ArticleMathematics (Basel, Switzerland)2025
Persistent Topological Laplacians-A Survey.
Article in Mathematics (Basel, Switzerland), 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 20 papers.
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Who cites it
20 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
- Correlated clustering and projection for dimensionality reduction.Machine learning: science and technology · 2026Article
- Spaces and sequences in the hippocampus: a homological perspective.Journal of computational neuroscience · 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 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
- Topological deep learning for enhancing peptide-protein complex prediction.Communications chemistry · 2025Article
- Article
- CAML: Commutative Algebra Machine Learning─A Case Study on Protein-Ligand Binding Affinity Prediction.Journal of chemical information and modeling · 2025Article
- Enhancing energy predictions in multi-atom systems with multiscale topological learning.Journal of materials chemistry. A · 2025Article
- A review of transformer models in drug discovery and beyond.Journal of pharmaceutical analysis · 2025Review
- Khovanov Laplacian and Khovanov Dirac for knots and links.Journal of physics. Complexity · 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
- Evolutionary Khovanov homology.AIMS mathematics · 2024Article
- Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning.AIMS mathematics · 2024Article
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Abstract
Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persistent homology when handling complex data. These Laplacians combine multiscale analysis with topological techniques to characterize the topological and geometrical features of functions and data. Their kernels fully retrieve the topological invariants of corresponding persistent homology, while their non-harmonic spectra provide supplementary information. Persistent topological Laplacians have demonstrated superior performance over persistent homology in the analysis of large-scale protein engineering datasets. In this survey, we offer a pedagogical review of persistent topological Laplacians formulated in various mathematical settings, including simplicial complexes, path complexes, flag complexes, digraphs, hypergraphs, hyperdigraphs, cellular sheaves, and
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