Linear Response of General Observables in Spiking Neuronal Network Models.

Bruno Cessac,Rodrigo Cofré,Ignacio Ampuero

doi:10.3390/e23020155

Abstract

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allow us to predict the influence of a weak amplitude time dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how the linear response is explicitly related to the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike train statistics. We illustrate our results with numerical simulations performed over a discrete time integrate and fire model.

Highlights

Neurons communicate by short-lasting electrical signals called action potentials or “spikes”, allowing the rapid propagation of information throughout the nervous system, with a minimal energy dissipation [1]
How are the spatiotemporal spike correlations modified by this stimulus? We address this question in the context of linear response theory using methods from ergodic theory and so-called chains with complete connections [30], extending the notion of Markov chains to infinite memory, providing a generalized notion of Gibbs distribution
We have addressed the following question: How is the average of an observable f (t, ω ) affected by a weak time-dependent stimulus. We studied this question in a theoretical setting, using the linear response theory and probability distributions with unbounded memory generalizing the usual definition (3) of Gibbs distributions in statistical physics courses

Summary

Introduction

Neurons communicate by short-lasting electrical signals called action potentials or “spikes”, allowing the rapid propagation of information throughout the nervous system, with a minimal energy dissipation [1].

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Methods

Results

Conclusion