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Journal of applied and computational topology最新文献

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Maximum persistent Betti numbers of Čech complexes. Čech复合体的最大持久贝蒂数。
Journal of applied and computational topology Pub Date : 2026-01-01 Epub Date: 2026-02-28 DOI: 10.1007/s41468-026-00233-3
Herbert Edelsbrunner, Matthew Kahle, Shu Kanazawa
{"title":"Maximum persistent Betti numbers of Čech complexes.","authors":"Herbert Edelsbrunner, Matthew Kahle, Shu Kanazawa","doi":"10.1007/s41468-026-00233-3","DOIUrl":"10.1007/s41468-026-00233-3","url":null,"abstract":"<p><p>This note proves that only a linear number of holes in a Čech complex of <i>n</i> points in <math> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> </math> can persist over an interval of constant length. Specifically, for any fixed dimension <math><mrow><mi>p</mi> <mo><</mo> <mi>d</mi></mrow> </math> and fixed   <math><mrow><mi>ε</mi> <mo>></mo> <mn>0</mn></mrow> </math> , the number of <i>p</i>-dimensional holes in the Čech complex at radius 1 that persist to radius <math><mrow><mn>1</mn> <mo>+</mo> <mi>ε</mi></mrow> </math> is bounded above by a constant times <i>n</i>, where <i>n</i> is the number of points. The proof uses a packing argument supported by relating the Čech complexes with corresponding snap complexes over the cells in a partition of space. The argument is self-contained and elementary, relying on geometric and combinatorial constructions rather than on the existing theory of sparse approximations or interleavings. The bound also applies to Alpha complexes and Vietoris-Rips complexes. While our result can be inferred from prior work on sparse filtrations, to our knowledge, no explicit statement or direct proof of this bound appears in the literature.</p>","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"10 1","pages":"5"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12950030/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147345991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Topological optimal transport for geometric cycle matching 几何周期匹配的拓扑最优输运
Journal of applied and computational topology Pub Date : 2025-04-01 DOI: 10.1007/s41468-025-00207-x
Stephen Y. Zhang, Michael P. H. Stumpf, Tom Needham, Agnese Barbensi
{"title":"Topological optimal transport for geometric cycle matching","authors":"Stephen Y. Zhang, Michael P. H. Stumpf, Tom Needham, Agnese Barbensi","doi":"10.1007/s41468-025-00207-x","DOIUrl":"https://doi.org/10.1007/s41468-025-00207-x","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"9 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147913509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The fiber of persistent homology for trees. 树木持久同源性的纤维。
Journal of applied and computational topology Pub Date : 2025-01-01 Epub Date: 2025-09-06 DOI: 10.1007/s41468-025-00213-z
David Beers, Jacob Leygonie
{"title":"The fiber of persistent homology for trees.","authors":"David Beers, Jacob Leygonie","doi":"10.1007/s41468-025-00213-z","DOIUrl":"10.1007/s41468-025-00213-z","url":null,"abstract":"<p><p>Consider the space of continuous functions on a geometric tree <i>X</i> whose persistent homology gives rise to a finite generic barcode <i>D</i>. We show that there are exactly as many path connected components in this space as there are merge trees whose barcode is <i>D</i>. We find that each component is homotopy equivalent to a configuration space on <i>X</i> with specialised constraints encoded by the merge tree. For barcodes <i>D</i> with either one or two intervals, our method also allows us to compute the homotopy type of this space of functions.</p>","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"9 3","pages":"22"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12414068/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145024820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tight quasi-universality of Reeb graph distances. Reeb图距离的紧拟普适性。
Journal of applied and computational topology Pub Date : 2025-01-01 Epub Date: 2025-02-12 DOI: 10.1007/s41468-025-00203-1
Ulrich Bauer, Håvard Bakke Bjerkevik, Benedikt Fluhr
{"title":"Tight quasi-universality of Reeb graph distances.","authors":"Ulrich Bauer, Håvard Bakke Bjerkevik, Benedikt Fluhr","doi":"10.1007/s41468-025-00203-1","DOIUrl":"10.1007/s41468-025-00203-1","url":null,"abstract":"<p><p>We establish tight bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, the functional distortion distance, and the functional contortion distance. The definition of the latter distance is a novel contribution, and for the special case of contour trees we also prove strict universality of this distance. Furthermore, we prove that for the special case of merge trees the functional contortion distance coincides with the interleaving distance, yielding universality of all four distances in this case.</p>","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"9 1","pages":"7"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11821802/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143434453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Expected Complexity of Barcode Reduction. 条码缩减的预期复杂度。
