ArticleAIMS mathematics2024
Evolutionary Khovanov homology.
Article in AIMS mathematics, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed.
- Topological data analysis and topological deep learning beyond persistent homology: a review.Artificial intelligence review · 2026Article
- Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data.Advanced intelligent discovery · 2025Article
- A Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences.Journal of chemical information and modeling · 2025Review
- Khovanov Laplacian and Khovanov Dirac for knots and links.Journal of physics. Complexity · 2025Article
- Persistent Topological Laplacians-A Survey.Mathematics (Basel, Switzerland) · 2025Article
- Knot data analysis using multiscale Gauss link integral.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning.AIMS mathematics · 2024Article
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3 authors.
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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.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the Socratic graph.