ArticleInternational journal for numerical methods in biomedical engineering2020
Persistent spectral graph.
Article in International journal for numerical methods in biomedical engineering, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 91 papers, 1 of them a synthesis that pooled it.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
91 citing papers in PubMed, 1 synthesis or guideline pooled it.
- Meta-Analysis and Topological Perturbation in Interactomic Network for Antiopioid Addiction Drug Repurposing.Journal of chemical information and modeling · 2025Pooled it
- Persistent Local Laplacian Prediction of Protein-Ligand Binding Affinities.Journal of chemical information and modeling · 2026Article
- Topological learning prediction of virus-like particle stoichiometry and stability.Biophysical journal · 2026Article
- Persistent sheaf Laplacian analysis of protein stability and solubility changes upon mutation.Protein science : a publication of the Protein Society · 2026Article
- Article
- Correlated clustering and projection for dimensionality reduction.Machine learning: science and technology · 2026Article
- Spectral Graph Features for Reference-free RNA 3D Quality Assessment.bioRxiv : the preprint server for biology · 2026Article
- Commutative Algebra Modeling in Materials Science - A Case Study on Metal-Organic Frameworks (MOFs).Journal of chemical information and modeling · 2026Article
- Persistent Stanley-Reisner Theory.Foundations of data science (Springfield, Mo.) · 2026Article
- Computational Drug Repurposing for Alzheimer's Disease via Sheaf Theoretic Population-Scale Analysis of snRNA-Seq Data.Journal of medicinal chemistry · 2026Article
- Topological data analysis and topological deep learning beyond persistent homology: a review.Artificial intelligence review · 2026Article
- Predicting protein-nucleic acid flexibility using persistent sheaf Laplacians.Physical chemistry chemical physics : PCCP · 2026Article
- Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data.Advanced intelligent discovery · 2025Article
- A geometric graph-based deep learning model for drug-target affinity prediction.BMC bioinformatics · 2025Article
- A Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences.Journal of chemical information and modeling · 2025Review
- CAP: Commutative algebra prediction of protein-nucleic acid binding affinities.Machine learning: science and technology · 2025Article
- Topological machine learning for protein-nucleic acid binding affinity changes upon mutation.Machine learning: science and technology · 2025Article
- Topological deep learning for enhancing peptide-protein complex prediction.Communications chemistry · 2025Article
- Multiscale Cell-Cell Interactive Spatial Transcriptomics Analysis.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2025Article
- Machine learning predictions from unpredictable chaos.Journal of the Royal Society, Interface · 2025Article
31 more citing papers are in PubMed but not listed here.
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
3 authors.
Funding
Abstract
Persistent homology is constrained to purely topological persistence, while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for revealing topological persistence and extracting geometric shapes from high-dimensional datasets. For a point-cloud dataset, a filtration procedure is used to generate a sequence of chain complexes and associated families of simplicial complexes and chains, from which we construct persistent combinatorial Laplacian matrices. We show that a full set of topological persistence can be completely recovered from the harmonic persistent spectra, that is, the spectra that have zero eigenvalues, of the persistent combinatorial Laplacian matrices. However, non-harmonic spectra of the Laplacian matrices induced by the filtration offer another powerful tool for data analysis, modeling, and prediction. In this work, fullerene stability is predicted by using both harmonic spectra and non-harmonic persistent spectra, while the latter spectra are successfully devised to analyze the structure of fullerenes and model protein flexibility, which cannot be straightforwardly extracted from the current persistent homology. The proposed method is found to provide excellent predictions of the protein B-factors for which current popular biophysical models break down.
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Registered trials
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.