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Mosc. Math. J., 2015, Volume 15, Number 4, Pages 741–748 (Mi mmj584)  

This article is cited in 5 scientific papers (total in 5 papers)

Neural codes and homotopy types: mathematical models of place field recognition

Yuri I. Manin

Max-Planck-Institut für Mathematik, Bonn, Germany

Abstract: 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.

DOI: https://doi.org/10.17323/1609-4514-2015-15-4-741-748

Full text: http://www.mathjournals.org/.../2015-015-004-010.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 94-02
Received: December 11, 2014; in revised form August 8, 2015
Language:

Citation: 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
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\by Yuri~I.~Manin
\paper Neural codes and homotopy types: mathematical models of place field recognition
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 4
\pages 741--748
\mathnet{http://mi.mathnet.ru/mmj584}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-4-741-748}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438831}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000368530900010}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. I. Manin, M. Marcolli, “Semantic spaces”, Math. Comput. Sci., 10:4 (2016), 459–477  crossref  mathscinet  zmath  isi  scopus
    2. 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  crossref  isi  elib
    3. V S. Kozyrev, “Biology as a constructive physics”, P-Adic Numbers Ultrametric Anal. Appl., 10:4 (2018), 305–311  crossref  mathscinet  isi  scopus
    4. Yu. I. Manin, “Error-correcting codes and neural networks”, Sel. Math.-New Ser., 24:1, SI (2018), 521–530  crossref  mathscinet  zmath  isi  scopus
    5. A. Port, I. Gheorghita, D. Guth, J. M. Clark, C. Liang, Sh. Dasu, M. Marcolli, “Persistent topology of syntax”, Math. Comput. Sci., 12:1 (2018), 33–50  crossref  mathscinet  zmath  isi  scopus
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