MaximumEntropy 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 Boltzmannlike equation governing the evolution of a oneparticle (i.e., oneneuron) probability density function. We demonstrate that this intuitive closure is a generalization of moment closures based on the maximumentropy principle. By invoking maximumentropy closures, we show how to systematically extend this kinetic theory to obtain higherorder (1+1)D kinetic equations and to include coupled networks of both excitatory and inhibitory neurons.
 Authors:
 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. MaximumEntropy 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. MaximumEntropy Closures for Kinetic Theories of Neuronal Network Dynamics. United States. doi:10.1103/PhysRevLett.96.178101.
Rangan, Aaditya V., and Cai, David. Fri .
"MaximumEntropy Closures for Kinetic Theories of Neuronal Network Dynamics". United States.
doi:10.1103/PhysRevLett.96.178101.
@article{osti_20777214,
title = {MaximumEntropy 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 Boltzmannlike equation governing the evolution of a oneparticle (i.e., oneneuron) probability density function. We demonstrate that this intuitive closure is a generalization of moment closures based on the maximumentropy principle. By invoking maximumentropy closures, we show how to systematically extend this kinetic theory to obtain higherorder (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}
}
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