J Neurophysiol 2012 import os from brian import x import numpy as np from brian library electrophysiology import working dir os path dirname jfile load data dt 0 1 ms current np load os path join working dir current npy 10000 long vector 1s duration rawtrace np load os path join working dir trace npy 10000 long vector 1s duration t linspace 0 1 len current find spikes and compute score Spikes scores find spikes rawtrace dt dt check quality True plot trace and spikes plot t rawtrace k plot t spikes rawtrace spikes or show Example AEC electrophysiology AEC experiment current clamp from brian import x from brian library electrophysiology import x from time import time myclock Clock dt 1 ms clock rec Clock dt 1 ms flog level debug taum 20 ms gl 20 nS Cm taum gl Re 50 Mohm
456. orted languages brian experimental codegen2 ArraySymbol attribute 381 supported languages brian experimental codegen2 DenseMatrixSymbols 1 attribute 370 supported languages brian experimental codegen2 SliceIndex attribute 382 supported languages brian experimental codegen2 S ymbol attribute 380 Symbol class in brian experimental codegen2 379 synapse index brian Synapses method 282 Synapses module Index 399 Brian Documentation Release 1 4 1 example usage 135 144 147 153 Synapses class in brian 282 SynapticDelay Variable class brian synapses synapticvariable 284 SynapticEquations class in brian 283 Synaptic Variable class brian synapses synapticvariable 283 T t brian Clock attribute 261 Tabulate class in brian 253 TabulateInterp class in brian 253 TanCarney example usage 113 125 128 TanCarney class in brian hears 327 tests 335 TextDocumentWriter class brian experimental model_documentation 342 threshold 268 empirical 268 functional 269 hodgkin huxley 268 linear 268 variable 268 Threshold class in brian 268 tick brian Clock method 262 Tile class in brian hears 318 time dependent differential equations 218 equations 218 TimedArray example usage 82 137 166 185 TimedArray class in brian 298 TimedArraySetter class in brian 298 times brian hears Sound attribute 312 times brian StateSpikeMonitor method 291
457. oth compile and freeze should be set to True for nonlinear differ ential equations freeze False If True parameters are replaced by their values at the time of initialization method None If not None the integration method is forced Possible values are linear nonlinear Euler exponential_Euler overrides implicit and order keywords unit_checking True Set to False to bypass unit checking order 1 The order to use for nonlinear differential equation solvers TODO more details implicit False Whether to use an implicit method for solving the differential equations TODO more details code_namespace None Namespace for the pre and post codes Methods state var Returns the vector of values for state variable var with length the number of synapses The vector is an instance of class SynapticVariable synapse_index Returns the synapse indexes correspond to i which can be a tuple or a slice If i is a tuple m n m and n can be an integer an array a slice or a subgroup The following usages are also possible for a Synapses object S 282 Chapter 8 Reference Brian Documentation Release 1 4 1 len S Returns the number of synapses in S Attributes delay The presynaptic delays for all synapses synapse gt delay If there are multiple presynaptic delays multiple pre codes this is a list delay pre Same as delay delay post The postsynaptic delays for all synapses synapse gt delay post lastupdate The
458. over some basic topics in writing Brian scripts in Python The complete source code for the examples is available in the examples folder in the extras package 3 2 1 frompapers Example Touboul Brette 2008 frompapers Chaos in the AdEx model Fig 8B from Touboul J and Brette R 2008 Dynamics and bifurcations of the adaptive exponential integrate and fire model Biological Cybernetics 99 4 5 319 34 This shows the bifurcation structure when the reset value is varied vertical axis shows the values of w at spike times for a given a reset value Vr from brian import x defaultclock dt 0 01 ms C 281 pF gL 30 nS EL 70 6 mV VT 2 50 4 mV DeltaT 2 mV tauw 40 ms a 4 nS b 0 08 nA I 8 nA Veut VT 5 DeltaT practical threshold condition N 500 eqs n dvm dt gL EL vm gL DeltaT exp vm VT DeltaT I w C volt 26 Chapter 3 Getting started Brian Documentation Release 1 4 1 dw dt ax vm EL w tauw amp Vr volt mnm neuron NeuronGroup N model eqs threshold Vcut reset vm Vr wt b neuron vm EL neuron w a neuron vm EL neuron Vr linspace 48 3 mV 47 7 mV N bifurcation parameter run 3 second report text we discard the first spikes M StateSpikeMonitor neuron Vr w record Vr and w at spike times run 2x second report text Vr w M values Vr M values w figure plot Vr mV w nA k xlabel Vr
459. ow down the simulations The units system can be disabled by inserting import brian no units as the first line of the script e g import brian no units from brian import etc Internally physical quantities are floats with an additional units information The float value is the value in the SI system For example float mV returns 0 001 After importing brian no units all units are converted to their float values For example mV is simply the number 0 001 This may also be a solution when using external libraries which are not compatible with units but see next section Unit checking can also be turned down locally when initializing a neuron group by passing the argument check units False In that case no error is raised if the differential equations are not homogeneous A good practice is to develop the script with units on then switch them off once the script runs correctly 4 1 6 Converting quantities In many situations physical quantities need to be expressed with given units For example one might want to plot a graph of the membrane potential in mV as a function of time in ms The following code plot t V displays the trace with time in seconds and potential in volts The simplest solution to have time in ms and potential in mV is to use units operations plot t ms V mV Here t ms is a unitless array containing the values of t in ms The same trick may be applied to use external functions which do not work wit
460. ownnoise in module brian hears 315 Bufferable class in brian hears 331 buffering interface 243 Butterworth example usage 112 Butterworth class in brian hears 324 C c data type in module brian experimental codegen2 378 Cascade example usage 115 Cascade class in brian hears 324 CCF in module brian 300 CCode class in brian experimental codegen2 370 CCVF in module brian 300 CDefineFromArray class in brian experimental codegen2 377 CForBlock class in brian experimental codegen2 368 channel brian hears Sound method 312 check_units in module brian 259 CIfBlock class in brian experimental codegen2 368 CLanguage class in brian experimental codegen2 376 clear example usage 168 389 Brian Documentation Release 1 4 1 clear in module brian 289 click example usage 128 click brian hears Sound static method 313 click in module brian hears 316 clicks brian hears Sound static method 313 clicks in module brian hears 316 Clock example usage 96 99 165 181 clock 212 260 default clock 261 262 multiple clocks 261 Clock class in brian 261 CMAES class in brian library modelfitting 309 cochlea modelling 240 code generation 358 Code class in brian experimental codegen2 369 code object brian experimental codegen2 Language method 376 CodeGenConnection class in brian experimental codegen2 370 CodeGenReset class in brian expe
461. ox used by modelfitting is implemented in the external Python package Playdoh It also supports distributed and parallel optimization across CPUs and machines Different optimization algorithms are supported the default one is CMAES All those algorithms require the evaluation of the fitness function for a large number of parameter sets Each iteration of the algorithm involves the simulation of a large number of neurons one neuron corresponding to one parameter set as well as the computation of the gamma factor for each neuron The quality of the result depends on the number of neurons used which is specified in the modelfitting function Playdoh supports the use of graphical processing units GPUs in order to accelerate the speed of convergence of the algorithm If multiple cores are detected the library will use all of them by default Also if a CUDA enabled GPU is present on the system and if PyCUDA is installed the library will automatically use the GPU by default In addition several computers can be networked over IP see Clusters 5 6 2 Usage example To import the library use 5 6 Model fitting 233 Brian Documentation Release 1 4 1 from brian library modelfitting import To fit the parameters of a neuron model with respect to some data use the modelfitting function results modelfitting model equations reset 0 threshold 1 data spikes input input dt 1 ms popsize 1000 maxiter 10 R
462. p i Pgp i 1 weight Cinput Synapses Pinput Pgp 0 model w volt pre y w Cinput True Cinput w weight Record the spikes Mgp SpikeMonitor p for p in Pgp Minput SpikeMonitor Pinput monitors Minput Mgp Setup the network and run it P V Vr rand len P Vt Vr 140 Chapter 3 Getting started Brian Documentation Release 1 4 1 run 100 ms Plot result raster plot showgrouplines True xmonitors show Example CUBA synapses CUBA example with delays Connection no delay 3 5 s DelayConnection 5 7 s Synapses with precomputed offsets 6 6 s 6 9 s Synapses with weave 6 4 s Synapses with zero delays 5 2 s from brian import import time start time time time taum 20 x ms taue 5 ms taui 10 ms Vt 50 mV Vr 60 mV El 49 mV eqs Equations dv dt getgi v El taum volt dge dt ge taue volt dgi dt gi taui volt II P NeuronGroup 4000 model eqs threshold Vt reset Vr refractory 5 ms P v Vr P ge 0 mV P gi 0 mV Pe P subgroup 3200 Pi P subgroup 800 we 60 0 27 10 mV excitatory synaptic weight voltage wi 20 4 5 10 mV inhibitory synaptic weight Se Synapses Pe P model w 1 pre ge we Si Synapses Pi P model w 1 pre gi wi Se 0 02 Si 0 02 Se delay rand ms
463. p to record from Has one attribute nspikes The number of recorded spikes class brian StateSpikeMonitor source var Counts or records spikes and state variables at spike times from a NeuronGroup Initialised as StateSpikeMonitor source var Where source A NeuronGroup to record from var The variable name or number to record from or a tuple of variable names or numbers if you want to record multiple variables for each spike Has two attributes nspikes The number of recorded spikes spikes A time ordered list of tuples i t v where neuron i fired at time t and the specified variable had value v If you specify multiple variables each tuple will be of the form i t v0 v1 v2 where the vi are the values corresponding in order to the variables you specified in the var keyword And two methods times i None Returns an array of the spike times for the whole monitored group or just for neuron i if specified values var i None Returns an array of the values of variable var for the whole monitored group or just for neuron i if specified class brian StateMonitor P varname clock None record False timestep 1 when end Records the values of a state variable from a NeuronGroup Initialise as StateMonitor P varname record False when end timestep 1 clock clock Where P The group to be recorded from 8 11 Monitors 291 Brian Documentation Release 1 4 1 varna
464. parallel to the Python Enhancement Proposals PEPs system for Python called Brian Enhancement Proposals BEPs These are stored in dev BEPs Ideas for new functionality for Brian are put in here for comment and discussion A BEP typically includes How the feature will look from user point of view with example scripts 345 Brian Documentation Release 1 4 1 Detailed implementation ideas and options We also use the Brian development mailing list 11 1 1 Contributing code First of all you should register to the developers mailing list If you want to modify existing modules you should make sure that you work on the latest SVN version We use the Eclipse IDE because it has a nice Python plugin Pydev and SVN plugin but of course you can use your preferred IDE The next step is to carefully read the guidelines in this guide Now that you wrote your code Write a test for it in brian tests testinterface If it is a new module create a new file test_mymodule py Write documentation both in the file see how it s done in existing modules and if appropriate in the relevant file in docs_sphinx We use the Sphinx documentation generator tools If you want to see how it looks generate the html docs by executing dev tools docs build_html py The html files will then be in docs e If it is a significant feature write an example script in examples and insert a line in xamples examples_guide txt Create a p
465. path_from_polys XY make a patch out of it patch patches PathPatch barpath facecolor blue edgecolor gray alpha 0 8 ax add_patch patch update the view limits ax set xlim left 0 right 1 ax set ylim bottom min top max uron parameters a 55 mV n 65 mV 5 ms 3 ms 15 ms a 4 mV input times tl t2 100 ms 120 ms simulation duration dur 200 ms number of neuron N bin EP int i int_ max we mo eqs V V0 dV0 dpsp dnoi rrr thr 10000 2 ms SP size EPSP taue EPSP2 tauextaue 2 taum taue _EPSP taum taue taum taue taum 3 0 mV max_EPSP del equations muy noise volt dt V0 psp taum volt dt psp taue volt se dt vmean noise tauntsigmas 2 taun 5 xi volt shold V theta rese in rein t vmean itialization of the NeuronGroup it_default_clock group NeuronGroup 2 N model eqs reset reset threshold threshold group VO group psp Oxvolt group noise vmean sigma randn 2xN 3 2 Examples 55 Brian Documentation Release 1 4 1 input spikes input spikes 0 t1 0 t2 1 t1 input SpikeGeneratorGroup 2 array input spikes connections C Connection input group psp C connect full input 0 group N weight we C connect full input 1 group N weight 2 we monitors prM1 PopulationRateMonito
466. perations supported M val is supported where val must be a scalar or an array of length nnz Implementation details The values are stored in an array alldata of length nnz number of nonzero entries The slice alldata rowind i rowind i 1 gives the values for row i These slices are stored in the list rowdata so that rowdata i is the data for row i The array rowj i gives the corresponding col umn j indices For row access the memory requirements are 12 bytes per entry 8 bytes for the float value and 4 bytes for the column indices The array a11 j of length nnz gives the column j coordinates for each element in alldata the elements of row are slices of this array so no extra memory is used If column access is being used then in addition to the above there are lists coli and coldataindices For column j the array coli j gives the row indices for the data values in column j while coldataindices j gives the indices in the array alldata for the values in column j Column ac cess therefore involves a copy operation rather than a slice operation Column access increases the memory requirements to 20 bytes per entry 4 extra bytes for the row indices and 4 extra bytes for the data indices TODO update size numbers when use minimal indices True for different architectures class brian DynamicConnectionMatrix val nnzmax None dynamic array constz2 kwds Dynamic sparse connection matrix See documentation for Connect
467. physiology import working dir os path dirname file load data dt 0 1 ms current np load os path join working dir current npy 10000 long vector 1s duration rawtrace np load os path join working dir trace npy 10000 1ong vector 1s duration compensatedtrace np load os path join working dir compensatedtrace npy obtained with examp t linspace 0 1 len current get trace quality of both raw and compensated traces r get trace quality rawtrace current full True rcomp get trace quality compensatedtrace current full True spikes r spikes print Quality coefficient for raw 3f and for compensated trace 3f r correlation rcomp correlation plot trace and spikes plot t rawtrace k plot t compensatedtrace g plot t spikes rawtrace spikes ok plot t spikes compensatedtrace spikes og show Example DCC electrophysiology An example of single electrode current clamp recording with discontinuous current clamp using the electrophysiology library from brian import x from brian library electrophysiology import x defaultclock dt 0 01 ms taum 20 ms membrane time constant gl 1 50 Mohm leak conductance Cm taum gl membrane capacitance Re 50 Mohm electrode resistance Ce 0 1 ms Re electrode capacitance 3 2 Examples 93 Brian Documentation Release 1 4 1 eqs Equati
468. pi I zeros barrelarraysize M23exc barrelarraysize M23exc around layer23exc x M23exc dtype int ix arr around layer23exc y M23exc dtype int ay iy array I iy ix imshow I hsv colorbar for i in range 1 barrelarraysizetl plot ixmax ix barrelarraysize i max ix barrelarraysize 0 max iy k plot 0 max ix ixmax iy barrelarraysize i xmax iy barrelarraysize k selectivity figure hist selectivity show 3 2 Examples 147 Brian Documentation Release 1 4 1 Example two_synapses Synapses One synapse within several possibilities Synapse from 0 gt 2 3 from brian import x P NeuronGroup 2 model dv dt 1 10 ms Q NeuronGroup 4 model v 1 S Synapses P Q model w 1 pre v w M StateMonitor Q v record True S 0 2 True S 0 3 True S w 0 1 7 S delay 0 5 ms 7 ms run 40 ms for i in range 4 plot M times ms M i i 2 k show Example multiple_delays synapses Multiple delays from brian import x P NeuronGroup 1 model dv dt 1 20 ms Q NeuronGroup 1 model v 1 S Synapses P Q model w l pre v t w M StateMonitor Q v record True 0 0 2 w 0 0 0 21 w 0 0 1 5 delay 0 0 0 2 5 ms delay 0 0 1 1 ms NNNN NN run 60 ms plot M times ms M 0 show Example short_term_plasticity2 synapses 1 threshold 1 reset 0 1 threshold 1 reset
469. pieces are put together A warning is issued at the preparation stage see below 11 4 2 Attributes after initialisation After initialisation an Equation object contains e a namespace namespace e a dictionary of units for all variables _units 11 4 Equations 355 Brian Documentation Release 1 4 1 a dictionary of strings corresponding to each variable right hand side of each equation including parameters and aliases string Parameters are defined as differential equations with RHS O unit second All comments are removed and multiline strings are concatenated e a list of variables of non differential equations eq names e a list of variables of differential equations including parameters diffeq names e a list of variables of differential equations excluding parameters diffeq names nonzero e a dictionary of aliases alias mapping a variable name to its alias There is no explicit list of parameters maybe it should be added Nothing more is done at initialisation time no units checking etc The reason is that the equation set might not be complete at this time in the case when equations are built in several pieces Various checks are done using the prepare method 11 4 3 Finalisation prepare The Equation object is finalised by an explicit call to the prepare method Finding Vm The first step is to find the name of the membrane potential variable getVm This is useful when the v
470. pike triggered average spikes stimulus max interval dt onset onset display True figure plot time axis filt max filt plot time axis sta max sta xlabel time axis ylabel sta legend real filter estimated filter show Example two_neurons misc Two connected neurons with delays from brian import x tau 10 ms w l mV vO 11 mV neurons NeuronGroup 2 model dv dt v0 v tau volt threshold 10 mV reset 0 mV max delay 5 ms neurons v rand 2 10 mV W Connection neurons neurons v delay 2 x ms W 0 1 w W 1 0 w S StateMonitor neurons v record True mymonitor SpikeMonitor neurons 0 mymonitor PopulationSpikeCounter neurons run 500 ms plot S times ms S 0 plot S times ms S 1 show mV mV Example topographic map2 misc Topographic map an example of complicated connections Two layers of neurons The first layer is connected randomly to the second one in a topographical way The second layer has random lateral connections Each neuron has a position x i from brian import x N 100 tau 10 ms tau_e 2 x ms AMPA synapse eqs dv dt I v tau volt dI dt I tau e volt 162 Chapter 3 Getting started Brian Documentation Release 1 4 1 rates zeros N Hz rates N 2 10 N 2 10 ones 20 x 30 gt Hz layerl PoissonGroup N rates rates layerl x
