Čech-Delaunay gradient flow and homology inference for self-maps

2020
journal article
article
3
cris.lastimport.scopus2024-04-07T13:46:38Z
cris.lastimport.wos2024-04-10T02:44:31Z
dc.abstract.enWe call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowejpl
dc.contributor.authorBauer, Ulrichpl
dc.contributor.authorEdelsbrunner, Herbertpl
dc.contributor.authorJabłoński, Grzegorz - 115499 pl
dc.contributor.authorMrozek, Marian - 130783 pl
dc.date.accessioned2021-03-23T19:20:02Z
dc.date.available2021-03-23T19:20:02Z
dc.date.issued2020pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.physical455-480pl
dc.description.versionostateczna wersja wydawcy
dc.description.volume4pl
dc.identifier.doi10.1007/s41468-020-00058-8pl
dc.identifier.eissn2367-1734pl
dc.identifier.issn2367-1726pl
dc.identifier.project2014/14/A/ST1/00453pl
dc.identifier.projectDEC-2013/09/N/ST6/02995pl
dc.identifier.project2621/7.PR/12/2013/2pl
dc.identifier.projectDFG Collaborative Research Center SFB/TRR 109pl
dc.identifier.projectROD UJ / OPpl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/267943
dc.languageengpl
dc.language.containerengpl
dc.rightsUdzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa*
dc.rights.licenceCC-BY
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/legalcode.pl*
dc.share.typeinne
dc.subject.encomputational topologypl
dc.subject.enpersistent homologypl
dc.subject.endynamical systemspl
dc.subtypeArticlepl
dc.titleČech-Delaunay gradient flow and homology inference for self-mapspl
dc.title.journalJournal of Applied and Computational Topologypl
dc.typeJournalArticlepl
dspace.entity.typePublication
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