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