Command: pp_pop_psc_delta

References

[1] Naud R Gerstner W (2012) Coding and decoding with adapting neurons:

a population approach to the peri-stimulus time histogram.

PLoS Compututational Biology 8: e1002711.

[2] Deger M Helias M Boucsein C Rotter S (2012) Statistical properties

of superimposed stationary spike trains. Journal of Computational

Neuroscience 32:3 443-463.

[3] Deger M Schwalger T Naud R Gerstner W (2014) Fluctuations and

information filtering in coupled populations of spiking neurons with

adaptation. Physical Review E 90:6 062704.

Description

pp_pop_psc_delta is an effective model of a population of neurons. The

N component neurons are assumed to be spike response models with escape

noise also known as generalized linear models. We follow closely the

nomenclature of [1]. The component neurons are a special case of

pp_psc_delta (with purely exponential rate function no reset and no

random dead_time). All neurons in the population share the inputs that it

receives and the output is the pooled spike train.

The instantaneous firing rate of the N component neurons is defined as

rate(t) = rho_0 * exp( (h(t) - eta(t))/delta_u )

where h(t) is the input potential (synaptic delta currents convolved with

an exponential kernel with time constant tau_m) eta(t) models the effect

of refractoriness and adaptation (the neuron's own spike train convolved with

a sum of exponential kernels with time constants taus_eta) and delta_u

sets the scale of the voltages.

To represent a (homogeneous) population of N inhomogeneous renewal process

neurons we can keep track of the numbers of neurons that fired a certain number

of time steps in the past. These neurons will have the same value of the

hazard function (instantaneous rate) and we draw a binomial random number

for each of these groups. This algorithm is thus very similar to

ppd_sup_generator and gamma_sup_generator see also [2].

However the adapting threshold eta(t) of the neurons generally makes the neurons

non-renewal processes. We employ the quasi-renewal approximation

[1] to be able to use the above algorithm. For the extension of [1] to

coupled populations see [3].

In effect in each simulation time step a binomial random number for each

of the groups of neurons has to be drawn independent of the number of

represented neurons. For large N it should be much more efficient than

simulating N individual pp_psc_delta models.

pp_pop_psc_delta emits spike events like other neuron models but no more

than one per time step. If several component neurons spike in the time step

the multiplicity of the spike event is set accordingly. Thus to monitor

its output the mulitplicity of the spike events has to be taken into account.

Alternatively the internal variable n_events gives the number of spikes

emitted in a time step and can be monitored using a multimeter.

A journal article that describes the model and algorithm in detail is

in preparation.

Parameters

The following parameters can be set in the status dictionary.

N int - Number of represented neurons.

tau_m double - Membrane time constant in ms.

C_m double - Capacitance of the membrane in pF.

rho_0 double - Base firing rate in 1/s.

delta_u double - Voltage scale parameter in mV.

I_e double - Constant input current in pA.

taus_eta list of doubles - time constants of post-spike kernel in ms.

vals_eta list of doubles - amplitudes of exponentials in post-spike-kernel in mV.

len_kernel double - post-spike kernel eta is truncated after max(taus_eta) * len_kernel.

The parameters correspond to the ones of pp_psc_delta as follows.

c_1 = 0.0

c_2 = rho_0

c_3 = 1/delta_u

q_sfa = vals_eta

tau_sfa = taus_eta

I_e = I_e

dead_time = simulation resolution

dead_time_random = False

with_reset = False

t_ref_remaining = 0.0

Author

May 2014
Setareh
Deger

Sends

SpikeEvent

File

models/pp_pop_psc_delta.h

Receives

SpikeEvent
CurrentEvent
DataLoggingRequest