# Command: mcculloch_pitts_neuron

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Name:

    mcculloch_pitts_neuron - Binary deterministic neuron with Heaviside
      activation function.

Description:

      The mcculloch_pitts_neuron is an implementation of a binary
      neuron that is irregularly updated as Poisson time points [1]. At
      each update point the total synaptic input h into the neuron is
      summed up, passed through a Heaviside gain function g(h) = H(h-theta),
      whose output is either 1 (if input is above) or 0 (if input is below
      threshold 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

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 decoding 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] W. McCulloch und W. Pitts (1943). A logical calculus of the ideas
      immanent in nervous activity. Bulletin of Mathematical Biophysics, 5:115-133.
      [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 2013

SeeAlso:

- pp_psc_delta

Source:

    /opt/conda/conda-bld/nest_1512421404550/work/nest-2.12.0/models/mcculloch_pitts_neuron.h

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