[{"language":[{"iso":"eng"}],"ec_funded":1,"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342"}],"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"János","last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János"}],"month":"06","ddc":["510"],"intvolume":"       293","publication_status":"published","conference":{"start_date":"2024-06-11","name":"SoCG: Symposium on Computational Geometry","end_date":"2024-06-14","location":"Athens, Greece"},"doi":"10.4230/LIPIcs.SoCG.2024.53","alternative_title":["LIPIcs"],"oa":1,"publication_identifier":{"isbn":["9783959773164"],"issn":["1868-8969"]},"article_processing_charge":"No","arxiv":1,"fulldoi":"https://doi.org/10.4230/LIPIcs.SoCG.2024.53","publication":"40th International Symposium on Computational Geometry","related_material":{"record":[{"status":"public","relation":"later_version","id":"20657"}]},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa_version":"Published Version","date_updated":"2026-10-02T11:48:01Z","quality_controlled":"1","supplementarymaterial":"no","external_id":{"arxiv":["2310.14801"]},"file":[{"date_updated":"2024-06-17T08:46:33Z","success":1,"file_id":"17152","checksum":"5442d44fb89d77477a87668d6e61aac9","file_size":766562,"file_name":"2024_LIPICS_Edelsbrunner.pdf","relation":"main_file","creator":"dernst","content_type":"application/pdf","access_level":"open_access","date_created":"2024-06-17T08:46:33Z"}],"volume":293,"year":"2024","abstract":[{"text":"The Upper Bound Theorem for convex polytopes implies that the p-th Betti number of the Čech complex of any set of N points in ℝ^d and any radius satisfies β_p = O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions, which prove that this upper bound is asymptotically tight. For example, we describe a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of the Čech complex at the other radius is n². In particular, there is an arrangement of n contruent balls in ℝ³ that enclose a quadratic number of voids, which answers a long-standing open question in computational geometry.","lang":"eng"}],"_id":"17146","researchdata_availability":"no","file_date_updated":"2024-06-17T08:46:33Z","has_accepted_license":"1","acknowledgement":"The first author is supported by the European Research Council (ERC), grant no. 788183, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. {I 02979-N35.} The second author is supported by the European Research Council (ERC), grant \"GeoScape\" and by the Hungarian Science Foundation (NKFIH), grant K-131529. Both authors are supported by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.\r\nThe authors thank Matt Kahle for communicating the question about extremal Čech complexes, Ben Schweinhart for early discussions on the linked circles construction in three dimensions, and Gábor Tardos for helpful remarks and suggestions.","department":[{"_id":"HeEd"}],"date_published":"2024-06-01T00:00:00Z","status":"public","article_number":"53","day":"01","title":"Maximum Betti numbers of Čech complexes","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","license":"https://creativecommons.org/licenses/by/4.0/","citation":{"chicago":"Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.53\">https://doi.org/10.4230/LIPIcs.SoCG.2024.53</a>.","ama":"Edelsbrunner H, Pach J. Maximum Betti numbers of Čech complexes. In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.53\">10.4230/LIPIcs.SoCG.2024.53</a>","ista":"Edelsbrunner H, Pach J. 2024. Maximum Betti numbers of Čech complexes. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 53.","ieee":"H. Edelsbrunner and J. Pach, “Maximum Betti numbers of Čech complexes,” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","apa":"Edelsbrunner, H., &#38; Pach, J. (2024). Maximum Betti numbers of Čech complexes. In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.53\">https://doi.org/10.4230/LIPIcs.SoCG.2024.53</a>","short":"H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","mla":"Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 53, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.53\">10.4230/LIPIcs.SoCG.2024.53</a>."},"date_created":"2024-06-16T22:01:06Z","das_tickbox":"0","type":"conference"},{"intvolume":"       293","publication_status":"published","month":"06","ddc":["510"],"conference":{"end_date":"2024-06-14","name":"SoCG: Symposium on Computational Geometry","start_date":"2024-06-11","location":"Athens, Greece"},"language":[{"iso":"eng"}],"author":[{"full_name":"Rote, Günter","first_name":"Günter","last_name":"Rote"},{"last_name":"Rüber","first_name":"Moritz","full_name":"Rüber, Moritz"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"oa":1,"alternative_title":["LIPIcs"],"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959773164"]},"fulldoi":"https://doi.org/10.4230/LIPIcs.SoCG.2024.76","arxiv":1,"article_processing_charge":"No","doi":"10.4230/LIPIcs.SoCG.2024.76","date_updated":"2026-10-02T11:47:18Z","quality_controlled":"1","oa_version":"Published Version","supplementarymaterial":"no","publication":"40th International Symposium on Computational Geometry","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"year":"2024","external_id":{"arxiv":["2402.15787"]},"volume":293,"file":[{"date_updated":"2024-06-17T08:40:04Z","file_size":1430896,"checksum":"fbad1de06383a6b7e8a1cb3e8c7205ce","file_id":"17151","success":1,"access_level":"open_access","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_name":"2024_LIPICS_Rote.pdf","date_created":"2024-06-17T08:40:04Z"}],"has_accepted_license":"1","file_date_updated":"2024-06-17T08:40:04Z","acknowledgement":"Part of this work was done while G.R. enjoyed the hospitality of the Institute of Science and Technology Austria (ISTA) as a visiting professor during his sabbatical in the winter semester 2022/23.","researchdata_availability":"no","_id":"17145","abstract":[{"text":"Grid peeling is the process of repeatedly removing the convex hull vertices of the grid points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes.","lang":"eng"}],"status":"public","article_number":"76","department":[{"_id":"HeEd"}],"date_published":"2024-06-01T00:00:00Z","scopus_import":"1","title":"Grid peeling of parabolas","day":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","das_tickbox":"0","type":"conference","date_created":"2024-06-16T22:01:06Z","citation":{"short":"G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","apa":"Rote, G., Rüber, M., &#38; Saghafian, M. (2024). Grid peeling of parabolas. In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">https://doi.org/10.4230/LIPIcs.SoCG.2024.76</a>","ieee":"G. Rote, M. Rüber, and M. Saghafian, “Grid peeling of parabolas,” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","mla":"Rote, Günter, et al. “Grid Peeling of Parabolas.” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 76, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">10.4230/LIPIcs.SoCG.2024.76</a>.","ama":"Rote G, Rüber M, Saghafian M. Grid peeling of parabolas. In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">10.4230/LIPIcs.SoCG.2024.76</a>","chicago":"Rote, Günter, Moritz Rüber, and Morteza Saghafian. “Grid Peeling of Parabolas.” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">https://doi.org/10.4230/LIPIcs.SoCG.2024.76</a>.","ista":"Rote G, Rüber M, Saghafian M. 2024. Grid peeling of parabolas. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 76."}},{"intvolume":"        26","month":"08","ddc":["510"],"article_type":"original","publication_status":"published","language":[{"iso":"eng"}],"author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4672-8297","last_name":"Ölsböck","first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","full_name":"Ölsböck, Katharina"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","orcid":"0009-0009-9111-8429","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"pmid":1,"publication_identifier":{"eissn":["1099-4300"]},"oa":1,"fulldoi":"https://doi.org/10.3390/e26080637","article_processing_charge":"Yes","doi":"10.3390/e26080637","quality_controlled":"1","date_updated":"2026-10-02T11:50:23Z","dataavailabilitystatement":"The software and data used for this study is available at: https://git.ista.ac.at/katharina.oelsboeck/wrap_2_3-public/ (accessed on 19 July 2024).","oa_version":"Published Version","supplementarymaterial":"yes","publication":"Entropy","publisher":"MDPI","related_material":{"link":[{"relation":"software","url":"https://git.ista.ac.at/katharina.oelsboeck/wrap_2_3-public/"}]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"year":"2024","file":[{"date_created":"2024-09-09T09:01:12Z","file_name":"2024_Entropy_Edelsbrunner.pdf","access_level":"open_access","creator":"dernst","relation":"main_file","content_type":"application/pdf","checksum":"624a9e2c5b49d6c38b88b0f675467ba3","file_id":"17948","success":1,"file_size":8025139,"date_updated":"2024-09-09T09:01:12Z"}],"external_id":{"isi":["001305543500001"],"pmid":["39202107"]},"volume":26,"has_accepted_license":"1","file_date_updated":"2024-09-09T09:01:12Z","acknowledgement":"We thank Anton Nikitenko for first observing that the Wrap complex can be characterized as stated in Claim (ii) of the Wrap Complex Lemma, and Ondrej Draganov for correcting a critical mistake in one of our formulas in Section 2.","abstract":[{"lang":"eng","text":"Abstract\r\nMethods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback–Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics."