Discrete morse theoretic algorithms for computing homology of complexes and maps

2014
journal article
article
56
cris.lastimport.wos2024-04-09T21:33:27Z
dc.abstract.enWe provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homology computation for a very general class of complexes. A set-valued map of top-dimensional cells between such complexes is a natural discrete approximation of an underlying (and possibly unknown) continuous function, especially when the evaluation of that function is subject to measurement errors. We introduce a new Morse theoretic preprocessing framework for deriving chain maps from such set-valued maps, and hence provide an effective scheme for computing the morphism induced on homology by the approximated continuous function.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowejpl
dc.contributor.authorHarker, Shaunpl
dc.contributor.authorMischaikow, Konstantinpl
dc.contributor.authorMrozek, Marian - 130783 pl
dc.contributor.authorNanda, Viditpl
dc.date.accessioned2015-03-03T08:40:48Z
dc.date.available2015-03-03T08:40:48Z
dc.date.issued2014pl
dc.description.number1pl
dc.description.physical151-184pl
dc.description.volume14pl
dc.identifier.doi10.1007/s10208-013-9145-0pl
dc.identifier.eissn1615-3383pl
dc.identifier.issn1615-3375pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/3446
dc.languageengpl
dc.language.containerengpl
dc.rights.licencebez licencji
dc.subtypeArticlepl
dc.titleDiscrete morse theoretic algorithms for computing homology of complexes and mapspl
dc.title.journalFoundations of Computational Mathematicspl
dc.typeJournalArticlepl
dspace.entity.typePublication
cris.lastimport.wos
2024-04-09T21:33:27Z
dc.abstract.enpl
We provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homology computation for a very general class of complexes. A set-valued map of top-dimensional cells between such complexes is a natural discrete approximation of an underlying (and possibly unknown) continuous function, especially when the evaluation of that function is subject to measurement errors. We introduce a new Morse theoretic preprocessing framework for deriving chain maps from such set-valued maps, and hence provide an effective scheme for computing the morphism induced on homology by the approximated continuous function.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej
dc.contributor.authorpl
Harker, Shaun
dc.contributor.authorpl
Mischaikow, Konstantin
dc.contributor.authorpl
Mrozek, Marian - 130783
dc.contributor.authorpl
Nanda, Vidit
dc.date.accessioned
2015-03-03T08:40:48Z
dc.date.available
2015-03-03T08:40:48Z
dc.date.issuedpl
2014
dc.description.numberpl
1
dc.description.physicalpl
151-184
dc.description.volumepl
14
dc.identifier.doipl
10.1007/s10208-013-9145-0
dc.identifier.eissnpl
1615-3383
dc.identifier.issnpl
1615-3375
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/3446
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights.licence
bez licencji
dc.subtypepl
Article
dc.titlepl
Discrete morse theoretic algorithms for computing homology of complexes and maps
dc.title.journalpl
Foundations of Computational Mathematics
dc.typepl
JournalArticle
dspace.entity.type
Publication

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