{"title":"Constructible sheaves and functions up to infinity","authors":"P. Schapira","doi":"10.1007/s41468-023-00121-0","DOIUrl":"https://doi.org/10.1007/s41468-023-00121-0","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"707 - 739"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42927274","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":"Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis.","authors":"Zixuan Cang, Elizabeth Munch, Guo-Wei Wei","doi":"10.1007/s41468-020-00057-9","DOIUrl":"https://doi.org/10.1007/s41468-020-00057-9","url":null,"abstract":"<p><p>While the spatial topological persistence is naturally constructed from a radius-based filtration, it has hardly been derived from a temporal filtration. Most topological models are designed for the global topology of a given object as a whole. There is no method reported in the literature for the topology of an individual component in an object to the best of our knowledge. For many problems in science and engineering, the topology of an individual component is important for describing its properties. We propose evolutionary homology (EH) constructed via a time evolution-based filtration and topological persistence. Our approach couples a set of dynamical systems or chaotic oscillators by the interactions of a physical system, such as a macromolecule. The interactions are approximated by weighted graph Laplacians. Simplices, simplicial complexes, algebraic groups and topological persistence are defined on the coupled trajectories of the chaotic oscillators. The resulting EH gives rise to time-dependent topological invariants or evolutionary barcodes for an individual component of the physical system, revealing its topology-function relationship. In conjunction with Wasserstein metrics, the proposed EH is applied to protein flexibility analysis, an important problem in computational biophysics. Numerical results for the B-factor prediction of a benchmark set of 364 proteins indicate that the proposed EH outperforms all the other state-of-the-art methods in the field.</p>","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"4 4","pages":"481-507"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-020-00057-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39033436","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":"Steady and ranging sets in graph persistence","authors":"Mattia G. Bergomi, M. Ferri, Antonella Tavaglione","doi":"10.1007/s41468-022-00099-1","DOIUrl":"https://doi.org/10.1007/s41468-022-00099-1","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"33 - 56"},"PeriodicalIF":0.0,"publicationDate":"2020-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53194263","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":"Dominance complexes and vertex cover numbers of graphs","authors":"Takahiro Matsushita","doi":"10.1007/s41468-022-00109-2","DOIUrl":"https://doi.org/10.1007/s41468-022-00109-2","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"363 - 368"},"PeriodicalIF":0.0,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48710837","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":"A directed persistent homology theory for dissimilarity functions","authors":"D. M'endez, Rub'en J. S'anchez-Garc'ia","doi":"10.1007/s41468-023-00124-x","DOIUrl":"https://doi.org/10.1007/s41468-023-00124-x","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"771 - 813"},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42739062","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":"Stratifications of real vector spaces from constructible sheaves with conical microsupport","authors":"Ezra Miller","doi":"10.1007/s41468-023-00112-1","DOIUrl":"https://doi.org/10.1007/s41468-023-00112-1","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"473 - 489"},"PeriodicalIF":0.0,"publicationDate":"2020-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47073296","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}
Michael J. Catanzaro, J. Curry, Brittany Terese Fasy, J. Lazovskis, Greg Malen, Hans Riess, Bei Wang, Matthew John Zabka
{"title":"Moduli spaces of morse functions for persistence","authors":"Michael J. Catanzaro, J. Curry, Brittany Terese Fasy, J. Lazovskis, Greg Malen, Hans Riess, Bei Wang, Matthew John Zabka","doi":"10.1007/s41468-020-00055-x","DOIUrl":"https://doi.org/10.1007/s41468-020-00055-x","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"4 1","pages":"353 - 385"},"PeriodicalIF":0.0,"publicationDate":"2020-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-020-00055-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49531871","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}
Shreya Arya, J. Boissonnat, Kunal Dutta, Martin Lotz
{"title":"Dimensionality reduction for k-distance applied to persistent homology","authors":"Shreya Arya, J. Boissonnat, Kunal Dutta, Martin Lotz","doi":"10.1007/s41468-021-00079-x","DOIUrl":"https://doi.org/10.1007/s41468-021-00079-x","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"5 1","pages":"671 - 691"},"PeriodicalIF":0.0,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44675318","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":"Computing persistent Stiefel–Whitney classes of line bundles","authors":"Raphaël Tinarrage","doi":"10.1007/s41468-021-00080-4","DOIUrl":"https://doi.org/10.1007/s41468-021-00080-4","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"6 1","pages":"65 - 125"},"PeriodicalIF":0.0,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42162639","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}