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 dynamical systems [Beurier, Pastor, Spivak 2019], before presenting the de-generacy paradigm, issued from biology [Edelman, Gally 1973] and mathematically formalized by [Ehresmann Vanbremeersch 2007] [Ehresmann Vanbremeersch 2019] 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.
Cite
@article{arxiv.2009.09666,
title = {A mathematical approach to resilience},
author = {Dominique Pastor and Erwan Beurier and Andrée C. Ehresmann and Roger Waldeck},
journal= {arXiv preprint arXiv:2009.09666},
year = {2020}
}
Comments
3 pages. In Proceedings of iTWIST'20, Paper-ID: 35, Nantes, France, December, 2-4, 2020