471. placed e g eqs Equations dx dt x tau volt tau 10 ms x Vm changes the variable name x to Vm This is useful for writing functions which return equations where the variable name is provided by the user Finally if the value is None then the name of the variable is replaced by a unique name e g eqs Equations dx dt x tau volt tau 10 ms x None This is useful to avoid conflicts in the names of hidden variables Issues There can be problems if a variable with the same name as the variable of a differential equation exists in the namespace where the Equations object was defined 4 14 More on equations 215 Brian Documentation Release 1 4 1 4 14 2 Combining equations Equations can be combined using the sum operator For example eqs Equations dx dt y x tau volt eqst Equations dy dt y tau volt Note that some variables may be undefined when defining the first equation No error is raised when variables are undefined and absent from the calling namespace When two Equations objects are added the consistency is checked For example it is not possible to add two Equations objects which define the same variable 4 14 3 Which variable is the membrane potential Several objects such as Threshold or Reset objects can be initialised without specifying which variable is the membrane potential in which case it is assumed that it is the first variable Internally
472. presented is sequence 1 odor A alone 2 odor B alone 3 odor B alone with twice stronger intensity 4 odor A with distracting odor C same intensity 5 odors A and B same intensity from brian import x bmin bmax 7 1 def odor N Returns a random vector of binding constants return 10 rand N bmax bmin bmin def hill function c K 1 n 23 prx Hill function C concentration E UK half activation constant choose K 1 for relative concentrations n Hill coefficient TRE return cx x n c x n K n N 5000 number of receptors Odors seed 31415 Get the same neurons every time intensity 3000 cl odor N c2 odor N c0 c1 Il I2 intensity intensity Odor plumes fluctuating concentrations tau plume 75 ms eq plumes dx dt x tau plume 2 tau plume x 5 xi 1 y clip x 0 inf 1 COR plume NeuronGroup 2 model eq plumes 2 odors 3 2 Examples 79 Brian Documentation Release 1 4 1 Receptor neurons Fmax 40 Hz maximum firing rate tau 20 ms Imax 1 1 exp 1 Fmax tau maximum input current eq receptors dv dt Imaxxhill function c v tau 1 C 1 concentrations relative to activation constant pow receptors NeuronGroup N model eq_receptors threshold 1 reset 0 receptors c cl Qnetwork operation def odor to nose Send odor plume to the receptors receptors c Il cl clip plume x 0 0 Inf I2 c2 clip plume x 1 0 1Inf
473. pressions Expression 364 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 Symbols symbols Symbol a UN UE symbols ArraySymbol symbols Slicelndex symbols RuntimeS ymbol symbols Arraylndex symbols NeuronGroupStateVariab eS ymbol Resolution and code output dependencies Dependency dependencies Write dependencies Read Integration integration EquationsContainer 11 5 Code generation 365 Brian Documentation Release 1 4 1 GPU codeobject Code management GPUSymbolMemoryManager management GPUManager languages Language management GPUKernel Y management GPUCode languages CLanguage Y management GPULanguage Brian objects Connection codegen2 connection SparseMatrixS ymbols brian base ObjectContainer brian magic InstanceTracker codegen2 connection DenseMatrixS ymbols connections connection Connection codegen2 connection CodeGenConnection Reset brian reset Reset codegen2 reset CodeGenReset 366 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 State updater brian stateupdater StateUpdater codegen2 stateupdater CodeGenStateUpdater Threshold codegen2 symbols Symbol b
474. prompt or shell window go to the directory where Brian is installed On Windows this will prob ably be C Python27 lib site packages brian Now go to the experimental cspikequeue folder If you re on Linux and this may also work for Mac run the command python setup py build_ext inplace If you re on Windows you ll need to have cygwin with gcc installed and then you run setup py 6 2 Compiled code 249 Brian Documentation Release 1 4 1 build ext inplace c mingw32 instead You should see some compilation possibly with some warnings but no errors If all works OK you should see a UserWarning when importing Brian You can uninstall and effectively switch off the use of the C SpikeQueue by removing the x so file in the experimental cspikequeue directory Repeating the steps above i e recompiling the object will re enable the C SpikeQueue The same steps can also be used for compiling the ccircular or fastexp if they were not already compiled automatically during installation just navigate to the respective directory 6 2 3 Automatically generated C code There is an experimental module for automatic generation of C code see Code generation 6 3 Projects with multiple files or functions Brian works with the minimal hassle if the whole of your code is in a single Python module py file This is fine when learning Brian or for quick projects but for larger more realistic projects with the source code separated int
475. provide your own callback function by setting report to be a function report elapsed complete oftwo variables elapsed the amount of time elapsed in seconds and complete the proportion of the run duration simulated between 0 and 1 The report function is guaranteed to be called at the end of the run with complete 1 0 so this can be used as a condition for reporting that the computation is finished report period How often the progress is reported by default every 10s Works by constructing a MagicNetwork object from all the suitable objects that could be found NeuronGroup Connection etc and then running that network Not suitable for repeated runs or situa tions in which you need precise control brian reinit states True Reinitialises any suitable objects that can be found Usage reinit states True 288 Chapter 8 Reference Brian Documentation Release 1 4 1 Works by constructing a MagicNetwork object from all the suitable objects that could be found NeuronGroup Connection etc and then calling reinit for each of them Not suitable for re peated runs or situations in which you need precise control If states False then NeuronGroup state variables will not be reinitialised brian stop Globally stops any running network this is reset the next time a network is run brian clear erase True all False Clears all Brian objects Specifically it stops all existing Brian objects from being collected
476. put PoissonGroup N rates F neurons NeuronGroup l model eqgs neurons threshold vt reset vr S Synapses input neurons model w l1 dApre dt Apre taupre 1 event driven dApost dt Apost taupost 1 event driven pre ge t w Apret dApre w clip wtApost 0 gmax post Apost dApost w clip wtApre 0 gmax neurons v vr S True S w rand gmax rate PopulationRateMonitor neurons start_time time run 100 second report text print Simulation time time start time subplot 311 plot rate times second rate smooth rate 100 ms subplot 312 plot S w gmax subplot 313 hist S w gmax 20 show Example transient sync synapses Transient synchronisation in a population of noisy IF neurons with distance dependent synaptic weights organised as aring from brian import x import time tau 10 ms N 100 v0 5 mV sigma 4 x mV group NeuronGroup N model dv dt v0 v tau sigma xxi tau x 5 volt threshold 10 mV reset 0 mV C Synapses group model w 1 pre v w C True C w 4 x mV x cos 2 x pi i j 1 N S SpikeMonitor group R PopulationRateMonitor group group v rand N 10 mV 152 Chapter 3 Getting started Brian Documentation Release 1 4 1 run 5000 ms report text subplot 211 raster_plot S subplot 2
477. quency are generated In the latter each harmonic parameter is set separately and the number of harmonics generated corresponds to the length of the array brian hears silence args kwds Returns a silent zero sound for the given duration Set nchannels to set the number of channels brian hears sequence sounds samplerate None Returns the sequence of sounds in the list sounds joined together dB class brian hears dB type The type of values in dB dB values are assumed to be RMS dB SPL assuming that the sound source is measured in Pascals class brian hears dB error Error raised when values in dB are used inconsistently with other units 8 21 2 Filterbanks class brian hears LinearFilterbank source b a Generalised linear filterbank Initialisation arguments source The input to the filterbank must have the same number of channels or just a single channel In the latter case the channels will be replicated b a The coeffs b a must be of shape nchannels m or nchannels m p Here mis the order of the filters and p is the number of filters in a chain first you apply O then 1 etc The filter parameters are stored in the modifiable attributes ilt b filt aandfilt state the variable z in the section below Has one method decascade ncascade 1 Reduces cascades of low order filters into smaller cascades of high order filters ncascade is the number of cascaded filters to use which should
478. quency t 1 missing fundamental frequency 200 200 t Hz Hz Hz increasing pitch pg receptors NeuronGroup 2 model eqs ear threshold 1 reset 0 refractory 2 ms Coincidence detectors min freq 50 Hz max freq 1000 Hz N 300 tau 1 ms Sigma 1 eqs neurons dv dt v tautsigmas 2 tau 5 xi 1 rrt neurons NeuronGroup N model eqs neurons threshold 1 reset 0 synapses Synapses receptors neurons model w 1 pre vt w synapses True synapses w 0 5 synapses delay 1 1 exp linspace log min freq Hz log max freq Hz N spikes SpikeMonitor neurons run 500 ms raster plot spikes ylabel Frequency yticks 0 99 199 299 array 1 synapses delay 1 0 99 199 299 dtype int show 3 2 15 misc Example delays misc Random network with external noise and transmission delays from brian import x tau 10 x ms sigma 5 mV eqs dv dt v tautsigma xi tauxx 5 volt P NeuronGroup 4000 model eqs threshold 10 mV reset 0 mV refractory 5 ms P v 60 mV Pe P subgroup 3200 Pi P subgroup 800 C Connection P P v delay 2 ms C connect random Pe 0 05 weight 7 mV C connect random Pi 0 05 weight 2 8 mV E P 154 Chapter 3 Getting started Brian Documentation Release 1 4 1 M SpikeMonitor P True run l second print Mean rate M
479. r xlabel k ylabel Firing rate Hz show Finally a more sophisticated solution for managing and tracking projects based on numerical simulation or analysis with the aim of supporting reproducible research is Sumatra For more detailed information see the reference chapter 4 16 Managing simulation runs and data 221 Brian Documentation Release 1 4 1 222 Chapter 4 User manual CHAPTER FIVE THE LIBRARY A number of standard models is defined in the library folder To use library elements use the following syntax from brian library module name import For example to import electrophysiology models from brian library electrophysiology import x 5 1 Library models 5 1 1 Membrane equations Library models are defined using the MembraneEquation class This is a subclass of Equations which is defined by a capacitance C and a sum of currents The following instruction eqs MembraneEquation 200 pF defines the equation C dvm dt 0 amp with the membrane capacitance C 200 pF The name of the membrane poten tial variable can be changed as follows eqs MembraneEquation 200 pF vm V The main interest of this class is that one can use it to build models by adding currents to a membrane equation The Current class is a subclass of Equations which defines a current to be added to a membrane equation For example eqs MembraneEquation 200 pF Current I V0 vm
480. r as described in Lopez Paveda E and Meddis R A human nonlinear cochlear filterbank JASA 2001 The entire pathway consists of the sum of a linear and a nonlinear pathway The linear path consists of a bank of bandpass filters second order gammatone a low pass function and a gain attenuation factor g in a cascade The nonlinear path is a cascade consisting of a bank of gammatone filters a compression function a second bank of gammatone filters and a low pass function in that order Initialised with arguments source Source of the cochlear model cf List or array of center frequencies type defines the parameters set corresponding to a certain fit It can be either type human The parameters come from Lopez Paveda E and Meddis R A human nonlinear cochlear filterbank JASA 2001 8 21 Brian hears 325 Brian Documentation Release 1 4 1 type guinea pig The parameters come from Summer et al A nonlinear filter bank model of the guinea pig cochlear nerve Rate responses JASA 2003 param Dictionary used to overwrite the default parameters given in the original papers The possible parameters to change and their default values for humans see Lopez Paveda E and Meddis R A human nonlinear cochlear filterbank JASA 2001 for notation are param stape_scale 0 00014 param order_linear 3 param order_nonlinear 3 from there on the parameters are given in the
481. r gammachirp filterbank and the resulting cochleogram is plotted The different impulse responses are also plotted from brian import x from brian hears import sound whitenoise 100 ms ramp sound level 50 dB nbr_center_frequencies 50 number of frequency channels in the filterbank 124 Chapter 3 Getting started Brian Documentation Release 1 4 1 cl 2 96 glide slope bl 1 81 factor determining the time constant of the filters ll center frequencies with a spacing following an ERB scale cf erbspace 100 Hz 1000 Hz nbr center frequencies gamma chirp LogGammachirp sound cf c cl b b1 gamma_chirp_mon gamma chirp process figure imshow flipud gamma chirp mon T aspect auto show 3 2 11 hears tan_carney_2003 Example tan_carney_Fig11 hears tan_carney_2003 Response area and phase response of a model fiber with CF 2200Hz in the Tan amp Carney model Reproduces Fig 11 from Tan Q and L H Carney A Phenomenological Model for the Responses of Auditory nerve Fibers II Nonlinear Tuning with a Frequency Glide The Journal of the Acoustical Society of America 114 2003 2007 import matplotlib pyplot as plt import numpy as np from brian import x set global preferences useweave True from brian hears import def product xargs Simple and inefficient variant of itertools product that works for Python 2 5 directly returns a list instead of y
482. r group N bin bin prM2 PopulationRateMonitor group N bin bin launch simulation run dur PSTH plot figure figsize 10 10 prMs prM1 prM2 for i in 0 1 prM prMs i r prM rate 1 bin m mean r len r 2 ax subplot 211 i histo prM times r ax plot 0 dur m m r title 2f extra spikes sum r tl bin t2 20 ms bin m xlim 05 2 ylim 0 125 show Example Brette Guigon 2003 frompapers Reliability of spike timing Adapted from Fig 10D E of Brette R and E Guigon 2003 Reliability of Spike Timing Is a General Property of Spiking Model Neurons Neural Computation 15 279 308 This shows that reliability of spike timing is a generic property of spiking neurons even those that are not leaky This is a non physiological model which can be leaky or anti leaky depending on the sign of the input I All neurons receive the same fluctuating input scaled by a parameter p that varies across neurons This shows 1 reproducibility of spike timing 2 robustness with respect to deterministic changes parameter 3 increased reproducibility in the fluctuation driven regime input crosses the threshold from brian import x N 500 tau 33 ms taux 20 ms sigma 0 02 56 Chapter 3 Getting started Brian Documentation Release 1 4 1 eqs input B 2 1texp 2 x 1 1 dx dt x taux 2 taux 5 xi 1 vee eqss dv dt v It l tau sigm
483. rd var The unbiased estimate of the variances as in mean std The square root of var as in mean values A 2D array of the values of all the recorded neurons each row is a single neuron s values In addition if M isa StateMonitor object you write M i for the recorded values of neuron i if it was specified with the record keyword It returns a numpy array Methods plot indicesz None cmap None refresh None showlast None redraw True Plots the recorded values using pylab You can specify an index or list of indices otherwise all the recorded values will be plotted The graph plotted will have legends of the form name i for name the variable name and i the neuron index If cmap is specified then the colours will be set according to the matplotlib colormap cmap refresh specifies how often in simulation time you would like the plot to refresh Note that this will only work if pylab is in interactive mode to ensure this call the pylab ion command If you are using the refresh option showlast specifies a fixed time window to display e g the last 100ms If you are using more than one realtime monitor only one of them needs to issue a redraw command therefore set redraw F alse for all but one of them Note that with some IDEs interactive plotting will not work with the default matplotlib backend try doing something like this at the beginning of your script before importing brian import matplotlib ma
484. rd the resting potential as well as the jumps when a spike was received 12 Chapter 3 Getting started Brian Documentation Release 1 4 1 Tutorial 1a The simplest Brian program Importing the Brian module The first thing to do in any Brian program is to load Brian and the names of its functions and classes The standard way to do this is to use the Python from import x statement from brian import x Integrate and Fire model The neuron model we will use in this tutorial is the simplest possible leaky integrate and fire neuron defined by the differential equation tau dV dt V El and with a threshold value Vt and reset value Vr Parameters Brian has a system for defining physical quantities quantities with a physical dimension such as time The code below illustrates how to use this system which mostly works just as you d expect tau 20 msecond membrane time constant Vt 50 mvolt spike threshold Vr 60 mvolt reset value El 60 mvolt resting potential same as the reset The built in standard units in Brian consist of all the fundamental SI units like second and metre along with a selection of derived SI units such as volt farad coulomb All names are lowercase following the SI standard In addition there are scaled versions of these units using the standard SI prefixes m 1 1000 K 1000 etc Neuron model and equations The simplest way to define a neuron model in Brian
485. rded if needed Finally all neurons from the NeuronGroup receive independent realizations of Poisson spike trains except if the keyword freeze True is used in which case all neurons receive the same Poisson input Initialised as PoissonInput target N rate weight state jitter reliability copies record with arguments target Thetarget NeuronGroup N The number of independent Poisson inputs rate The rate of each Poisson process weight The synaptic weight state The name or the index of the synaptic variable of the NeuronGroup jitter is None by default There is the possibility to consider copies presynaptic spikes at each Pois son event randomly shifted according to an exponential law with parameter jitter taujitter in second reliability is None by default There is the possibility to consider copies presynaptic spikes at each Poisson event where each of these spikes is unreliable i e it occurs with probability jitter alpha between 0 and 1 copies The number of copies of each Poisson event This is identical to weight copies w except if jitterorreliability are specified record True if the input has to be recorded In this case the recorded events are stored in the recorded events attribute as a list of pairs 1 t where i is the neuron index and t is the event time freeze True if the input must be the same for all neurons of the NeuronGroup class brian PulsePacket args kwds Fires a Gau
