**Name:**

ginzburg_neuron - Binary stochastic neuron with sigmoidal activation

function.

**Description:**

The ginzburg_neuron is an implementation of a binary neuron that

is irregularly updated as Poisson time points. At each update

point the total synaptic input h into the neuron is summed up,

passed through a gain function g whose output is interpreted as

the probability of the neuron to be in the active (1) state.

The gain function g used here is g(h) = c1*h + c2 * 0.5*(1 +

tanh(c3*(h-theta))) (output clipped to [0,1]). This allows to

obtain affin-linear (c1!=0, c2!=0, c3=0) or sigmoidal (c1=0,

c2=1, c3!=0) shaped gain functions. The latter choice

corresponds to the definition in [1], giving the name to this

neuron model.

The choice c1=0, c2=1, c3=beta/2 corresponds to the Glauber

dynamics [2], g(h) = 1 / (1 + exp(-beta (h-theta))).

The time constant tau_m is defined as the mean

inter-update-interval that is drawn from an exponential

distribution with this parameter. Using this neuron to reprodce

simulations with asynchronous update [1], the time constant needs

to be chosen as tau_m = dt*N, where dt is the simulation time

step and N the number of neurons in the original simulation with

asynchronous update. This ensures that a neuron is updated on

average every tau_m ms. Since in the original paper [1] neurons

are coupled with zero delay, this implementation follows this

definition. It uses the update scheme described in [3] to

maintain causality: The incoming events in time step t_i are

taken into account at the beginning of the time step to calculate

the gain function and to decide upon a transition. In order to

obtain delayed coupling with delay d, the user has to specify the

delay d+h upon connection, where h is the simulation time step.

**Parameters:**

tau_m double - Membrane time constant (mean inter-update-interval)

in ms.

theta double - threshold for sigmoidal activation function mV

c1 double - linear gain factor (probability/mV)

c2 double - prefactor of sigmoidal gain (probability)

c3 double - slope factor of sigmoidal gain (1/mV)

**Receives:**

SpikeEvent, PotentialRequest

**Sends:**

SpikeEvent

**Remarks:**

This neuron has a special use for spike events to convey the

binary state of the neuron to the target. The neuron model

only sends a spike if a transition of its state occurs. If the

state makes an up-transition it sends a spike with multiplicity 2,

if a down transition occurs, it sends a spike with multiplicity 1.

The decoding scheme relies on the feature that spikes with multiplicity

larger 1 are delivered consecutively, also in a parallel setting.

The creation of double connections between binary neurons will

destroy the deconding scheme, as this effectively duplicates

every event. Using random connection routines it is therefore

advisable to set the property 'multapses' to false.

The neuron accepts several sources of currents, e.g. from a

noise_generator.

**References:**

[1] Iris Ginzburg, Haim Sompolinsky. Theory of correlations in stochastic

neural networks (1994). PRE 50(4) p. 3171

[2] Hertz Krogh, Palmer. Introduction to the theory of neural computation.

Westview (1991).

[3] Abigail Morrison, Markus Diesmann. Maintaining Causality in Discrete Time

Neuronal

Simulations.

In: Lectures in Supercomputational Neuroscience, p. 267. Peter beim Graben,

Changsong Zhou, Marco Thiel, Juergen Kurths (Eds.), Springer 2008.

**Author:**

Moritz Helias

**FirstVersion:**

February 2010

**SeeAlso:**

**Source:**

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