| Naslov: | Rigidity of terminal simplices in persistent homology |
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| Avtorji: | ID Franc, Aleksandra (Avtor)
ID Virk, Žiga (Avtor) |
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| Datoteke: |  URL - Izvorni URL, za dostop obiščite https://link.springer.com/article/10.1007/s13398-023-01473-z
 PDF - Predstavitvena datoteka, prenos (476,36 KB)
MD5: BA951B107E513AAEE2E68383B2703D7D
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | Given a filtration function on a finite simplicial complex, stability theorem of persistent homology states that the corresponding barcode is continuous with respect to changes in the filtration function. However, due to the discrete setting of simplicial complexes, the simplices terminating matched bars cannot change continuously for arbitrary perturbations of filtration functions. In this paper we provide a sufficient condition for rigidity of a terminal simplex, i.e., a condition on $\varepsilon > 0$ implying that the terminal simplex of a homology class or a bar in persistent homology remains constant through $\varepsilon$-perturbations of filtration function. The condition for a homology class or a bar in dimension $n$ depends only on the barcodes in dimensions $n$ and $n+1$. |
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| Ključne besede: | persistent homology, stability theorem, terminal simplex, rigidity |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.10.2023 |
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| Leto izida: | 2023 |
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| Št. strani: | str. 1-16 |
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| Številčenje: | Vol. 117, iss. 4, article no. 141 |
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| PID: | 20.500.12556/DiRROS-18417  |
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| UDK: | 515.1 |
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| ISSN pri članku: | 1578-7303 |
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| DOI: | 10.1007/s13398-023-01473-z |
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| COBISS.SI-ID: | 157780483 |
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| Datum objave v DiRROS: | 15.03.2024 |
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| Število ogledov: | 470 |
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| Število prenosov: | 227 |
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| Metapodatki: |    |
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