Merge Trees of Periodic Filtrations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929478603636736 |
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| author | Edelsbrunner, Herbert Heiss, Teresa |
| author_facet | Edelsbrunner, Herbert Heiss, Teresa |
| contents | Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability under perturbations and provide an algorithm that under mild geometric conditions typically satisfied by crystalline materials takes $\mathcal{O}({(n+m) \log n})$ time, in which $n$ and $m$ are the numbers of vertices and edges in the quotient complex, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16575 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Merge Trees of Periodic Filtrations Edelsbrunner, Herbert Heiss, Teresa Algebraic Topology Computational Geometry Combinatorics Metric Geometry 55N31 (Primary), 55-08, 05C05, 05C38, 05C40, 05C63, 05C85, 05C90, 05C92, 52C22, 68W05, 92E10 (Secondary) G.2.2; G.2.3; F.2.2 Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability under perturbations and provide an algorithm that under mild geometric conditions typically satisfied by crystalline materials takes $\mathcal{O}({(n+m) \log n})$ time, in which $n$ and $m$ are the numbers of vertices and edges in the quotient complex, respectively. |
| title | Merge Trees of Periodic Filtrations |
| topic | Algebraic Topology Computational Geometry Combinatorics Metric Geometry 55N31 (Primary), 55-08, 05C05, 05C38, 05C40, 05C63, 05C85, 05C90, 05C92, 52C22, 68W05, 92E10 (Secondary) G.2.2; G.2.3; F.2.2 |
| url | https://arxiv.org/abs/2408.16575 |