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Brian Documentation, Release 1.2.1 where nu is the vector of rates of the source spike trains, P is the mixture matrix (entries between 0 and 1), tauc is the correlation time constant, t is the duration. It returns a list of (neuron_number,spike_time), which can be passed to SpikeGeneratorGroup. This method is appropriate for short time constants and is explained in the paper mentioned above. 4.7.3 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=[(0,1*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 be ordered in time). Spike times may also be provided separately for each neuron, using the MultipleSpikeGeneratorGroup class: S0=[1*ms, 2*ms] S1=[3*ms] S2=[1*ms, 3*ms, 5*ms] input=MultipleSpikeGeneratorGroup([S0,S1,S2]) The object is initialised with a list of spike containers, one for each neuron. Each container can be a sorted list of spike times or any iterable object returning the spike times (ordered in time). 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. 4.7.4 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: eqs = ’’’ dv/dt = (I-v)/tau : volt I : volt ’’’ group = NeuronGroup(100, model=eqs, reset=0*mV, threshold=15*mV) group.I = linspace(0*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). 4.7. Inputs 107