{"type":"journal_article","year":"2022","ddc":["510"],"author":[{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","full_name":"Biswas, Ranita","last_name":"Biswas"},{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"_id":"11660","title":"A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs","month":"07","date_updated":"2024-03-20T09:36:56Z","date_created":"2022-07-27T09:31:15Z","has_accepted_license":"1","file":[{"date_updated":"2022-07-27T09:30:30Z","creator":"scultrer","relation":"main_file","file_id":"11661","file_name":"window 1.pdf","content_type":"application/pdf","date_created":"2022-07-27T09:30:30Z","access_level":"open_access","checksum":"95903f9d1649e8e437a967b6f2f64730","file_size":564836}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"acknowledgement":"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. ","publication_status":"submitted","oa":1,"oa_version":"Submitted Version","status":"public","ec_funded":1,"day":"25","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"date_published":"2022-07-25T00:00:00Z","quality_controlled":"1","alternative_title":["LIPIcs"],"publication":"LIPIcs","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"15094"}]},"article_processing_charge":"No","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","abstract":[{"lang":"eng","text":"We characterize critical points of 1-dimensional maps paired in persistent homology geometrically and this way get elementary proofs of theorems about the symmetry of persistence diagrams and the variation of such maps. In particular, we identify branching points and endpoints of networks as the sole source of asymmetry and relate the cycle basis in persistent homology with a version of the stable marriage problem. Our analysis provides the foundations of fast algorithms for maintaining collections of interrelated sorted lists together with their persistence diagrams. "}],"file_date_updated":"2022-07-27T09:30:30Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.).","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. LIPIcs.","mla":"Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” <i>LIPIcs</i>, Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, n.d.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. <i>LIPIcs</i>.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs,” <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik."}}