}],"_id":"17891","researchdata_availability":"yes","status":"public","article_number":"637","department":[{"_id":"HeEd"}],"date_published":"2024-08-01T00:00:00Z","scopus_import":"1","isi":1,"issue":"8","title":"Understanding higher-order interactions in information space","day":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","das_tickbox":"1","type":"journal_article","citation":{"short":"H. Edelsbrunner, K. Ölsböck, H. Wagner, Entropy 26 (2024).","ieee":"H. Edelsbrunner, K. Ölsböck, and H. Wagner, “Understanding higher-order interactions in information space,” <i>Entropy</i>, vol. 26, no. 8. MDPI, 2024.","apa":"Edelsbrunner, H., Ölsböck, K., &#38; Wagner, H. (2024). Understanding higher-order interactions in information space. <i>Entropy</i>. MDPI. <a href=\"https://doi.org/10.3390/e26080637\">https://doi.org/10.3390/e26080637</a>","mla":"Edelsbrunner, Herbert, et al. “Understanding Higher-Order Interactions in Information Space.” <i>Entropy</i>, vol. 26, no. 8, 637, MDPI, 2024, doi:<a href=\"https://doi.org/10.3390/e26080637\">10.3390/e26080637</a>.","chicago":"Edelsbrunner, Herbert, Katharina Ölsböck, and Hubert Wagner. “Understanding Higher-Order Interactions in Information Space.” <i>Entropy</i>. MDPI, 2024. <a href=\"https://doi.org/10.3390/e26080637\">https://doi.org/10.3390/e26080637</a>.","ama":"Edelsbrunner H, Ölsböck K, Wagner H. Understanding higher-order interactions in information space. <i>Entropy</i>. 2024;26(8). doi:<a href=\"https://doi.org/10.3390/e26080637\">10.3390/e26080637</a>","ista":"Edelsbrunner H, Ölsböck K, Wagner H. 2024. Understanding higher-order interactions in information space. Entropy. 26(8), 637."},"date_created":"2024-09-08T22:01:11Z"},{"department":[{"_id":"HeEd"}],"date_published":"2024-01-01T00:00:00Z","status":"public","researchdata_availability":"no","_id":"15012","abstract":[{"text":"We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than n-1 star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs.","lang":"eng"}],"acknowledgement":"János Pach’s Research partially supported by European Research Council (ERC), grant “GeoScape” No. 882971 and by the Hungarian Science Foundation (NKFIH), grant K-131529. Work by Morteza Saghafian is partially supported by the European Research Council (ERC), grant No. 788183, and by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31.","citation":{"ista":"Pach J, Saghafian M, Schnider P. 2024. Decomposition of geometric graphs into star-forests. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14465, 339–346.","chicago":"Pach, János, Morteza Saghafian, and Patrick Schnider. “Decomposition of Geometric Graphs into Star-Forests.” In <i>31st International Symposium on Graph Drawing and Network Visualization</i>, 14465:339–46. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">https://doi.org/10.1007/978-3-031-49272-3_23</a>.","ama":"Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests. In: <i>31st International Symposium on Graph Drawing and Network Visualization</i>. Vol 14465. Springer Nature; 2024:339-346. doi:<a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">10.1007/978-3-031-49272-3_23</a>","ieee":"J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs into star-forests,” in <i>31st International Symposium on Graph Drawing and Network Visualization</i>, Isola delle Femmine, Palermo, Italy, 2024, vol. 14465, pp. 339–346.","apa":"Pach, J., Saghafian, M., &#38; Schnider, P. (2024). Decomposition of geometric graphs into star-forests. In <i>31st International Symposium on Graph Drawing and Network Visualization</i> (Vol. 14465, pp. 339–346). Isola delle Femmine, Palermo, Italy: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">https://doi.org/10.1007/978-3-031-49272-3_23</a>","short":"J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.","mla":"Pach, János, et al. “Decomposition of Geometric Graphs into Star-Forests.” <i>31st International Symposium on Graph Drawing and Network Visualization</i>, vol. 14465, Springer Nature, 2024, pp. 339–46, doi:<a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">10.1007/978-3-031-49272-3_23</a>."},"date_created":"2024-02-18T23:01:03Z","das_tickbox":"0","type":"conference","day":"01","title":"Decomposition of geometric graphs into star-forests","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"scopus_import":"1","doi":"10.1007/978-3-031-49272-3_23","oa":1,"alternative_title":["LNCS"],"publication_identifier":{"isbn":["9783031492716"],"issn":["0302-9743"],"eissn":["1611-3349"],"eisbn":["9783031492723"]},"article_processing_charge":"No","arxiv":1,"fulldoi":"https://doi.org/10.1007/978-3-031-49272-3_23","ec_funded":1,"language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"author":[{"full_name":"Pach, János","last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza"},{"last_name":"Schnider","first_name":"Patrick","full_name":"Schnider, Patrick"}],"publication_status":"published","intvolume":"     14465","month":"01","conference":{"name":"GD: Graph Drawing and Network Visualization","start_date":"2023-09-20","end_date":"2023-09-22","location":"Isola delle Femmine, Palermo, Italy"},"volume":14465,"external_id":{"arxiv":["2306.13201"],"isi":["001207939600023"]},"page":"339-346","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.13201"}],"year":"2024","related_material":{"record":[{"status":"public","id":"21253","relation":"later_version"}]},"publisher":"Springer Nature","publication":"31st International Symposium on Graph Drawing and Network Visualization","oa_version":"Preprint","quality_controlled":"1","date_updated":"2026-10-02T11:50:59Z","supplementarymaterial":"no"},{"ec_funded":1,"language":[{"iso":"eng"}],"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073","name":"Learning and triangulating manifolds via collapses"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342"}],"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Garber","first_name":"Alexey","full_name":"Garber, Alexey"},{"full_name":"Ghafaris, Mohadese","last_name":"Ghafaris","first_name":"Mohadese"},{"full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","first_name":"Teresa","orcid":"0000-0002-1780-2689"},{"full_name":"Saghafiant, Morteza","first_name":"Morteza","last_name":"Saghafiant"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"month":"06","intvolume":"        38","article_type":"original","publication_status":"published","doi":"10.1137/22M1489071","publication_identifier":{"issn":["0895-4801"]},"oa":1,"arxiv":1,"article_processing_charge":"No","fulldoi":"https://doi.org/10.1137/22M1489071","corr_author":"1","publication":"SIAM Journal on Discrete Mathematics","publisher":"Society for Industrial and Applied Mathematics","oa_version":"Preprint","quality_controlled":"1","date_updated":"2026-10-02T11:49:10Z","supplementarymaterial":"no","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2204.01077"}],"page":"1784-1807","external_id":{"arxiv":["2204.01077"],"isi":["001292728600001"]},"volume":38,"year":"2024","abstract":[{"lang":"eng","text":"For a locally finite set, 𝐴⊆ℝ𝑑\r\n, the 𝑘\r\nth Brillouin zone of 𝑎∈𝐴\r\n is the region of points 𝑥∈ℝ𝑑\r\n for which ‖𝑥−𝑎‖\r\n is the 𝑘\r\nth smallest among the Euclidean distances between 𝑥\r\n and the points in 𝐴\r\n. If 𝐴\r\n is a lattice, the 𝑘\r\nth Brillouin zones of the points in 𝐴\r\n are translates of each other, and together they tile space. Depending on the value of 𝑘\r\n, they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our results include the stability of a Brillouin zone under perturbations, a linear upper bound on the number of chambers in a zone for lattices in ℝ2\r\n, and the convergence of the maximum volume of a chamber to zero for the integer lattice."