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.
Highlights
Introduction and summaryRecently it became technically possible to record simultaneously spiking activity of large neural populations
The data supplied by these studies show “signatures of criticality”. This means that the respective neural populations are functioning near the point of a phase transition if one chooses appropriate statistic models of their behaviour
In this note I test the philosophy relating criticality with optimality using the results of recent works suggesting models of encoding of stimulus space that utilise the basic notions of the theory of error-correcting codes
Summary
It became technically possible to record simultaneously spiking activity of large neural populations (cf. Refs. 1, 2 in [21]). The data supplied by these studies show “signatures of criticality” This means that the respective neural populations are functioning near the point of a phase transition if one chooses appropriate statistic models of their behaviour. The recent collaboration of neurobiologists and mathematicians, in particular, led to the consideration of binary codes used by brain for encoding and storing a stimuli domain such as a rodent’s territory through the combinatorics of its covering by local neighbourhoods: see [1,2, 24] These binary codes as they are described in [1,2,24] (cf a brief survey for mathematicians [14]) are not good error-correcting codes themselves. I approach the problem of relating criticality to optimality of such neural activities using a new statistical model of error-correcting codes explained in [15]. I am happy to dedicate this paper to the inspired researcher Sasha Beilinson, who is endowed with almost uncanny empathy for living inhabitants of this planet!
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