Étude d'un processus d'auto-organisation. (Study of a self-organization process)
type: Item
instance of: scholarly article
title: Étude d'un processus d'auto-organisation. (Study of a self-organization process)
zbMATH Open document ID: 0605.92002
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77289
review text: \textit{T. Kohonen} defined in Biol. Cybern. 43, 59-69 (1982; Zbl 0466.92002) a mathematical algorithm in order to modelize the biological phenomena called retinotopy: that is the self-organized formation of maps between retina and cortex preserving the topological structure of the retina. He observed the convergence of the algorithm by simulation and presented in ''Self-organization and associative memory'' (1984; Zbl 0528.68062) a sketch of proof. In this paper we prove the convergence toward an invariant distribution in the one-dimensional case.
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 92F05
Mathematics Subject Classification ID: 92Cxx
zbMATH DE Number: 3978885
zbMATH Keywords: self-organization process
zbMATH Keywords: formation of feature maps
zbMATH Keywords: retinotopy
zbMATH Keywords: cortex
zbMATH Keywords: topological structure of the retina
zbMATH Keywords: convergence of the algorithm
zbMATH Keywords: invariant distribution
zbMATH Keywords: one-dimensional case
author: Marie Cottrell
author: Jean-Claude Fort
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3978885