Journal of applied and computational topology Pub Date : 2025-01-01 Epub Date: 2025-11-25 DOI: 10.1007/s41468-025-00218-8
Barbara Giunti, Guillaume Houry, Michael Kerber, Matthias Söls
{"title":"Expected Complexity of Barcode Reduction.","authors":"Barbara Giunti, Guillaume Houry, Michael Kerber, Matthias Söls","doi":"10.1007/s41468-025-00218-8","DOIUrl":"10.1007/s41468-025-00218-8","url":null,"abstract":"<p><p>We study the algorithmic complexity of computing the persistence barcode of a randomly generated filtration. We provide a general technique to bound the expected complexity of reducing the boundary matrix in terms of the density of its reduced form. We apply this technique finding upper bounds for the average fill-in (number of non-zero entries) of the boundary matrix on Čech, Vietoris-Rips and Erdős-Rényi filtrations after matrix reduction, thus obtaining bounds on the expected complexity of the barcode computation. Our method is based on previous results on the expected Betti numbers of the corresponding complexes. Our fill-in bounds for Čech and Vietoris-Rips complexes are asymptotically tight up to a logarithmic factor. In particular, both our fill-in and computation bounds are better than the worst-case estimates. We also provide an Erdős-Rényi filtration realizing the worst-case fill-in and computation.</p>","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"9 4","pages":"29"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12647303/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145643700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Proceedings of ATMCS10 ATMCS10 会议记录
Journal of applied and computational topology Pub Date : 2024-07-15 DOI: 10.1007/s41468-024-00187-4
Ulrike Tillmann, Gunnar Carlsson
{"title":"Proceedings of ATMCS10","authors":"Ulrike Tillmann, Gunnar Carlsson","doi":"10.1007/s41468-024-00187-4","DOIUrl":"https://doi.org/10.1007/s41468-024-00187-4","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"10 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141646285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Homotopy, homology, and persistent homology using closure spaces 使用闭合空间的同调、同调和持久同调
Journal of applied and computational topology Pub Date : 2024-07-01 DOI: 10.1007/s41468-024-00183-8
Peter Bubenik, Nikola Milićević
{"title":"Homotopy, homology, and persistent homology using closure spaces","authors":"Peter Bubenik, Nikola Milićević","doi":"10.1007/s41468-024-00183-8","DOIUrl":"https://doi.org/10.1007/s41468-024-00183-8","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"4 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141698290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ambiguities in neural-network-based hyperedge prediction 基于神经网络的超edge 预测中的模糊性
Journal of applied and computational topology Pub Date : 2024-05-07 DOI: 10.1007/s41468-024-00172-x
Changlin Wan, Muhan Zhang, Pengtao Dang, Weiyu Hao, Sha Cao, Pan Li, Chi Zhang
{"title":"Ambiguities in neural-network-based hyperedge prediction","authors":"Changlin Wan, Muhan Zhang, Pengtao Dang, Weiyu Hao, Sha Cao, Pan Li, Chi Zhang","doi":"10.1007/s41468-024-00172-x","DOIUrl":"https://doi.org/10.1007/s41468-024-00172-x","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"129 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141002946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Depth in arrangements: Dehn–Sommerville–Euler relations with applications 排列的深度Dehn-Sommerville-Euler 关系及其应用
Journal of applied and computational topology Pub Date : 2024-05-03 DOI: 10.1007/s41468-024-00173-w
R. Biswas, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, M. Saghafian
{"title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","authors":"R. Biswas, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, M. Saghafian","doi":"10.1007/s41468-024-00173-w","DOIUrl":"https://doi.org/10.1007/s41468-024-00173-w","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"44 188","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141016743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Torsion-weighted spanning acycle entropy in cubical lattices and Mahler measures 立方晶格中的扭转加权跨循环熵和马勒度量
Journal of applied and computational topology Pub Date : 2024-02-24 DOI: 10.1007/s41468-024-00163-y
Yasuaki Hiraoka, Tomoyuki Shirai
{"title":"Torsion-weighted spanning acycle entropy in cubical lattices and Mahler measures","authors":"Yasuaki Hiraoka, Tomoyuki Shirai","doi":"10.1007/s41468-024-00163-y","DOIUrl":"https://doi.org/10.1007/s41468-024-00163-y","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"13 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140435018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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