Coincidence detector

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Main :: Neuron Models :: Coincidence Detector

Coincidence detector receiving three weighted inputs.
Coincidence detectors, also known equivalently as linear threshold gates, McCulloch-Pitts neurons, or Perceptrons, are a type of neuron model that fires at time t if the weighted sum of inputs received within the window (t,t + δt) equals or exceeds the threshold θ. This is a very simplified model of the neuron, but it is analytically tractable, and

there has accumulated considerable experimental evidence indicating that, under certain conditions, such as high background synaptic activity, neurons can function as coincidence detectors. Thus, even though our model neuron is very simple, it carries biological significance and may be considered biologically realistic under certain experimental conditions.

In many cases, it makes sense to think of δt as of a period on the order of 5-10 ms. This is the time scale of fast ionic synaptic conductances and it is at this time scale that synaptic events superpose and interact.

[edit] Coincidence detector receiving non-correlated inputs

The coincidence detector is a computational unit that fires if the number of input spikes received within a given time bin equals or exceeds the threshold, θ. It is instructive to first derive a solution for independent inputs (q=0) with mean rate p / δt. Using the binomial distribution and elementary combinatorics, we find that the probability of obtaining exactly j coincident input spikes from a set of m input spike trains with probability p for a spike (to exist within each time bin) is:

P(j)={m \choose j} p^{j} (1-p)^{m-j}

Since we are only interested in cases where the coincidence detector receives at least θ coincident input spikes, the probability for the coincidence detector to produce an output spike is:

P_{out}(p,m,\theta;q=0)=\sum_{j=\theta}^m{m \choose j} p^{j}(1-p)^{m-j}

Dividing by δt, we obtain the mean output rate of a coincidence detector in the case of non-correlated inputs: N_{out}(p,m,\theta;q=0)=\frac{1}{\delta t}\sum_{j=\theta}^m{m \choose j} p^{j} (1-p)^{m-j}

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