Pub Date : 2019-06-01Epub Date: 2019-05-16DOI: 10.1007/s41468-019-00026-x
Shaun Harker, Miroslav Kramár, Rachel Levanger, Konstantin Mischaikow
We present a generalization of the induced matching theorem of as reported by Bauer and Lesnick (in: Proceedings of the thirtieth annual symposium computational geometry 2014) and use it to prove a generalization of the algebraic stability theorem for -indexed pointwise finite-dimensional persistence modules. Via numerous examples, we show how the generalized algebraic stability theorem enables the computation of rigorous error bounds in the space of persistence diagrams that go beyond the typical formulation in terms of bottleneck (or log bottleneck) distance.
{"title":"A comparison framework for interleaved persistence modules.","authors":"Shaun Harker, Miroslav Kramár, Rachel Levanger, Konstantin Mischaikow","doi":"10.1007/s41468-019-00026-x","DOIUrl":"https://doi.org/10.1007/s41468-019-00026-x","url":null,"abstract":"<p><p>We present a generalization of the induced matching theorem of as reported by Bauer and Lesnick (in: Proceedings of the thirtieth annual symposium computational geometry 2014) and use it to prove a generalization of the algebraic stability theorem for <math><mi>ℝ</mi></math> -indexed pointwise finite-dimensional persistence modules. Via numerous examples, we show how the generalized algebraic stability theorem enables the computation of rigorous error bounds in the space of persistence diagrams that go beyond the typical formulation in terms of bottleneck (or log bottleneck) distance.</p>","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"3 1-2","pages":"85-118"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-019-00026-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37687528","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}
Pub Date : 2019-06-01DOI: 10.1007/s41468-019-00029-8
J. Boissonnat, A. Lieutier, M. Wintraecken
{"title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","authors":"J. Boissonnat, A. Lieutier, M. Wintraecken","doi":"10.1007/s41468-019-00029-8","DOIUrl":"https://doi.org/10.1007/s41468-019-00029-8","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"3 1","pages":"29 - 58"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-019-00029-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41491289","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}
Pub Date : 2019-05-11DOI: 10.1007/s41468-020-00056-w
Peter Bubenik, Alexander Wagner
{"title":"Embeddings of persistence diagrams into Hilbert spaces","authors":"Peter Bubenik, Alexander Wagner","doi":"10.1007/s41468-020-00056-w","DOIUrl":"https://doi.org/10.1007/s41468-020-00056-w","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"4 1","pages":"339 - 351"},"PeriodicalIF":0.0,"publicationDate":"2019-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-020-00056-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47034247","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}
Pub Date : 2019-01-10DOI: 10.1007/s41468-020-00061-z
Vincent Divol, Théo Lacombe
{"title":"Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport","authors":"Vincent Divol, Théo Lacombe","doi":"10.1007/s41468-020-00061-z","DOIUrl":"https://doi.org/10.1007/s41468-020-00061-z","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"5 1","pages":"1 - 53"},"PeriodicalIF":0.0,"publicationDate":"2019-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-020-00061-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48187857","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}
Pub Date : 2018-12-28DOI: 10.1007/s41468-019-00030-1
A. Dickstein, F. Zapolsky
{"title":"Approximation of quasi-states on manifolds","authors":"A. Dickstein, F. Zapolsky","doi":"10.1007/s41468-019-00030-1","DOIUrl":"https://doi.org/10.1007/s41468-019-00030-1","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"3 1","pages":"221 - 248"},"PeriodicalIF":0.0,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-019-00030-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43678219","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}
Pub Date : 2018-12-01DOI: 10.1007/s41468-019-00024-z
J. Curry
{"title":"The fiber of the persistence map for functions on the interval","authors":"J. Curry","doi":"10.1007/s41468-019-00024-z","DOIUrl":"https://doi.org/10.1007/s41468-019-00024-z","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"215 1","pages":"301 - 321"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-019-00024-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53193666","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}
Pub Date : 2018-12-01DOI: 10.1007/s41468-018-0022-4
Peter Bubenik, T. Vergili
{"title":"Topological spaces of persistence modules and their properties","authors":"Peter Bubenik, T. Vergili","doi":"10.1007/s41468-018-0022-4","DOIUrl":"https://doi.org/10.1007/s41468-018-0022-4","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"2 1","pages":"233 - 269"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-018-0022-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53193539","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}
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