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Spike-train spectra and network response functions for nonlinear integrate-and-fire neurons. (English) Zbl 1161.92014
Summary: Reduced models have long been used as a tool for the analysis of the complex activity taking place in neurons and their coupled networks. Recent advances in experimental and theoretical techniques have further demonstrated the usefulness of this approach. Despite the often gross simplification of the underlying biophysical properties, reduced models can still present significant difficulties in their analysis, with the majority of exact and perturbative results available only for the leaky integrate-and-fire model.
Here an elementary numerical scheme is demonstrated which can be used to calculate a number of biologically important properties of a general class of nonlinear integrate-and-fire models. Exact results for the first-passage-time density and spike-train spectrum are derived, as well as the linear response properties and emergent states of recurrent networks. Given that the exponential integrate-fire model has recently been shown to agree closely with the experimentally measured response of pyramidal cells, the methodology presented here promises to provide a convenient tool to facilitate the analysis of cortical-network dynamics.

92C20 Neural biology
92C05 Biophysics
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
92-08 Computational methods for problems pertaining to biology
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