486. re S is Synapses object S w 12 Value of variable w for synapse 12 S w 1 3 Value of variable w for synapses from neuron to neuron 3 This is an array as there can be several synapses for a given neuron pair e g with different delays S w 1 3 4 Value of variable w for synapse 4 from neuron 1 to neuron 3 Indexes can be integers slices arrays or groups Synaptic variables can be assigned values as follows S w P Q x where x is a float or a 1D array The number of elements in the array must equal the number of selected synapses 8 9 Synapses 283 Brian Documentation Release 1 4 1 S w P Q s where s is a string The string is Python code that is executed in a single vectorised operation where i is the presynaptic neuron index a vector of length the number of synapses j is the postsynaptic neuron index and n is the number of synapses The methods rand and randn return arrays of n random values Initialised with arguments data Vector of values synapses The Synapses object to matrix multiple synapses last Returns the wanted state as a matrix of shape presynaptic neurons postsynaptic neurons for visu alization purposes The returned array value at i j is the value of the wanted synaptic variable for the synapse between i j If not synapse exists between those two neurons then the value is np nan Dealing with multiple synapses between two neurons Outputting a 2D matrix is not generally possible
487. re time constants and U is a parameter in 0 1 Each a presynaptic spike triggers modifications of the variables x xx 1 u u gt utUx 1 u Note that the update order is important Synaptic weights are modulated by the product u x in 0 1 which is taken before updating the variables This model describes both depression and facilitation To introduce short term plasticity into an existing connection C use the class STP mystp STP C taud 100 ms tauf 5 ms U 6 4 6 Synapses Starting from Brian 1 4 there is a new class Synapses in which everything synaptic can be defined The Synapses is similar to the Connection class but it is more general and flexible In particular synaptic plas ticity can be defined in the same object 4 6 1 Defining synaptic models The basic syntax is as follows S Synapses P Q model w 1 pre v w This defines a set of synapses between NeuronGroup P and NeuronGroup Q If the target group is not specified it is identical to the source group by default The model keyword is similar as in NeuronGroup it defines synaptic variables and possibly their dynamics with differential equations as in NeuronGroup Here synaptic variable w is created there is one value for each synapse The pre keyword defines what happens when a presynaptic spike arrives at a synapse In this case variable w is added to variable v Because v is not defined as a synaptic variable it is assumed by defaul
488. reate rectangle 0 0 0 30 fill ffaaaa width 0 t can create text width 2 15 text self progressbars append can r t self results text Tkinter Label self text Computed 0 results time taken 0s self results text grid column 0 row processes 1 self title Simulation control def update results self elapsed complete RE Method to update the total number of results computed and the amount of time taken Fa self results text config text Computed str complete time taken str int elaps self update def update process self i elapsed complete msg To Method to update the status of a given process OR F can r t self progressbars i can itemconfigure t text Process str i make text report elapsed complete can coords r 0 0 int self pb width complete 30 self update def sim mainloop pool results message queue Kor Monitors results of a simulation as they arrive pool is the multiprocessing Pool that the processes are running in results is the AsyncResult object returned by Pool imap unordered which returns simulation results asynchronously as and when they are ready and message queue is a multiprocessing Queue used to communicate between child processes and the server process In this case we use this Queue to send messages about the percent complete and time elapsed for each run put We use this
489. rian Documentation Release 1 4 1 The first statement creates synapses between all pairs of neurons The second statement creates synapses between all neurons in the source group and neuron 1 in the target group The third statement connects all pairs of neurons in the subgroups Pe and Pi One can also create synapses using code S i Sle j i 1 N The code is a boolean statement that should return True when a synapse must be created where i is the presynaptic neuron index and j is the postsynaptic neuron index special variables Here the first statement creates one to one connections the second statement creates connections with a ring structure N is the number of neurons assumed to defined elsewhere by the user This way of creating synapses is generally much faster than using loops because it is internally vectorised Two high level construction methods are implemented S connect random groupl group2 sparseness 0 1 S connect one to one groupl group2 The first one randomly connects pairs of neurons with probability given by the sparseness argument The second one is equivalent to the instruction S groupl group2 i j The groupl and group2 arguments are subgroups of the source and target groups 4 6 3 Accessing synaptic variables Synaptic variables can be accessed in a similar way as NeuronGroup variables They can indexed with two indexes corresponding to the indexes of pre and postsynaptic ne
490. rian threshold Threshold codegen2 threshold NumSpikesS ymbol codegen2 threshold CodeGenThreshold 11 5 7 Reference blocks class brian experimental codegen2 Block args Contains a list of CodeItem objects which are considered to be executed in serial order The list is passed as arguments to the init method so if you want to pass a list you can initialise as block Block items class brian experimental codegen2 ControlBlock start end contents dependencies re solved Helper class used as the base for various control structures such as for loops if statements These are typically not language invariant and should only be output in the resolution process by symbols which know the language they are resolving to Consists of strings start and end a list of contents as for Block and explicit sets of dependencies and resolved these are self dependencies resolved The output code consists of the start string the indented converted contents and then the end string For example for a C for loop we would have start for and end convert to language symbols namespace class brian experimental codegen2 ForBlock start end contents dependencies resolved Simply a base class does nothing 11 5 Code generation 367 Brian Documentation Release 1 4 1 class brian experimental codegen2 PythonForBlock var container content dependen cie
491. rimental codegen2 376 CodeGenStateUpdater class in brian experimental codegen2 378 CodeGenThreshold class in brian experimental codegen2 384 Codeltem class in brian experimental codegen2 368 CodeObjectClass brian experimental codegen2 CLanguage attribute 376 CodeObjectClass brian experimental codegen2 GPULanguage attribute 375 CodeObjectClass brian experimental codegen2 PythonLanguage attribute 376 CodeStatement class in brian experimental codegen2 377 CoincidenceCounter class in brian 295 CombinedFilterbank class in brian hears 321 combining equations 215 Compartments example usage 177 compilation differential equations 218 equations 218 compile brian experimental codegen2 Code method 370 compile brian experimental codegen2 GPUCode method 374 brian experimental codegen2 GPUManager method 373 compile compile brian experimental codegen2 PythonCode method 370 computation online 242 connect from sparse brian Connection method 275 Connection example usage 31 39 40 45 46 49 54 63 66 68 74 77 79 82 84 97 99 102 106 109 130 132 154 156 158 160 162 164 165 167 170 172 174 177 179 181 185 187 connection matrix 277 Connection class in brian 273 connection matrix 277 ConnectionMatrix class in brian 277 Connection Vector class in brian 279 ConstructionMatrix class in brian 278 contained objects protocol exte
492. rimental codegen2 CodeGenConnection args kwds propagate spikes class brian experimental codegen2 DenseMatrixSymbols class SynapseIndex M name weightname language sourceindex source index tar getlen target len resolve read write vectorisable item namespace class DenseMatrixSymbols TargetIndex M name weightname language in dex synapse index targetlenz target len dependencies load read write vectorisable supported languages python c class DenseMatrixSymbols Value M name language index _synapse_index class brian experimental codegen2 SparseMatrixSymbols E class SynapseIndex M name weightname language sourceindex source index resolve read write vectorisable item namespace 370 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 class SparseMatrixSymbols TargetIndex M name weightname language in dex synapse index E class SparseMatrixSymbols Value M name language index synapse index dependencies class brian experimental codegen2 Dependency name Base class for Read and Write dependencies A dependency marks that a Code1tem depends on a given symbol Each dependency has a name class brian experimental codegen2 Read name Used to indicate a read dependency i e the value of the symbol is read class brian experimental codegen2 Write name Used to indicate a write dependency i e the
493. rious sizes optimising Ideas for making Brian faster speedtracking A sort of testing framework which tracks over time the speed of various Brian features tests A few scripts to run Brian s tests tools The main folder for developer tools docs Scripts for invoking Sphinx and building the documentation Includes script to automatically gen erate documentation for examples and tutorials and to build index entries for these newrelease Tools for creating a new public release of Brian searchreplace Some tools for doing global changes to the code e g syntax changes dist Automatically generated distribution files docs Automatically generated documentation files in HTML PDF format docs_sphinx Sources for Sphinx documentation examples Examples of Brian s use Documentation is automatically generated from all of these examples tutorials Source files for the tutorials documentation is automatically generated from these Each tutorial has a directory possibly containing an int roduction txt Sphinx source followed by a series of files in alpha betical order e g la Ib 1c etc Multi line strings are treated as Sphinx source code take a look at a few examples to get the idea See also the reference sheet You can download a PDF version of the documentation here 386 Chapter 11 Developer s guide PYTHON MODULE INDEX brian brian experimental model documentation 341 387 Brian Documentation Release 1 4
494. riterion 3 dt vc spike criterion Criterion dV dt gt 3 V s Spike triggered average of V STA spike shape V onsets onsets before 100 after 100 print Spike duration float spike_duration V onsets onsets dt ms ms 94 Chapter 3 Getting started Brian Documentation Release 1 4 1 print Reset potential float reset_potential V peaks peaks mV mv Spike threshold statistics slope slope threshold V onsets onsets T int 5 ms dt Subthreshold trace subthreshold spike_mask V t arange len V dt subplot 221 plot t ms V mV k plot t peaks ms V peaks mV b plot t onsets ms V onsets mV r subplot 222 plot arange len STA 100 dt ms STA mV k subplot 223 plot t subthreshold ms V subthreshold mV k subplot 224 plot slope ms V onsets mvV show Example voltageclamp electrophysiology Voltage clamp experiment from brian import x from brian library electrophysiology import defaultclock dt 01 ms taum 20 ms gl 20 nS Cm taum gl Re 50 Mohm Ce 0 2 x ms Re N 1 Rs 9 Re tauc Rs x Ce critical tau_u eqs Equations dvm dt gl vmti_inj Cm volt Eer qs electrode 2 Re Ce eqs voltage clamp vm v el v cmd 20 mV i inj i cmd Re 8 x Re Rs 9 x Re tau u 2 ms setup NeuronGroup N model eqs setup v 0 mV rec
495. rk operation decorator Models equations etc do not need to be passed to the Network object The most important method is the run duration method which runs the simulation for the given length of time see below for details about what happens when you do this Example usage 8 10 Network 285 Brian Documentation Release 1 4 1 G NeuronGroup C Connection net Network G C net run l second Methods add Add additional objects after initialisation works the same way as initialisation remove Remove objects from the Network run duration report report period Runs the network for the given duration See be low for details about what happens when you do this See documentation for run for an explanation of the report and report period keywords reinit states True Reinitialises the network runs each objects reinit and each clock s reinit method resetting them to 0 If states False then it will not reinitialise the NeuronGroup state variables stop Can be called from a network operation for example to stop the network from running len Returns the number of neurons in the network call obj Similar to add but you can only pass one object and that object is returned You would only need this in obscure circumstances where objects needed to be added to the network but were either not stored elsewhere or were stored in a way that made them difficult to extract for examp
496. roup Nin rates 2 Hz tau 10 ms neurons NeuronGroup Nout model dv dt v tau 1 threshold 35 50 5 reset 0 S Synapses input neurons model w 1 PSP size for one quantum nvesicles 1 Number of vesicles n is reserved p l Release probability pre v t binomial nvesicles p w S True all to all S w rand S nvesicles 50 S p rand S SpikeMonitor neurons run 1000 ms raster_plot S show Example one_synapse Synapses One synapse 136 Chapter 3 Getting started Brian Documentation Release 1 4 1 from brian import x P NeuronGroup 1 model dv dt 1 10 ms 1 threshold 1 reset 0 Q NeuronGroup 1 model v 1 S Synapses P Q model w 1 pre v t w M StateMonitor Q v record True S 0 0 True S w 0 0 1 S delay 0 0 5 ms run 40 ms plot M times ms M 0 show Example noisy_ring synapses Integrate and fire neurons with noise from brian import x tau 10 ms sigma 5 N 100 J 1 eqs wen dv dt mu tautsigma tau x 5 xi 1 wwe group NeuronGroup N model eqs threshold 1 reset 0 C Synapses group model w 1 pre vt w Cli tl J 141 N C w J S SpikeMonitor group trace StateMonitor group v record True run 500 ms i t S spikes 1 subplot 211 raster plot S subplot 212 plot trace times ms trace 0 show
497. ry random processes import For the moment only the Ornstein Uhlenbeck process has been included The function OrnsteinUhlenbeck returns an Equations object The following example defines a membrane equation with an Ornstein Uhlenbeck current I coloured noise eqs Equations dv dt v tau I C volt qs OrnsteinUhlenbeck I mu 1 nA sigma 2 nA tau 10 ms where mu is the mean of the current sigma is the standard deviation and t au is autocorrelation time constant 226 Chapter 5 The library Brian Documentation Release 1 4 1 5 3 Electrophysiology models The electrophysiology library contains a number of models of electrodes amplifiers and recording protocols to simu late intracellular electrophysiological recordings To import the electrophysiology library from brian library electrophysiology import x There is a series of example scripts in the examples electrophysiology folder 5 3 1 Electrodes Electrodes are defined as resistor capacitor RC circuits or multiple RC circuits in series Define a simple RC elec trode with resistance Re and capacitance Ce possibly 0 pF as follows l electrode Re Ce The elect rode function returns an Equat ions object containing the electrode model where the electrode poten tial is v e1 the recording the membrane potential is vm the electrode current entering the membrane is i inj and command current is i_cmd These names can be overriden
498. s plot cf rms xlabel Frequency Hz ylabel RMS show Example linear_gammachirp hears Example of the use of the class LinearGammachirp available in the library It implements a filterbank of FIR gammatone filters with linear frequency sweeps as described in Wagner et al 2009 Auditory responses in the barn owl s nucleus laminaris to clicks impulse response and signal analysis of neurophonic potential J Neurophysiol 3 2 Examples 111 Brian Documentation Release 1 4 1 In this example a white noise is filtered by a gammachirp filterbank and the resulting cochleogram is plotted The different impulse responses are also plotted from brian import x from brian hears import sound whitenoise 100 ms ramp sound level 50 dB nbr_center_frequencies 10 number of frequency channels in the filterbank center frequencies with a spacing following an ERB scale center frequencies erbspace 100 Hz 1000 Hz nbr center frequencies c 0 0 glide slope time constant linspace 3 0 3 nbr center frequencies ms gamma chirp LinearGammachirp sound center frequencies time constant c gamma chirp mon gamma chirp process figure imshow gamma chirp mon T aspect auto figure plot gamma chirp impulse response T show Example butterworth hears Example of the use of the class Butterworth available in the library In this example a wh
499. s In the following we suppose that an Equat ions object is defined as follows eqs Equations dx dt y x 10 ms volt dy dt z 5xms volt Z 2 xty volt FEF 218 Chapter 4 User manual Brian Documentation Release 1 4 1 Applying an equation The value of z can be calculated using the apply method z eqs apply z dict x 3 mV y 5 mV The second argument is a dictionary containing the values of all dependent variables here the result is 8 mV The right hand side of differential equations can also be calculated in the same way x eqs apply x dict x 2 mV y 3 mvV y eqs apply y dict x 2 mV y 3 mV Note in the second case that only the values of the dynamic variables should be passed Calculating a fixed point A fixed point of the equations can be calculated as follows fp eqs fixedpoint x 2 mV y 3 mV where the optional keywords give the initial point zero if not provided Internally the function optimize fsolve from the Scipy package is used to find a zero of the set of differential equations thus convergence is not guaranteed in that case the initial values are returned A dictionary with the values of the dynamic variables at the fixed point is returned Issues If the equations were previously frozen then the units disappear from the equations and unit consistency prob lems may arise Equations objects need to be prepared before use as follows
500. s You may want to use either of the following two solutions if you think your code may be used by someone else or if you want to make it into an extension to Brian 337 Brian Documentation Release 1 4 1 9 1 2 Use the magic return decorator or magic_register function The magic return decorator is used as follows Qmagic return def f return obj Any object returned by a function decorated by magic return will be considered to have been instantiated in the execution frame that called the function In other words the magic functions will find that object even though it was really instantiated in a different execution frame In more complicated scenarios you may want to use the magic register function For example def f magic register obj1l obj2 return obj1 obj2 This does the same thing as magic return but can be used with multiple objects Also you can specify a level see documentation on magic register for more details 9 1 3 Use derived classes Rather than writing a function which returns an object you could instead write a derived class of the object type So suppose you wanted to have an object that emitted N equally spaced spikes with an interval dt between them you could use the 5pikeGeneratorGroup class as follows Qmagic return def equally spaced spike group N dt spikes 0 i xdt for i in range N return SpikeGeneratorGroup spikes Or alternatively you could derive
