There are various ways of providing “external” input to a network. Brian does not yet provide all the features of Brian1 in this regard, but there is already a range of options, detailed below.
For generating spikes according to a Poisson point process, PoissonGroup can be used. It takes a rate or an array of rates (one rate per neuron) as an argument and can be connected to a NeuronGroup via the usual Synapses mechanism. At the moment, using PoissonGroup(N, rates) is equivalent to NeuronGroup(N, 'rates : Hz', threshold='rand()<rates*dt') and setting the group’s rates attribute. The explicit creation of such a NeuronGroup might be useful if the rates for the neurons are not constant in time, since it allows using the techniques mentioned below (formulating rates as equations or referring to a timed array). In the future, the implementation of PoissonGroup will change to a more efficient spike generation mechanism, based on the calculation of inter-spike intervals. Note that, as can be seen in its equivalent NeuronGroup formulation, a PoissonGroup does not work for high rates where more than one spike might fall into a single timestep. Use several units with lower rates in this case (e.g. use PoissonGroup(10, 1000*Hz) instead of PoissonGroup(1, 10000*Hz)).
P = PoissonGroup(100, np.arange(100)*Hz + 10*Hz) G = NeuronGroup(100, 'dv/dt = -v / (10*ms) : 1') S = Synapses(P, G, pre='v+=0.1', connect='i==j')
For simulations where the PoissonGroup is just used as a source of input to a neuron (i.e., the individually generated spikes are not important, just their impact on the target cell), the PoissonInput class provides a more efficient alternative. Instead of generating spikes, it directly updates a target variable based on the sum of independent Poisson processes:
G = NeuronGroup(100, 'dv/dt = -v / (10*ms) : 1') P = PoissonInput(G, 'v', 100, 100*Hz, weight=0.1)
The PoissonInput class is however more restrictive than PoissonGroup, it only allows for a constant rate across all neurons (but you can create several PoissonInput objects, targeting different subgroups). It internally uses BinomialFunction which will draw a random number each time step, either from a binomial distribution or from a normal distribution as an approximation to the binomial distribution if \(n p > 5 \wedge n (1 - p) > 5\), where \(n\) is the number of inputs and \(p = dt \cdot rate\) the spiking probability for a single input.
You can also generate an explicit list of spikes given via arrays using SpikeGeneratorGroup. This object behaves just like a NeuronGroup in that you can connect it to other groups via a Synapses object, but you specify three bits of information: N the number of neurons in the group; indices an array of the indices of the neurons that will fire; and times an array of the same length as indices with the times that the neurons will fire a spike. The indices and times arrays are matching, so for example indices=[0,2,1] and times=[1*ms,2*ms,3*ms] means that neuron 0 fires at time 1 ms, neuron 2 fires at 2 ms and neuron 1 fires at 3 ms. Example use:
indices = array([0, 2, 1]) times = array([1, 2, 3])*ms G = SpikeGeneratorGroup(3, indices, times)
If the input can be explicitly expressed as a function of time (e.g. a sinusoidal input current), then its description can be directly included in the equations of the respective group:
G = NeuronGroup(100, '''dv/dt = (-v + I)/(10*ms) : 1 rates : Hz # each neuron's input has a different rate size : 1 # and a different amplitude I = size*sin(2*pi*rates*t) : 1''') G.rates = '10*Hz + i*Hz' G.size = '(100-i)/100. + 0.1'
If the time dependence of the input cannot be expressed in the equations in the way shown above, it is possible to create a TimedArray. Such an objects acts as a function of time where the values at given time points are given explicitly. This can be especially useful to describe non-continuous stimulation. For example, the following code defines a TimedArray where stimulus blocks consist of a constant current of random strength for 30ms, followed by no stimulus for 20ms. Note that in this particular example, numerical integration can use exact methods, since it can assume that the TimedArray is a constant function of time during a single integration time step. Also note that the semantics of TimedArray changed slightly compared to Brian1: for TimedArray([x1, x2, ...], dt=my_dt), the value x1 will be returned for all 0<=t<my_dt, x2 for my_dt<=t<2*my_dt etc., whereas Brian1 returned x1 for 0<=t<0.5*my_dt, x2 for 0.5*my_dt<=t<1.5*my_dt, etc.
stimulus = TimedArray(np.hstack([[c, c, c, 0, 0] for c in np.random.rand(1000)]), dt=10*ms) G = NeuronGroup(100, 'dv/dt = (-v + stimulus(t))/(10*ms) : 1', threshold='v>1', reset='v=0') G.v = '0.5*rand()' # different initial values for the neurons
TimedArray can take a one-dimensional value array (as above) and therefore return the same value for all neurons or it can take a two-dimensional array with time as the first and (neuron/synapse/...-)index as the second dimension.
In the following, this is used to implement shared noise between neurons, all the “even neurons” get the first noise instantiation, all the “odd neurons” get the second:
runtime = 1*second stimulus = TimedArray(np.random.rand(int(runtime/defaultclock.dt), 2), dt=defaultclock.dt) G = NeuronGroup(100, 'dv/dt = (-v + stimulus(t, i % 2))/(10*ms) : 1', threshold='v>1', reset='v=0')
An alternative to specifying a stimulus in advance is to run explicitly specified code at certain points during a simulation. This can be achieved with a custom_operation(). One can think of these statements as equivalent to reset statements but executed unconditionally (i.e. for all neurons) and possibly on a different clock than the rest of the group. The following code changes the stimulus strength of half of the neurons (randomly chosen) to a new random value every 50ms. Note that the statement uses logical expressions to have the values only updated for the chosen subset of neurons (where the newly introduced auxiliary variable change equals 1):
G = NeuronGroup(100, '''dv/dt = (-v + I)/(10*ms) : 1 I : 1 # one stimulus per neuron''') stim_updater = G.custom_operation('''change = int(rand() < 0.5) I = change*(rand()*2) + (1-change)*I''', dt=50*ms)
Arbitrary Python code (network operations)¶
If none of the above techniques is general enough to fulfill the requirements of a simulation, Brian allows you to write a NetworkOperation, an arbitrary Python function that is executed every time step (possible on a different clock than the rest of the simulation). This function can do arbitrary operations, use conditional statements etc. and it will be executed as it is (i.e. as pure Python code even if weave code generation is active). Note that one cannot use network operations in combination with the C++ standalone mode. Network operations are particularly useful when some condition or calculation depends on operations across neurons, which is currently not possible to express in abstract code. The following code switches input on for a randomly chosen single neuron every 50 ms:
G = NeuronGroup(10, '''dv/dt = (-v + active*I)/(10*ms) : 1 I = sin(2*pi*100*Hz*t) : 1 (shared) #single input active : 1 # will be set in the network function''') @network_operation(dt=50*ms) def update_active(): print defaultclock.t index = np.random.randint(10) # index for the active neuron G.active_ = 0 # the underscore switches off unit checking G.active_[index] = 1
Note that the network operation (in the above example: update_active) has to be included in the Network object if one is constructed explicitly.