}],"_id":"17190","researchdata_availability":"no","acknowledgement":"The second author is partially supported by the Alexander von Humboldt Foundation. The sixth author is supported by the European Union's Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement 754411, and by Austrian Science Fund(FWF) grant M-3073. All other authors are supported by European Research Council (ERC) grant 788183, by the Wittgenstein Prize, by Austrian Science Fund (FWF) grant Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF) grant I 02979-N35.","department":[{"_id":"HeEd"}],"date_published":"2024-06-07T00:00:00Z","status":"public","day":"07","title":"Brillouin zones of integer lattices and their perturbations","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"scopus_import":"1","issue":"2","citation":{"apa":"Edelsbrunner, H., Garber, A., Ghafaris, M., Heiss, T., Saghafiant, M., &#38; Wintraecken, M. (2024). Brillouin zones of integer lattices and their perturbations. <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/22M1489071\">https://doi.org/10.1137/22M1489071</a>","short":"H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, M. Wintraecken, SIAM Journal on Discrete Mathematics 38 (2024) 1784–1807.","ieee":"H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, and M. Wintraecken, “Brillouin zones of integer lattices and their perturbations,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 38, no. 2. Society for Industrial and Applied Mathematics, pp. 1784–1807, 2024.","mla":"Edelsbrunner, Herbert, et al. “Brillouin Zones of Integer Lattices and Their Perturbations.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 38, no. 2, Society for Industrial and Applied Mathematics, 2024, pp. 1784–807, doi:<a href=\"https://doi.org/10.1137/22M1489071\">10.1137/22M1489071</a>.","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafaris, Teresa Heiss, Morteza Saghafiant, and Mathijs Wintraecken. “Brillouin Zones of Integer Lattices and Their Perturbations.” <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/22M1489071\">https://doi.org/10.1137/22M1489071</a>.","ama":"Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. Brillouin zones of integer lattices and their perturbations. <i>SIAM Journal on Discrete Mathematics</i>. 2024;38(2):1784-1807. doi:<a href=\"https://doi.org/10.1137/22M1489071\">10.1137/22M1489071</a>","ista":"Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. 2024. Brillouin zones of integer lattices and their perturbations. SIAM Journal on Discrete Mathematics. 38(2), 1784–1807."},"date_created":"2024-06-30T22:01:05Z","das_tickbox":"0","type":"journal_article"},{"ec_funded":1,"language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"Z00342","name":"Mathematics, Computer Science","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"author":[{"full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","last_name":"Cultrera di Montesano","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Draganov, Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0464-3823","first_name":"Ondrej","last_name":"Draganov"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza"}],"month":"10","ddc":["510"],"publication_status":"published","intvolume":"       320","OA_type":"gold","conference":{"location":"Vienna, Austria","start_date":"2024-09-18","name":"GD: Graph Drawing and Network Visualization","end_date":"2024-09-20"},"doi":"10.4230/LIPIcs.GD.2024.3","oa":1,"alternative_title":["LIPIcs"],"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959773430"]},"article_processing_charge":"Yes","arxiv":1,"fulldoi":"https://doi.org/10.4230/LIPIcs.GD.2024.3","corr_author":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication":"32nd International Symposium on Graph Drawing and Network Visualization","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa_version":"Published Version","quality_controlled":"1","date_updated":"2026-10-02T11:52:23Z","OA_place":"publisher","supplementarymaterial":"no","file":[{"date_created":"2024-11-18T07:49:25Z","access_level":"open_access","content_type":"application/pdf","creator":"dernst","relation":"main_file","file_name":"2024_LIPIcs_CultreradiMontesano.pdf","file_size":908541,"checksum":"5f9b35e115c3d375e99be78da9054cb4","file_id":"18560","success":1,"date_updated":"2024-11-18T07:49:25Z"}],"external_id":{"isi":["001540278400001"],"arxiv":["2403.10204"]},"volume":320,"year":"2024","_id":"18556","abstract":[{"lang":"eng","text":"Given a finite set, A ⊆ ℝ², and a subset, B ⊆ A, the MST-ratio is the combined length of the minimum spanning trees of B and A⧵B divided by the length of the minimum spanning tree of A. The question of the supremum, over all sets A, of the maximum, over all subsets B, is related to the Steiner ratio, and we prove this sup-max is between 2.154 and 2.427. Restricting ourselves to 2-dimensional lattices, we prove that the sup-max is 2, while the inf-max is 1.25. By some margin the most difficult of these results is the upper bound for the inf-max, which we prove by showing that the hexagonal lattice cannot have MST-ratio larger than 1.25."}],"researchdata_availability":"no","file_date_updated":"2024-11-18T07:49:25Z","has_accepted_license":"1","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.","department":[{"_id":"HeEd"}],"date_published":"2024-10-28T00:00:00Z","status":"public","article_number":"3","day":"28","title":"The Euclidean MST-ratio for bi-colored lattices","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"scopus_import":"1","citation":{"mla":"Cultrera di Montesano, Sebastiano, et al. “The Euclidean MST-Ratio for Bi-Colored Lattices.” <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, vol. 320, 3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">10.4230/LIPIcs.GD.2024.3</a>.","ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “The Euclidean MST-ratio for bi-colored lattices,” in <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, Vienna, Austria, 2024, vol. 320.","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (2024). The Euclidean MST-ratio for bi-colored lattices. In <i>32nd International Symposium on Graph Drawing and Network Visualization</i> (Vol. 320). Vienna, Austria: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">https://doi.org/10.4230/LIPIcs.GD.2024.3</a>","ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. The Euclidean MST-ratio for bi-colored lattices. In: <i>32nd International Symposium on Graph Drawing and Network Visualization</i>. Vol 320. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">10.4230/LIPIcs.GD.2024.3</a>","chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “The Euclidean MST-Ratio for Bi-Colored Lattices.” In <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, Vol. 320. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">https://doi.org/10.4230/LIPIcs.GD.2024.3</a>.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2024. The Euclidean MST-ratio for bi-colored lattices. 32nd International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LIPIcs, vol. 320, 3."