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A mathematical approach to resilience

Abstract : In this paper, we evolve from sparsity, a key concept in robust statistics, to concepts and theoretical results of what we call the mathematics of resilience, at the interface between category theory, the theory of dynamical systems, statistical signal processing and biology. We first summarize a recent result on dy-namical systems [2], before presenting the de-generacy paradigm, issued from biology [4] and mathematically formalized by [5, 6] as the Multiplicity Principle (MP). We then make the connection with statistical signal processing by showing that two distinct and structurally different families of tests satisfy the MP.
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https://hal-imt-atlantique.archives-ouvertes.fr/hal-02557647
Contributor : Dominique Pastor <>
Submitted on : Tuesday, April 28, 2020 - 9:18:43 PM
Last modification on : Tuesday, October 6, 2020 - 9:40:04 AM

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Dominique Pastor, Erwan Beurier, Andrée Ehresmann, Roger Waldeck. A mathematical approach to resilience. iTWIST'20 (international Traveling Workshop on Interactions between low-complexity data models and Sensing Techniques), Jun 2020, Nantes, France. ⟨hal-02557647⟩

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