Application of a generalised Levy residence time problem to neuronal dynamics

Waxman, David and Feng, J. F. (2004) Application of a generalised Levy residence time problem to neuronal dynamics. Europhysics Letters (EPL), 65 (3). p. 434. ISSN 0295-5075

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Abstract

The distribution of bursting lengths of neuron spikes, in a two-component integrate-and-fire model, is investigated. The stochastic process underlying this model corresponds to a generalisation of the Brownian motion underlying Levy's arcsine law of residence times. The generalisation involves the inclusion of a quadratic potential of strength γ and γ = 0 corresponds to Levy's original problem. In the generalised problem, the distribution of the residence times, T, over a time window t, is related to spectral properties of a complex, non-relativistic Hamiltonian of quantum mechanics. The distribution of T depends on γt and varies from a U-shaped distribution for small γt to a bell-shaped distribution for large γt. The first two moments of T of the generalised problem are explicitly calculated and the crossover point between the two forms of the distribution is calculated. The distribution of residence times is shown to be independent of the magnitude of the stochastic force. This corresponds, in the neuron model, to exactly balanced synaptic inputs and, in this case, the distribution of residence times contains no information on synaptic inputs.

Item Type: Article
Schools and Departments: School of Life Sciences > Biology and Environmental Science
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Depositing User: David Waxman
Date Deposited: 14 Feb 2007
Last Modified: 14 Oct 2019 09:53
URI: http://sro.sussex.ac.uk/id/eprint/766
Google Scholar:2 Citations
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