},"date_created":"2024-11-17T23:01:47Z","das_tickbox":"0","type":"conference"},{"supplementarymaterial":"yes","date_updated":"2026-10-02T11:51:50Z","quality_controlled":"1","oa_version":"Published Version","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication":"40th International Symposium on Computational Geometry","year":"2024","volume":293,"file":[{"date_created":"2024-09-19T10:30:37Z","file_name":"2024_LIPICs_Attali.pdf","creator":"dernst","relation":"main_file","content_type":"application/pdf","access_level":"open_access","success":1,"checksum":"9355c2e60b8ec285e1b22719c5b73f1a","file_id":"18098","file_size":3507177,"date_updated":"2024-09-19T10:30:37Z"}],"conference":{"location":"Athens, Greece","end_date":"2024-06-14","name":"SoCG: Symposium on Computational Geometry","start_date":"2024-06-11"},"publication_status":"published","intvolume":"       293","ddc":["000"],"month":"06","author":[{"full_name":"Attali, Dominique","last_name":"Attali","first_name":"Dominique"},{"full_name":"Kourimska, Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","first_name":"Hana","last_name":"Kourimska","orcid":"0000-0001-7841-0091"},{"first_name":"Christopher D","last_name":"Fillmore","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","full_name":"Fillmore, Christopher D"},{"full_name":"Ghosh, Ishika","first_name":"Ishika","last_name":"Ghosh","id":"ee449b28-344d-11ef-a6d5-9ca430e9e9ff"},{"full_name":"Lieutier, Andre","last_name":"Lieutier","first_name":"Andre"},{"first_name":"Elizabeth R","last_name":"Stephenson","orcid":"0000-0002-6862-208X","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","full_name":"Stephenson, Elizabeth R"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"name":"Learning and triangulating manifolds via collapses","grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"language":[{"iso":"eng"}],"ec_funded":1,"corr_author":"1","fulldoi":"https://doi.org/10.4230/LIPIcs.SoCG.2024.87","article_processing_charge":"Yes","alternative_title":["LIPIcs"],"oa":1,"publication_identifier":{"isbn":["9783959773164"]},"doi":"10.4230/LIPIcs.SoCG.2024.87","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"The ultimate frontier: An optimality construction for homotopy inference (media exposition)","day":"06","type":"conference","das_tickbox":"0","citation":{"ista":"Attali D, Kourimska H, Fillmore CD, Ghosh I, Lieutier A, Stephenson ER, Wintraecken M. 2024. The ultimate frontier: An optimality construction for homotopy inference (media exposition). 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 87.","ama":"Attali D, Kourimska H, Fillmore CD, et al. The ultimate frontier: An optimality construction for homotopy inference (media exposition). In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">10.4230/LIPIcs.SoCG.2024.87</a>","chicago":"Attali, Dominique, Hana Kourimska, Christopher D Fillmore, Ishika Ghosh, Andre Lieutier, Elizabeth R Stephenson, and Mathijs Wintraecken. “The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition).” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">https://doi.org/10.4230/LIPIcs.SoCG.2024.87</a>.","short":"D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","apa":"Attali, D., Kourimska, H., Fillmore, C. D., Ghosh, I., Lieutier, A., Stephenson, E. R., &#38; Wintraecken, M. (2024). The ultimate frontier: An optimality construction for homotopy inference (media exposition). In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">https://doi.org/10.4230/LIPIcs.SoCG.2024.87</a>","ieee":"D. Attali <i>et al.</i>, “The ultimate frontier: An optimality construction for homotopy inference (media exposition),” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","mla":"Attali, Dominique, et al. “The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition).” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 87, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">10.4230/LIPIcs.SoCG.2024.87</a>."},"date_created":"2024-09-19T10:29:48Z","acknowledgement":"This research has been supported by the European Research Council (ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant No. I02979-N35. Mathijs Wintraecken: Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant No. M-3073, and the welcome package from IDEX of the Université Côte d’Azur.\r\nWe thank Jean-Daniel Boissonnat, Herbert Edelsbrunner, and Mariette Yvinec for discussion.","has_accepted_license":"1","file_date_updated":"2024-09-19T10:30:37Z","_id":"18097","abstract":[{"lang":"eng","text":"In our companion paper \"Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds\" we gave optimal bounds (in terms of the two one-sided Hausdorff distances) on a sample P of an input shape 𝒮 (either manifold or general set with positive reach) such that one can infer the homotopy of 𝒮 from the union of balls with some radius centred at P, both in Euclidean space and in a Riemannian manifold of bounded curvature. The construction showing the optimality of the bounds is not straightforward. The purpose of this video is to visualize and thus elucidate said construction in the Euclidean setting."}],"researchdata_availability":"no","article_number":"87","status":"public","date_published":"2024-06-06T00:00:00Z","department":[{"_id":"HeEd"}]},{"date_created":"2023-07-02T22:00:44Z","citation":{"ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. 8, 1101–1119.","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>. 2024;8:1101-1119. doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>","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, 2024. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). 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>","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.","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>, vol. 8. Springer Nature, pp. 1101–1119, 2024.","mla":"Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>, vol. 8, Springer Nature, 2024, pp. 1101–19, doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>."},"type":"journal_article","das_tickbox":"0","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Geometric characterization of the persistence of 1D maps","day":"01","scopus_import":"1","date_published":"2024-10-01T00:00:00Z","department":[{"_id":"HeEd"}],"status":"public","_id":"13182","researchdata_availability":"no","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"}],"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.","file_date_updated":"2025-01-09T07:39:41Z","has_accepted_license":"1","external_id":{"pmid":["39678706"]},"page":"1101-1119","volume":8,"file":[{"date_updated":"2025-01-09T07:39:41Z","success":1,"file_id":"18783","checksum":"d493df5088c222b88d9ca46b623ad0ee","file_size":476896,"file_name":"2024_JourApplCompTopo_Biswas.pdf","creator":"dernst","content_type":"application/pdf","relation":"main_file","access_level":"open_access","date_created":"2025-01-09T07:39:41Z"}],"year":"2024","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"related_material":{"record":[{"id":"11660","relation":"earlier_version","status":"public"},{"id":"15094","relation":"dissertation_contains","status":"public"}]},"publisher":"Springer Nature","publication":"Journal of Applied and Computational Topology","supplementarymaterial":"no","date_updated":"2026-10-02T11:52:56Z","quality_controlled":"1","OA_place":"publisher","oa_version":"Published Version","doi":"10.1007/s41468-023-00126-9","corr_author":"1","fulldoi":"https://doi.org/10.1007/s41468-023-00126-9","article_processing_charge":"Yes (via OA deal)","pmid":1,"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"oa":1,"author":[{"full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas","orcid":"0000-0002-5372-7890"},{"full_name":"Cultrera Di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","last_name":"Cultrera Di Montesano","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"grant_number":"I4887","name":"Persistent Homology, Algorithms and Stochastic Geometry","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"grant_number":"Z00342","name":"Mathematics, Computer Science","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"language":[{"iso":"eng"}],"OA_type":"hybrid","article_type":"original","ddc":["000"],"intvolume":"         8","month":"10","publication_status":"published"},{"article_processing_charge":"Yes (via OA deal)","fulldoi":"https://doi.org/10.1007/s41468-024-00173-w","corr_author":"1","oa":1,"publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"pmid":1,"doi":"10.1007/s41468-024-00173-w","publication_status":"published","article_type":"original","month":"09","ddc":["510"],"intvolume":"         8","OA_type":"hybrid","author":[{"full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","last_name":"Biswas","first_name":"Ranita"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera Di Montesano","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","full_name":"Cultrera Di Montesano, Sebastiano"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"language":[{"iso":"eng"}],"ec_funded":1,"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","name":"Mathematics, Computer Science","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"year":"2024","volume":8,"external_id":{"pmid":["39308789"]},"page":"557-578","file":[{"checksum":"0ee15c1493a6413cf356ab2f32c81a9e","file_id":"19612","success":1,"file_size":522831,"date_updated":"2025-04-23T08:01:36Z","date_created":"2025-04-23T08:01:36Z","file_name":"2024_JourApplCompTopo_BiswasRa.pdf","access_level":"open_access","content_type":"application/pdf","creator":"dernst","relation":"main_file"}],"supplementarymaterial":"no","oa_version":"Published Version","OA_place":"publisher","quality_controlled":"1","date_updated":"2026-10-02T11:55:12Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"related_material":{"record":[{"relation":"earlier_version","id":"11658","status":"public"}]},"publication":"Journal of Applied and Computational Topology","publisher":"Springer Nature","status":"public","date_published":"2024-09-01T00:00:00Z","department":[{"_id":"HeEd"}],"acknowledgement":"The authors thank Uli Wagner and Emo Welzl for comments on an earlier version of this paper, and for pointing out related work in the prior literature.