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}
Pub Date : 2021-11-26DOI: 10.1007/s41468-022-00108-3
T. Chaplin
{"title":"First Betti number of the path homology of random directed graphs","authors":"T. Chaplin","doi":"10.1007/s41468-022-00108-3","DOIUrl":"https://doi.org/10.1007/s41468-022-00108-3","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45684147","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 : 2021-11-05DOI: 10.1007/s41468-022-00094-6
Emile Jacquard, Vidit Nanda, U. Tillmann
{"title":"The space of barcode bases for persistence modules","authors":"Emile Jacquard, Vidit Nanda, U. Tillmann","doi":"10.1007/s41468-022-00094-6","DOIUrl":"https://doi.org/10.1007/s41468-022-00094-6","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"1 - 30"},"PeriodicalIF":0.0,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46174981","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 : 2021-10-21DOI: 10.1007/s41468-023-00117-w
Michael J. Catanzaro, Brantley Vose
{"title":"Harmonic representatives in homology over arbitrary fields","authors":"Michael J. Catanzaro, Brantley Vose","doi":"10.1007/s41468-023-00117-w","DOIUrl":"https://doi.org/10.1007/s41468-023-00117-w","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"643 - 670"},"PeriodicalIF":0.0,"publicationDate":"2021-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47689181","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 : 2021-10-11DOI: 10.1007/s41468-022-00088-4
Sam Hughes, Kevin Li
{"title":"Higher topological complexity of hyperbolic groups","authors":"Sam Hughes, Kevin Li","doi":"10.1007/s41468-022-00088-4","DOIUrl":"https://doi.org/10.1007/s41468-022-00088-4","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"6 1","pages":"323 - 329"},"PeriodicalIF":0.0,"publicationDate":"2021-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48749727","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 : 2021-09-27DOI: 10.1007/s41468-023-00125-w
E. Lasalle
{"title":"Heat diffusion distance processes: a statistically founded method to analyze graph data sets","authors":"E. Lasalle","doi":"10.1007/s41468-023-00125-w","DOIUrl":"https://doi.org/10.1007/s41468-023-00125-w","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53194487","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 : 2021-09-24DOI: 10.1007/s41468-023-00119-8
I. Obayashi
{"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}
Pub Date : 2021-09-12DOI: 10.1007/s41468-022-00110-9
M. B. Botnan, C. Hirsch
{"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}
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