Input stimuli
There are various ways of providing “external” input to a network.
Poisson inputs
For generating spikes according to a Poisson point process, PoissonGroup can
be used, e.g.:
P = PoissonGroup(100, np.arange(100)*Hz + 10*Hz)
G = NeuronGroup(100, 'dv/dt = -v / (10*ms) : 1')
S = Synapses(P, G, on_pre='v+=0.1')
S.connect(j='i')
See More on Poisson inputs below for further information.
For simulations where the individually generated spikes are just used as a
source of input to a neuron, the PoissonInput class provides a more efficient
alternative: see Efficient Poisson inputs via PoissonInput below for details.
Spike generation
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)
The spikes that will be generated by SpikeGeneratorGroup can be changed
between runs with the
set_spikes method. This
can be useful if the input to a system should depend on its previous output or
when running multiple trials with different input:
inp = SpikeGeneratorGroup(N, indices, times)
G = NeuronGroup(N, '...')
feedforward = Synapses(inp, G, '...', on_pre='...')
feedforward.connect(j='i')
recurrent = Synapses(G, G, '...', on_pre='...')
recurrent.connect('i!=j')
spike_mon = SpikeMonitor(G)
# ...
run(runtime)
# Replay the previous output of group G as input into the group
inp.set_spikes(spike_mon.i, spike_mon.t + runtime)
run(runtime)
Explicit equations
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'
Timed arrays
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. This 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.
Note
The semantics of TimedArray changed slightly compared
to Brian 1: 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')
Regular operations
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 run_regularly().
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''')
G.run_regularly('''change = int(rand() < 0.5)
I = change*(rand()*2) + (1-change)*I''',
dt=50*ms)
The following topics are not essential for beginners.
More on Poisson inputs
Setting rates for Poisson inputs
PoissonGroup takes either a constant rate, an array of rates (one rate per
neuron, as in the example above), or a string expression evaluating to a rate
as an argument.
If the given value for rates is a constant, then using
PoissonGroup(N, rates) is equivalent to:
NeuronGroup(N, 'rates : Hz', threshold='rand()<rates*dt')
and setting the group’s rates attribute.
If rates is a string, then this is equivalent to:
NeuronGroup(N, 'rates = ... : Hz', threshold='rand()<rates*dt')
with the respective expression for the rates. This expression will be evaluated
at every time step and therefore allows the use of time-dependent rates, i.e.
inhomogeneous Poisson processes. For example, the following code
(see also Timed arrays) uses a TimedArray to define the rates of a
PoissonGroup as a function of time, resulting in five 100ms blocks of 100 Hz
stimulation, followed by 100ms of silence:
stimulus = TimedArray(np.tile([100., 0.], 5)*Hz, dt=100.*ms)
P = PoissonGroup(1, rates='stimulus(t)')
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)).
Efficient Poisson inputs via PoissonInput
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, PoissonInput 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)
Each input of the PoissonInput is connected to all the neurons of the target
NeuronGroup but each neuron receives independent realizations of the Poisson
spike trains. Note that 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.
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 cython 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 operation''')
@network_operation(dt=50*ms)
def update_active():
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.
Only functions with zero or one arguments can be used as a NetworkOperation.
If the function has one argument then it will be passed the current time t:
@network_operation(dt=1*ms)
def update_input(t):
if t>50*ms and t<100*ms:
pass # do something
Note that this is preferable to accessing defaultclock.t from within the
function – if the network operation is not running on the defaultclock
itself, then that value is not guaranteed to be correct.
Instance methods can be used as network operations as well, however in this case
they have to be constructed explicitly, the network_operation() decorator
cannot be used:
class Simulation(object):
def __init__(self, data):
self.data = data
self.group = NeuronGroup(...)
self.network_op = NetworkOperation(self.update_func, dt=10*ms)
self.network = Network(self.group, self.network_op)
def update_func(self):
pass # do something
def run(self, runtime):
self.network.run(runtime)