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). 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.","file_date_updated":"2025-04-23T08:01:36Z","has_accepted_license":"1","_id":"15380","researchdata_availability":"no","abstract":[{"text":"The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements.","lang":"eng"}],"type":"journal_article","das_tickbox":"0","date_created":"2024-05-12T22:01:03Z","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. 2024;8:557-578. doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Journal of Applied and Computational Topology. 8, 557–578.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” <i>Journal of Applied and Computational Topology</i>, vol. 8. Springer Nature, pp. 557–578, 2024.","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>, vol. 8, Springer Nature, 2024, pp. 557–78, doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>."},"scopus_import":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications"},{"issue":"8","isi":1,"scopus_import":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01","title":"Odd-sunflowers","type":"journal_article","das_tickbox":"1","date_created":"2024-03-31T22:01:11Z","license":"https://creativecommons.org/licenses/by-nc/4.0/","citation":{"apa":"Frankl, P., Pach, J., &#38; Pálvölgyi, D. (2024). Odd-sunflowers. <i>Journal of Combinatorial Theory, Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">https://doi.org/10.1016/j.jcta.2024.105889</a>","ieee":"P. Frankl, J. Pach, and D. Pálvölgyi, “Odd-sunflowers,” <i>Journal of Combinatorial Theory, Series A</i>, vol. 206, no. 8. Elsevier, 2024.","short":"P. Frankl, J. Pach, D. Pálvölgyi, Journal of Combinatorial Theory, Series A 206 (2024).","mla":"Frankl, Peter, et al. “Odd-Sunflowers.” <i>Journal of Combinatorial Theory, Series A</i>, vol. 206, no. 8, 105889, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">10.1016/j.jcta.2024.105889</a>.","ista":"Frankl P, Pach J, Pálvölgyi D. 2024. Odd-sunflowers. Journal of Combinatorial Theory, Series A. 206(8), 105889.","chicago":"Frankl, Peter, János Pach, and Dömötör Pálvölgyi. “Odd-Sunflowers.” <i>Journal of Combinatorial Theory, Series A</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">https://doi.org/10.1016/j.jcta.2024.105889</a>.","ama":"Frankl P, Pach J, Pálvölgyi D. Odd-sunflowers. <i>Journal of Combinatorial Theory, Series A</i>. 2024;206(8). doi:<a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">10.1016/j.jcta.2024.105889</a>"},"acknowledgement":"We are grateful to Balázs Keszegh, and to the members of the Miklós Schweitzer Competition committee of 2022 for valuable discussions, and Shira Zerbib for pointing out several important mathematical typos.","has_accepted_license":"1","file_date_updated":"2025-01-09T08:37:20Z","researchdata_availability":"not applicable","_id":"15247","abstract":[{"lang":"eng","text":"Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant <2 such that every family of subsets of an n-element set that contains no odd-sunflower consists of at most n sets. We construct such families of size at least 1.5021n. We also characterize minimal odd-sunflowers of triples."}],"article_number":"105889","status":"public","date_published":"2024-08-01T00:00:00Z","department":[{"_id":"HeEd"}],"supplementarymaterial":"yes","oa_version":"Published Version","dataavailabilitystatement":"No data was used for the research described in the article.","quality_controlled":"1","date_updated":"2026-10-02T11:54:47Z","OA_place":"publisher","tmp":{"short":"CC BY-NC (4.0)","image":"/images/cc_by_nc.png","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"},"publisher":"Elsevier","publication":"Journal of Combinatorial Theory, Series A","year":"2024","volume":206,"file":[{"file_size":366029,"file_id":"18791","checksum":"ffc29d65e712849f0d31009271e06a63","success":1,"date_updated":"2025-01-09T08:37:20Z","date_created":"2025-01-09T08:37:20Z","access_level":"open_access","relation":"main_file","content_type":"application/pdf","creator":"dernst","file_name":"2024_JourCombiTheoryA_Frankl.pdf"}],"external_id":{"arxiv":["2310.16701"],"isi":["001217739200001"]},"intvolume":"       206","publication_status":"published","article_type":"original","month":"08","ddc":["510"],"OA_type":"hybrid","author":[{"full_name":"Frankl, Peter","last_name":"Frankl","first_name":"Peter"},{"full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach","first_name":"János"},{"full_name":"Pálvölgyi, Dömötör","last_name":"Pálvölgyi","first_name":"Dömötör"}],"language":[{"iso":"eng"}],"arxiv":1,"article_processing_charge":"No","corr_author":"1","fulldoi":"https://doi.org/10.1016/j.jcta.2024.105889","oa":1,"publication_identifier":{"issn":["0097-3165"],"eissn":["1096-0899"]},"doi":"10.1016/j.jcta.2024.105889"},{"file":[{"checksum":"247bb057aed2fba1cd4711917aaa2d77","file_id":"18686","success":1,"file_size":7752253,"date_updated":"2024-12-19T10:24:46Z","date_created":"2024-12-19T10:24:46Z","file_name":"Teresa_Heiss_PhD_Thesis_final.pdf","access_level":"open_access","content_type":"application/pdf","creator":"theiss","relation":"main_file"},{"date_updated":"2024-12-19T10:24:50Z","file_size":17197731,"checksum":"9648b45c07a008ee11a07f99856a139d","file_id":"18687","creator":"theiss","relation":"source_file","content_type":"application/zip","access_level":"closed","file_name":"PhD_Thesis.zip","date_created":"2024-12-19T10:24:50Z"}],"page":"111","doi_confirm":"1","year":"2024","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"publisher":"Institute of Science and Technology Austria","related_material":{"record":[{"relation":"part_of_dissertation","id":"10828","status":"public"},{"status":"public","id":"11440","relation":"part_of_dissertation"},{"id":"9345","relation":"part_of_dissertation","status":"public"},{"id":"18673","relation":"part_of_dissertation","status":"public"}]},"supplementarymaterial":"no","date_updated":"2026-10-02T11:55:42Z","OA_place":"publisher","oa_version":"Published Version","doi":"10.15479/at:ista:18667","corr_author":"1","fulldoi":"https://doi.org/10.15479/at:ista:18667","degree_awarded":"PhD","article_processing_charge":"No","publication_identifier":{"isbn":["978-3-99078-052-7"],"issn":["2663-337X"]},"alternative_title":["ISTA Thesis"],"oa":1,"author":[{"full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","last_name":"Heiss","first_name":"Teresa"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"}],"ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","month":"12","ddc":["514","516","004"],"citation":{"apa":"Heiss, T. (2024). <i>New methods for applying topological data analysis to materials science</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>","short":"T. Heiss, New Methods for Applying Topological Data Analysis to Materials Science, Institute of Science and Technology Austria, 2024.","ieee":"T. Heiss, “New methods for applying topological data analysis to materials science,” Institute of Science and Technology Austria, 2024.","mla":"Heiss, Teresa. <i>New Methods for Applying Topological Data Analysis to Materials Science</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>.","ista":"Heiss T. 2024. New methods for applying topological data analysis to materials science. Institute of Science and Technology Austria.","ama":"Heiss T. New methods for applying topological data analysis to materials science. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>","chicago":"Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials Science.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>."