A directed persistent homology theory for dissimilarity functions

DOI10.1007/s41468-023-00124-xzbMath1528.55004arXiv2008.00711OpenAlexW3046717611WikidataQ122911570 ScholiaQ122911570MaRDI QIDQ6082668

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Publication date: 30 November 2023

Published in: Journal of Applied and Computational Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.00711

zbMATH Keywords

persistent homologydissimilarity functionsdirected cyclesdirected simplicial complexes

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Semirings (16Y60) Simplicial sets and complexes in algebraic topology (55U10) Other homology theories in algebraic topology (55N35)

Cites Work

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• The persistent homology of a self-map
• Generalized fuzzy matrices
• Omega-categories and chain complexes
• Computing persistent homology
• Topological persistence and simplification
• Path complexes and their homologies
• Cohomology monoids of monoids with coefficients in semimodules. I
• Rips filtrations for quasimetric spaces and asymmetric functions with stability results
• A functorial Dowker theorem and persistent homology of asymmetric networks
• Hierarchical clustering of asymmetric networks
• Bases in semimodules over commutative semirings
• Directed algebraic topology and concurrency. With a foreword by Maurice Herlihy and a preface by Samuel Mimram
• The Structure and Stability of Persistence Modules
• Topology and data
• Persistent Path Homology of Directed Networks
• Induced Matchings of Barcodes and the Algebraic Stability of Persistence
• Proximity of persistence modules and their diagrams