**Name:**

gif_pop_psc_exp - Population of generalized integrate-and-fire neurons

with exponential postsynaptic currents and adaptation

**Description:**

This model simulates a population of spike-response model neurons with

multi-timescale adaptation and exponential postsynaptic currents, as

described in [1].

The single neuron model is defined by the hazard function

lambda_0 * exp[ ( V_m - E_sfa ) / Delta_V ]

After each spike the membrane potential V_m is reset to V_reset. Spike

frequency

adaptation is implemented by a set of exponentially decaying traces, the

sum of which is E_sfa. Upon a spike, all adaptation traces are incremented

by the respective q_sfa each and decay with the respective time constant

tau_sfa.

The corresponding single neuron model is available in NEST as gif_psc_exp.

The default parameters, although some are named slightly different, are not

matched in both models due to historical reasons. See below for the parameter

translation.

As gif_pop_psc_exp represents many neurons in one node, it may send a lot

of spikes. In each time step, it sends at most one spike though, the

multiplicity of which is set to the number of emitted spikes. Postsynaptic

neurons and devices in NEST understand this as several spikes, but

communication effort is reduced in simulations.

This model uses a new algorithm to directly simulate the population activity

(sum of all spikes) of the population of neurons, without explicitly

representing each single neuron (see [1]). The computational cost is largely

independent of the number N of neurons represented. The algorithm used

here is fundamentally different from and likely much faster than the one

used in the previously added population model pp_pop_psc_delta.

Connecting two population models corresponds to full connectivity of every

neuron in each population. An approximation of random connectivity can be

implemented by connecting populations through a spike_dilutor.

**Parameters:**

The following parameters can be set in the status dictionary.

V_reset double - Membrane potential is reset to this value in mV after a

spike.

V_T_star double - Threshold level of the membrane potential in mV.

E_L double - Resting potential in mV

Delta_V double - Noise level of escape rate in mV.

C_m double - Capacitance of the membrane in pF.

tau_m double - Membrane time constant in ms.

t_ref double - Duration of refractory period in ms.

I_e double - Constant input current in pA.

N long - Number of neurons in the population.

len_kernel long - Refractory effects are accounted for up to len_kernel

time steps

lambda_0 double - Firing rate at threshold in 1/s.

tau_syn_ex double - Time constant for excitatory synaptic currents in ms.

tau_syn_in double - Time constant for inhibitory synaptic currents in ms.

tau_sfa double vector - Adaptation time constants in ms.

q_sfa double vector - Adaptation kernel amplitudes in ms.

BinoRand bool - If True, binomial random numbers are used, otherwise

we use Poisson distributed spike counts.

Parameter translation to gif_psc_exp:

gif_pop_psc_exp gif_psc_exp relation

----------------------------------------------------

tau_m g_L tau_m = C_m / g_L

N --- use N gif_psc_exp

**Require:**

HAVE_GSL

**Receives:**

SpikeEvent, CurrentEvent, DataLoggingRequest

Authors: Nov 2016, Moritz Deger, Tilo Schwalger, Hesam Setareh

**Sends:**

SpikeEvent

**References:**

[1] Towards a theory of cortical columns: From spiking neurons to

interacting neural populations of finite size

Tilo Schwalger, Moritz Deger, Wulfram Gerstner

PLoS Comput Biol 2017

https://doi.org/10.1371/journal.pcbi.1005507

**SeeAlso:**

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/models/gif_pop_psc_exp.h