},"date_created":"2024-12-17T16:17:55Z","type":"dissertation","das_tickbox":"0","supervisor":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"New methods for applying topological data analysis to materials science","day":"17","date_published":"2024-12-17T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"status":"public","keyword":["persistent homology","topological data analysis","periodic","crystalline materials","images","fingerprint"],"abstract":[{"text":"Many chemical and physical properties of materials are determined by the material’s shape,\r\nfor example the size of its pores and the width of its tunnels. This makes materials science\r\na prime application area for geometrical and topological methods. Nevertheless many\r\nmethods in topological data analysis have not been satisfyingly extended to the needs of\r\nmaterials science. This thesis provides new methods and new mathematical theorems\r\ntargeted at those specific needs by answering four different research questions. While the\r\nmotivation for each of the research questions arises from materials science, the methods\r\nare versatile and can be applied in different areas as well. \r\n\r\nThe first research question is concerned with image data, for example a three-dimensional\r\ncomputed tomography (CT) scan of a material, like sand or stone. There are two commonly\r\nused topologies for digital images and depending on the application either of them might be\r\nrequired. However, software for computing the topological data analysis method persistence\r\nhomology, usually supports only one of the two topologies. We answer the question how to\r\ncompute persistent homology of an image with respect to one of the two topologies using\r\nsoftware that is intended for the other topology. \r\n\r\nThe second research question is concerned with image data as well, and asks how much\r\nof the topological information of an image is lost when the resolution is coarsened. As\r\ncomputer tomography scanners are more expensive the higher the resolution, it is an\r\nimportant question in materials science to know which resolution is enough to get satisfying\r\npersistent homology. We give theoretical bounds on the information loss based on different\r\ngeometrical properties of the object to be scanned. In addition, we conduct experiments on\r\nsand and stone CT image data. \r\n\r\nThe third research question is motivated by comparing crystalline materials efficiently. As\r\nthe atoms within a crystal repeat periodically, crystalline materials are either modeled by\r\nunmanageable infinite periodic point sets, or by one of their fundamental domains, which is\r\nunstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with\r\nappropriate properties such that comparing the crystals can be eased by comparing the\r\nfingerprints instead. We define the density fingerprint and prove the necessary properties. \r\n\r\nThe fourth research question is motivated by studying the hole-structure or connectedness,\r\ni.e. persistent homology or merge trees, of crystalline materials. A common way to deal\r\nwith periodicity is to take a fundamental domain and identify opposite boundaries to form a\r\ntorus. However, computing persistent homology or merge trees on that torus loses some\r\nof the information materials scientists are interested in and is additionally not stable under\r\ncertain noise. We therefore decorate the merge tree stemming from the torus with additional\r\ninformation describing the density and growth rate of the periodic copies of a component\r\nwithin a growing spherical window. We prove all desired properties, like stability and efficient\r\ncomputability.","lang":"eng"}],"_id":"18667","researchdata_availability":"no","acknowledgement":"I was supported by the European Research Council (ERC) Horizon 2020 project\r\n“Alpha Shape Theory Extended” No. 788183 and by the Pöttinger Scholarship. In addition,\r\nI am very thankful for having been able to attend the second Workshop for Women in\r\nComputational Topology in July 2019, funded by the Mathematical Sciences Institute at\r\nANU, the US National Science Foundation through the award CCF-1841455, the Australian\r\nMathematical Sciences Institute and the Association for Women in Mathematics. Two of the\r\nprojects presented in this thesis started there. One of them reached completion thanks to\r\nfunding from the MSRI Summer Research in Mathematics program awarded to me and my\r\ncollaborators in 2020.","has_accepted_license":"1","file_date_updated":"2024-12-19T10:24:50Z"},{"type":"dissertation","das_tickbox":"0","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"}],"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","date_created":"2024-03-08T15:28:10Z","citation":{"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>.","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>","ista":"Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria.","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>.","short":"S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024.","ieee":"S. Cultrera di Montesano, “Persistence and Morse theory for discrete geometric structures,” Institute of Science and Technology Austria, 2024.","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>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Persistence and Morse theory for discrete geometric structures","day":"08","status":"public","date_published":"2024-03-08T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"has_accepted_license":"1","file_date_updated":"2024-03-14T14:14:35Z","_id":"15094","researchdata_availability":"no","abstract":[{"lang":"eng","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"}],"year":"2024","file":[{"access_level":"open_access","content_type":"application/pdf","relation":"main_file","creator":"scultrer","file_name":"Thesis Sebastiano.pdf","date_created":"2024-03-14T08:55:07Z","date_updated":"2024-03-14T08:55:07Z","file_size":4106872,"file_id":"15112","checksum":"1e468bfa42a7dcf04d89f4dadc621c87","success":1},{"relation":"source_file","creator":"scultrer","content_type":"application/zip","access_level":"closed","file_name":"Thesis (1).zip","date_created":"2024-03-14T08:56:24Z","date_updated":"2024-03-14T14:14:35Z","file_size":4746234,"file_id":"15113","checksum":"bcbd213490f5a7e68855a092bbce93f1"}],"page":"108","doi_confirm":"1","supplementarymaterial":"no","date_updated":"2026-10-02T11:57:31Z","OA_place":"publisher","oa_version":"Published Version","tmp":{"image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)"},"related_material":{"record":[{"status":"public","id":"15090","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"11658","status":"public"},{"relation":"part_of_dissertation","id":"11660","status":"public"},{"id":"13182","relation":"part_of_dissertation","status":"public"},{"id":"15091","relation":"part_of_dissertation","status":"public"},{"id":"15093","relation":"part_of_dissertation","status":"public"}]},"publisher":"Institute of Science and Technology Austria","fulldoi":"https://doi.org/10.15479/at:ista:15094","degree_awarded":"PhD","corr_author":"1","article_processing_charge":"No","alternative_title":["ISTA Thesis"],"publication_identifier":{"issn":["2663-337X"]},"oa":1,"doi":"10.15479/at:ista:15094","ddc":["514","500","516"],"publication_status":"published","month":"03","author":[{"full_name":"Cultrera di Montesano, Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","last_name":"Cultrera di Montesano"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Persistent Homology, Algorithms and Stochastic Geometry"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"language":[{"iso":"eng"}],"ec_funded":1},{"das_tickbox":"0","type":"conference","date_created":"2024-03-08T10:27:39Z","citation":{"ista":"Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. 2024. Dynamically maintaining the persistent homology of time series. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). SODA: Symposium on Discrete Algorithms, 243–295.","chicago":"Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika Henzinger, and Lara Ost. “Dynamically Maintaining the Persistent Homology of Time Series.” In <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, edited by David P. Woodruff, 243–95. