ArticleJournal of applied and computational topology2020
Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis.
Article in Journal of applied and computational topology, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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12 citing papers in PubMed, 19 citations in OpenAlex.
- Topological data analysis and topological deep learning beyond persistent homology: a review.Artificial intelligence review · 2026Article
- A Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences.Journal of chemical information and modeling · 2025Review
- Machine learning predictions from unpredictable chaos.Journal of the Royal Society, Interface · 2025Article
- Persistent Sheaf Laplacian Analysis of Protein Flexibility.The journal of physical chemistry. B · 2025Article
- Multiscale Differential Geometry Learning for Protein Flexibility Analysis.Journal of computational chemistry · 2025Article
- Multi-scale Jones polynomial and persistent Jones polynomial for knot data analysis.AIMS mathematics · 2025Article
- Knot data analysis using multiscale Gauss link integral.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- ADCdb: the database of antibody-drug conjugates.Nucleic acids research · 2024Article
- Artificial intelligence-aided protein engineering: from topological data analysis to deep protein language models.Briefings in bioinformatics · 2023Review
- Article
- The topology of data: opportunities for cancer research.Bioinformatics (Oxford, England) · 2021Article
- EVOLUTIONARY DE RHAM-HODGE METHOD.Discrete and continuous dynamical systems. Series B · 2021Article
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3 authors at 1 institution in 1 country.
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Abstract
While the spatial topological persistence is naturally constructed from a radius-based filtration, it has hardly been derived from a temporal filtration. Most topological models are designed for the global topology of a given object as a whole. There is no method reported in the literature for the topology of an individual component in an object to the best of our knowledge. For many problems in science and engineering, the topology of an individual component is important for describing its properties. We propose evolutionary homology (EH) constructed via a time evolution-based filtration and topological persistence. Our approach couples a set of dynamical systems or chaotic oscillators by the interactions of a physical system, such as a macromolecule. The interactions are approximated by weighted graph Laplacians. Simplices, simplicial complexes, algebraic groups and topological persistence are defined on the coupled trajectories of the chaotic oscillators. The resulting EH gives rise to time-dependent topological invariants or evolutionary barcodes for an individual component of the physical system, revealing its topology-function relationship. In conjunction with Wasserstein metrics, the proposed EH is applied to protein flexibility analysis, an important problem in computational biophysics. Numerical results for the B-factor prediction of a benchmark set of 364 proteins indicate that the proposed EH outperforms all the other state-of-the-art methods in the field.
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