On Information Links
| Autor: | Pierre Baudot |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Mutual information Brunnian link 01 natural sciences 010305 fluids & plasmas Interaction information Maxima and minima Joint probability distribution Kirkwood approximation 0103 physical sciences Multivariate mutual information 010306 general physics Divergence (statistics) Mathematics |
| Zdroj: | Lecture Notes in Computer Science ISBN: 9783030802080 GSI |
| DOI: | 10.1007/978-3-030-80209-7_68 |
| Popis: | In a joint work with D. Bennequin [8], we suggested that the (negative) minima of the 3-way multivariate mutual information correspond to Borromean links, paving the way for providing probabilistic analogs of linking numbers. This short note generalizes the correspondence of the minima of k multivariate interaction information with k Brunnian links in the binary variable case. Following [16], the negativity of the associated K-L divergence of the joint probability law with its Kirkwood approximation implies an obstruction to local decomposition into lower order interactions than k, defining a local decomposition inconsistency that reverses Abramsky’s contextuality local-global relation [1]. Those negative k-links provide a straightforward definition of collective emergence in complex k-body interacting systems or dataset. |
| Databáze: | OpenAIRE |
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