ArticleProceedings. Mathematical, physical, and engineering sciences2022
A statistical approach to knot confinement via persistent homology.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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1 citing paper in PubMed.
- Homology of homologous knotted proteins.Journal of the Royal Society, Interface · 2023Article
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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.
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