In this paper we present computational simulations of a mathematical model describing the
time evolution of membrane potentials in a GABAergic neural network. This model, with …

This paper is a survey of recent developments in the application of stochastic modeling and
statistical analysis of biological and artificial neuron systems. We focus first on a general …

In this book we describe a large number of open problems in the theory of stochastic neural
systems, with the aim of enticing probabilists to work on them. These include problems …

We consider applications of path-integral methods to the analysis of a stochastic hybrid
model representing a network of synaptically coupled spiking neuronal populations. The …

The brain is a very complex system in the strong sense. It features a huge amount of
individual cells, in particular the neurons presenting a highly nonlinear dynamics …

An analytical approach is presented for determining the response of a neuron or of the
activity in a network of connected neurons, represented by systems of nonlinear ordinary …

A stochastic model for describing the firing activity of a couple of interacting neurons subject
to time-dependent stimuli is proposed. Two stochastic differential equations suitably coupled …

We present for the first time an analytical approach for determining the time of firing of
multicomponent nonlinear stochastic neuronal models. We apply the theory of first exit times …

Artificial neuronal networks provide attractive models for cortical function, in particular, if
“cognitive” properties emerge from their structure. Unfortunately, it turns out difficult to set up …

We discuss the statistics of spikes trains for different types of integrate-and-fire neurons and
different types of synaptic noise models. In contrast with the usual approaches in …