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Hyperbolic bumps

Grégory Faye 1, * Pascal Chossat 1, 2 Olivier Faugeras 1
* Corresponding author
1 NEUROMATHCOMP
CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Rocquencourt, ENS Paris - École normale supérieure - Paris, UNS - Université Nice Sophia Antipolis (... - 2019), CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : In many models of working memory, transient stimuli are encoded by feature-selective persistent neural activity. Such stimuli are imagined to induce the formation of a spatially localised bump of persistent activity which coexists with a stable uniform state. As an example, Camperi and Wang have proposed and studied a network model of visuo-spatial working memory in prefontal cortex adapted from the ring model of orientation of Ben-Yishai and colleagues. It is therefore natural to study the emergence of spatially localised bumps for the structure tensor model. This modelization was introduced by Chossat and Faugeras to describe the representation and the processing of image edges and textures in the hypercolumns of the cortical area V1. The key entity, the structure tensor, intrinsically lives in a non-Euclidean, in effect hyperbolic, space. Its spatio-temporal behaviour is governed by nonlinear integro-differential equations defined on the Poincaré disc model of the two-dimensional hyperbolic space. In this paper, we present an original study, based on non-Euclidean, hyperbolic, analysis, of a spatially localised bump solution.
keyword : System dynamics
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Grégory Faye, Pascal Chossat, Olivier Faugeras. Hyperbolic bumps. Cinquième conférence plénière française de Neurosciences Computationnelles, "Neurocomp'10", Aug 2010, Lyon, France. ⟨hal-00553402⟩

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