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/1.9781611977912.11\">https://doi.org/10.1137/1.9781611977912.11</a>.","ama":"Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. Dynamically maintaining the persistent homology of time series. In: Woodruff DP, ed. <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>. Society for Industrial and Applied Mathematics; 2024:243-295. doi:<a href=\"https://doi.org/10.1137/1.9781611977912.11\">10.1137/1.9781611977912.11</a>","ieee":"S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, and L. Ost, “Dynamically maintaining the persistent homology of time series,” in <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, Alexandria, VA, USA, 2024, pp. 243–295.","short":"S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, L. Ost, in:, D.P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics, 2024, pp. 243–295.","apa":"Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M., &#38; Ost, L. (2024). Dynamically maintaining the persistent homology of time series. In D. P. Woodruff (Ed.), <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i> (pp. 243–295). Alexandria, VA, USA: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611977912.11\">https://doi.org/10.1137/1.9781611977912.11</a>","mla":"Cultrera di Montesano, Sebastiano, et al. “Dynamically Maintaining the Persistent Homology of Time Series.” <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, edited by David P. Woodruff, Society for Industrial and Applied Mathematics, 2024, pp. 243–95, doi:<a href=\"https://doi.org/10.1137/1.9781611977912.11\">10.1137/1.9781611977912.11</a>."},"scopus_import":"1","title":"Dynamically maintaining the persistent homology of time series","day":"04","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","department":[{"_id":"HeEd"},{"_id":"MoHe"}],"date_published":"2024-01-04T00:00:00Z","acknowledgement":"The  first  and  second  authors  are  funded  by  the  European  Research  Council  under  the European Union’s Horizon 2020 research and innovation programme, ERC grant no. 788183,“Alpha Shape Theory Extended (Alpha)”, by the Wittgenstein Prize, FWF grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.The third author received funding by the European Research Council under the European Union’s Horizon 2020research  and  innovation  programme,  ERC  grant  no.  101019564,  “The  Design  of  Modern  Fully  Dynamic  DataStructures (MoDynStruct)”, and by the Austrian Science Fund through the Wittgenstein Prize with FWF grant no. Z 422-N, and also by FWF grant no. I 5982-N, and by FWF grant no. P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024.  The fourth author is funded by the Vienna Graduate School on Computational Optimization, FWF project no. W1260-N35.","researchdata_availability":"no","_id":"15093","abstract":[{"text":"We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right.","lang":"eng"}],"year":"2024","external_id":{"arxiv":["2311.01115"]},"page":"243 - 295","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2311.01115"}],"date_updated":"2026-10-02T11:57:32Z","quality_controlled":"1","oa_version":"Preprint","supplementarymaterial":"no","publisher":"Society for Industrial and Applied Mathematics","publication":"Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)","related_material":{"record":[{"id":"15094","relation":"dissertation_contains","status":"public"}]},"editor":[{"full_name":"Woodruff, David P.","last_name":"Woodruff","first_name":"David P."}],"oa":1,"publication_identifier":{"eisbn":["9781611977912"]},"fulldoi":"https://doi.org/10.1137/1.9781611977912.11","corr_author":"1","arxiv":1,"article_processing_charge":"No","doi":"10.1137/1.9781611977912.11","publication_status":"published","month":"01","conference":{"location":"Alexandria, VA, USA","name":"SODA: Symposium on Discrete Algorithms","start_date":"2024-01-07","end_date":"2024-01-10"},"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342"},{"call_identifier":"H2020","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564","name":"The design and evaluation of modern fully dynamic data structures"},{"name":"Efficient algorithms","grant_number":"Z00422","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"ec_funded":1,"language":[{"iso":"eng"}],"author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","last_name":"Henzinger","first_name":"Monika H"},{"last_name":"Ost","first_name":"Lara","full_name":"Ost, Lara"}]},{"doi":"10.48550/arXiv.2209.14993","corr_author":"1","fulldoi":"https://doi.org/10.48550/arXiv.2209.14993","arxiv":1,"article_processing_charge":"No","oa":1,"author":[{"first_name":"Adam","last_name":"Brown","full_name":"Brown, Adam"},{"full_name":"Draganov, Ondrej","orcid":"0000-0003-0464-3823","last_name":"Draganov","first_name":"Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87"}],"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"ec_funded":1,"month":"06","publication_status":"draft","external_id":{"arxiv":["2209.14993"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2209.14993","open_access":"1"}],"year":"2024","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"related_material":{"record":[{"status":"public","relation":"later_version","id":"20323"},{"status":"public","relation":"dissertation_contains","id":"18979"}]},"publication":"arXiv","supplementarymaterial":"no","date_updated":"2026-10-02T11:57:00Z","OA_place":"repository","oa_version":"Preprint","date_published":"2024-06-09T00:00:00Z","department":[{"_id":"HeEd"}],"status":"public","_id":"18981","researchdata_availability":"no","abstract":[{"text":"We establish several results combining discrete Morse theory and microlocal sheaf theory in the setting of finite posets and simplicial complexes. Our primary tool is a computationally tractable description of the bounded derived category of sheaves on a poset with the Alexandrov topology. We prove that each bounded complex of sheaves on a finite poset admits a unique (up to isomorphism of complexes) minimal injective resolution, and we provide algorithms for computing minimal injective resolution of an injective complex, as well as several useful functors between derived categories of sheaves. For the constant sheaf on a simplicial complex, we give asymptotically tight bounds on the complexity of computing the minimal injective resolution using those algorithms. Our main result is a novel definition of the discrete microsupport of a bounded complex of sheaves on a finite poset. We detail several foundational properties of the discrete microsupport, as well as a microlocal generalization of the discrete homological Morse theorem and Morse inequalities.","lang":"eng"}],"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European\r\nUnion’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize,\r\nAustrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR\r\n109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.","date_created":"2025-01-31T17:03:04Z","citation":{"short":"A. Brown, O. Draganov, ArXiv (n.d.).","apa":"Brown, A., &#38; Draganov, O. (n.d.). Discrete microlocal Morse theory. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2209.14993\">https://doi.org/10.48550/arXiv.2209.14993</a>","ieee":"A. Brown and O. Draganov, “Discrete microlocal Morse theory,” <i>arXiv</i>. .","mla":"Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2209.14993\">10.48550/arXiv.2209.14993</a>.","chicago":"Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2209.14993\">https://doi.org/10.48550/arXiv.2209.14993</a>.","ama":"Brown A, Draganov O. Discrete microlocal Morse theory. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2209.14993\">10.48550/arXiv.2209.14993</a>","ista":"Brown A, Draganov O. Discrete microlocal Morse theory. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2209.14993\">10.48550/arXiv.2209.14993</a>."},"type":"preprint","das_tickbox":"0","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Discrete microlocal Morse theory","day":"09"},{"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Merge trees of periodic filtrations","day":"29","date_created":"2024-12-18T14:06:57Z","citation":{"mla":"Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2408.16575\">10.48550/arXiv.2408.16575</a>.","short":"H. Edelsbrunner, T. Heiss, ArXiv (n.d.).","apa":"Edelsbrunner, H., &#38; Heiss, T. (n.d.). Merge trees of periodic filtrations. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2408.16575\">https://doi.org/10.48550/arXiv.2408.16575</a>","ieee":"H. Edelsbrunner and T. Heiss, “Merge trees of periodic filtrations,” <i>arXiv</i>. .","ama":"Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2408.16575\">10.48550/arXiv.2408.16575</a>","chicago":"Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2408.16575\">https://doi.org/10.48550/arXiv.2408.16575</a>.","ista":"Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2408.16575\">10.48550/arXiv.2408.16575</a>."