501. s M nspikes 204 Chapter 4 User manual Brian Documentation Release 1 4 1 Custom monitoring To process the spikes in a specific way one can pass a function at initialisation of the SoikeMonitor object def f spikes print spikes M SpikeMonitor group function f The function f is called every time step with the argument spikes being the list of indexes of neurons that just spiked 4 7 2 Recording state variables State variables can be recorded continuously by defining a Stat eMonitor object as follows M StateMonitor group v Here the state variables v of the defined group are monitored By default only the statistics are recorded The list of time averages for all neurons is M mean the standard deviations are stored in M std and the variances in M var Note that these are averages over time not over the neurons To record the values of the state variables over the whole simulation use the keyword record Ml StateMonitor group v record True M2 StateMonitor group v record 3 5 9 The first monitor records the value of v for all neurons while the second one records v for neurons 3 5 and 9 only The list of times is stored in M1 times and the lists of values are stored in M1 i where i the index of the neuron Means and variances are no longer recorded if you record traces By default the values of the state variables are recorded every timestep but one may record every n timesteps by settin
502. s None resolved None A for loop in Python the structure is for var in container content Where var and container are strings and content is a CodeItem or list of items Dependencies can be given explicitly or by default they are Read x for each word x in container Re solved can be given explicitly or by default itis set var class brian experimental codegen2 CForBlock var spec content dependencies None re solved None A for loop in C the structure is for spec content You specify a string var which is the variable the loop is iterating over and a string spec should be of the form int i 0 i lt n i The content is a CodeItem or list of items The dependencies and resolved sets can be given explicitly or by default they are extracted respectively from the set of words in spec and set var class brian experimental codegen2 IfBlock start end contents dependencies resolved Just a base class class brian experimental codegen2 PythonIfBlock cond content dependencies None re solved None If statement in Python structure is if cond content Dependencies can be specified explicitly or are automatically extracted as the words in string cond and re solved can be specified explicitly or by default is set class brian experimental codegen2 CIfBlock cond content dependencies None re solved None If statement in C structure is if cond content
503. s all hand written Sphinx source files are stored in the docs sphinx folder in the repository and compiled HTML files are stored in the docs folder Most of the documentation is stored directly in the Sphinx source text files but reference documentation for important Brian classes and functions are kept in the documentation strings of those classes themselves This is automatically pulled from these classes for the reference manual section of the documentation The idea is to keep the definitive reference documentation near the code that it documents serving as both a comment for the code itself and to keep the documentation up to date with the code In the code every class or function should start with an explanation of what it does unless it is trivial A good idea is to use explicit names rather than abbreviations so that you instantly understand what it is about Inside a function important chunks should also be commented lesting Brian uses the nose package for its testing framework Tests are stored in the brian tests directory Tests associated to a Brian module are stored in brian tests testinterface and tests of the mathematical correctness of Brian s algorithms are stored in brian tests testcorrectness Errors It is a good idea to start an important function e g object initialisation with a check of the arguments and possibly issue errors This way errors are more understandable by the user Enhancements Brian uses a system
504. s features such as StateMonitor NeuronGroup update The NeuronGroup update method does the following three things First of all it calls the StateUpdater to update the state variables Then it calls its Threshold object if one exists to extract the indices of the spiking neurons Finally it pushes these into the LS attribute for extraction by any Connect ion objects NeuronGroup reset The Reset call method pulls spike from the NeuronGroup s LS attribute and then resets the state variables for those Spike propagation The Connection do propagate method does two things it gets the spike indices to propagate with homogeneous delays if chosen from the LS attribute of the NeuronGroup and then passes these to its Connection propagate method This method extracts a list of connection matrix rows using the ConnectionMatrix get rows method This method returns a list of ConnectionVector instances There are two types of ConnectionVector dense and sparse Dense ones are simply numpy arrays sparse ones consist of two numpy arrays an array of values and an array of corresponding column indices The SparseConnectionVector class has some methods which make this distinction seamless to the user in most instances although developers need to be aware of it Finally the Connection propagate method goes through this list applying the row vectors one by one The pure Python version of this is straightforward but there is also a C acceler
505. s object has attributes best pos best_fit info but only for group an or i key where i is a group index is the same as or i best_pos key For more details on the gamma factor see Jolivet et al 2008 A benchmark test for a quantitative assessment of simple neuron models J Neurosci Methods available in PDF here brian library modelfitting print table results precision 4 colwidth 16 Displays the results of an optimization in a table 306 Chapter 8 Reference Brian Documentation Release 1 4 1 Arguments results The results returned by the minimize of maximize function precision 4 The number of decimals to print for the parameter values colwidth 16 The width of the columns in the table brian library modelfitting open server port None maxcpu None maxgpu None lo cal None Start the Playdoh server Arguments port DEFAULT PORT The port integer of the Playdoh server The default is DEFAULT PORT which is 2718 maxcpu MAXCPU The total number of CPUs the Playdoh server can use MAXCPU is the total number of CPUs on the computer maxgpu MAXGPU The total number of GPUs the Playdoh server can use MAXGPU is the total number of GPUs on the computer if PyCUDA is installed brian library modelfitting get spikes model None reset None threshold None input None input var T dt None ini tial valueszNone params Retrieves the spike times corresponding to the best parameters found by t
506. s run by repeatedly evaluating the update schedule and updating the clock or clocks The update schedule is user specifiable but usually consists of the following sequence of operations interspersed with optional user network operation calls Update state variables of NeuronGroup Call thresholding function Push spikes into SpikeContainer Propagate spikes possibly with delays via Connection Update state variables of Synapses possibly includes updating the state of targeted NeuronGroup objects Call reset function on neurons which have spiked 11 3 2 Details of network construction Construction of NeuronGroup The NeuronGroup object is responsible for storing the state variables of each of its neurons for updating them each time step generating spikes via a thresholding mechanism storing spikes so that they can be accessed with a delay and resetting state variables after spiking State variable update is done by a StateUpdaater class defined in brian stateupdater py Thresholding is done by a Threshold class defined in brian threshold py and resetting is done by a Reset class defined in brian reset py The init methodof NeuronGroup takes these objects as arguments but it also has various additional keywords which can be used more intuitively In this case the appropriate object is selected automatically For example if you specify reset 0 mV in the keyword arguments Brian generates a Reset OxmV object The N
507. s spikes 1 Mf SpikeMonitor P function ratemonitor M SpikeMonitor P Simulation and plotting run 10 second print Rates after 10s print ns 10 second ns 0 run 10 second print Rates after 20s print ns 10 second raster_plot show Example non reliability misc Reliability of spike timing See e g Mainen amp Sejnowski 1995 for experimental results in vitro Here a constant current is injected in all trials 18 Brette 3 2 Examples 169 Brian Documentation Release 1 4 1 from brian import x N 25 tau 20 ms sigma 015 eqs neurons dx dt 1 1 x tautsigmax 2 tau xx 5xxi 1 rrt neurons NeuronGroup N model eqs neurons threshold 1 reset 0 refractory 5 ms spikes SpikeMonitor neurons run 500 ms raster plot spikes show Example named_threshold misc Example with named threshold and reset variables from brian import x FIT eqs dge dt ge 5 ms volt dgi dt gi 10 ms volt dx dt getgi x 49 mV 20 ms volt P NeuronGroup 4000 model eqs threshold x gt 50 mv reset Refractoriness 60 mV 5 ms state x P NeuronGroup 4000 model eqs threshold Threshold 50 mV state x reset Reset 60 mV state x without refractoriness P x 60 mV Pe P subgroup 3200 Pi P subgroup 800 Ce Connection Pe P ge weight 1 62 x mV sp
508. s value between 0 and to insert a space between each group on the y axis refresh Specify how often in simulation time you would like the plot to refresh Note that this will only work if pylab is in interactive mode to ensure this call the pylab ion command showlast If you are using the refresh option above plots are much quicker if you specify a fixed time window to display e g the last 100ms redraw If you are using more than one realtime monitor only one of them needs to issue a redraw command therefore set this to False for all but one of them Note that with some IDEs interactive plotting will not work with the default matplotlib backend try doing something like this at the beginning of your script before importing brian import matplotlib matplotlib use WXAgg You may need to experiment try WXAgg GTKAgg QTAgg TkAgg brian hist plot histmon None plotoptions Plot a histogram Usage hist plot histmon options Plotthe given histogram monitor hist plot options Guesses which histogram monitor to use with argument histmon is a monitor of histogram type Notes Plots only the first n 1 of n bars in the histogram because the nth bar is for the interval infinity Options Any of PyLab options for bar can be given as well as showplot False setto True to run pylab s show function newfigure True set to False not to create a new figure with pylab s figure function 8 12 Plotting 297
509. samples minimum buffer size This can be useful to ensure that the buffering is done ef ficiently internally even if the user request buffered chunks that are too small If the filterbank has a maximum buffer size attribute then buffer fetch next samples will always be called with samples maximum buffer size this can be useful for either memory consumption reasons or for implementing time varying filters that need to update on a shorter time window than the overall buffer size The following attributes will automatically be maintained self cached buffer start self cached buffer end The start and end of the cached segment of the buffer self cached buffer output Anarray of shape cached buffer end cached buffer start nchannels with the current cached segment of the buffer Note that this array can change size class brian hears Filterbank source Generalised filterbank object Documentation common to all filterbanks Filterbanks all share a few basic attributes source The source of the filterbank a Buf ferable object e g another Filterbank ora Sound It can also be a tuple of sources Can be changed after the object is created although note that for some filterbanks this may cause problems if they do make assumptions about the input based on the first source object they were passed If this is causing problems you can insert a dummy filterbank DoNothingFilterbank which is guaranteed to work if you change the source nchanne
510. sation is used by both Python and GPU but not C Each resolution step calls CodeItem resolve on the output of the previous stage statements class brian experimental codegen2 Statement Just a base class supposed to indicate single line statements class brian experimental codegen2 CodeStatement code dependencies resolved A language specific single line of code which should only be used in the resolution step by a Symbol which knows the language it is resolving to The string code and the set of dependencies and resolved have to be given explicitly convert to language symbols namespace class brian experimental codegen2 CDefineFromArray var arr index dependencies None resolved None dtype None refer ence True const False Define a variable from an array and an index in C For example double amp V arr V neuron index Initialisation arguments are var The variable being defined a string arr A string representing the array index A string giving the index dependencies Given explicitly or by default use set Read arr Read index resolved Given explicitly or by default use set var dtype The numpy data type of the variable being defined reference Whether the variable should be treated as a C reference e g double amp V rather than double V Ifthe variable is being written to as well as read from use reference True const Whether the variable can
511. so changes made on either the CPU or GPU won t automatically be reflected in the other Since only numerical integration is done on the GPU any state variable that is modified by incoming synapses for example should be copied to and from the GPU each time step In addition any variables used for thresholding or resetting need to be appropriately copied GPU gt CPU for thresholding and both for resetting 10 3 Multilinear state updater class brian experimental multilinearstateupdater MultiLinearNeuronGroup eqs subs clock None level 0 kwds Make a NeuronGroup with a linear differential equation for each neuron You give a single set of differential equations with parameters the variables you want substituted should be defined as parameters in the equations but they will not be treated as parameters instead they will be substituted You also pass a list of variables to have their values substituted and these names should exist in the namespace initialising the MultiLinearNeuronGroup Arguments eqs should be the equations and must be a string not an Equations object subs A list of variables to be substituted with values level How many levels up to look for the equations namespace clock If you want kwds Any additonal arguments to pass to NeuronGroup init Example eqs PI dv dt k v 1 xsecond 1 dw dt k w 1 xsecond 1 Kos L vee k array 1 2 3 340 Chapter 10 Experiment
512. somewhat under developed logging capabilities magic Classes and functions for tracking and finding instances of classes membrane equations More code for compartmental modelling see user docs monitor All the monitors including SpikeMonitor and StateMonitor network The Network and MagicNetwork classes as well as the NetworkOperation class Also includes the run etc functions neurongroup The NeuronGroup definition and some related stuff including linked variables the LinkedVar class and PoissonGroup optimiser Some tools for freezing expressions converting e g 3 ms into 0 003 and simplifying some equations e g a 10 ms converted to a 100 plotting Plotting tools mostly raster plot quantityarray A leftover from the day when Brian had support for arrays with units will be removed when practical reset Reset classes stateupdater State update classes and the magic state updater function stdp STDP features 384 Chapter 11 Developer s guide Brian Documentation Release 1 4 1 stdunits Standard unit names such as mV for mvolt etc stp Short term plasticity features threshold Threshold classes timedarray The TimedArray class and related functions units The Brian units package including the Quantity class unitsafefunctions Some functions which override the numpy ones which are safe to use with units e g sin 3 volt raises a dimensionality error library subpackage electrophys
513. sponses are normalized with respect to the transmitted power i e the rms of the filter taps is 1 Initialisation parameters source Source sound or filterbank f List or array of the sweep starting frequencies finstantaneous f ct time constant Determines the duration of the envelope and consequently the length of the impulse re sponse c 1 The glide slope or sweep rate given in Hz second The time dependent instantaneous frequency is f cx t and is therefore going upward when c gt 0 and downward when c 0 c can either be a scalar and will be the same for every channel or an array with the same length as f phase 0 Phase shift of the carrier Has attributes length impulse response Number of samples in the impulse responses impulse response Array of shape nchannels length impulse response with each row being an impulse response for the corresponding channel class brian hears LinearGaborchirp source f time constant c phase 0 Bank of gammachirp filters with linear frequency sweeps and gaussian envelope as described in Wagner et al 2009 Auditory responses in the barn owl s nucleus laminaris to clicks impulse response and signal analysis of neurophonic potential J Neurophysiol The impulse response IR is defined as follows IR t e 29 cos 2z ft 4 c 212 where o corresponds totime constant and to phase see definition of parameters These filters are implemented as FIR filters using truncated time
514. ss brian Connection source target state 0 delay 0 0 second modulation None struc ture sparse weight None sparseness None max_delay 5 0 msecond kwds Mechanism for propagating spikes from one group to another A Connection object declares that when spikes in a source group are generated certain neurons in the target group should have a value added to specific states See Tutorial 2 Connections to understand this better With arguments source The group from which spikes will be propagated target The group to which spikes will be propagated state The state variable name or number that spikes will be propagated to in the target group delay The delay between a spike being generated at the source and received at the target Depending on the type of delay it has different effects If delay is a scalar value then the connection will be initialised with all neurons having that delay For very long delays this may raise an error If delay True then the connection will be initialised as a DelayConnection allowing heterogeneous delays a different delay for each synapse delay can also be a pair min max or a function of one or two variables in both cases it will be initialised as a DelayConnection see the documentation for that class for details Note that in these cases initialisation of delays will only have the intended effect if used with the weight and sparseness arguments below max delay If you are using a conn
