HomogeneousCorrelatedSpikeTrains

inputs.SpikeTrains.HomogeneousCorrelatedSpikeTrains(
    self,
    geometry,
    rates,
    corr,
    tau,
    schedule=None,
    period=-1.0,
    name=None,
    refractory=None,
    copied=False,
)

Population of spiking neurons following a homogeneous distribution with correlated spike trains.

The method describing the generation of homogeneous correlated spike trains is described in:

Brette, R. (2009). Generation of correlated spike trains. Neural Computation 21(1). http://romainbrette.fr/WordPress3/wp-content/uploads/2014/06/Brette2008NC.pdf

The implementation is based on the one provided by Brian http://briansimulator.org.

To generate correlated spike trains, the population rate of the group of Poisson-like spiking neurons varies following a stochastic differential equation:

\frac{dx}{dt} = \frac{\mu - x}{\tau} + \sigma \, \frac{\xi}{\sqrt{\tau}}

where \xi is a random sample from the standard normal distribution. In short, x will randomly vary around \mu over time, with an amplitude determined by \sigma and a speed determined by \tau.

This doubly stochastic process is called a Cox process or Ornstein-Uhlenbeck process.

To avoid that x becomes negative, the values of mu and sigma are computed from a rectified Gaussian distribution, parameterized by the desired population rate rates, the desired correlation strength corr and the time constant tau. See Brette’s paper for details.

In short, you should only define the parameters rates, corr and tau, and let the class compute mu and sigma for you. Changing rates, corr or tau after initialization automatically recomputes mu and sigma.

Example:

import ANNarchy as ann
ann.setup(dt=0.1)

pop_corr = ann.HomogeneousCorrelatedSpikeTrains(200, rates=10., corr=0.3, tau=10.)

ann.compile()

ann.simulate(1000.)

pop_corr.rates=30.

ann.simulate(1000.)

Alternatively, a schedule can be provided to change automatically the value of rates and corr (but not tau) at the required times (as in TimedArray or TimedPoissonPopulation):

pop_corr = ann.HomogeneousCorrelatedSpikeTrains(
    geometry=200, 
    rates= [10., 30.], 
    corr=[0.3, 0.5], 
    tau=10.,
    schedule=[0., 1000.]
)

ann.compile()

ann.simulate(2000.)

Even when using a schedule, corr accepts a single constant value. The first value of schedule must be 0. period specifies when the schedule “loops” back to its initial value.

Parameters

Name	Type	Description	Default
geometry	int \| tuple[int]	population geometry as tuple.	required
rates	float \| list[float]	rate in Hz of the population (must be a positive float or a list)	required
corr	float \| list[float]	total correlation strength (float in [0, 1], or a list)	required
tau	float	correlation time constant in ms.	required
schedule	list[float]	list of times where new values of `rates`and `corr`will be used to computre mu and sigma.	`None`
period	float	time when the array will be reset and start again, allowing cycling over the schedule. Default: no cycling (-1.)	`-1.0`
name	str	unique name of the population (optional).	`None`
refractory	float	refractory period in ms (careful: may break the correlation)	`None`