This article is cited in 2 scientific papers (total in 2 papers)
Neural codes and homotopy types: mathematical models of place field recognition
Yuri I. Manin
Max-Planck-Institut für Mathematik, Bonn, Germany
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.
Key words and phrases:
neural codes, place field recognition.
Received: December 11, 2014; in revised form August 8, 2015
Yuri I. Manin, “Neural codes and homotopy types: mathematical models of place field recognition”, Mosc. Math. J., 15:4 (2015), 741–748
Citation in format AMSBIB
\paper Neural codes and homotopy types: mathematical models of place field recognition
\jour Mosc. Math.~J.
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Yu. I. Manin, M. Marcolli, “Semantic spaces”, Math. Comput. Sci., 10:4 (2016), 459–477
V. I. Volchikhin, A. I. Ivanov, A. V. Serikov, Yu. I. Serikova, “Kvantovaya superpozitsiya diskretnogo spektra sostoyanii matematicheskoi molekuly korrelyatsii dlya malykh vyborok biometricheskikh dannykh”, Vestnik Mordovskogo universiteta, 27:2 (2017), 224–238
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