Neural fields and visual texture perception

Olivier Faugeras 1
1 NEUROMATHCOMP
CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Rocquencourt, ENS Paris - École normale supérieure - Paris, UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of even approximate solutions to such models is of interest to the broad mathematical neuroscience community. Here we develop one such scheme, for stationary and travelling wave solutions, that can deal with a certain class of smoothed Heaviside functions. The distribution that smoothes the Heaviside is viewed as a fundamental object, and all expressions describing the scheme are constructed in terms of integrals over this distribution. The comparison of our scheme and results from direct numerical simulations is used to highlight the very good levels of approximation that can be achieved by iterating the process only a small number of times.
Type de document :
Communication dans un congrès
AIMS Conference Spatially Structured Oscillations and Waves in Neural Media, May 2010, Dresden, Germany. 2010, 〈http://aimsciences.org/AIMS-Conference/conf-reg2010/ss/detail.php?absₙo=1486〉
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https://hal.inria.fr/hal-00847443
Contributeur : Pierre Kornprobst <>
Soumis le : mardi 23 juillet 2013 - 15:41:06
Dernière modification le : jeudi 11 janvier 2018 - 15:56:40

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  • HAL Id : hal-00847443, version 1

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Olivier Faugeras. Neural fields and visual texture perception. AIMS Conference Spatially Structured Oscillations and Waves in Neural Media, May 2010, Dresden, Germany. 2010, 〈http://aimsciences.org/AIMS-Conference/conf-reg2010/ss/detail.php?absₙo=1486〉. 〈hal-00847443〉

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