Approximate maximizers of intricacy functionals

Abstract : G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. This functional is a special case of intricacy, i.e., an average of the mutual information of subsystems whose weights have good mathematical properties. Moreover, its maximum value grows at a definite speed with the size of the system. In this work, we compute exactly this speed of growth by building "approximate maximizers" subject to an entropy condition. These approximate maximizers work simultaneously for all intricacies. We also establish some properties of arbitrary approximate maximizers, in particular the existence of a threshold in the size of subsystems of approximate maximizers: most smaller subsystems are almost equidistributed, most larger subsystems determine the full system. The main ideas are a random construction of almost maximizers with a high statistical symmetry and the consideration of entropy profiles, i.e., the average entropies of sub-systems of a given size. The latter gives rise to interesting questions of probability and information theory.
Type de document :
Pré-publication, Document de travail
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Contributeur : Lorenzo Zambotti <>
Soumis le : lundi 14 septembre 2009 - 09:54:35
Dernière modification le : mercredi 21 mars 2018 - 18:56:48

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  • HAL Id : hal-00416395, version 1
  • ARXIV : 0909.2120



Jerome Buzzi, Lorenzo Zambotti. Approximate maximizers of intricacy functionals. 2009. 〈hal-00416395〉



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