| Name: | mcculloch_pitts_neuron - Binary deterministic neuron with Heaviside activation function.
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| 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 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) = H(h-theta), with H the
Heaviside function. 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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| Parameters: |
tau_m double - Membrane time constant (mean inter-update-interval) in ms.
theta double - threshold for sigmoidal activation function mV
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| 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.
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| Sends: | SpikeEvent
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| Receives: | SpikeEvent, PotentialRequest
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| FirstVersion: | February 2013
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| Author: | Moritz Helias
| SeeAlso: | binary_neuron pp_psc_delta |
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| Source: | /home/abuild/rpmbuild/BUILD/nest-2.4.1/models/mcculloch_pitts_neuron.h
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