Statistics of spike trains in conductance-based neural networks: Rigorous results

TL;DR

This paper rigorously establishes the existence and uniqueness of a Gibbs distribution for spike train statistics in conductance-based neural networks, providing explicit formulas and applicable to non-stationary stimuli.

Contribution

It introduces a rigorous mathematical framework for spike train statistics in conductance-based neural networks, including explicit Gibbs potential computation.

Findings

Existence and uniqueness of Gibbs distribution for spike trains.

Explicit computation of the Gibbs potential.

Applicability to non-stationary stimuli.

Abstract

We consider a conductance based neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe. We show the existence and uniqueness of a unique Gibbs distribution characterizing spike train statistics. The corresponding Gibbs potential is explicitly computed. These results hold in presence of a time-dependent stimulus and apply therefore to non-stationary dynamics.