{"status":"public","day":"31","article_type":"original","date_updated":"2024-10-09T21:00:33Z","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"187"}]},"publication":"Discrete and Computational Geometry","corr_author":"1","publisher":"Springer Nature","ec_funded":1,"has_accepted_license":"1","scopus_import":"1","language":[{"iso":"eng"}],"type":"journal_article","license":"https://creativecommons.org/licenses/by/4.0/","citation":{"chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-021-00281-9\">https://doi.org/10.1007/s00454-021-00281-9</a>.","apa":"Edelsbrunner, H., &#38; Osang, G. F. (2021). The multi-cover persistence of Euclidean balls. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-021-00281-9\">https://doi.org/10.1007/s00454-021-00281-9</a>","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “The Multi-Cover Persistence of Euclidean Balls.” <i>Discrete and Computational Geometry</i>, vol. 65, Springer Nature, 2021, pp. 1296–1313, doi:<a href=\"https://doi.org/10.1007/s00454-021-00281-9\">10.1007/s00454-021-00281-9</a>.","short":"H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.","ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. <i>Discrete and Computational Geometry</i>. 2021;65:1296–1313. doi:<a href=\"https://doi.org/10.1007/s00454-021-00281-9\">10.1007/s00454-021-00281-9</a>","ista":"Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 65, 1296–1313.","ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” <i>Discrete and Computational Geometry</i>, vol. 65. Springer Nature, pp. 1296–1313, 2021."},"abstract":[{"text":"Given a locally finite X⊆Rd and a radius r≥0, the k-fold cover of X and r consists of all points in Rd that have k or more points of X within distance r. We consider two filtrations—one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k—and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in Rd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.","lang":"eng"}],"date_published":"2021-03-31T00:00:00Z","file":[{"date_updated":"2021-12-01T10:56:53Z","access_level":"open_access","success":1,"creator":"cchlebak","content_type":"application/pdf","file_name":"2021_DisCompGeo_Edelsbrunner_Osang.pdf","checksum":"59b4e1e827e494209bcb4aae22e1d347","file_id":"10394","date_created":"2021-12-01T10:56:53Z","file_size":677704,"relation":"main_file"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"isi":1,"oa_version":"Published Version","year":"2021","ddc":["516"],"volume":65,"doi":"10.1007/s00454-021-00281-9","page":"1296–1313","article_processing_charge":"Yes (via OA deal)","publication_status":"published","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"03","title":"The multi-cover persistence of Euclidean balls","date_created":"2021-04-11T22:01:15Z","oa":1,"_id":"9317","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"external_id":{"isi":["000635460400001"]},"file_date_updated":"2021-12-01T10:56:53Z","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Osang","full_name":"Osang, Georg F","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"intvolume":"        65","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha), and by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF)\r\nOpen Access funding provided by the Institute of Science and Technology (IST Austria).","quality_controlled":"1"}