论文标题
弹性的数学方法
A mathematical approach to resilience
论文作者
论文摘要
在本文中，我们从稀疏性（稳健统计数据中的关键概念）演变为我们所谓的弹性数学的概念和理论结果，在类别理论，动力学系统，统计信号处理和生物学之间的界面上。我们首先总结了动态系统的最新结果[Beurier，Pastor，Spivak，2019年]，然后介绍了生物学发行的De-eneracy范式[Edelman，Gally，1973年]，并由[Ehresmann vanbremesch 2007] [Ehresmann vanbremesch 2007] [Ehresmann vanbremeersch 2019] [ehresmann vanbremesch 2019]正式化。然后，我们通过表明两个不同的和结构上不同的测试家族满足MP来与统计信号处理建立联系。
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.
