5 papers
A Persistent Homology Signature of Knotting
Aurelie Jodelle Kemme, Collins A. Agyingi, Colleen Farrelly +1
We ask whether knotting can be recognised using persistent homology. Starting from a point-cloud representation of a curve, we compute one-dimensional persistent homology, extract…
An exploration of low crossing and chiral cosmetic bands with grid diagrams
Agnese Barbensi, Daniele Celoria, Christopher Ktenidis +3
We computationally explore non-coherent band attachments between low crossing number knots, using grid diagrams. We significantly improve the current H(2)-distance table. In partic…
Topologically Directed Simulations Reveal the Impact of Geometric Constraints on Knotted Proteins
Agnese Barbensi, Alexander R. Klotz, Dimos Gkountaroulis
Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological…
Topological Optimal Transport for Geometric Cycle Matching
Stephen Y Zhang, Michael P H Stumpf, Tom Needham +1
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant t…
Geometry of the Space of Partitioned Networks: A Unified Theoretical and Computational Framework
Stephen Y Zhang, Fangfei Lan, Youjia Zhou +4
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however,…