A statistical approach to knot confinement via persistent homology

Author:

Celoria Daniele1ORCID,Mahler Barbara I.1ORCID

Affiliation:

1. Mathematical Institute, University of Oxford, Radcliffe Observatory, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, UK

Abstract

In this paper, we study how randomly generated knots occupy a volume of space using topological methods. To this end, we consider the evolution of the first homology of an immersed metric neighbourhood of a knot’s embedding for growing radii. Specifically, we extract features from the persistent homology (PH) of the Vietoris–Rips complexes built from point clouds associated with knots. Statistical analysis of our data shows the existence of increasing correlations between geometric quantities associated with the embedding and PH-based features, as a function of the knots’ lengths. We further study the variation of these correlations for different knot types. Finally, this framework also allows us to define a simple notion of deviation from ideal configurations of knots.

Funder

H2020 European Research Council

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Study of Inter-Channel Knowledge Distillation Based on Inheritance and Exploration;2023 42nd Chinese Control Conference (CCC);2023-07-24

2. Homology of homologous knotted proteins;Journal of The Royal Society Interface;2023-04

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