{"title":"Stable volumes for persistent homology","authors":"I. Obayashi","doi":"10.1007/s41468-023-00119-8","DOIUrl":"https://doi.org/10.1007/s41468-023-00119-8","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"671 - 706"},"PeriodicalIF":0.0,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44237817","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}
{"title":"On the consistency and asymptotic normality of multiparameter persistent Betti numbers","authors":"M. B. Botnan, C. Hirsch","doi":"10.1007/s41468-022-00110-9","DOIUrl":"https://doi.org/10.1007/s41468-022-00110-9","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48416520","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}
{"title":"Fiber of persistent homology on morse functions","authors":"Jacob Leygonie, David Beers","doi":"10.1007/s41468-022-00100-x","DOIUrl":"https://doi.org/10.1007/s41468-022-00100-x","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"89 - 102"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47085147","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}
{"title":"Correction to: A higher Boltzmann distribution","authors":"Michael J. Catanzaro, V. Chernyak, John R. Klein","doi":"10.1007/s41468-021-00074-2","DOIUrl":"https://doi.org/10.1007/s41468-021-00074-2","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"5 1","pages":"531 - 532"},"PeriodicalIF":0.0,"publicationDate":"2021-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-021-00074-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47821214","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}
J. Curry, Haibin Hang, W. Mio, Tom Needham, Osman Berat Okutan
{"title":"Decorated merge trees for persistent topology","authors":"J. Curry, Haibin Hang, W. Mio, Tom Needham, Osman Berat Okutan","doi":"10.1007/s41468-022-00089-3","DOIUrl":"https://doi.org/10.1007/s41468-022-00089-3","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"6 1","pages":"371 - 428"},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47446113","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}
{"title":"On Vietoris–Rips complexes of hypercube graphs","authors":"Michal Adamaszek, Henry Adams","doi":"10.1007/s41468-021-00083-1","DOIUrl":"https://doi.org/10.1007/s41468-021-00083-1","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"6 1","pages":"177 - 192"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46961623","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}
{"title":"Geodesic complexity of motion planning","authors":"David Recio-Mitter","doi":"10.1007/s41468-020-00064-w","DOIUrl":"https://doi.org/10.1007/s41468-020-00064-w","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"79 1","pages":"141 - 178"},"PeriodicalIF":0.0,"publicationDate":"2021-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-020-00064-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53194030","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}
Aruni Choudhary, Michael Kerber, Sharath Raghvendra
{"title":"Improved approximate rips filtrations with shifted integer lattices and cubical complexes.","authors":"Aruni Choudhary, Michael Kerber, Sharath Raghvendra","doi":"10.1007/s41468-021-00072-4","DOIUrl":"https://doi.org/10.1007/s41468-021-00072-4","url":null,"abstract":"<p><p>Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes is expensive because of a combinatorial explosion in the complex size. For <i>n</i> points in <math> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> </math> , we present a scheme to construct a 2-approximation of the filtration of the Rips complex in the <math><msub><mi>L</mi> <mi>∞</mi></msub> </math> -norm, which extends to a <math><mrow><mn>2</mn> <msup><mi>d</mi> <mrow><mn>0.25</mn></mrow> </msup> </mrow> </math> -approximation in the Euclidean case. The <i>k</i>-skeleton of the resulting approximation has a total size of <math><mrow><mi>n</mi> <msup><mn>2</mn> <mrow><mi>O</mi> <mo>(</mo> <mi>d</mi> <mo>log</mo> <mi>k</mi> <mo>+</mo> <mi>d</mi> <mo>)</mo></mrow> </msup> </mrow> </math> . The scheme is based on the integer lattice and simplicial complexes based on the barycentric subdivision of the <i>d</i>-cube. We extend our result to use cubical complexes in place of simplicial complexes by introducing <i>cubical maps</i> between complexes. We get the same approximation guarantee as the simplicial case, while reducing the total size of the approximation to only <math><mrow><mi>n</mi> <msup><mn>2</mn> <mrow><mi>O</mi> <mo>(</mo> <mi>d</mi> <mo>)</mo></mrow> </msup> </mrow> </math> (cubical) cells. There are two novel techniques that we use in this paper. The first is the use of <i>acyclic carriers</i> for proving our approximation result. In our application, these are maps which relate the Rips complex and the approximation in a relatively simple manner and greatly reduce the complexity of showing the approximation guarantee. The second technique is what we refer to as <i>scale balancing</i>, which is a simple trick to improve the approximation ratio under certain conditions.</p>","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"5 3","pages":"425-458"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-021-00072-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39580559","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}
{"title":"Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces","authors":"Peter Bubenik, Alex Elchesen","doi":"10.1007/s41468-022-00091-9","DOIUrl":"https://doi.org/10.1007/s41468-022-00091-9","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"6 1","pages":"429 - 474"},"PeriodicalIF":0.0,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46803814","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}