# 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:

- 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}

}

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