A First-Order Non-Homogeneous Markov Model for the Response of Spiking Neurons Stimulated by Small Phase-Continuous Signals

TL;DR

This paper introduces a first-order non-homogeneous Markov model for predicting the interspike-interval density of stimulated neurons, capturing signal and neuron characteristics separately, and demonstrating applications in cross-correlation systems.

Contribution

It presents a novel Markov model that separates neuron and signal effects, enabling response prediction without detailed neuron models.

Findings

Model captures autocorrelations and cross-correlations naturally.

Effective in predicting responses for small signals and moderate noise.

Simplifies design of neuron cross-correlation systems.

Abstract

We present a first-order non-homogeneous Markov model for the interspike-interval density of a continuously stimulated spiking neuron. The model allows the conditional interspike-interval density and the stationary interspike-interval density to be expressed as products of two separate functions, one of which describes only the neuron characteristics, and the other of which describes only the signal characteristics. This allows the use of this model to predict the response when the underlying neuron model is not known or well determined. The approximation shows particularly clearly that signal autocorrelations and cross-correlations arise as natural features of the interspike-interval density, and are particularly clear for small signals and moderate noise. We show that this model simplifies the design of spiking neuron cross-correlation systems, and describe a four-neuron mutual inhibition network that generates a cross-correlation output for two input signals.