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Selecta Mathematica

pp 1–10

First Online: 19 October 2016

Abstract

Encoding, transmission and decoding of information are ubiquitous in biology and human history: from DNA transcription to spoken-written languages and languages of sciences. During the last decades, the study of neural networks in brain performing their multiple tasks was providing more and more detailed pictures of fragments of this activity. Mathematical models of this multifaceted process led to some fascinating problems about -good codes- in mathematics, engineering, and now biology as well. The notion of -good- or -optimal- codes depends on the technological progress and criteria defining optimality of codes of various types: error-correcting ones, cryptographic ones, noise-resistant ones etc. In this note, I discuss recent suggestions that activity of some neural networks in brain, in particular those responsible for space navigation, can be well approximated by the assumption that these networks produce and use good error-correcting codes. I give mathematical arguments supporting the conjecture that search for optimal codes is built into neural activity and is observable.

Mathematics Subject Classification92C20 97M60 To Sasha Beilinson, most cordially

Io mirava, e chiedea: Musa, la lima ov’è? Disse la Dea: lima è consumata; or facciam senza. Ed io, ma di rifarla Non vi cal, soggiungea, quand’ella è stanca? Rispose: hassi a rifar, ma il tempo manca.

Giacomo Leopardi, Canti. XXXVI, Scherzo

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Author: Yuri I. Manin

Source: https://link.springer.com/







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