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Information cohomology: an overview

Juan Pablo Vigneaux ( Institut de Mathématiques de Jussieu – Paris Rive Gauche, Université Paris Diderot – Paris 7 )

In this talk, I introduce spaces (Grothendieck topoi) related to random experiments and an adapted cohomology theory, called "information cohomology". These spaces serve as "graphical models" for several applications in physics and computer science, and they also formalize the notion of "context". I describe the cohomological characterization of Shannon entropy, Tsallis entropy and the Fontené-Ward multinomial coefficients (a generalized version of the usual ones), as well as a functorial relation between them. Finally, I comment about a generalization of Shannon theory in which messages are finite vector spaces, inspired by this correspondence.

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