Statistical physics approaches to neuronal network dynamics.

David Cai, Louis Tao

Research output: Contribution to journalArticle

Abstract

We review a statistical physics approach for reduced descriptions of neuronal network dynamics. From a network of all-to-all coupled, excitatory integrate-and-fire neurons, we derive a (2+1)-D advection-diffusion equation for a probability distribution function, which describes neuronal population dynamics. We further show how to derive a (1+1)-D kinetic equation, using a moment closure scheme, without introducing any new parameters to the system. We demonstrate the numerical accuracy of our kinetic theory by comparing its results to Monte Carlo simulations of the full integrate-and-fire neuronal network.

Original languageEnglish (US)
Pages (from-to)453-462
Number of pages10
JournalSheng li xue bao : [Acta physiologica Sinica]
Volume63
Issue number5
StatePublished - Oct 25 2011

Fingerprint

Physics
Population Dynamics
Neurons

ASJC Scopus subject areas

  • Physiology

Cite this

Statistical physics approaches to neuronal network dynamics. / Cai, David; Tao, Louis.

In: Sheng li xue bao : [Acta physiologica Sinica], Vol. 63, No. 5, 25.10.2011, p. 453-462.

Research output: Contribution to journalArticle

@article{adf32618201342d1bbe6dacf5589f6b6,
title = "Statistical physics approaches to neuronal network dynamics.",
abstract = "We review a statistical physics approach for reduced descriptions of neuronal network dynamics. From a network of all-to-all coupled, excitatory integrate-and-fire neurons, we derive a (2+1)-D advection-diffusion equation for a probability distribution function, which describes neuronal population dynamics. We further show how to derive a (1+1)-D kinetic equation, using a moment closure scheme, without introducing any new parameters to the system. We demonstrate the numerical accuracy of our kinetic theory by comparing its results to Monte Carlo simulations of the full integrate-and-fire neuronal network.",
author = "David Cai and Louis Tao",
year = "2011",
month = "10",
day = "25",
language = "English (US)",
volume = "63",
pages = "453--462",
journal = "Acta Physiologica Sinica",
issn = "0371-0874",
publisher = "Kexue Chubaneshe/Science Press",
number = "5",

}

TY - JOUR

T1 - Statistical physics approaches to neuronal network dynamics.

AU - Cai, David

AU - Tao, Louis

PY - 2011/10/25

Y1 - 2011/10/25

N2 - We review a statistical physics approach for reduced descriptions of neuronal network dynamics. From a network of all-to-all coupled, excitatory integrate-and-fire neurons, we derive a (2+1)-D advection-diffusion equation for a probability distribution function, which describes neuronal population dynamics. We further show how to derive a (1+1)-D kinetic equation, using a moment closure scheme, without introducing any new parameters to the system. We demonstrate the numerical accuracy of our kinetic theory by comparing its results to Monte Carlo simulations of the full integrate-and-fire neuronal network.

AB - We review a statistical physics approach for reduced descriptions of neuronal network dynamics. From a network of all-to-all coupled, excitatory integrate-and-fire neurons, we derive a (2+1)-D advection-diffusion equation for a probability distribution function, which describes neuronal population dynamics. We further show how to derive a (1+1)-D kinetic equation, using a moment closure scheme, without introducing any new parameters to the system. We demonstrate the numerical accuracy of our kinetic theory by comparing its results to Monte Carlo simulations of the full integrate-and-fire neuronal network.

UR - http://www.scopus.com/inward/record.url?scp=84874174650&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874174650&partnerID=8YFLogxK

M3 - Article

VL - 63

SP - 453

EP - 462

JO - Acta Physiologica Sinica

JF - Acta Physiologica Sinica

SN - 0371-0874

IS - 5

ER -