Cortical Maps

[Hans-Otto Carmesin]

The paper

TOPOLOGY-PRESERVATION EMERGENCE BY THE HEBB RULE 
WITH INFINITESIMAL SHORT RANGE SIGNALS

by 

Hans-Otto Carmesin, 
Institute for Theoretical Physics and Center for Cognitive Sciences, 
University Bremen, 28334 Bremen, Germany

is available.

ABSTRACT: Topology preservation is an ubiquitous phenomenon
in the mammalian nervous system.
What are the necessary
and sufficient conditions for the self- organized formation
of topology preservation due to a Hebb- mechanism?
A relatively realistic Hebb- rule
and neurons with stochastic fluctuations are modeled.
Moreover, the reasonable growth law  is used for coupling growth
that the biomass increase is
proportional to the present biomass under the constraint that
the biomass is limited at a neuron.
It is proven for such general Hebb- type
networks that infinitesimal lateral
signal transfer to neighbouring neurons
is necessary and sufficient for the emergence
of topology preservation.
As a consequence, observed topology preservation in nervous systems
may emerge with or without purpose as a byproduct of
infinitesimal lateral signal transfer to neighbouring neurons
due to ubiquitous chemical and electrical leakage.

Otainable via WWW at  http://www.schoner.physik.uni-bremen.de/~carmesin/

The paper appeared in Phys. Rev. E, Vol.53, 993-1002 (1996).