Moment neuronal networks : stochastic computation in neuronal systems

Spike trains recorded in cortical neurons in vivo can be approximated by renewal processes, but are generally not Poisson. Besides, the spiking activity of neighboring neurons display small yet not negligible correlations. The Artificial Neuronal Network theory has traditionally neglected such observations, assuming that neurons could simply be described by their mean firing rate. Here we present a theoretical framework in which the dynamics of a system of neurons is specified in terms of higher-order moments of their spiking activity beyond the mean firing rate