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- B Cessac
- Journal of mathematical biology
- 2008

We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in Soula et al. (Neural Comput. 18, 1, 2006). Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns ("raster plots"). Moreover, though the dynamics… (More)

- Olivier D. Faugeras, Jonathan Touboul, Bruno Cessac
- Front. Comput. Neurosci.
- 2009

We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the time variations of their membrane potentials. They are coupled by synaptic connections acting on their resulting… (More)

- B Cessac, T Viéville
- 2008

We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some finite precision, we propose a model where spikes are effective at times multiple of a characteristic time scale δ, where δ can be arbitrary small (in particular,… (More)

- B Cessac
- Journal of mathematical biology
- 2011

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also… (More)

- Benoît Siri, Hugues Berry, Bruno Cessac, Bruno Delord, Mathias Quoy
- Neural Computation
- 2008

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule, including passive forgetting and different timescales, for neuronal activity and learning dynamics. Previous numerical work has reported that Hebbian learning drives the system from chaos to a steady state through… (More)

- Emmanuel Daucé, Mathias Quoy, Bruno Cessac, Bernard Doyon, Manuel Samuelides
- Neural Networks
- 1998

- Benoît Siri, Mathias Quoy, Bruno Delord, Bruno Cessac, Hugues Berry
- Journal of physiology, Paris
- 2007

The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore consider that the neuron dynamics may occur at a (shorter) time scale than synaptic plasticity and consider the… (More)

- Bruno Cessac, Hélène Paugam-Moisy, Thierry Viéville
- Journal of physiology, Paris
- 2010

In the present overview, our wish is to demystify some aspects of coding with spike-timing, through a simple review of well-understood technical facts regarding spike coding. Our goal is a better understanding of the extent to which computing and modeling with spiking neuron networks might be biologically plausible and computationally efficient. We… (More)

- Bruno Cessac
- I. J. Bifurcation and Chaos
- 2010

We present some recent investigations resulting from the modelling of neural networks as dynamical systems, and dealing with the following questions, adressed in the context of specific models. (ii). Statistical analysis of spikes trains; (iii). Interplay between dynamics and network structure; (iv). Effects of synaptic plasticity.

- Bruno Cessac, Manuel Samuelides
- ArXiv
- 2006

This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the Hodgkin-Huxley description, which is somehow the canonical description for the " biological neuron ". We discuss some… (More)