Microscopic approach of a time elapsed neural model

Julien Chevallier; Maria Jose Caceres; Marie Doumic; Patricia Reynaud-Bouret

doi:10.1142/S021820251550058X

Microscopic approach of a time elapsed neural model

Julien Chevallier
, Maria Jose Caceres
, Marie Doumic
, Patricia Reynaud-Bouret

Research output: Contribution to journal › Article › peer-review

Abstract

The spike trains are the main components of the information processing in the brain. To model spike trains several point processes have been investigated in the literature. And more macroscopic approaches have also been studied, using partial differential equation models. The main aim of the present paper is to build a bridge between several point processes models (Poisson, Wold, Hawkes) that have been proved to statistically fit real spike trains data and age-structured partial differential equations as introduced by Pakdaman, Perthame and Salort.

Original language	English
Pages (from-to)	2669-2719
Number of pages	51
Journal	Mathematical Models and Methods in Applied Sciences
Volume	25
Issue number	14
DOIs	https://doi.org/10.1142/S021820251550058X
Publication status	Published - 30 Dec 2015

Keywords

Hawkes process
Wold process
neural network
renewal equation

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title = "Microscopic approach of a time elapsed neural model",

abstract = "The spike trains are the main components of the information processing in the brain. To model spike trains several point processes have been investigated in the literature. And more macroscopic approaches have also been studied, using partial differential equation models. The main aim of the present paper is to build a bridge between several point processes models (Poisson, Wold, Hawkes) that have been proved to statistically fit real spike trains data and age-structured partial differential equations as introduced by Pakdaman, Perthame and Salort.",

keywords = "Hawkes process, Wold process, neural network, renewal equation",

author = "Julien Chevallier and Caceres, \{Maria Jose\} and Marie Doumic and Patricia Reynaud-Bouret",

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AU - Chevallier, Julien

AU - Caceres, Maria Jose

AU - Doumic, Marie

AU - Reynaud-Bouret, Patricia

PY - 2015/12/30

Y1 - 2015/12/30

N2 - The spike trains are the main components of the information processing in the brain. To model spike trains several point processes have been investigated in the literature. And more macroscopic approaches have also been studied, using partial differential equation models. The main aim of the present paper is to build a bridge between several point processes models (Poisson, Wold, Hawkes) that have been proved to statistically fit real spike trains data and age-structured partial differential equations as introduced by Pakdaman, Perthame and Salort.

AB - The spike trains are the main components of the information processing in the brain. To model spike trains several point processes have been investigated in the literature. And more macroscopic approaches have also been studied, using partial differential equation models. The main aim of the present paper is to build a bridge between several point processes models (Poisson, Wold, Hawkes) that have been proved to statistically fit real spike trains data and age-structured partial differential equations as introduced by Pakdaman, Perthame and Salort.

KW - Hawkes process

KW - Wold process

KW - neural network

KW - renewal equation

U2 - 10.1142/S021820251550058X

DO - 10.1142/S021820251550058X

M3 - Article

AN - SCOPUS:84944278123

SN - 0218-2025

VL - 25

SP - 2669

EP - 2719

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 14

ER -

Microscopic approach of a time elapsed neural model

Abstract

Keywords

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