# Moscow Mathematical Journal

Volume 15, Issue 4, October–December 2015  pp. 741–748.

Neural Codes and Homotopy Types: Mathematical Models of Place Field Recognition

Authors:  Yuri I. Manin
Author institution:Max-Planck-Institut für Mathematik, Bonn, Germany

Summary:

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.

Keywords: Neural codes, place field recognition.