{"department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Ranita","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas"},{"last_name":"Cultrera Di Montesano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera Di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","first_name":"Sebastiano"},{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"language":[{"iso":"eng"}],"file_date_updated":"2023-07-03T09:41:05Z","date_published":"2023-06-17T00:00:00Z","article_processing_charge":"Yes (via OA deal)","year":"2023","file":[{"checksum":"697249d5d1c61dea4410b9f021b70fce","creator":"alisjak","file_id":"13185","access_level":"open_access","success":1,"relation":"main_file","content_type":"application/pdf","date_updated":"2023-07-03T09:41:05Z","file_size":487355,"date_created":"2023-07-03T09:41:05Z","file_name":"2023_Journal of Applied and Computational Topology_Biswas.pdf"}],"ddc":["000"],"date_created":"2023-07-02T22:00:44Z","publication":"Journal of Applied and Computational Topology","citation":{"short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology (2023).","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2023). Geometric characterization of the persistence of 1D maps. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2023. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization of the persistence of 1D maps. <i>Journal of Applied and Computational Topology</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>","mla":"Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric characterization of the persistence of 1D maps,” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2023.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>."},"type":"journal_article","oa_version":"Published Version","month":"06","title":"Geometric characterization of the persistence of 1D maps","doi":"10.1007/s41468-023-00126-9","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"_id":"13182","publication_status":"epub_ahead","oa":1,"scopus_import":"1","publisher":"Springer Nature","ec_funded":1,"related_material":{"record":[{"status":"public","id":"15094","relation":"dissertation_contains"}]},"acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of this paper thank anonymous reviewers for their constructive criticism and Monika Henzinger for detailed comments on an earlier version of this paper.","quality_controlled":"1","day":"17","status":"public","abstract":[{"text":"We characterize critical points of 1-dimensional maps paired in persistent homology\r\ngeometrically and this way get elementary proofs of theorems about the symmetry\r\nof persistence diagrams and the variation of such maps. In particular, we identify\r\nbranching points and endpoints of networks as the sole source of asymmetry and\r\nrelate the cycle basis in persistent homology with a version of the stable marriage\r\nproblem. Our analysis provides the foundations of fast algorithms for maintaining a\r\ncollection of sorted lists together with its persistence diagram.","lang":"eng"}],"date_updated":"2024-03-20T09:36:56Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"article_type":"original","has_accepted_license":"1","project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","grant_number":"Z00342","call_identifier":"FWF"}]}