515. ss in brian hears 318 313 harmoniccomplex in module brian hears 316 L have same dimensions in module brian 259 labels from namespace in module HeadlessDatabase class in brian hears 330 brian experimental model documentation hist plot in module brian 297 343 histogram Language class in brian experimental codegen2 376 language invariant symbol method n module brian experimental codegen2 383 plotting 297 Hodgin Huxley type equations numerical integration 217 394 Index Brian Documentation Release 1 4 1 latex_equation brian experimental model_documentation LaTedkbopimesm eritad 124 static method 342 LogGammachirp class in brian hears 322 latex_equations brian experimental model documentationldg liaK D cumentWriter static method 342 LaTeXDocumentWriter class in brian experimental model documentation 342 LazyStateUpdater class in brian 270 left brian hears Sound attribute 312 level sound 240 316 level brian hears Sound attribute 314 linear equations 216 integration 270 threshold 268 LinearFilterbank example usage 108 118 LinearFilterbank class in brian hears 316 LinearGaborchirp class in brian hears 323 LinearGammachirp example usage 111 LinearGammachirp class in brian hears 322 LinearStateUpdater class in brian 270 linked var example usage 56 60 178 184 linked var in module brian 299 load brian experimen
516. ssian distributed packet of n spikes with given spread Initialised as PulsePacket t n sigma clock with arguments t The mean firing time n The number of spikes in the packet sigma The standard deviation of the firing times clock The clock to use omit to use default or local clock Methods This class is derived from SpikeGeneratorGroup and has all its methods as well as one additional method 8 6 Standard Groups 271 Brian Documentation Release 1 4 1 generate f n sigma Change the parameters and or generate a new pulse packet class brian SpikeGeneratorGroup N spiketimes clock None period None sort True gather None Emits spikes at given times Initialised as SpikeGeneratorGroup N spiketimes clock period with arguments N The number of neurons in the group spiketimes An object specifying which neurons should fire and when It can be a container such as a list containing tuples i t meaning neuron i fires at time t or a callable object which returns such a container which allows you to use generator objects even though this is slower see below i can be an integer or an array list of neurons that spike at the same time If spiketimes is not a list or tuple the pairs i t need to be sorted in time You can also pass a numpy array spiketimes where the first column of the array is the neuron indices and the second column is the times in seconds Alternatively you can pass a tuple
517. stant choose K 1 for relative concentrations Hill coefficient return cx n c x n K n N 5000 number of receptors seed 31415 Get the same neurons every time intensity 3000 Odor plumes tau_plume 75 ms eq plumes 3 2 Examples 75 Brian Documentation Release 1 4 1 dx dt x tau_plumet 2 tau_plume 5 xi 1 y clip x 0 inf 1 EFF plume NeuronGroup 2 model eq plumes 1 odor Receptor neurons Fmax 40 Hz maximum firing rate tau 20 ms Imax 1 1 exp 1 Fmax tau maximum input current eq receptors dv dt Imaxxhill function c v tau 1 c 1 4 concentrations relative to activation constant PEF receptors NeuronGroup N model eq_receptors threshold 1 reset 0 Qnetwork operation def odor to nose Send odor plume to the receptors receptors c Il cl clip plume x 0 0 Inf I2 xc2 clip plume x 0 0 1Inf odors odor N odor N cl c2 odors Decoder neurons M len tuning eq_decoders dv dt v taud sigmax 2 taud 5 xi 1 CCF decoders NeuronGroup M model eq_decoders threshold 1 reset 0 S2 SpikeMonitor decoders Synapses syn Connection receptors decoders v for i in range len decoders for j in weights i nonzero 0 syn j i weights j i Run I1 12 intensity 0 print Started Odor A increasing concentration for I1 in intensity xexp linspace log 1 log 10 20 run 1 second report text
518. sting simulation be patient run T print Simulation completed If you did not see any firing rate population burst lower panel then Plot nice spikes adapted from Brette s code vm trace 0 spikesO t for i t in M spikes if i 0 for i in range 0 len spikes0 k int spikesO i defaultclock dt vm k 80 mV subplot 311 membrane potential of neuron 0 plot trace times ms vm mV 60 subplot 312 raster plot raster_plot M subplot 313 smoothed population rate plot R times ms R smooth rate 5 ms Hz tracex times ms tracex 0 10 ylim 0 120 show Example anonymous twister Anonymous entry for the 2012 Brian twister 3 2 Examples 103 Brian Documentation Release 1 4 1 vier My contribution to the brian twister I meant to give it more thought but I forgot about the deadline ELF from brian import x from brian hears import import pygame _mixer_status 1 1 class SoundMonitor SpikeMonitor mmm Listen to you networks Plays pure tones whenever a neuron spikes frequency is set according to the neuron number mmm def init self source record False delay 0 frange 100 Hz 5000 xHz duration 50 ms samplerate 44100 Hz super SoundMonitor self init source record record delay delay self samplerate samplerat self nsamples np rint duration samplerate p linspace 0 1 len source reshape 1
519. t choose K 1 for relative concentrations n Hill coefficient FW return cxxn c n Kx n N 5000 number of receptors seed 31415 Get the same neurons every time intensity 3000 Odor plumes tau_plume 75x ms eq_plumes dx dt x tau_plumet 2 tau_plume 5 xi 1 y elip x 0 in f X rrt plume NeuronGroup 1 model eq plumes 1 odor Receptor neurons Fmax 40 Hz maximum firing rate tau 20 ms Imax 1 1 exp 1 Fmax tau maximum input current eq receptors dv dt Imaxxhill function c v tau 1 c 1 4 concentrations relative to activation constant EEF 3 2 Examples 77 Brian Documentation Release 1 4 1 receptors NeuronGroup N model eq_receptors threshold 1 reset 0 Qnetwork operation def odor to nose Send odor plume to the receptors receptors c Il cl clip plume x 0 0 Inf odors odor N odor N two odors cl odors 0 stimuli A random odor is presented every 200 ms network_operation clock EventClock dt 200 ms def change_odor global cl nodor randint len odors cl odors nodor stimuli append float defaultclock t float nodor Decoder neurons M 30 eq decoders dv dt v taud sigmax 2 taud 5 xi 1 CEF decoders NeuronGroup M model eq_decoders threshold 1 reset 0 S2 SpikeMonitor decoders Random synapses syn Connection receptors decoders v sparseness Nsynapses 1 N wei
520. t clamp misc An example of single electrode current clamp recording with bridge compensation using the electrophysiology li brary from brian import x from brian library electrophysiology import taum 20 ms membrane time constant gl 1 50 Mohm leak conductance Cm taum gl membrane capacitance Re 50 Mohm electrode resistance Ce 0 5 ms Re electrode capacitance eqs Equations dvm dt glxvm i inj Cm volt Rbridge ohm bridge resistance I amp command current Fay eqs current clamp i cmd I Re Re Ce Ce bridge Rbridge setup NeuronGroup 1 model eqs soma StateMonitor setup vm record True recording StateMonitor setup v rec record True No compensation run 50 ms setup I 5 nA run 100 ms 3 2 Examples 171 Brian Documentation Release 1 4 1 setup I 0 nA run 50 ms Full compensation setup Rbridge Re run 50 ms setup I 5 nA run 100 x ms setup I 0 nA run 50 ms plot recording times ms mV plot soma times ms soma 0 show recording 0 mV er Example CUBA misc rts This is a Brian script implementing a benchmark described in the following review paper Simulation of networks of spiking neurons A review of tools and strategies 2007 Brette Rudolph Carnevale Hines Beeman Bower Diesmann Goodman Harris Zirpe Natschlager Pecevski Ermentrout Djurfeldt
521. t that it is a postsynaptic variable defined in the target NeuronGroup Q Note that this does not does create synapses see next section only the synaptic models The more general syntax is S Synapses P Q model model_string pre pre_code post post_code Model syntax The model follows exactly the same syntax as for NeuronGroup There can be parameters e g synaptic variable w above but there can also be static equations and differential equations describing the dynamics of synaptic variables In all cases synaptic variables are created one value per synapse Internally these are stored as arrays There are a few specificities 200 Chapter 4 User manual Brian Documentation Release 1 4 1 A variable with the post suffix is looked up in the postsynaptic target neuron That is v post means variable v in the postsynaptic neuron A variable with the pre suffix is looked up in the presynaptic source neuron A variable not defined as a synaptic variable is considered to be postsynaptic A variable not defined as a synaptic variable and not defined in the postsynaptic neuron is considered external For the integration of differential equations one can use the same keywords as for NeuronGroup Event driven updates By default differential equations are integrated in a clock driven fashion as for a NeuronGroup This is po tentially very time consuming because all synapses are updated at every timestep It is
522. tabase 5 7 Brian hears 245 Brian Documentation Release 1 4 1 246 Chapter 5 The library CHAPTER SIX ADVANCED CONCEPTS 6 1 How to write efficient Brian code There are a few keys to writing fast and efficient Brian code The first is to use Brian itself efficiently The second is to write good vectorised code which is using Python and NumPy efficiently For more performance tips see also Compiled code 6 1 1 Brian specifics You can switch off Brian s entire unit checking module by including the line import brian_no_units before importing Brian itself Good practice is to leave unit checking on most of the time when developing and debugging a model but switching it off for long runs once the basic model is stable Another way to speed up code is to store references to arrays rather than extracting them from Brian objects each time you need them For example if you know the custom reset object in the code above is only ever applied to a group custom_group say then you could do something like this def myreset P spikes custom group V spikes OxmvV custom group Vt spikes 2 mV custom group custom group V custom group V custom group Vt custom group Vt In this case the speed increase will be quite small and probably not worth doing because it makes it less readable but in more complicated examples where you repeatedly refer to custom group V it could add up 6 1 2 Vectorisation
523. tal codegen2 ArraySymbol method 380 LowPass example usage 115 123 LowPass class in brian hears 325 Lp compensate in brian library electrophysiology 310 module M magic 334 magic functions extending brian 250 337 multiple files 250 337 magic register extending brian 250 337 multiple files 250 337 magic register in module brian 334 magic return extending brian 250 337 multiple files 250 337 magic return in module brian 334 MagicNetwork class in brian 289 make c integrator in brian experimental codegen2 376 make combined kernel brian experimental codegen2 GPUManager method 373 make coordinates in module brian hears 330 module load brian experimental codegen2 DenseMatrixS ymbols Target nakeeration_step in module method 370 brian experimental codegen2 375 load brian experimental codegen2 Symbol method MathematicalStatement class in 379 brian experimental codegen2 377 load brian hears Sound static method 311 matrix load_aer connection 277 example usage 168 maxlevel brian hears Sound attribute 314 load_aer in module brian 301 membrane potential load cQ brian experimental codegen2 ArraySymbol equations 216 method 381 MembraneEquation load python brian experimental codegen2 ArraySymbol example usage 167 177 method 381 methods loadsound in module brian hears 315 integration 269 log 255 MiddleEar example usa
524. tances of different cell types in nS maximal_conductances dict typelc 1000 150 0 0 0 5 0 2 typelt 1000 80 0 65 0 5 0 2 typel2 1000 150 20 0 2 0 2 type21 1000 150 35 0 3 5 0 2 type2 1000 150 200 0 20 0 2 type20 1000 150 600 0 0 40 2 octopus cell gnabar gkhtbar gkltbar gkabar ghbar gbarno gl x nS for x in maximal conductances neuron t Classical Na channel eqs_na nnm ina gnabar m 3xh ENa v amp dm dt q10 minf m mtau 1 dh dt q10 hinf h htau 1 minf l ltexp vu 38 T s 1 hinf 1 1 exp vu 65 6 1 mtau 10 5xexp vu 60 18 36 exp vut60 25 0 04 ms ms htau 100 7xexp vu 60 11 10 exp vu 60 25 0 6 ms ms mnm KHT channel delayed rectifier K eqs kht wm ikht gkhtbarx nfxn 2 dn dt ql0 ninf n ntau 1 dp dt q10 pinf p ptau 1 1 nf p EK v amp ninf 1 exp vu 4 15 5 0 5 s 1 pinf 1 1 exp vu 23 6 1 ntau 100 11l exp vut60 24 21 exp vu 60 23 0 7 ms ms ptau 100 4 exp vut60 32 5xexp vu 60 22 5 ms ms wee Ih channel subthreshold adaptive non inactivating eqs_ih ih ghbar r Eh v amp dr dt ql0 rinf r rtau 1 rinf 1 ltexp vu 76 7 1 rtau 100000 237 xexp vu
525. te b post 5 Hz target firing rate 5 Hz Simulation control record_period 1 second duration 100 second 3 2 5 frompapers computing with neural synchrony hearing Example Fig7A_Jeffress frompapers computing with neural synchrony hearing Brette R 2012 Computing with neural synchrony PLoS Comp Biol 8 6 e1002561 doi 10 1371 journal pcbi 1002561 Figure 7A Jeffress model adapted with spiking neuron models A sound source white noise is moving around the head Delay differences between the two ears are used to determine the azimuth of the source Delays are mapped to a neural place code using delay lines each neuron receives input from both ears with different delays from brian import x defaultclock dt 02 x ms dt defaultclock dt Sound sound TimedArray 10 x randn 50000 white noise Ears and sound motion around the head constant angular speed sound speed 300 metre second interaural distance 20 cm big head max delay interaural distance sound speed print Maximum interaural delay max delay angular speed 2 x pi x radian second 1 turn second tau ear 1 ms sigma ear 05 eqs ears dx dt sound t delay x tau eartsigma ear 2 tau ear x x 5 xxi 1 delay distance sin theta second distance second distance to the centre of the head in time units dtheta dt angular speed radian rrt ears NeuronGroup 2 model eqs ears threshold 1
526. tep In fact the number of firings is bounded above by 200 000 The reason for this is that the network updates in the following way 1 Integration step 2 Find neurons above threshold 3 Propagate spikes 4 Reset neurons which spiked You can see then that if neuron i has spiked at time t then it will not spike at time t dt even if it receives spikes from another neuron Those spikes it receives will be added at step 3 at time t then reset to Vr at step 4 of time t then the thresholding function at time t dt is applied at step 2 before it has received any subsequent inputs So the most a neuron can spike is every other time step Tutorial 1f Recording spikes In the previous part of the tutorial we defined a network with not entirely trivial behaviour and printed the number of spikes In this part we ll record every spike that the network generates and display a raster plot of them We start as before from brian import x tau 20 msecond membrane time constant Vt 50 mvolt spike threshold Vr 60 mvolt reset value El 49 x mvolt resting potential same as the reset psp 0 5 mvolt postsynaptic potential size G NeuronGroup N 40 model dV dt V El tau volt threshold Vt reset Vr C Connection G G C connect_random sparseness 0 1 weight psp M SpikeMonitor G G V Vr rand 40 Vt Vr 16 Chapter 3 Getting started Brian Documentation Release 1
527. that dX dt M X B are calculated with the function get linear equations Third the matrix A such that X t dt A X t B B is calculated at initialisation of a specific state updater object LinearStateUpdater as A expm M dt where expm is the matrix exponential Note that this approach raises an issue when dX dt B We currently temporarily solve this problem by adding a small diagonal matrix to M to make it invertible 216 Chapter 4 User manual Brian Documentation Release 1 4 1 Important remark since the update matrix and vector are precalculated the values of all external variables in the equations are frozen at initialisation If external variables are modified after initialisation those modifications are not taken into account during the simulation Inexact exact integration If the equation cannot be put into the form dX dt M X B for example if the equation is dX dt MX A where M is not invertible then the equations are not integrated exactly but using a system equivalent to Euler integration but with dt 100 times smaller than specified Updates are of the form X t dt A X t C where the matrix A and vector C are computed by applying Euler integration 100 times to the differential equations Euler integration The Euler is a first order explicit integration method It is the default one for nonlinear equations It is simply implemented as X t dt X th f X dt Exponential Euler integration The exponential E
528. the default clock values then you should not specify clock start or dt see Technical notes below Arbitrary slicing of the array is supported but the clock will only be preserved where the intervals can be guaranteed to be fixed that is except for the case where lists or numpy arrays are used on the time index Timed arrays can be called as if they were a function of time if the array times are based on a clock but not if the array times are arbitrary as the look up costs would be excessive If x t is called where times i lt t lt times i dt for some index i then x t will have the value x i You can also call x t with t a ID array If x is 1D then x t i x t il ifxis2D then x t i x t i1 i Has one method See also TimedArraySetter set group var by array and NeuronGroup Technical notes Note that specifying a new clock or values of start and dt will mean that if you use this TimedArray to set the value of a NeuronGroup variable it will be updated on the schedule of this clock which can due to floating point errors induce some timing problems This rarely happens but if an occasional inaccuracy of order dt might conceivably be critical for your simulation you should use RegularClock objects instead of Clock objects class brian TimedArraySetter args kwds Sets NeuronGroup values with a TimedArray At the beginning of each update step this object will set the values of a given state varia
529. the individuals in the population to create mutation children Mutation provides genetic diversity and enable the genetic algorithm to search a broader space Different options are available gaussian adds a random number taken from a Gaussian distribution with mean 0 to each entry of the parent vector The scale mutation parameter 0 8 by default determines the standard deviation at the first generation by scale mutation Xmax Xmin where Xmax and Xmin are the boundaries The shrink mutation parameter 0 2 by default controls how the standard deviation shrinks as generations go by math sigma i Nsigma i 1 1 shrink mutation i maxiter at iteration i uniform The algorithm selects a fraction of the vector entries of an individual for mutation where each entry has a probability nutation rate default is 0 1 of being mutated In the second step the algorithm replaces each selected entry by a random number selected uniformly from the range for that entry class brian library modelfitting CMAES Covariance Matrix Adaptation Evolution Strategy algorithm See the wikipedia entry on CMAES and also the author s website lt http www lri fr hansen cmaesintro html gt Optimization parameters proportion selective 0 5 This parameter refered to as mu in the CMAES algorithm is the pro portion out of 1 of the entire population that is selected and used to update the generative distribution note for different
530. the plot The most strongly responding assembly is indicated by the green x which is the estimate of the location by the model from brian import x from brian hears import Download the IRCAM database http recherche ircam fr equipes salles listen download html and replace this filename with the location you downloaded it to hrtfdb IRCAM_LISTEN r Z HRTF IRCAM subject 1002 hrtfset hrtfdb load_subject subject This gives the number of spatial locations in the set of HRTFs num indices hrtfset num indices Choose a random location for the sound to come from index randint num indices A sound to test the model with sound Sound whitenoise 500 ms This is the specific HRTF for the chosen location hrtf hrtfset hrtf index We apply the chosen HRTF to the sound the output has 2 channels hrtf fb hrtf filterbank sound We swap these channels equivalent to swapping the channels in the subsequent filters but simpler to do it with the inputs swapped channels RestructureFilterbank hrtf fb indexmapping 1 0 Now we apply all of the possible pairs of HRTFs in the set to these swapped channels which means repeating them num indices times first hrtfset fb hrtfset filterbank Repeat swapped channels num indices Now we apply cochlear filtering logically this comes before the HRTF filtering but since convolution is commutative it is more efficient to do the cochlear filtering
