81 citations · 318 across the 48 of their papers we have counts for
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Computability questions in the sphere packing problem
Yuri Manin, Matilde Marcolli
We consider the sets of dimensions for which there is an optimal sphere packing with special regularity properties (respectively, a lattice, or a periodic set with a given bound on…
Geometry of Information: classical and quantum aspects
Noemie Combe, Yuri I. Manin, Matilde Marcolli
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and…
Moufang Patterns and Geometry of Information
Noemie Combe, Yuri I. Manin, Matilde Marcolli
Technology of data collection and information transmission is based on various mathematical models of encoding. The words "Geometry of information" refer to such models, whereas th…
Zipf's law and L. Levin's probability distributions
Yuri I. Manin
Zipf's law in its basic incarnation is an empirical probability distribution governing the frequency of usage of words in a language. As Terence Tao recently remarked, it still lac…
Kolmogorov complexity and the asymptotic bound for error-correcting codes
Yuri I. Manin, Matilde Marcolli
The set of all error--correcting block codes over a fixed alphabet with letters determines a recursively enumerable set of rational points in the unit square with coordinates $…
A computability challenge: asymptotic bounds and isolated error-correcting codes
Yuri I. Manin
Consider the set of all error--correcting block codes over a fixed alphabet with letters. It determines a recursively enumerable set of points in the unit square with coordinat…
Error-correcting codes and phase transitions
Yuri I. Manin, Matilde Marcolli
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requiremen…