Moscow Mathematical Journal
Volume 15, Issue 4, October–December 2015 pp. 741–748.
Neural Codes and Homotopy Types: Mathematical Models of Place Field Recognition
This note is a brief survey of some results of the recent
collaboration of neurobiologists and mathematicians dedicated to stimulus reconstruction from neuronal spiking activity. This collaboration,
in particular, led to the consideration of binary codes used by brain
for encoding a stimuli domain such as a rodent’s territory through the
combinatorics of its covering by local neighborhoods. The survey is addressed to mathematicians (cf. [DS01]) and focusses
on the idea that stimuli spaces are represented by the relevant neural
codes as simplicial sets and thus encode say, the homotopy type of space
if local neighbourhoods are convex. 2010 Math. Subj. Class. 94-02.
Authors:
Yuri I. Manin
Author institution:Max-Planck-Institut für Mathematik, Bonn, Germany
Summary:
Keywords: Neural codes, place field recognition.
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