Pub Date : 2022-06-17DOI: 10.1007/s41468-022-00106-5
Henry Adams, F. Frick, Žiga Virk
{"title":"Vietoris thickenings and complexes have isomorphic homotopy groups","authors":"Henry Adams, F. Frick, Žiga Virk","doi":"10.1007/s41468-022-00106-5","DOIUrl":"https://doi.org/10.1007/s41468-022-00106-5","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"221 - 241"},"PeriodicalIF":0.0,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41830677","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 : 2022-06-15DOI: 10.1007/s41468-022-00107-4
Stephan Mescher, Maximilian Stegemeyer
{"title":"Geodesic complexity via fibered decompositions of cut loci","authors":"Stephan Mescher, Maximilian Stegemeyer","doi":"10.1007/s41468-022-00107-4","DOIUrl":"https://doi.org/10.1007/s41468-022-00107-4","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"397 - 425"},"PeriodicalIF":0.0,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43618460","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 : 2022-06-07DOI: 10.1007/s41468-023-00130-z
Michael Moy
{"title":"Vietoris–Rips metric thickenings of the circle","authors":"Michael Moy","doi":"10.1007/s41468-023-00130-z","DOIUrl":"https://doi.org/10.1007/s41468-023-00130-z","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"831 - 877"},"PeriodicalIF":0.0,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42933298","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 : 2022-04-01DOI: 10.1007/s41468-023-00118-9
L. Caputi, H. Riihimäki
{"title":"Hochschild homology, and a persistent approach via connectivity digraphs","authors":"L. Caputi, H. Riihimäki","doi":"10.1007/s41468-023-00118-9","DOIUrl":"https://doi.org/10.1007/s41468-023-00118-9","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47528002","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 : 2022-02-16DOI: 10.1007/s41468-023-00113-0
Mishal Assif
{"title":"Singularities of gaussian random maps into the plane","authors":"Mishal Assif","doi":"10.1007/s41468-023-00113-0","DOIUrl":"https://doi.org/10.1007/s41468-023-00113-0","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"491 - 525"},"PeriodicalIF":0.0,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46963855","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 : 2022-02-01DOI: 10.1007/s41468-022-00086-6
J. Wiseman
{"title":"Persistence of Morse decompositions over grid resolution for maps and time series","authors":"J. Wiseman","doi":"10.1007/s41468-022-00086-6","DOIUrl":"https://doi.org/10.1007/s41468-022-00086-6","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"6 1","pages":"247 - 269"},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53193803","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 : 2022-01-13DOI: 10.1007/s41468-023-00115-y
Hee Rhang Yoon, R. Ghrist, Chad Giusti
{"title":"Persistent extensions and analogous bars: data-induced relations between persistence barcodes","authors":"Hee Rhang Yoon, R. Ghrist, Chad Giusti","doi":"10.1007/s41468-023-00115-y","DOIUrl":"https://doi.org/10.1007/s41468-023-00115-y","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"571 - 617"},"PeriodicalIF":0.0,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48622069","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 : 2022-01-03DOI: 10.1007/s41468-022-00111-8
Nicholas Wawrykow
{"title":"On the symmetric group action on rigid disks in a strip","authors":"Nicholas Wawrykow","doi":"10.1007/s41468-022-00111-8","DOIUrl":"https://doi.org/10.1007/s41468-022-00111-8","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"427 - 472"},"PeriodicalIF":0.0,"publicationDate":"2022-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46563603","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 : 2022-01-01Epub Date: 2021-12-18DOI: 10.1007/s41468-021-00085-z
Kohei Tanaka
In this paper, parametrized motion planning algorithms for a fiberwise space over a poset P are studied. Such an algorithm assigns paths in a space X decomposed into subspaces with the index set P, that do not cross the boundaries of the separated regions. We compute the parametrized topological complexity of , which is one less than the minimal number of local parametrized motion planning algorithms used for designing non-cross-border robot motions in X.
{"title":"Parametrized topological complexity of poset-stratified spaces.","authors":"Kohei Tanaka","doi":"10.1007/s41468-021-00085-z","DOIUrl":"https://doi.org/10.1007/s41468-021-00085-z","url":null,"abstract":"<p><p>In this paper, parametrized motion planning algorithms for a fiberwise space <math><mrow><mi>X</mi> <mo>→</mo> <mi>P</mi></mrow> </math> over a poset <i>P</i> are studied. Such an algorithm assigns paths in a space <i>X</i> decomposed into subspaces with the index set <i>P</i>, that do not cross the boundaries of the separated regions. We compute the parametrized topological complexity of <math><mrow><mi>X</mi> <mo>→</mo> <mi>P</mi></mrow> </math> , which is one less than the minimal number of local parametrized motion planning algorithms used for designing non-cross-border robot motions in <i>X</i>.</p>","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"6 2","pages":"221-246"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8683837/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39765269","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 : 2021-12-20DOI: 10.1007/s41468-022-00104-7
Benjamin Brück, A. Garin
{"title":"Stratifying the space of barcodes using Coxeter complexes","authors":"Benjamin Brück, A. Garin","doi":"10.1007/s41468-022-00104-7","DOIUrl":"https://doi.org/10.1007/s41468-022-00104-7","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"369 - 395"},"PeriodicalIF":0.0,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43907398","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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