Evolutionary Khovanov homology
Year: 2024
Type: article
Abstract: Knot theory, a subfield in geometric topology, is the study of the embedding of closed circles into three-dimensional Euclidean space, motivated by the ubiquity of knots in daily life and human civilization. However, focusing on topology, the current knot theory lacks metric analysis. As a result, the application of knot theory has remained largely primitive and qualitative. Motivated by the need of quantitative knot data analysis (KDA), this work implemented the evolutionary Khovanov homology (EKH) to facilitate a multiscale KDA of real-world data. EKH considers specific metrics to filter links, capturing multiscale topological features of knot configurations beyond traditional invariants. It is demonstrated that EKH can reveal non-trivial knot invariants at appropriate scales, even when the global topological structure of a knot is simple. The proposed EKH holds great potential for KDA and machine learning applications related to knot-type data, in contrast to other data forms, such as point cloud data and data on manifolds.
Source: AIMS Mathematics
Authors: Li Shen, Jian Liu, Guo-Wei Wei
Institutions: Michigan State University, Chongqing University of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
Funders: National Science Foundation, National Aeronautics and Space Administration, Bristol-Myers Squibb, Michigan State University, Nuclear Safety and Security Commission, National Institutes of Health, College of Engineering, Michigan State University, National Institute of General Medical Sciences, National Institute of Allergy and Infectious Diseases
Awards: AI-based platform for predicting emerging vaccine-escape variants and designing mutation-proof antibodies, G2333693723, G2551507366, G4604530488, G4934647071, Collaborative Research: Integrating Algebraic Topology, Graph Theory, and Multiscale Analysis for Learning Complex and Diverse Datasets, G5117234996, Kinetics-Driven Drug Discovery Using Persistent Homology, Rare-Event Molecular Dynamics and Experimental Data, G6065440738, III: Medium: De Rham-Hodge theory modeling and learning of biomolecular data, Discovery-Driven Mathematics and Artificial Intelligence for Biosciences and Drug Discovery, G754965114, G9000094880, G9000099788, G9000294604, G965062884
OpenAlex ID: W4402415082