531. the short labels making it easier to link the model description and the actual code 10 5 Automatic Model Documentation 343 Brian Documentation Release 1 4 1 344 Chapter 10 Experimental features CHAPTER ELEVEN DEVELOPER S GUIDE This section is intended as a guide to how Brian functions internally for people developing Brian itself or extensions to Brian It may also be of some interest to others wishing to better understand how Brian works internally 11 1 Guidelines The basic principles of developing Brian are 1 For the user the emphasis is on making the package flexible readable and easy to use See the paper The Brian simulator in Frontiers in Neuroscience for more details 2 For the developer the emphasis is on keeping the package maintainable by a small number of people To this end we use stable well maintained existing open source packages whenever possible rather than writing our own code Coding conventions We use the PEP 8 coding conventions for our code Syntax is chosen as much as possible from the user point of view to reflect the concepts as directly as possible Ideally a Brian script should be readable by someone who doesn t know Python or Brian although this isn t always possible Function and class names should be explicit rather than abbreviated Documentation It is very important to maintain documentation We use the Sphinx documentation generator tools The documentation i
532. the stopband in dB Can be a scalar or an array of length nchannels gstop 10 xdB farrays of shape 2 x nchannels defining the passband frequencies Hz passband vstack center frequencies bw 2 center frequencies tbw 2 farrays of shape 2 x nchannels defining the stopband frequencies Hz stopband vstack center frequencies 1 1 bw center frequencies 1l 1 bw filterbank IIRFilterbank sound nchannels passband stopband gpass gstop bandstop chebyl filterbank mon filterbank process 3 2 Examples 117 Brian Documentation Release 1 4 1 figure subplot 211 imshow flipud filterbank mon T aspect auto example of a bank of lowpass filter tet tt et nchannels 50 cutoff frequencies linspace 100 Hz 1000 Hz nchannels bandwidth of the transition region between the en of the pass band and the begin of the stop band width transition linspace 50 Hz 300 Hz nchannels The maximum loss in the passband in dB Can be a scalar or an array of length nchannels gpass 1 dB The minimum attenuation in the stopband in dB Can be a scalar or an array of length nchannels gstop 10 dB passband cutoff frequencies width transition 2 stopband cutoff frequencies width transition 2 filterbank IIRFilterbank sound nchannels passband stopband gpass gstop low cheby1 filterbank mon filterbank process subplot 212 imshow flipud filter
533. the weight sparseness and delay keywords For example myconnection Connection groupl group2 ge weight 1 nS sparseness 0 1 delay O ms 5 xms max delay 5 ms This would be equivalent to myconnection Connection groupl group2 ge delay True max delay 5 ms myconnection connect random groupl group2 weight l1 nS delay O ms 5xms If the sparseness value is omitted or set to value 1 full connectivity is assumed otherwise random connectivity NOTE in this case the delay keyword used without the weight keyword has no effect 4 4 Spike timing dependent plasticity Synaptic weights can be modified by spiking activity Weight modifications at a given synapse depend on the relative timing between presynaptic and postsynaptic spikes Down to the biophysical level there is a number of synaptic 198 Chapter 4 User manual Brian Documentation Release 1 4 1 variables which are continuously evolving according to some differential equations and those variables can be mod ified by presynaptic and postsynaptic spikes In spike timing dependent plasticity STDP rules the synaptic weight changes at the times of presynaptic and postsynaptic spikes only as a function of the other synaptic variables In Brian an STDP rule can be specified by defining an STDP object as in the following example eqs stdp dA pre dt A pre tau pre 1 dA post dt A post tau post 1 EFT stdp STDP myconnectio
534. tical operations and numpy functions work as you would expect with sounds e g soundl1 sound2 3 soundor abs sound Level level Can be used to get or set the level of a sound which should be in dB For single channel sounds a value in dB is used for multiple channel sounds a value in dB can be used for setting the level all channels will be set to the same level or a list tuple array of levels It is assumed that the unit of the sound is Pascals atlevel level Returns the sound at the given level in dB SPL RMS assuming array is in Pascals level should be a value in dB or a tuple of levels one for each channel maxlevel Can be used to set or get the maximum level of a sound For mono sounds this is the same as the level but for multichannel sounds it 1s the maximum level across the channels Relative level differences will be preserved The specified level should be a value in dB and it is assumed that the unit of the sound is Pascals atmaxlevel level Returns the sound with the maximum level across channels set to the given level Relative level differences will be preserved The specified level should be a value in dB and it is assumed that the unit of the sound is Pascals Ramping ramp when onset durationz 10 0 msecond envelope None inplace True Adds a ramp on off to the sound when onset Can take values onset offset or both duration 10 ms The time over which the ramping happ
535. times ms rate smooth rate 5 ms Hz show Example remotecontrolserver misc Example of using RemoteControlServer and RemoteControlClient to control a simulation as it runs in Brian After running this script run remotecontrolclient py or paste the code from that script into an IPython shell for inter active control from brian import x eqs a dV dt I V 10 ms 0 1 xi 2 10 ms 5 1 I oi Far G NeuronGroup 3 qs reset 0 threshold 1 M RecentStateMonitor G V duration 50 ms server RemoteControlServer run lel10 second Example COBAHH misc This is an implementation of a benchmark described in the following review paper Simulation of networks of spiking neurons A review of tools and strategies 2006 Brette Rudolph Carnevale Hines Beeman Bower Diesmann Goodman Harris Zirpe NatschlAger Pecevski Ermentrout Djurfeldt Lansner Rochel Vibert Alvarez Muller Davison El Boustani and Destexhe Journal of Computational Neuroscience Benchmark 3 random network of HH neurons with exponential synaptic conductances Clock driven implementation no spike time interpolation 18 Brette Dec 2007 70s for dt 0 1 ms with exponential Euler 174 Chapter 3 Getting started Brian Documentation Release 1 4 1 from brian import Parameters area 20000 umetre 2 Cm 1 ufarad x cm 2 area gl 5e 5 siemens cm 2 x area El
536. tion graph_connections connections groups Draw a graph visualizing the connection structure of the network intro Is called before any other output function useful for the start of an HTML or LaTeX document outro Is called after all other output function useful for the end of an HTML or LaTeX document static to_sympy_expression eq_string Simple helper function for converting an Equation string eg_string only the right hand side of an equation into a sympy expression by calling x Symbol x for every variable x in the equation class brian experimental model_documentation TextDocumentWriter kwargs Documents the network by printing to stdout uses sympy for formatting the equations including nice Unicode symbols class brian experimental model documentation LaTeXDocumentWriter kwargs Documents the network by printing LaTeX code to stdout Prints a full document i e including preamble etc The resulting LaTeX file needs the amsmath package Note that if you use the graph_connections True option you additionally need the tikz and dot2texi packages part of texlive core and texlive pictures on Linux systems and the dot2tex tool To make the conversion from dot code to LaTeX automatically happen on document creation you have to pass the shell escape option to your LaTeX call e g pdflatex shell escape network doc tex static format equation lhs rhs unit Helper function to convert an equ
537. tion Release 1 4 1 8 5 1 StateUpdaters Typically you don t need to worry about StateUpdater objects because they are automatically created from the differential equations defining your model TODO more details about this class brian LinearStateUpdater M B None clock None A linear model with dynamics dX dt M X B or dX dt MX Initialised as LinearStateUpdater M B clock with arguments M Matrix defining the differential equation B Optional linear term in the differential equation clock Optional clock Computes an update matrix A exp M dt for the linear system and performs the update step TODO more mathematical details class brian LazyStateUpdater numstatevariables 1 clock None A StateUpdater that does nothing Initialised as LazyStateUpdater numstatevariables 1 clock with arguments numstatevariables The number of state variables to create clock An optional clock to determine when it updates although the update function does nothing so TODO write docs for these StateUpdaters e StateUpdater LinearStateUpdater more details NonlinearStateUpdater NonlinearStateUpdater2 Exponen tialEulerStateUpdater NonlinearStateUpdaterRK2 NonlinearStateUpdaterBE SynapticNoise 8 6 Standard Groups Some standard types of NeuronGroup have already been defined PoissonGroup and PoissonInput to generate spikes with Poisson statistics PulsePacket to generate pulse packets with specified para
538. tion and then emit graded amounts of neurotransmitter variable y to the auditory nerve fibres input current variable I from brian import x N5 f 50 Hz a_min 1 0 a_max 100 0 tau_haircell 50 ms tau 10 ms duration 100 ms eqs haircells input axsin 2x xpixfxt 1 x eclip input 0 Inf 1 0 3 0 2 1 Bird 184 Chapter 3 Getting started Brian Documentation Release 1 4 1 dy dt x y tau haircell 1 qa haircells NeuronGroup N eqs haircells haircells a linspace a min a max N M haircells MultiStateMonitor haircells vars input y record True qs nervefibres dv dt I V tau 1 I EL Kw nervefibres NeuronGroup N qs_nervefibres reset 0 threshold 1 nervefibres I linked var haircells y M_nervefibres MultiStateMonitor nervefibres record True run duration subplot 221 haircells input plot ylabel haircell input subplot 222 haircells y plot ylabel haircell y subplot 223 nervefibres I plot ylabel nervefibres I subplot 224 nervefibres V plot ylabel nervefibres V show 3 2 16 audition Example jeffress audition Jeffress model adapted with spiking neuron models A sound source white noise is moving around the head Delay differences between the two ears are used to determine the azimuth of the source Delays are
539. tion is simulated Its overall emerging firing rate activity replicates some of the features of spontaneous patterned electrical activity observed experimentally in cultured networks of neurons dissociated from the neocortex Se SR SR OS CH Hz CH OSE CH CH SHR SHR CHR CHO SR from brian import x Parameters of the simulation T 30000 ms life time of the simulation N 100 total number of excitatory integrate and fire model neurons in the network Parameters of each model neuron voltage dynamics C 67 95 pF Membrane capacitance of single model neurons tau 22 25 x ms Membrane time constant of single model neurons H 2 39 xmv theta 20 mV tauarp 7 76 ms Reset voltage mimicking hyperpolarization potential following a spike Threshold voltage for spike initiation Absolute refractory period Sh cH CH CHE Parameters of each model neuron spike frequency adaptation dynamics taua 2100 ms Adaptation time constant a 0 75 pA Adaptation scaling factor NO ADAPTATION D l1x ms Unit consistency factor temp 1 ms x 5 Unit consistency factor Parameters of network connectivity Cee 0 38 Sparseness of all to all random connectivity taue 5 ms Decay time constant of excitatory EPSPs delta 1 5 ms Conductiontsynaptic propagation delay J 14 5 pA Strenght of synaptic coupling up to 18 xpA Parameters of background synaptic activity modelled as a identical and independe
540. tions defined in brian stateupdater py Finally note that equations strings can contain references to names of objects that are defined in the namespace of the string and the Equations object can pick these out It does this by inspecting the call stack extracting the namespace for the appropriate level which has to be kept track of and plucking out the appropriate name The level keywords you see dotted around Brian s code are there to keep track of these levels for this reason Construction of Connection Connection objects provide methods for storing weight matrices and propagating spikes Spike propagation is done via the Connection do propagate and Connection propagate methods Weight ma trices are stored in the W attribute Initially weight matrices are Const ructionMatrix objects and are con verted by the Connection compress method via the matrices connection matrix methods to ConnectionMatrix objects The idea is to have two data structures one appropriate to the construction of a matrix supporting adding and removing new synapses and one appropriate to runtime behaviour focussing on fast row access above all else There are three matrix structures dense sparse and dynamic and computed may be added later The dense matrix is just a full 2D array and the matrix objects just reproduce the functionality of numpy arrays The sparse and dynamic structures are sparse matrices T
541. to demonstrate stopping a simulation during a run Have a fully connected network of integrate and fire neurons with input fed by a group of Poisson neurons with a steadily increasing rate want to determine the point in time at which the network of integrate and fire neurons switches from no firing to all neurons firing so we have a network operation called stop condition that calls the stop function if the monitored network firing rate is above a minimum threshold from brian import x clk Clock Vr 0 x mV El 0 mV Vt 10 mV tau 10 ms weight 0 2 x mV duration 100 msecond max input rate 10000 Hz num input neurons 1000 input connection p 0 1 rate per neuron max input rate num input neurons input connection p P PoissonGroup num input neurons lambda t rate per neuron t duration 3 2 Examples 165 Brian Documentation Release 1 4 1 NeuronGroup 1000 model dV dt V El tau volt threshold Vt reset Vr V Vr Vt Vr rand len G Q Q CPG Connection P G weight weight sparseness input connection p CGG Connection G G weight weight MP PopulationRateMonitor G bin 1 ms network_operation def stop_condition if MP rate 1 Hz gt 10 Hz stop run duration print Reached population rate gt 10 Hz by time clk t 1 ms Example timed_array misc An example of the TimedArray class used for applying
542. to enumerate the processes mapping their process IDs to an int in the range 0 num processes pid to id dict pid i for i pid in enumerate p pid for p in pool pool num processes len pid to id start time time stoprunningsim False This function terminates all the pool s child processes it is used as the callback function called when the terminate button on the GUI is clicked def terminate sim pool terminate stoprunningsim 0 True controller SimulationController num_processes terminate_sim for i in range num_processes controller update_process i 0 0 no info yet i 0 3 2 Examples 87 Brian Documentation Release 1 4 1 while True try If there is a new result the 0 1 means wait 0 1 seconds for a result before giving up then this try clause will execute otherwise a TimeoutError will occur and the except clause afterwards will execute weight numspikes results next 0 1 if we reach here we have a result to plot so we plot it and update the GUI plot_result weight numspikes i i 1 controller update results time time start i except multiprocessing TimeoutError if we re still waiting for a new result we can process events in the message queue and update the GUI if there are any while not message queue empty try messages here are of the form pid elapsed complete where pid is the process ID of the child process elapsed
543. tplotlib use WXAgg You may need to experiment try WXAgg GTKAgg QTAgg TkAgg insert spikes spikemonitor value 0 Inserts spikes into recorded traces for plotting State values at spike times are replaced with the given value peak value of spike 292 Chapter 8 Reference Brian Documentation Release 1 4 1 class brian MultiStateMonitor G vars None clock None kwds Monitors multiple state variables of a group This class is a container for multiple Stat eMonitor objects one for each variable in the group You can retrieve individual StateMonitor objects using M name or retrieve the recorded values using M name i for neuron i Initialised with a group G and a list of variables vars If vars is omitted then all the variables of G will be recorded Any additional keyword argument used to initialise the object will be passed to the individual StateMonitor objects e g the when keyword Methods items iteritems Returns the pairs var mon plot indices cmap Plots all the monitors note that real time plotting is not supported for this class Attributes vars The list of variables recorded times The times at which recordings were made monitors The dictionary of monitors indexed by variable name Usage G NeuronGroup N eqs M MultiStateMonitor G record True runi plot M V times M V 0 figure for name m in M iteritems plot m times m 0 label name
544. trode time constant the sampling period should be two orders of magnitude larger than the electrode time constant It is defined and used in the same way as an acquisition board above board DCC P neuron V V I I frequency 2 kHz where frequency is the sampling frequency The duty cycle is 1 3 meaning current is injected during 1 3 of each sampling step Discontinuous voltage clamp The discontinuous voltage clamp or single electrode voltage clamp SEVC is an implementation of the voltage clamp using a feedback current with a DCC amplifier It is defined as the DCC board SEVC P neuron V V I I frequency 2 kHz gain 10 nS except that a gain parameter is included The SEVC injects a negative feedback current I gain Vcommand V The quality of the clamp improves with higher gains but there is a maximum value above which the system is unstable be cause of the finite temporal resolution The recorded current is stored in board record and the command voltage is 228 Chapter 5 The library Brian Documentation Release 1 4 1 sent with the instruction board command 20 mvV With this implementation of the SEVC the membrane is never perfectly clamped A better clamp is obtained by adding an integral controller with the keyword gain2 10 nS ms The additional current J t is governed by the differential equation dJ dt gain2 Vcommand V so that it ensures perfect clamping in the stationary state However this c
