# Command: ginzburg_neuron

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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:

- pp_psc_delta

Source:

    /opt/conda/conda-bld/nest_1512418773968/work/nest-2.14.0/models/ginzburg_neuron.h

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