Persistent Cup-Length

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.contributorThe Ohio State University-
Autor(es): dc.contributorUniversity of Bremen-
Autor(es): dc.creatorContessoto, Marco-
Autor(es): dc.creatorMémoli, Facundo-
Autor(es): dc.creatorStefanou, Anastasios-
Autor(es): dc.creatorZhou, Ling-
Data de aceite: dc.date.accessioned2025-08-21T19:17:37Z-
Data de disponibilização: dc.date.available2025-08-21T19:17:37Z-
Data de envio: dc.date.issued2023-03-01-
Data de envio: dc.date.issued2023-03-01-
Data de envio: dc.date.issued2022-06-01-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.4230/LIPIcs.SoCG.2022.31-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/11449/240472-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/240472-
Descrição: dc.descriptionCohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by the software Ripser. The cup product operation which is available at cohomology level gives rise to a graded ring structure that extends the usual vector space structure and is therefore able to extract and encode additional rich information. The maximum number of cocycles having non-zero cup product yields an invariant, the cup-length, which is useful for discriminating spaces. In this paper, we lift the cup-length into the persistent cup-length function for the purpose of capturing ring-theoretic information about the evolution of the cohomology (ring) structure across a filtration. We show that the persistent cup-length function can be computed from a family of representative cocycles and devise a polynomial time algorithm for its computation. We furthermore show that this invariant is stable under suitable interleaving-type distances.-
Descrição: dc.descriptionNational Sleep Foundation-
Descrição: dc.descriptionDepartment of Mathematics São Paulo State University-UNESP-
Descrição: dc.descriptionDepartment of Computer Science and Engineering The Ohio State University-
Descrição: dc.descriptionDepartment of Mathematics and Computer Science University of Bremen-
Descrição: dc.descriptionDepartment of Mathematics The Ohio State University-
Descrição: dc.descriptionDepartment of Mathematics São Paulo State University-UNESP-
Descrição: dc.descriptionNational Sleep Foundation: CCF-1740761-
Descrição: dc.descriptionNational Sleep Foundation: DMS-1440386-
Descrição: dc.descriptionNational Sleep Foundation: RI-1901360-
Idioma: dc.languageen-
Relação: dc.relationLeibniz International Proceedings in Informatics, LIPIcs-
???dc.source???: dc.sourceScopus-
Palavras-chave: dc.subjectcohomology-
Palavras-chave: dc.subjectcup length-
Palavras-chave: dc.subjectcup product-
Palavras-chave: dc.subjectGromov-Hausdorff distance-
Palavras-chave: dc.subjectpersistence-
Título: dc.titlePersistent Cup-Length-
Tipo de arquivo: dc.typeaula digital-
Aparece nas coleções:Repositório Institucional - Unesp

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