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, kinetic equations and to include coupled networks of both excitatory and inhibitory neurons.
authors.affiliation: Courant Institute of Mathematical Sciences, New York University, New York 10012, USA.
authors.forename: Aaditya V
authors.initials: AV
authors.lastname: Rangan
authors.forename: David
authors.initials: D
authors.lastname: Cai
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D019277:Entropy; D007700:Kinetics; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D011336:Probability