Brain state in a convex body

Author

Bohner, Martin ; Hui, Stefen

Author_Institution

Abteilung Math. V, Ulm Univ., Germany

Volume

6

Issue

5

fYear

1995

fDate

9/1/1995 12:00:00 AM

Firstpage

1053

Lastpage

1060

Abstract

We study a generalization of the brain-state-in-a-box (BSB) model for a class of nonlinear discrete dynamical systems where we allow the states of the system to lie in an arbitrary convex body. The states of the classical BSB model are restricted to lie in a hypercube. Characterizations of equilibrium points of the system are given using the support function of a convex body. Also, sufficient conditions for a point to be a stable equilibrium point are investigated. Finally, we study the system in polytopes. The results in this special case are more precise and have simpler forms than the corresponding results for general convex bodies. The general results give one approach of allowing pixels in image reconstruction to assume more than two values

Keywords

content-addressable storage; generalisation (artificial intelligence); hypercube networks; image reconstruction; neural nets; nonlinear dynamical systems; brain-state-in-a-box model; convex body; equilibrium points; generalization; hypercube; image reconstruction; neural model; nonlinear discrete dynamical systems; polytopes; sufficient conditions; Associative memory; Brain modeling; Equations; Helium; Hypercubes; Image reconstruction; Neural networks; Pixel; Stability; Sufficient conditions;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.410350

Filename

410350