ArticleFoundations of data science (Springfield, Mo.)2025
PERSISTENT DIRECTED FLAG LAPLACIAN.
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 6 papers.
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Who cites it
6 citing papers in PubMed.
- 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
- Drug Resistance Predictions Based on a Directed Flag Transformer.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2025Article
- Persistent Topological Laplacians-A Survey.Mathematics (Basel, Switzerland) · 2025Article
- Persistent Mayer Dirac.Journal of physics. Complexity · 2024Article
- Preventing future zoonosis: SARS-CoV-2 mutations enhance human-animal cross-transmission.Computers in biology and medicine · 2024Article
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Authors and funding
2 authors.
Funding
Abstract
Topological data analysis (TDA) has had enormous success in science and engineering in the past decade. Persistent topological Laplacians (PTLs) overcome some limitations of persistent homology, a key technique in TDA, and provide substantial insight to the behavior of various geometric and topological objects. This work extends PTLs to directed flag complexes, which are an exciting generalization to flag complexes, also known as clique complexes, that arise naturally in many situations. We introduce the directed flag Laplacian and show that the proposed persistent directed flag Laplacian (PDFL) is a distinct way of analyzing these flag complexes. Example calculations are provided to demonstrate the potential of the proposed PDFL in real world applications.
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Registered trials
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