Skip to Main content Skip to Navigation
Other publications

Stochastic Processes and Hitting Times in Mathematical Neurosciences

Jonathan Touboul 1, 2
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : In this research report we define a new event-based mathematical framework for studying the dynamics of networks of integrate-and-fire neuron driven by external noise. Such networks are classically studied using the Fokker-Planck equation (Brunel, Hakim). In this study, we use the powerful tools developed for communication networks theory and define a formalism for the study of spiking neuron networks driven by an external noise. With this formalism, we address biological questions to characterize the different network regimes. In this framework, the probability distribution of the interspike interval is a fundamental parameter. We developed and apply several tools for defining and computing the probability density function (pdf) of the time of the first spike, using stochastic analysis. This point of view gives us an event-driven strategy for simulating this type of random networks. This strategy has been implemented in an extension of the event-driven simulator Mvaspike.
Document type :
Other publications
Complete list of metadata

Cited literature [1 references]  Display  Hide  Download

https://hal.inria.fr/inria-00311967
Contributor : Jonathan Touboul <>
Submitted on : Friday, August 22, 2008 - 5:32:48 PM
Last modification on : Thursday, July 1, 2021 - 5:58:02 PM
Long-term archiving on: : Thursday, June 3, 2010 - 5:31:18 PM

File

masterThesis.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00311967, version 1

Collections

Citation

Jonathan Touboul. Stochastic Processes and Hitting Times in Mathematical Neurosciences. 2006. ⟨inria-00311967⟩

Share

Metrics

Record views

305

Files downloads

98