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Title: Maximum-Entropy Closures for Kinetic Theories of Neuronal Network Dynamics

Abstract

We analyze (1+1)D kinetic equations for neuronal network dynamics, which are derived via an intuitive closure from a Boltzmann-like equation governing the evolution of a one-particle (i.e., one-neuron) probability density function. We demonstrate that this intuitive closure is a generalization of moment closures based on the maximum-entropy principle. By invoking maximum-entropy closures, we show how to systematically extend this kinetic theory to obtain higher-order (1+1)D kinetic equations and to include coupled networks of both excitatory and inhibitory neurons.

Authors:
;  [1]
  1. Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
Publication Date:
OSTI Identifier:
20777214
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 96; Journal Issue: 17; Other Information: DOI: 10.1103/PhysRevLett.96.178101; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY FUNCTIONAL METHOD; ENTROPY; KINETIC EQUATIONS; MATHEMATICAL EVOLUTION; NERVE CELLS; NEURAL NETWORKS; PARTICLES; PROBABILITY

Citation Formats

Rangan, Aaditya V., and Cai, David. Maximum-Entropy Closures for Kinetic Theories of Neuronal Network Dynamics. United States: N. p., 2006. Web. doi:10.1103/PhysRevLett.96.178101.
Rangan, Aaditya V., & Cai, David. Maximum-Entropy Closures for Kinetic Theories of Neuronal Network Dynamics. United States. doi:10.1103/PhysRevLett.96.178101.
Rangan, Aaditya V., and Cai, David. Fri . "Maximum-Entropy Closures for Kinetic Theories of Neuronal Network Dynamics". United States. doi:10.1103/PhysRevLett.96.178101.
@article{osti_20777214,
title = {Maximum-Entropy Closures for Kinetic Theories of Neuronal Network Dynamics},
author = {Rangan, Aaditya V. and Cai, David},
abstractNote = {We analyze (1+1)D kinetic equations for neuronal network dynamics, which are derived via an intuitive closure from a Boltzmann-like equation governing the evolution of a one-particle (i.e., one-neuron) probability density function. We demonstrate that this intuitive closure is a generalization of moment closures based on the maximum-entropy principle. By invoking maximum-entropy closures, we show how to systematically extend this kinetic theory to obtain higher-order (1+1)D kinetic equations and to include coupled networks of both excitatory and inhibitory neurons.},
doi = {10.1103/PhysRevLett.96.178101},
journal = {Physical Review Letters},
number = 17,
volume = 96,
place = {United States},
year = {Fri May 05 00:00:00 EDT 2006},
month = {Fri May 05 00:00:00 EDT 2006}
}