545. trols everything on the GPU It uses a GPUKernel object for managing kernels and a GPUSymbolMemoryManager object for managing symbol memory The class is used by 1 Adding several kernels using add kernel 2 Calling prepare see method documentation for details 3 Run code with run Memory is mirrored on GPU and CPU In the present implementation in the development phase only each call to run will copy all symbols from CPU to GPU before running the GPU kernel and afterwards copy all symbols from GPU back to CPU In the future this will be disabled and symbol memory copies will be handled explicitly by calls to methods copy to device andcopby to host add kernel name code namespace Adds a kernel with the given name code and namespace Creates a GPUKernel object add symbols items Proxy to GPUSymbolMemoryManager add symbols compile Compiles code using pycuda compiler SourceModule and extracts kernel functions with pycuda compiler SourceModule get function The GPUKernel gpu func at tribute is set for each kernel copy to device symname Proxy to GPUSymbolMemoryManager copy to device copy to host symname Proxy to GPUSymbolMemoryManager copy to host generate code Combines kernel source into one source file and adds memory management kernel functions These simple kernels simply copy a pointer to a previously specified name This is necessary because when pycuda is used to allocate memory
546. ts 335 units 259 array 260 inconsistent 259 update brian ProgressReporter method 304 xi 264 noise 264 Z ZhangSynapse example usage 125 128 ZhangSynapse class in brian hears 327 400 Index
547. ts as inputs but this is very slow and memory consuming from brian import x Poisson inputs M 1000 number of Poisson inputs max rate 100 3 2 Examples 149 Brian Documentation Release 1 4 1 Neurons N 50 number of neurons tau 10 ms BR exc 0 mV EL 70 mV G NeuronGroup N model dvm dt vm E L tau mv G rest Dummy neuron group P NeuronGroup l v 1 threshold 1 reset 0 spikes every timestep time varying rate def varying rate t return defaultclock dt max rate 0 5 0 5 sin 2 x pi x 5 x t Synaptic connections binomial cellM varying rate t gives the number of events per timestep The synapse model is a conductance based instanteneous jump in postsynaptic membrane potential S Synapses P G model J g d cellM 1 da pre vm binomial cellM varying rate t J E exc vm S True S cellM M we need one value for M per cell so that binomial is vectorized S J 0 0005 mon StateMonitor G vm record True run 1 second report text mon plot show Example short term plasticity synapses Example with short term plasticity from brian import x tau_e 3 ms taum 10 ms A SE 250 pA Rm 100 Mohm N 10 eqs dx dt rate 1 rate Hz pore input NeuronGroup N model eqs threshold 1 reset 0 input rate linspace 5 Hz 30 x Hz N
548. twork from brian import x class PoissonDrivenGroup NeuronGroup E E ud This class is a group of leaky integrate and fire neurons driven by external Poisson inputs The class creates the Poisson inputs and 182 Chapter 3 Getting started Brian Documentation Release 1 4 1 connects them to itself Lr def J init self N rate weight tau 10 ms eqs Eg dV dt V tau 1 PRL It s essential to call the initialiser of the base class super PoissonDrivenGroup self init N qs reset 0 threshold 1 self poisson group PoissonGroup N rate self conn Connection self poisson group self V self conn connect one to one weight weight self contained objects self poisson group self conn G PoissonDrivenGroup 100 100 Hz 3 M SpikeMonitor G M pg SpikeMonitor G poisson group trace StateMonitor G V record 0 run l second subplot 311 raster_plot M_pg title Input spikes subplot 312 raster plot M title Output spikes subplot 313 plot trace times trace 0 title Sample trace show Example pulsepacket misc This example basically replicates what the Brian PulsePacket object does and then compares to that object from brian import x from random import gauss shuffle Generator for pulse packet def pulse packet t n sigma generate a list of n times with Gaussian distribution sort them in time and th
549. twork for debugging purposes level Where to find objects level 1 means look for objects where the MagicNetwork object was created The level argument says how many steps back in the stack to look 8 10 Network 289 Brian Documentation Release 1 4 1 8 11 Monitors Monitors are used to record properties of your network The two most important are SpikeMonitor which records spikes and St ateMonitor which records values of state variables These objects are just added to the network like aNeuronGroup or Connection Implementation note monitors that record spikes are classes derived from Connection and overwrite the propagate method to store spikes If you want to write your own custom spike monitors you can do the same or just use Spi keMonitor with a custom function Monitors that record values are classes derived from NetworkOperationandimplementthe call methodto store values each time the network updates Custom state monitors are most easily written by just writing your own network operation using the network operation decorator class brian SpikeMonitor source record True delay 0 functionz None Counts or records spikes from a NeuronGroup Initialised as one of SpikeMonitor source record True SpikeMonitor source function function Where source A NeuronGroup to record from record True or False to record all the spikes or just summary statistics function A function f spikes which is passed the arra
550. types above Notes This class implements post synaptic delays This means that the spike is propagated immediately from the presynaptic neuron with the synaptic weight at the time of the spike but arrives at the postsynaptic neuron with the given delay At the moment Brian only provides support for presynaptic delays if they are homogeneous using the delay keyword of a standard Connect ion Implementation DelayConnection stores an array of size n m where n is max delay dt for dt of the target NeuronGroup s clock and m is the number of neurons in the target This array can potentially be quite large Each row in this array represents the array that should be added to the target state variable at some particular future time Which row corresponds to which time is tracked using a circular indexing scheme When a spike from neuron i in the source is encountered the delay time of neuron i is looked up the row corresponding to the current time plus that delay time is found using the circular indexing scheme and then the spike is propagated to that row as for a standard connection although this won t be propagated to the target until a later time Warning 276 Chapter 8 Reference Brian Documentation Release 1 4 1 If you are using a dynamic connection matrix it is your responsibility to ensure that the nonzero entries of the weight matrix and the delay matrix exactly coincide This is not an issue for sparse or dense matrices
551. u to define a cascade of computed parameters that depend on the values of other parameters so that changing one will automatically update the others See the synfire chain example examples sfc py for a demonstration of how it can be used class brian Parameters kwds A storage class for keeping track of parameters Example usage 252 Chapter 6 Advanced concepts Brian Documentation Release 1 4 1 p Parameters a 5 b 6 computed_parameters c atb ap FE print p c p a 1 print p c The first print statement will give 11 the second gives 7 Details Call as p Parameters Where the consists of a list of keyword value pairs like a dict Keywords must not start with the underscore _ character Any keyword that starts with computed_ should be a string of valid Python state ments that compute new values based on the given ones Whenever a non computed value is changed the computed parameters are recomputed in alphabetical order of their keyword names so computed a is com puted before computed b for example Non computed values can be accessed and set via p x p x 1 for example whereas computed values can only be accessed and not set New parameters can be added after the Parameters object is created including new computed x parameters You can derive a new parameters object from a given one as follows pl Parameters x 1 p2 Parameters y 2 x x pl print p2 x Note th
552. uations object is initialised a dictionary is built with the values of all external variables These values are taken from the namespace where the Equations object was defined It is possible to go one or several levels up in the namespaces by specifying the keyword level default 0 The value of these parameters can in general be changed during the simulation and the modifications are taken into account except in two situations when the equations are frozen see below or when the integration is exact linear equations In those cases the values of the parameters are the ones at initialisation time Alternatively the string defining the equations can be evaluated within a given namespace by providing keywords at initialisation time e g eqs Equations dx dt x tau volt tau 10 ms In that case the values of all external variables are taken from the specified dictionary given by the keyword argu ments even if variables with the same name exist in the namespace where the string was defined The two methods for passing the values of external variables are mutually exclusive that is either all external variables are explicitly spec ified with keywords if not they are left unspecified even if there are variables with the same names in the namespace where the string was defined or all values are taken from the calling namespace More can be done with keyword arguments If the value is a string then the name of the variable is re
553. ubplot 221 ind M times lt 500 ms plot M times ind ms M 0 ind mV k plot Mt times ind ms Mt 0 ind mV r xlabel Time ms 3 2 Examples 51 Brian Documentation Release 1 4 1 ylabel Voltage mV subplot 222 plot slope array threshold mV r sx lLinspace 0 5 volt second 4 volt second 100 t array thresh_ex s volt second for s in sx plot sx t mV k xlim 0 5 4 xlabel Depolarization slope ms ylabel Threshold mV ms show Example Muller et al 2011 frompapers Interplay of STDP and input oscillations Figure 4 from Muller L Brette R and Gutkin B 2011 Spike timing dependent plasticity and feed forward input oscillations produce precise and invariant spike phase locking Front Comput Neurosci 5 45 doi 10 3389 fn com 2011 00045 Description In this simulation a group of IF neurons is given a tonic DC input and a tonic AC input The DC input is mediated by current injection neurons I line 62 and the AC input is mediated by Poisson processes whose rate parameters are oscillating in time Each neuron in the group is given a different DC input ensuring a unique initial phase After two seconds of simulation to integrate out any initial transients the STDP rule is turned on ExponentialS TDP line 68 and the population of neurons converges to the theoretically predicted fixed point As there is some noise in the phase due to the random inputs the simulati
554. uler method is used for Hodgkin Huxley type equations are which stiff Equations of that type are conditionally linear that is the differential equation for each variable is linear in that variable i e linear if all other variables are considered constant The idea is thus to solve the differential equation for each variable over one time step assuming that all other variables are constant over that time step The numerical scheme is still first order but it is more stable than the forward Euler method Each equation can be written as dx dt a x b where a and b depend on the other variables and thus change after each time step The values of a and b are obtained during the update phase by calculating a x b for x 0 and x 1 note that these values are different for every neuron thus we calculate vectors A and B Then x t dt is calculated in the same way as for the exact integration method above 4 14 5 Stochastic differential equations Noise is introduced in differential equations with the keyword xi which means normalised gaussian noise the deriva tive of the Brownian term Currently this is implemented simply by adding a normal random number to the vari able at the end of the integration step independently for each neuron The unit of white noise is non trivial it is secondx 5 Thus a typical stochastic equation reads dx dt x taut tsigma xi taux 5 where sigma is in the same units as x We note the following two facts
555. ultipleSpikeGeneratorGroup class in brian 273 Euler 217 MultiStateMonitor exact 216 example usage 166 184 exponential Euler 217 MultiStateMonitor class in brian 293 Hodgin Huxley type equations 217 semi exact 216 N numpy NaiveClock class in brian 262 analysis 189 259 names brian experimental codegen2 GPUSymbolMemoryManag merical computation 189 259 attribute 374 namespaces O equations 215 online nchannels brian hears Filterbank attribute 332 computation 242 nchannels brian hears Sound attribute 312 OnlineSound class in brian hears 333 Network open_server in module brian library modelfitting 307 example usage 27 125 128 outro brian experimental model_documentation DocumentWriter network method 342 multiple files 250 337 Network class in brian 285 P network_operation parameter example usage 46 60 74 77 79 144 165 173 equations 192 181 Parameters network_operation in module brian 287 example usage 27 NetworkOperation class in brian 288 Parameters class in brian 252 Neuron pause brian RemoteControlClient method 303 dat file 302 peek brian SpikeQueue method 285 neuron pinknoise brian hears Sound static method 312 equations 263 pinknoise in module brian hears 315 group 263 play model 263 example usage 114 124 NeuronGroup play brian hears Sound method 311 example usage 26 31 35 39 41 43 45 46 49 50 play in module brian hears
556. umentation Release 1 4 1 one point chooses a random integer n between 1 and ndimensions and then selects vector entries numbered less than or equal to n from the first parent It then Selects vector entries numbered greater than n from the second parent Finally it concatenates these entries to form a child vector two points it selects two random integers m and n between 1 and ndimensions The func tion selects vector entries numbered less than or equal to m from the first parent Then it selects vector entries numbered from m 1 to n inclusive from the second parent Then it selects vector entries numbered greater than n from the first parent The algorithm then concatenates these genes to form a single gene heuristic returns a child that lies on the line containing the two parents a small distance away from the parent with the better fitness value in the direction away from the parent with the worse fitness value You can specify how far the child is from the better parent by the parameter ratio xover which is 0 5 by default linear combination creates children that are linear combinations of the two parents with the parameter ratio xover which is 0 5 by default and should be between 0 and 1 child parentl Ratio parent2 parenti For ratio xover 0 5 every child is an arithmetic mean of two parents func mutation gaussian This function define how the genetic algorithm makes small random changes in
557. units will raise an error gt gt gt from brian import gt gt gt 3 x second 2 metre Traceback most recent call last File lt pyshell 38 gt line 1 in lt module gt 189 Brian Documentation Release 1 4 1 3 second 2 metre File C Documents and Settings goodman Mes documents Programming Python simulator Brian units py if dim self dim DimensionMismatchError Addition dimensions were s m 4 1 2 Units defined in Brian The following fundamental SI unit names are defined metre meter US spelling kilogram second amp kelvin mole candle These derived SI unit names are also defined radian steradian hertz newton pascal joule watt coulomb volt farad ohm siemens weber tesla henry celsius lumen lux becquerel gray sievert katal In addition you can form scaled versions of these units with any of the standard SI prefixes Factor Name Symbol Factor Name Symbol 10424 yotta Y 104 24 yocto y 10421 zetta Z 104 21 zepto Z 10 18 exa E 10 21 zepto Z 10 15 peta P 10 15 femto f 10 12 tera T 10 12 pico p 10 9 giga G 10 9 nano n 10 6 mega M 10 6 micro u mu in SI 10 3 kilo k 10 3 milli m 10 2 hecto h 10 2 centi c 1041 deka da 10 1 deci d So for example you could write fnewt on for femto newtons Mwatt for megawatt etc There are also units for 2nd and 3rd powers of each of the above units for
558. uns in parallel The Python multiprocessing module can be used for relatively simply distributing simulation runs over multiple CPUs Alternatively you could use Playdoh produced by our group to distribute work over multiple CPUs and multiple machines For other solutions see the Parallel and distributed programming section of the Scipy Topical Software page Brian provides a simple single machine technique that works with the Dat aManager object run tasks With this you provide a function and a sequence of arguments to that function and the function calls will be evaluated across multiple CPUs with the results being stored in the data manager It also features a GUI which gives feedback on simulations as they run and can be used to safely stop the processes without risking losing any data A simple example of using this technique from brian import x from brian tools datamanager import x from brian tools taskfarm import x def find rate k report eqs EFT dV dt k V 10xms 1 Cee G NeuronGroup 1000 eqs reset 0 threshold 1 M SpikeCounter G 220 Chapter 4 User manual Brian Documentation Release 1 4 1 run 30 second report report return k mean M count 30 if name main N 20 dataman DataManager taskfarmexample if dataman itemcount lt N M N dataman itemcount run tasks dataman find rate rand M 19 1 X Y zip dataman values plot x Y Ca
559. uples arrays in which case there is one frequency or phase for each channel static whitenoise args kwds Returns a white noise If the samplerate is not specified the global default value will be used static powerlawnoise args kwds Returns a power law noise for the given duration Spectral density per unit of bandwidth scales as 1 f alpha Sample usage noise powerlawnoise 200 ms 1 samplerate 44100 Hz Arguments duration Duration of the desired output alpha Power law exponent samplerate Desired output samplerate static brownnoise args kwds Returns brown noise i e powerlawnoise with alpha 2 static pinknoise args kwds Returns pink noise i e powerlawnoise with alpha 1 312 Chapter 8 Reference Brian Documentation Release 1 4 1 static silence args kwds Returns a silent zero sound for the given duration Set nchannels to set the number of channels static click args kwds Returns a click of the given duration If peak is not specified the amplitude will be 1 otherwise peak refers to the peak dB SPL of the click according to the formula 28e 6 10 peak 20 static clicks args kwds Returns a series of n clicks see c1ick separated by interval static harmoniccomplex args kwds Returns a harmonic complex composed of pure tones at integer multiples of the fundamental frequency 0 The amplitude and phase keywords can be set to either a single va
560. urons and optionally with a third index in the case of multiple synapses Here are a few examples which follows essentially the same syntax as for creating synapses S w 2 5 1 nS S w 1 2 nS S w l nS all synapses assigned w0 S w 2 3 1 second synapse for connection 2 gt 3 S w 2 3 1 nS 2x nS S w groupl group2 1l cos i j 2 nS S w l rand nS 4 6 4 Delays There is a special synaptic variable that is automatically created delay It is the propagation delay from the presy naptic neuron to the synapse i e the presynaptic delay An alias is delay_pre When there is a postsynaptic code keyword post the variable delay_post is created These can be accessed and modified in the same way as other synaptic variables If delays can change during the simulation one should specify the maximum allowed delay with the keyword max_delay synapses Synapses P Q model w 1 pre v w max_delay 1 ms Otherwise this maximum delay is automatically calculated the first time the model is run 4 6 5 Multiple pathways It is possible to have multiple pathways with different update codes from the same presynaptic neuron group This may be interesting in cases when different operations must be applied at different times for the same presynaptic spike 4 6 Synapses 203 Brian Documentation Release 1 4 1 To do this simply specify a tuple or list of pre codes pre get w w
