title: A first-order nonhomogeneous Markov model for the response of spiking neurons stimulated by small phase-continuous signals.
abstract: We present a first-order nonhomogeneous 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. 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.
authors.affiliation: Department of Electrical Engineering, University of Cape Town, Rondebosch 7701, South Africa. jonathan.tapson@uct.ac.za
authors.forename: Jonathan
authors.initials: J
authors.lastname: Tapson
authors.forename: Craig
authors.initials: C
authors.lastname: Jin
authors.forename: André
authors.initials: A
authors.lastname: van Schaik
authors.forename: Ralph
authors.initials: R
authors.lastname: Etienne-Cummings
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D003198:Computer Simulation; D008390:Markov Chains; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology; D009433:Neural Inhibition / Q000502:physiology; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D010812:Physical Stimulation; D013997:Time Factors