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Journal of applied and computational topology最新文献

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Homotopical decompositions of simplicial and Vietoris Rips complexes 单纯复形和Vietoris-Rips复形的同态分解
Journal of applied and computational topology Pub Date : 2020-02-09 DOI: 10.1007/s41468-021-00066-2
W. Chachólski, Alvin Jin, Martina Scolamiero, Francesca Tombari
{"title":"Homotopical decompositions of simplicial and Vietoris Rips complexes","authors":"W. Chachólski, Alvin Jin, Martina Scolamiero, Francesca Tombari","doi":"10.1007/s41468-021-00066-2","DOIUrl":"https://doi.org/10.1007/s41468-021-00066-2","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"5 1","pages":"215 - 248"},"PeriodicalIF":0.0,"publicationDate":"2020-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-021-00066-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48581391","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: 7
Contractibility of a persistence map preimage. 持久性映射原映像的可收缩性。
Journal of applied and computational topology Pub Date : 2020-01-01 Epub Date: 2020-08-28 DOI: 10.1007/s41468-020-00059-7
Jacek Cyranka, Konstantin Mischaikow, Charles Weibel
{"title":"Contractibility of a persistence map preimage.","authors":"Jacek Cyranka,&nbsp;Konstantin Mischaikow,&nbsp;Charles Weibel","doi":"10.1007/s41468-020-00059-7","DOIUrl":"https://doi.org/10.1007/s41468-020-00059-7","url":null,"abstract":"<p><p>This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of snapshots of solutions, what conclusions can be drawn about solutions of the original dynamical system? We address this challenge in the context of an <i>N</i> dimensional system of ordinary differential equation defined in <math> <msup><mrow><mi>R</mi></mrow> <mi>N</mi></msup> </math> . To each point in <math> <msup><mrow><mi>R</mi></mrow> <mi>N</mi></msup> </math> (e.g. an initial condition) we associate a persistence diagram. The main result of this paper is that under this association the preimage of every persistence diagram is contractible. As an application we provide conditions under which multiple time series of persistence diagrams can be used to conclude the existence of a fixed point of the differential equation that generates the time series.</p>","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"4 4","pages":"509-523"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-020-00059-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38520536","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: 6
On the hardness of finding normal surfaces 关于寻找法向表面的硬度
Journal of applied and computational topology Pub Date : 2019-12-19 DOI: 10.1007/s41468-021-00076-0
Benjamin A. Burton, Alexander He
{"title":"On the hardness of finding normal surfaces","authors":"Benjamin A. Burton, Alexander He","doi":"10.1007/s41468-021-00076-0","DOIUrl":"https://doi.org/10.1007/s41468-021-00076-0","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"5 1","pages":"583 - 619"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44026380","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 Rado simplicial complex 拉多简单复合体
Journal of applied and computational topology Pub Date : 2019-12-05 DOI: 10.1007/s41468-021-00069-z
M. Farber, Lewis Mead, Lewin Strauss
{"title":"The Rado simplicial complex","authors":"M. Farber, Lewis Mead, Lewin Strauss","doi":"10.1007/s41468-021-00069-z","DOIUrl":"https://doi.org/10.1007/s41468-021-00069-z","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"5 1","pages":"339 - 356"},"PeriodicalIF":0.0,"publicationDate":"2019-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-021-00069-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47478105","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: 7
Digital fundamental groups and edge groups of clique complexes 集团复合体的数字基群和边群
Journal of applied and computational topology Pub Date : 2019-10-17 DOI: 10.1007/s41468-022-00095-5
G. Lupton, N. Scoville
{"title":"Digital fundamental groups and edge groups of clique complexes","authors":"G. Lupton, N. Scoville","doi":"10.1007/s41468-022-00095-5","DOIUrl":"https://doi.org/10.1007/s41468-022-00095-5","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"6 1","pages":"529-558"},"PeriodicalIF":0.0,"publicationDate":"2019-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44776240","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: 5
Spaces of directed paths on pre-cubical sets II 前立方集上有向路径的空间Ⅱ
Journal of applied and computational topology Pub Date : 2019-08-30 DOI: 10.1007/s41468-019-00040-z
Krzysztof Ziemiański
{"title":"Spaces of directed paths on pre-cubical sets II","authors":"Krzysztof Ziemiański","doi":"10.1007/s41468-019-00040-z","DOIUrl":"https://doi.org/10.1007/s41468-019-00040-z","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"4 1","pages":"45 - 78"},"PeriodicalIF":0.0,"publicationDate":"2019-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-019-00040-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42632343","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: 14
Configuration spaces of disks in an infinite strip 配置无限条带中的磁盘空间
Journal of applied and computational topology Pub Date : 2019-08-12 DOI: 10.1007/s41468-021-00070-6
H. Alpert, Matthew Kahle, R. Macpherson
{"title":"Configuration spaces of disks in an infinite strip","authors":"H. Alpert, Matthew Kahle, R. Macpherson","doi":"10.1007/s41468-021-00070-6","DOIUrl":"https://doi.org/10.1007/s41468-021-00070-6","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"100 1","pages":"357 - 390"},"PeriodicalIF":0.0,"publicationDate":"2019-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-021-00070-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53194217","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: 9
On the topology of complexes of injective words 关于内射词复数的拓扑
Journal of applied and computational topology Pub Date : 2019-08-09 DOI: 10.1007/s41468-019-00039-6
W. Chachólski, R. Levi, R. Meshulam
{"title":"On the topology of complexes of injective words","authors":"W. Chachólski, R. Levi, R. Meshulam","doi":"10.1007/s41468-019-00039-6","DOIUrl":"https://doi.org/10.1007/s41468-019-00039-6","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"4 1","pages":"29 - 44"},"PeriodicalIF":0.0,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-019-00039-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42407909","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: 3
Ripser: efficient computation of Vietoris–Rips persistence barcodes Ripser: Vietoris-Rips持久性条码的高效计算
Journal of applied and computational topology Pub Date : 2019-08-07 DOI: 10.1007/s41468-021-00071-5
Ulrich Bauer
{"title":"Ripser: efficient computation of Vietoris–Rips persistence barcodes","authors":"Ulrich Bauer","doi":"10.1007/s41468-021-00071-5","DOIUrl":"https://doi.org/10.1007/s41468-021-00071-5","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"5 1","pages":"391 - 423"},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-021-00071-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48169470","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: 246
A fundamental group for digital images 数字图像的基本组
Journal of applied and computational topology Pub Date : 2019-06-14 DOI: 10.1007/s41468-021-00067-1
G. Lupton, J. Oprea, N. Scoville
{"title":"A fundamental group for digital images","authors":"G. Lupton, J. Oprea, N. Scoville","doi":"10.1007/s41468-021-00067-1","DOIUrl":"https://doi.org/10.1007/s41468-021-00067-1","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"5 1","pages":"249 - 311"},"PeriodicalIF":0.0,"publicationDate":"2019-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-021-00067-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41606414","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: 14
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