ArticleJournal of computational chemistry2015
Multidimensional persistence in biomolecular data.
Article in Journal of computational chemistry, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 28 papers.
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Who cites it
28 citing papers in PubMed, 87 citations in OpenAlex.
- Spectral Graph Features for Reference-free RNA 3D Quality Assessment.bioRxiv : the preprint server for biology · 2026Article
- 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
- Spatial and Sequential Topological Analysis of Molecular Dynamics Simulations of IgG1 Fc Domains.Journal of chemical theory and computation · 2025Article
- Persistent Topological Laplacians-A Survey.Mathematics (Basel, Switzerland) · 2025Article
- Morphological multiparameter filtration and persistent homology in mitochondrial image analysis.PloS one · 2024Article
- Article
- Persistent Homology for RNA Data Analysis.Methods in molecular biology (Clifton, N.J.) · 2023Article
- Topological data analysis gives two folding paths in HP35(nle-nle), double mutant of villin headpiece subdomain.Scientific reports · 2022Article
- Biomolecular Topology: Modelling and Analysis.Acta mathematica Sinica, English series · 2022Article
- Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash.Entropy (Basel, Switzerland) · 2021Article
- EVOLUTIONARY DE RHAM-HODGE METHOD.Discrete and continuous dynamical systems. Series B · 2021Article
- Exact Probability Landscapes of Stochastic Phenotype Switching in Feed-Forward Loops: Phase Diagrams of Multimodality.Frontiers in genetics · 2021Article
- Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis.Journal of applied and computational topology · 2020Article
- Protein-Folding Analysis Using Features Obtained by Persistent Homology.Biophysical journal · 2020Article
- A review of mathematical representations of biomolecular data.Physical chemistry chemical physics : PCCP · 2020Review
- Atom-specific persistent homology and its application to protein flexibility analysis.Computational and mathematical biophysics · 2020Article
- Persistent Cohomology for Data With Multicomponent Heterogeneous Information.SIAM journal on mathematics of data science · 2020Article
- Generative network complex (GNC) for drug discovery.Communications in information and systems · 2019Article
- Article
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Authors and funding
2 authors at 1 institution in 1 country.
Funding
Abstract
Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology. However, its practical and robust construction has been a challenge. We introduce two families of multidimensional persistence, namely pseudomultidimensional persistence and multiscale multidimensional persistence. The former is generated via the repeated applications of persistent homology filtration to high-dimensional data, such as results from molecular dynamics or partial differential equations. The latter is constructed via isotropic and anisotropic scales that create new simiplicial complexes and associated topological spaces. The utility, robustness, and efficiency of the proposed topological methods are demonstrated via protein folding, protein flexibility analysis, the topological denoising of cryoelectron microscopy data, and the scale dependence of nanoparticles. Topological transition between partial folded and unfolded proteins has been observed in multidimensional persistence. The separation between noise topological signatures and molecular topological fingerprints is achieved by the Laplace-Beltrami flow. The multiscale multidimensional persistent homology reveals relative local features in Betti-0 invariants and the relatively global characteristics of Betti-1 and Betti-2 invariants.
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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 OpenQuestion graph.