ArticleFoundations of data science (Springfield, Mo.)2025
PERSISTENT SHEAF LAPLACIANS.
Article in Foundations of data science (Springfield, Mo.), 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 23 papers.
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Who cites it
23 citing papers in PubMed.
- Persistent sheaf Laplacian analysis of protein stability and solubility changes upon mutation.Protein science : a publication of the Protein Society · 2026Article
- Article
- 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 Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences.Journal of chemical information and modeling · 2025Review
- Topological machine learning for protein-nucleic acid binding affinity changes upon mutation.Machine learning: science and technology · 2025Article
- Machine learning predictions from unpredictable chaos.Journal of the Royal Society, Interface · 2025Article
- Article
- PERSISTENT DIRECTED FLAG LAPLACIAN.Foundations of data science (Springfield, Mo.) · 2025Article
- PERSISTENT INTERACTION TOPOLOGY IN DATA ANALYSIS.Foundations of data science (Springfield, Mo.) · 2025Article
- Persistent Sheaf Laplacian Analysis of Protein Flexibility.The journal of physical chemistry. B · 2025Article
- Persistent Directed Flag Laplacian (PDFL)-Based Machine Learning for Protein-Ligand Binding Affinity Prediction.Journal of chemical theory and computation · 2025Article
- Persistent Topological Laplacians-A Survey.Mathematics (Basel, Switzerland) · 2025Article
- Rapid response to fast viral evolution using AlphaFold 3-assisted topological deep learning.Virus evolution · 2025Article
- PERSISTENT MAYER HOMOLOGY AND PERSISTENT MAYER LAPLACIAN.Foundations of data science (Springfield, Mo.) · 2024Article
- Persistent Mayer Dirac.Journal of physics. Complexity · 2024Article
- Rapid response to fast viral evolution using AlphaFold 3-assisted topological deep learning.ArXiv · 2024Article
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2 authors.
Funding
Abstract
Recently, various types of topological Laplacians have been studied from the perspective of data analysis. The spectral theory of these Laplacians has significantly extended the scope of algebraic topology and data analysis. Inspired by the theory of persistent Laplacians and cellular sheaves, this work develops the theory of persistent sheaf Laplacians for cellular sheaves and describes how to construct sheaves for a point cloud where each point is associated with a quantity that can be devised to embed physical properties. The spectra of persistent sheaf Laplacians encode both geometrical and non-geometrical information of the given point cloud. The theory of persistent sheaf Laplacians provides an elegant method for fusing different types of data and has significant potential for future development.
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