DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kim, Woojin | ko |
dc.contributor.author | Mémoli, Facundo | ko |
dc.date.accessioned | 2023-07-06T02:00:10Z | - |
dc.date.available | 2023-07-06T02:00:10Z | - |
dc.date.created | 2023-07-06 | - |
dc.date.created | 2023-07-06 | - |
dc.date.created | 2023-07-06 | - |
dc.date.created | 2023-07-06 | - |
dc.date.issued | 2021-12 | - |
dc.identifier.citation | Journal of Applied and Computational Topology, v.5, no.4, pp.533 - 581 | - |
dc.identifier.issn | 2367-1726 | - |
dc.identifier.uri | http://hdl.handle.net/10203/310335 | - |
dc.description.abstract | When a category C satisfies certain conditions, we define the notion of rank invariant for arbitrary poset-indexed functors F: P→ C from a category theory perspective. This generalizes the standard notion of rank invariant as well as Patel’s recent extension. Specifically, the barcode of any interval decomposable persistence modules F: P→ vec of finite dimensional vector spaces can be extracted from the rank invariant by the principle of inclusion-exclusion. Generalizing this idea allows freedom of choosing the indexing poset P of F: P→ C in defining Patel’s generalized persistence diagram of F. Of particular importance is the fact that the generalized persistence diagram of F is defined regardless of whether F is interval decomposable or not. By specializing our idea to zigzag persistence modules, we also show that the zeroth level set barcode of a Reeb graph can be obtained in a purely set-theoretic setting without passing to the category of vector spaces. This leads to a promotion of Patel’s semicontinuity theorem about type A persistence diagram to Lipschitz continuity theorem for the category of sets. | - |
dc.language | English | - |
dc.publisher | Springer International Publishing | - |
dc.title | Generalized persistence diagrams for persistence modules over posets | - |
dc.type | Article | - |
dc.identifier.scopusid | 2-s2.0-85117543944 | - |
dc.type.rims | ART | - |
dc.citation.volume | 5 | - |
dc.citation.issue | 4 | - |
dc.citation.beginningpage | 533 | - |
dc.citation.endingpage | 581 | - |
dc.citation.publicationname | Journal of Applied and Computational Topology | - |
dc.identifier.doi | 10.1007/s41468-021-00075-1 | - |
dc.contributor.localauthor | Kim, Woojin | - |
dc.contributor.nonIdAuthor | Mémoli, Facundo | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
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