erfc_neuron.h

Go to the documentation of this file.

/*
 *  erfc_neuron.h
 *
 *  This file is part of NEST.
 *
 *  Copyright (C) 2004 The NEST Initiative
 *
 *  NEST is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  NEST is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with NEST.  If not, see <http://www.gnu.org/licenses/>.
 *
 */
 
#ifndef ERFC_NEURON_H
#define ERFC_NEURON_H
 
// Includes from models:
#include "binary_neuron.h"
 
namespace nest
{
 
/* BeginUserDocs: neuron, binary
 
Short description
+++++++++++++++++
 
Binary stochastic neuron with complementary error function as
activation function
 
Description
+++++++++++
 
The ``erfc_neuron`` is an implementation of a binary neuron that
is irregularly updated at Poisson time points. At each update
point, the total synaptic input :math:`h` into the neuron is summed up,
passed through a gain function :math:`g` whose output is interpreted as
the probability of the neuron to be in the active (1) state.
 
The gain function used here is
 
.. math::
 
 g(h) = \frac{1}{2} \mathrm{erfc} \frac{h - \theta}{\sqrt{2}\sigma}\;.
 
This corresponds to a McCulloch-Pitts neuron receiving additional
Gaussian noise with mean 0 and standard deviation :math:`\sigma`.  The time
constant :math:`\tau_m` is defined as the mean of the inter-update-interval
that is drawn from an exponential distribution with this
parameter. Using this neuron to reproduce simulations with
asynchronous update (similar to :footcite:p:`Ginzburg1994` :footcite:p:`McCulloch1943`), the time constant needs to be
chosen as :math:`\tau_m = dt \times N`, where :math:`dt` is the simulation
time step and :math:`N` the number of neurons in the original simulation with asynchronous
update. This ensures that a neuron is updated on average every :math:`\tau_m`
ms. Since in the original papers :footcite:p:`Ginzburg1994` :footcite:p:`McCulloch1943` neurons are coupled with zero
delay, this implementation follows that definition. It uses the update
scheme described in :footcite:p:`Morrison2007b` 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 :math:`d`, the user has to specify
the delay :math:`d+h` upon connection, where :math:`h` is the simulation time step.
 
 
Parameters
++++++++++
 
======  ======  =========================================================
 tau_m  ms      Membrane time constant (mean inter-update-interval)
 theta  mV      threshold for sigmoidal activation function
 sigma  mV      1/sqrt(2pi) x inverse of maximal slope
======  ======  =========================================================
 
.. admonition:: Special requirements for binary neurons
 
   As the ``erfc_neuron`` is a binary neuron, the user must
   ensure that the following requirements are observed. NEST does not
   enforce them. Breaching the requirements can lead to meaningless
   results.
 
   1. Binary neurons must only be connected to other binary neurons.
 
   #. No more than one connection must be created between any pair of
      binary neurons. When using probabilistic connection rules, specify
      ``'allow_autapses': False`` to avoid accidental creation of
      multiple connections between a pair of neurons.
 
   #. Binary neurons can be driven by current-injecting devices, but
      *not* by spike generators.
 
   #. Activity of binary neurons can only be recored using a ``spin_detector``
      or ``correlospinmatrix_detector``.
 
 
References
++++++++++
 
.. footbibliography::
 
Receives
++++++++
 
CurrentEvent
 
See also
++++++++
 
Examples using this model
+++++++++++++++++++++++++
 
.. listexamples:: erfc_neuron
 
 
EndUserDocs */
 
class gainfunction_erfc
{
private:
  double theta_;
 
  double sigma_;
 
public:
  gainfunction_erfc()
    : theta_( 0.0 )
    , sigma_( 1.0 )
  {
  }
 
  void get( Dictionary& ) const;              
  void set( const Dictionary&, Node* node );  
 
  bool operator()( RngPtr rng, double h );
};
 
inline bool
gainfunction_erfc::operator()( RngPtr rng, double h )
{
  return rng->drand() < 0.5 * erfc( -( h - theta_ ) / ( sqrt( 2. ) * sigma_ ) );
}
 
typedef binary_neuron< gainfunction_erfc > erfc_neuron;
void register_erfc_neuron( const std::string& name );
 
 
template <>
void RecordablesMap< erfc_neuron >::create();
 
}  // namespace nest
 
 
#endif /* #ifndef ERFC_NEURON_H */