{"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","publisher":"Institute of Science and Technology Austria","supervisor":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"publication_status":"published","alternative_title":["ISTA Thesis"],"month":"03","date_created":"2024-03-08T15:28:10Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","type":"dissertation","date_updated":"2024-03-20T09:36:57Z","doi":"10.15479/at:ista:15094","oa_version":"Published Version","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"project":[{"call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"},{"call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"file_date_updated":"2024-03-14T14:14:35Z","file":[{"content_type":"application/pdf","relation":"main_file","file_id":"15112","checksum":"1e468bfa42a7dcf04d89f4dadc621c87","file_name":"Thesis Sebastiano.pdf","date_created":"2024-03-14T08:55:07Z","access_level":"open_access","creator":"scultrer","date_updated":"2024-03-14T08:55:07Z","success":1,"file_size":4106872},{"date_created":"2024-03-14T08:56:24Z","file_size":4746234,"access_level":"closed","creator":"scultrer","date_updated":"2024-03-14T14:14:35Z","relation":"source_file","file_id":"15113","content_type":"application/zip","checksum":"bcbd213490f5a7e68855a092bbce93f1","file_name":"Thesis (1).zip"}],"_id":"15094","degree_awarded":"PhD","status":"public","year":"2024","oa":1,"abstract":[{"text":"Point sets, geometric networks, and arrangements of hyperplanes are fundamental objects in\r\ndiscrete geometry that have captivated mathematicians for centuries, if not millennia. This\r\nthesis seeks to cast new light on these structures by illustrating specific instances where a\r\ntopological perspective, specifically through discrete Morse theory and persistent homology,\r\nprovides valuable insights.\r\n\r\nAt first glance, the topology of these geometric objects might seem uneventful: point sets\r\nessentially lack of topology, arrangements of hyperplanes are a decomposition of Rd, which\r\nis a contractible space, and the topology of a network primarily involves the enumeration\r\nof connected components and cycles within the network. However, beneath this apparent\r\nsimplicity, there lies an array of intriguing structures, a small subset of which will be uncovered\r\nin this thesis.\r\n\r\nFocused on three case studies, each addressing one of the mentioned objects, this work\r\nwill showcase connections that intertwine topology with diverse fields such as combinatorial\r\ngeometry, algorithms and data structures, and emerging applications like spatial biology.\r\n\r\n","lang":"eng"}],"page":"108","day":"08","language":[{"iso":"eng"}],"author":[{"last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano"}],"tmp":{"short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode"},"has_accepted_license":"1","ddc":["514","500","516"],"publication_identifier":{"issn":["2663 - 337X"]},"article_processing_charge":"No","citation":{"mla":"Cultrera di Montesano, Sebastiano. <i>Persistence and Morse Theory for Discrete Geometric Structures</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:15094\">10.15479/at:ista:15094</a>.","ista":"Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria.","ieee":"S. Cultrera di Montesano, “Persistence and Morse theory for discrete geometric structures,” Institute of Science and Technology Austria, 2024.","ama":"Cultrera di Montesano S. Persistence and Morse theory for discrete geometric structures. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:15094\">10.15479/at:ista:15094</a>","apa":"Cultrera di Montesano, S. (2024). <i>Persistence and Morse theory for discrete geometric structures</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:15094\">https://doi.org/10.15479/at:ista:15094</a>","chicago":"Cultrera di Montesano, Sebastiano. “Persistence and Morse Theory for Discrete Geometric Structures.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:15094\">https://doi.org/10.15479/at:ista:15094</a>.","short":"S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024."},"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"11660"},{"status":"public","relation":"part_of_dissertation","id":"11658"},{"relation":"part_of_dissertation","status":"public","id":"13182"},{"id":"15090","status":"public","relation":"part_of_dissertation"},{"id":"15091","relation":"part_of_dissertation","status":"public"},{"id":"15093","status":"public","relation":"part_of_dissertation"}]},"title":"Persistence and Morse theory for discrete geometric structures","date_published":"2024-03-08T00:00:00Z"}