.. currentmodule:: brian
Inputs
======
Some specific types of neuron groups are available to provide inputs to a network.
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: :class:`PoissonInput`, which updates
the state variable of a :class:`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 :class:`PoissonInput` objects can be
created for a given :class:`NeuronGroup`, in which case all the independent
inputs are linearly superimposed.
Other features of the :class:`PoissonInput` class include the following (see the reference):
* record the individual Poisson events (``record=True`` keyword),
* having identical Poisson events for all neurons, instead of having
independent copies for every neuron (``freeze=True`` keyword)
* 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.
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 :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 ``tauc`` 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(i,j)*exp(-|s|/tauc)`, use the class :class:`CorrelatedSpikeTrains`::
group=CorrelatedSpikeTrains(rates,C,tauc)
where ``rates`` is the vector of rates r(i), ``C`` is the correlation matrix (which must be
symmetrical) and ``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 :class:`HomogeneousCorrelatedSpikeTrains` and :class:`CorrelatedSpikeTrains`
define neuron groups, which can be directly used with :class:`Connection` 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
:func:`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),
``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.
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
:class:`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).
Gaussian spike packets
^^^^^^^^^^^^^^^^^^^^^^
There is a subclass of :class:`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.
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).
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 :class:`TimedArray` to specify the values the variable will
have at each time interval, for example::
eqs = '''
dv/dt = (I-v)/tau : volt
I : volt
'''
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(linspace(0*mV, 20*mV, 100), dt=10*ms)
eqs = '''
dv/dt = (I(t) * volt - v)/tau : volt
'''
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
:func:`linked_var`, for example::
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).