Related papers: A discrete time neural network model with spiking …
We briefly review and highlight the consequences of rigorous and exact results obtained in \cite{cessac:10}, characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where…
We investigate the effect of electric synapses (gap junctions) on collective neuronal dynamics and spike statistics in a conductance-based Integrate-and-Fire neural network, driven by a Brownian noise, where conductances depend upon spike…
We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one…
In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature…
This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials…
Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire (LIF) model. The method is valid in a wide parameter regime beyond the restraining…
We introduce a mathematical framework where the statistics of spikes trains, produced by neural networks evolving under synaptic plasticity, can be analysed.
Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of…
This paper is based on a lecture given in the LACONEU summer school, Valparaiso, January 2012. We introduce Gibbs distribution in a general setting, including non stationary dynamics, and present then three examples of such Gibbs…
We consider a new class of non Markovian processes with a countable number of interacting components, both in discrete and continuous time. Each component is represented by a point process indicating if it has a spike or not at a given…
We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky…
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…
A single neuron is known to generate almost identical spike trains when the same fluctuating input is repeatedly applied. Here, we study the reliability of spike firing in a pulse-coupled network of oscillator neurons receiving fluctuating…
The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train…
A common way of studying the relationship between neural activity and behavior is through the analysis of neuronal spike trains that are recorded using one or more electrodes implanted in the brain. Each spike train typically contains…
We study in this paper the effect of an unique initial stimulation on random recurrent networks of leaky integrate and fire neurons. Indeed given a stochastic connectivity this so-called spontaneous mode exhibits various non trivial…
We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…
Spiking neural networks (SNNs) have emerged as energy-efficient neural networks with temporal information. SNNs have shown a superior efficiency on neuromorphic devices, but the devices are susceptible to noise, which hinders them from…
The nervous system represents time-dependent signals in sequences of discrete action potentials or spikes, all spikes are identical so that information is carried only in the spike arrival times. We show how to quantify this information, in…
Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and…