561. urons per row N Nx Nx number of neurons rest_time l second initial time duration 500 ms delta_t 2x ms Size of synchronous groups maximum time difference Se OS Duration selective neurons eqss dv dt El v gmax gK gmax2 gK2 ginh EK v tau volt dgK dt gKinf gK tauK 1 4 IKLT dgK2 dt gK2 tauK2 1 Delayed rectifier gKinf 1 1 exp Va v ka 1 ginh ginh max t rest time amp t lt rest_timetduration 1 tauK ms tau ms gmax 1 EEP uniform lambda N rand N 5 2 uniform between 1 and 1 seed 31418 Get the same neurons every time neurons NeuronGroup N model eqs threshold v gt Vt reset v Vr gK2 1 neurons v Vr neurons gK 1 1 exp Va E1 ka neurons tauk 400 mstuniform N tauK_spread alpha El Vt Vt EK neurons gmax alphax minx maxx minx rand N neurons tau 30 mstuniform N tau_spread 70 Chapter 3 Getting started Brian Documentation Release 1 4 1 spikes SpikeMonitor neurons run rest_time 1 1 second Calculate first spike time of each neuron times zeros N First spike time of each neuron times Inf Inf means no response or response before the start of the stimulus blacklist neurons that fire spontaneously for i t in spikes spikes if times i Inf times i t duration rest time if times i 0 blacklist append i times blacklist Inf tmin tmax min times times I
562. urons that just spiked 4 2 Models and neuron groups 193 Brian Documentation Release 1 4 1 Functional reset To define a specific reset the generic method is define a function as follows def myreset P spikes P v spikes rand len spikes 5 mV group NeuronGroup 100 model eqs reset myreset threshold 10 mvV or faster def myreset P spikes P v_ spikes rand len spikes 5 mV Every time step the user defined function is called with arguments P the neuron group and spikes the list of indexes of the neurons that just spiked The function above resets the neurons that just spiked to a random value Resetting another variable It is possible to specify the reset variable explicitly group NeuronGroup 100 model eqs reset Reset O mV state w threshold 10 mvV Here the variable w is reset Resetting to the value of another variable The value of the reset can be given by another state variable group NeuronGroup 100 model eqs reset VariableReset 0 mV state v resetvaluestate w threshold 10 Here the value of the variable w is used to reset the variable v 4 2 4 Threshold As for the reset the threshold can be customised Threshold as Python expression The simplest way to customise the threshold is to define it as a Python expression e g eqs r dv dt v tau volt dw dt v w tau volt pu group NeuronGroup 100 model eqs reset 0 mV threshold v gt w
563. using the corresponding keywords For example a membrane equation with a 5 nA current injected through an electrode is defined as follows eqs Equations dv dt gl vti_inj Cm volt electrode 50 Mohm 10 pF vm v i_cmd 5 nA Specify i_cmd None if the electrode is only used to record no current injection More complex electrodes can be defined by passing lists of resistances and capacitances e g el electrode 50 Mohm 20 Mohm 5 pF 3 pF 5 3 2 Amplifiers Current clamp amplifier A current clamp amplifier injects a current through an intracellular electrode and records the membrane potential Two standard circuits are included to compensate for the electrode voltage bridge compensation and capacitance neutralization see e g the Axon guide The following command amp current clamp Re 80 Mohm Ce 10 pF defines a current clamp amplifier with an electrode modelled as a RC circuit The function returns an Equations object where the recording potential is v_rec the membrane potential is vm the electrode current entering the mem brane is i inj and command current is i cmd These names can be overriden using the corresponding keywords For implementation reasons the amplifier always includes an electrode Optionally bridge compensation can be used with the bridge keyword and capacitance neutralization with the capa_comp keyword For example the following instruction defines a partially compensated recordin
564. value of the symbol is written to brian experimental codegen2 get read or write dependencies dependencies Returns the set of names of the variables which are either read to or written to in a set of dependencies equations brian experimental codegen2 freeze with equations inputcode eqs ns Returns a frozen version of inputcode with equations and namespace Replaces each occurrence in inputcode of a variable name in the namespace ns with its value if it is of int or float type Variables with names in brian Equations eqs are not replaced and neither are dt or t brian experimental codegen2 frozen equations eqs Returns a frozen set of equations Each expression defining an equation is frozen as in reeze with equations expressions class brian experimental codegen2 Expression expr A mathematical expression such as x y z Has an attribute dependencies which is Read var for all words var in expr Has a method convert to defined the same way as CodeItem convert to convert to language symbols namespace Converts expression into a string for the given language using the given set of symbols Replaces each Symbol appearing in the expression with sym read and if the language is C or GPU then uses sympy CCodePrinter doprint to convert the syntax e g x xy becomes pow x y formatting brian experimental codegen2 word substitute expr substitutions Applies a dict of word substitutions The di
565. ve the gcc compiler installed on Cygwin if you are running on Windows Mac users The Enthought Python Distribution EPD is free for academics and contains all the libraries necessary to run Brian Otherwise the Scipy Superpack for Intel OS X also includes versions of Numpy Scipy Pylab and IPython Windows users the Python x y distribution includes all the packages including Eclipse and IPython above except Brian which is available as an optional plugin Another option is the Anaconda distribution which also includes all the packages above except Brian and Eclipse 2 2 1 Installing Python packages On Windows Python packages including Brian are generally installed simply by running an exe file On other operating systems you can download the source release typically a compressed archive tar gz or zip that you need to unzip and then install the package by typing the following in your shell python setup py install 2 2 2 Installing Eclipse Eclipse is an Integrated Development Environment IDE for any programming language PyDev is a plugin for Eclipse with features specifically for Python development The combination of these two is excellent for Python development it s what we use for writing Brian To install Eclipse go to their web page and download any of the base language IDEs It doesn t matter which one but Python is not one of the base languages so you have to choose an alternative language Probably the most
566. where is a list of keyword assignments brian get global preference k Get the value of the named global preference 6 7 2 Global configuration file If you have a module named brian global config anywhere on your Python path Brian will attempt to import it to define global preferences For example to automatically enable weave compilation for all your Brian projects create a file brian global config py somewhere in the Python path with the following contents from brian globalprefs import set global preferences useweave True 6 7 3 Global preferences for Brian The following global preferences have been defined defaultclock Clock dtz0 1 msecond The default clock to use if none is provided or defined in any enclosing scope useweave linear diffeq False Whether to use weave C acceleration for the solution of linear dif ferential equations Note that on some platforms typically older ones this is faster and on some platforms typically new ones this is actually slower useweave False Defines whether or not functions should use inlined compiled C code where defined Re quires a compatible C compiler The gcc and g compilers are probably the easiest option use Cygwin on Windows machines See also the weavecompiler global preference weavecompiler gcc Defines the compiler to use for weave compilation On Windows machines installing Cygwin is the easiest way to get access to the gcc compiler 254
567. which update as the simulation runs for example G NeuronGroup spikemon SpikeMonitor G statemon StateMonitor G V record range 5 ion subplot 211 raster plot spikemon refresh 10 ms showlast 200 ms subplot 212 statemon plot refresh 10 ms showlast 200 ms run 1 second ioff show The ion and ioff command activate and deactivate Pylab s interactive plotting mode The refresh param eter specifies how often in simulation time to refresh the plot smaller values will slow down the simulation The showlast option only plots the most recent values With some IDEs you may need to do something like the following at the beginning of your script to make interactive mode work import matplotlib matplotlib use WXAgg This is because the default graphical backend can sometimes interact badly with the IDE Other options to try are GTKAgg OTAgg TkAgg 4 10 4 Statistics Here are a few functions to analyse first and second order statistical properties of spike trains defined as ordered lists of spike times e Firing rate firing_rate spikes where spikes is a spike train list of spike times Coefficient of variation CV spikes e Cross correlogram correlogram T1 T2 width 20 ms bin 1l ms T None returns the cross correlogram of spike trains T1 and T2 with lag in width width and given bin size T is the total duration optional and should be greater than the duration of T1 and
568. width 20 0 msecond bin 1 0 msecond T None Returns the cross correlation function with lag in width width and given bin size T is the total duration optional The result is in Hz 2 CCF T1 T2 lt T1 t T2 t s gt N B units are discarded brian ACF TO width 20 0 msecond bin 1 0 msecond T None Returns the autocorrelation function with lag in width width and given bin size T is the total duration op tional The result is in Hz 2 ACF T0 lt TO t TO t s gt N B units are discarded brian CCVF T1 T2 width 20 0 msecond bin 1 0 msecond T None Returns the cross covariance function with lag in width width and given bin size T is the total duration optional The result is in Hz 2 CCVF T1 T2 lt T1 t T2 t s gt lt T1 gt lt T2 gt N B units are discarded brian ACVF T0 width 20 0 msecond bin 1 0 msecond T None Returns the autocovariance function with lag in width width and given bin size T is the total duration op tional The result is in Hz 2 ACVF T0 lt TO t TO t s gt lt T0 gt 2 N B units are discarded brian total correlation T1 T2 width 20 0 msecond T None Returns the total correlation coefficient with lag in width width T is the total duration optional The result is a real typically in 0 1 total_correlation T1 T2 int CCVF T1 T2 rate T1 brian spike triggered average spikes stimulus max interval dt onset None display False Spi
569. will update it compile False Whether or not to attempt to compile the differential equation solvers into Python code Typically for best performance both compile and freeze should be set to True for nonlinear differ ential equations freeze False If True parameters are replaced by their values at the time of initialization method None If not None the integration method is forced Possible values are linear nonlinear Euler exponential_Euler overrides implicit and order keywords unit checking True Set to False to bypass unit checking Methods subgroup N Returns the next sequential subgroup of N neurons See the section on subgroups below state var Returns the array of values for state variable var with length the number of neurons in the group rest Sets the neuron state values at rest for their differential equations The following usages are also possible for a group G G i j Returns the subgroup of neurons from i to j len G Returns the number of neurons in G G x For any valid Python variable name x corresponding to a state variable of the the NeuronGroup this returns the array of values for the state variable x as for the state method above Writing G x arr for arr a TimedArray will set the values of variable x to be arr t at time t See TimedArraySetter for details Subgroups A subgroup is a view on a group It isn t a new group it s just a convenient way of referring to a subset of the neur
570. www labbookpages co uk audio beamforming fractionalDelay html will be used in troducing some small numerical errors With this method you can specify the filter_length larger values are slower but more accurate especially at higher frequencies The large default value of 2048 samples provides good accuracy for sounds with frequencies above 20 Hz but not for lower frequency sounds If you are restricted to high frequency sounds a smaller value will be more efficient Note that if fractional True then duration is assumed to be a time not a number of samples resized L Returns the Sound with length extended or contracted to have L samples Slicing One can slice sound objects in various ways for example sound 100 ms 200 ms returns the part of the sound between 100 ms and 200 ms not including the right hand end point If the sound is less than 200 ms long it will be zero padded You can also set values using slicing e g sound 50 ms 0 will silence the first 50 ms of the sound The syntax is the same as usual for Python slicing In addition you can select a subset 8 21 Brian hears 313 Brian Documentation Release 1 4 1 of the channels by doing for example sound 5 would be the last 5 channels For time indices either times or samples can be given e g sound 100 gives the first 100 samples In addition steps can be used for example to reverse a sound as sound 1 Arithmetic operations Standard aritheme
571. x phases f idx 1l idx np angle np sum temp phases plt subplot 2 1 1 rate reshaped mean axis 2 plt plot freqs rate plt ylabel Spikes sec plt legend 0f dB level for level in levels 0 plt xlim 0 4000 plt ylim 0 250 plt subplot 2 1 2 relative phases phases T phases 1 T relative phases relative phases gt pi relative phases relative phases gt pi 2 pi relative phases relative phases lt pi relative phases relative phases lt pi 2x pi plt plot freq subset relative phases pi plt ylabel Phase Re 90dB pi radians plt xlabel Frequency Hz plt legend 0f dB level for level in levels 0 plt xlim 0 4000 plt ylim 0 5 0 75 plt show Example tan carney Fig7 hears tan carney 2003 CF dependence of compressive nonlinearity in the Tan amp Carney model Reproduces Fig 7 from Tan Q and L H Carney A Phenomenological Model for the Responses of Auditory nerve Fibers II Nonlinear Tuning with a Frequency Glide The Journal of the Acoustical Society of America 114 2003 2007 import numpy as np import matplotlib pyplot as plt from scipy interpolate import interpld from brian import x fZset global preferences useweave True from brian hears import from brian hears filtering tan carney import TanCarneySignal MiddleEar samplerate 50 kHz set default samplerate samplerate duration 50 ms
572. xi 1 pag neurons NeuronGroup N model eqs neurons threshold 1 reset 0 synapses Synapses ears neurons model w 1 pre vt w synapses True synapses w 5 synapses delay 0 linspace 0 x ms 1 1 max delay N synapses delay 1 linspace 0 ms 1 1 max delay N 1 Spikes SpikeMonitor neurons run l1 ms tl time run 1000 ms t2 time print It took t2 rtl s raster plot spikes show Example synapse construction synapses An example of constructing synapses 138 Chapter 3 Getting started Brian Documentation Release 1 4 1 from brian import x import time N 10 P NeuronGroup N model dv dt 1 10 ms 1 threshold 1 reset 0 Q NeuronGroup N model v 1 S Synapses P Q model w 1 pre v w S efaej S w 2xi M StateMonitor Q v record True run 40 ms for i in range N plot M times ms M i ix2 k show Example one_synapse_bis Synapses One synapse within several possibilities Synapse from 2 gt 3 from brian import x P NeuronGroup 5 model dv dt 1 10 ms 1 threshold 1 reset 0 Q NeuronGroup 4 model v 1 S Synapses P Q model w l pre v c w M StateMonitor Q v record True S 2 3 True S w 2 3 1 S delay 2 3 5 ms run 40 ms for i in range 4 plot M times ms M i ix2 k show Example probabilistic_synapses synapses Proba
573. y of neuron numbers that have fired called each step to define custom spike monitoring Has attributes nspikes The number of recorded spikes spikes A time ordered list of pairs i t where neuron i fired at time t spiketimes A dictionary with keys the indices of the neurons and values an array of the spike times of that neuron For example t M spiketimes 3 gives the spike times for neuron 3 it Return a tuple i t where i and t are the arrays of spike indices and corresponding spike times int and float ForMa SpikeMonitor you can also write M i An array of the spike times of neuron i Notes SpikeMonitor is subclassed from Connect ion To define a custom monitor either define a subclass and rewrite the propagate method or pass the monitoring function as an argument function myfunction with de myfunction spikes class brian SpikeCounter source Counts spikes from a NeuronGroup Initialised as SpikeCounter source With argument source A NeuronGroup to record from Has two attributes 290 Chapter 8 Reference Brian Documentation Release 1 4 1 nspikes The number of recorded spikes count An array of spike counts for each neuron For a SpikeCounter M you can also write M i for the number of spikes counted for neuron i class brian PopulationSpikeCounter source delay 0 Counts spikes from a NeuronGroup Initialised as PopulationSpikeCounter source With argument source A NeuronGrou
574. ynaptic weight wi 2 5 x we inhibitory synaptic weight Ce Connection Pe P ge weight we sparseness 0 05 Ci Connection Pi P gi weight wi sparseness 0 05 Initialization P vm randn len P 10 mV 70 mV refractory 2 180 Chapter 3 Getting started Brian Documentation Release 1 4 1 P ge randn len P 2 5 we P gi randn len P 2 5 wi ll Excitatory input to a subset of excitatory and inhibitory neurons Excitatory neurons are excited for the first 200 ms Inhibitory neurons are excited for the first 100 ms input_layerl Pe subgroup 200 input_layer2 Pi subgroup 200 inputl PoissonGroup 200 rates lambda t t lt 200 ms and 2000 Hz or 0 x Hz input2 PoissonGroup 200 rates lambda t t lt 100 ms and 2000 Hz or 0 x Hz input col IdentityConnection inputl input_layerl ge weight we input co2 IdentityConnection input2 input layer2 ge weight we Record the number of spikes M SpikeMonitor P print Simulation running start time time time run 500 ms duration time time start time print Simulation time duration seconds print M nspikes 4000 spikes per neuron raster plot M show Example transient sync misc Transient synchronisation in a population of noisy IF neurons with distance dependent synaptic weights organised as aring from brian import x tau 10 ms N
575. ype int return 1 brian letters tmp x tmp y print Building network with wrapped 2D gaussian profiles Ce Connection exc cells all cells ge weight g exc max delay max delay Sparseness lambda i j probas i j exc cells position all cells position delay lambda i j delays i j exc cells position all cells position Ci Connection inh cells all cells gi weight g inh max delay max delay Sparseness lambda i j probas i j inh cells position all cells position delay lambda i j delays i j inh cells position all cells position Cext Connection sources all cells ge weight g ext max delay max delay Sparseness lambda i j is in brian i j sources position all cells position print mean probability from excitatory synapses Ce W getnnz float n exc n cells 100 print mean probability from inhibitory synapses Ci W getnnz float n cells n exc xn cell print Setting the recorders V exc RecentStateMonitor exc cells v record True S exc SpikeCounter exc cells ion To enter the interactive mode print Initializing the plots figl pylab subplot 211 im figl scatter all cells position n exc 0 all cells position n exc 1 c 0 n exc im set clim 0 1 figl set ylabel spikes pylab colorbar im fig2 pylab subplot 212 im fig2 scatter all cells position n exc 0 all cells position n exc 1 c

Here`s - The Brian spiking neural network simulator

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