**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:**

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/models/mcculloch_pitts_neuron.h