},"type":"preprint","das_tickbox":"0","_id":"18673","abstract":[{"text":"Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability under perturbations and provide an algorithm that under mild geometric conditions typically satisfied by crystalline materials takes O((n+m)logn) time, in which n and m are the numbers of vertices and edges in the quotient complex, respectively.\r\n","lang":"eng"}],"researchdata_availability":"no","acknowledgement":"Both authors are partially supported by the European Research Council (ERC) Horizon 2020 project\r\n‘Alpha Shape Theory Extended’, grant no. 788183. The first author is also partially supported by the DFG\r\nCollaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund\r\n(FWF), grant no. I 02979-N35.","date_published":"2024-08-29T00:00:00Z","department":[{"_id":"HeEd"}],"status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"18667"}]},"publication":"arXiv","supplementarymaterial":"no","OA_place":"repository","date_updated":"2026-10-02T11:55:43Z","oa_version":"Preprint","external_id":{"arxiv":["2408.16575"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2408.16575"}],"year":"2024","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","last_name":"Heiss","first_name":"Teresa","full_name":"Heiss, Teresa"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"language":[{"iso":"eng"}],"ec_funded":1,"month":"08","publication_status":"draft","doi":"10.48550/arXiv.2408.16575","fulldoi":"https://doi.org/10.48550/arXiv.2408.16575","corr_author":"1","arxiv":1,"article_processing_charge":"No","oa":1},{"supplementarymaterial":"no","oa_version":"Preprint","date_updated":"2026-10-02T11:56:13Z","OA_place":"repository","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"publication":"arXiv","related_material":{"record":[{"id":"18979","relation":"dissertation_contains","status":"public"},{"id":"20585","relation":"later_version","status":"public"},{"status":"public","relation":"dissertation_contains","id":"15094"}]},"year":"2024","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2212.03128"}],"external_id":{"arxiv":["2212.03128"]},"month":"02","publication_status":"draft","author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano"},{"orcid":"0000-0003-0464-3823","last_name":"Draganov","first_name":"Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"language":[{"iso":"eng"}],"arxiv":1,"article_processing_charge":"No","corr_author":"1","fulldoi":"https://doi.org/10.48550/arXiv.2212.03128","oa":1,"doi":"10.48550/arXiv.2212.03128","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"07","title":"Chromatic alpha complexes","type":"preprint","das_tickbox":"0","citation":{"ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2212.03128\">10.48550/arXiv.2212.03128</a>","chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2212.03128\">https://doi.org/10.48550/arXiv.2212.03128</a>.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. arXiv, 2212.03128.","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). Chromatic alpha complexes. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2212.03128\">https://doi.org/10.48550/arXiv.2212.03128</a>","ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” <i>arXiv</i>. .","mla":"Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” <i>ArXiv</i>, 2212.03128, doi:<a href=\"https://doi.org/10.48550/arXiv.2212.03128\">10.48550/arXiv.2212.03128</a>."},"date_created":"2024-03-08T10:13:59Z","_id":"15091","researchdata_availability":"no","abstract":[{"text":"Motivated by applications in the medical sciences, we study finite chromatic\r\nsets in Euclidean space from a topological perspective. Based on the persistent\r\nhomology for images, kernels and cokernels, we design provably stable\r\nhomological quantifiers that describe the geometric micro- and macro-structure\r\nof how the color classes mingle. These can be efficiently computed using\r\nchromatic variants of Delaunay and alpha complexes, and code that does these\r\ncomputations is provided.","lang":"eng"}],"article_number":"2212.03128","status":"public","date_published":"2024-02-07T00:00:00Z","department":[{"_id":"HeEd"}]},{"file":[{"file_name":"2023_Algorithmica_Edelsbrunner.pdf","relation":"main_file","content_type":"application/pdf","creator":"dernst","access_level":"open_access","date_created":"2023-01-20T10:02:48Z","date_updated":"2023-01-20T10:02:48Z","success":1,"file_id":"12322","checksum":"71685ca5121f4c837f40c3f8eb50c915","file_size":911017}],"external_id":{"pmid":["36687803"],"isi":["000846967100001"]},"page":"277-295","volume":85,"year":"2023","publisher":"Springer Nature","publication":"Algorithmica","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa_version":"Published Version","quality_controlled":"1","date_updated":"2025-04-23T08:46:48Z","doi":"10.1007/s00453-022-01027-6","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"oa":1,"pmid":1,"article_processing_charge":"Yes (via OA deal)","corr_author":"1","fulldoi":"https://doi.org/10.1007/s00453-022-01027-6","language":[{"iso":"eng"}],"ec_funded":1,"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"Mathematics, Computer Science"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Osang, Georg F","first_name":"Georg F","last_name":"Osang","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"ddc":["510"],"intvolume":"        85","publication_status":"published","article_type":"original","month":"01","citation":{"chicago":"Edelsbrunner, Herbert, and Georg F Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” <i>Algorithmica</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00453-022-01027-6\">https://doi.org/10.1007/s00453-022-01027-6</a>.","ama":"Edelsbrunner H, Osang GF. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. <i>Algorithmica</i>. 2023;85:277-295. doi:<a href=\"https://doi.org/10.1007/s00453-022-01027-6\">10.1007/s00453-022-01027-6</a>","ista":"Edelsbrunner H, Osang GF. 2023. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 85, 277–295.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” <i>Algorithmica</i>, vol. 85, Springer Nature, 2023, pp. 277–95, doi:<a href=\"https://doi.org/10.1007/s00453-022-01027-6\">10.1007/s00453-022-01027-6</a>.","short":"H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.","ieee":"H. Edelsbrunner and G. F. Osang, “A simple algorithm for higher-order Delaunay mosaics and alpha shapes,” <i>Algorithmica</i>, vol. 85. Springer Nature, pp. 277–295, 2023.","apa":"Edelsbrunner, H., &#38; Osang, G. F. (2023). A simple algorithm for higher-order Delaunay mosaics and alpha shapes. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00453-022-01027-6\">https://doi.org/10.1007/s00453-022-01027-6</a>"},"date_created":"2022-09-11T22:01:57Z","type":"journal_article","day":"01","title":"A simple algorithm for higher-order Delaunay mosaics and alpha shapes","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"scopus_import":"1","department":[{"_id":"HeEd"}],"date_published":"2023-01-01T00:00:00Z","status":"public","_id":"12086","abstract":[{"text":"We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets.","lang":"eng"}],"file_date_updated":"2023-01-20T10:02:48Z","has_accepted_license":"1","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."},{"type":"journal_article","date_created":"2023-01-16T10:04:06Z","citation":{"short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete &#38; Computational Geometry 69 (2023) 156–191.","apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., &#38; Wintraecken, M. (2023). Local criteria for triangulating general manifolds. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00431-7\">https://doi.org/10.1007/s00454-022-00431-7</a>","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for triangulating general manifolds,” <i>Discrete &#38; Computational Geometry</i>, vol. 69. Springer Nature, pp. 156–191, 2023.","mla":"Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.” <i>Discrete &#38; Computational Geometry</i>, vol. 69, Springer Nature, 2023, pp. 156–91, doi:<a href=\"https://doi.org/10.1007/s00454-022-00431-7\">10.1007/s00454-022-00431-7</a>.","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken. “Local Criteria for Triangulating General Manifolds.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-022-00431-7\">https://doi.org/10.1007/s00454-022-00431-7</a>.","ama":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating general manifolds. <i>Discrete &#38; Computational Geometry</i>. 2023;69:156-191. doi:<a href=\"https://doi.org/10.1007/s00454-022-00431-7\">10.1007/s00454-022-00431-7</a>","ista":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete &#38; Computational Geometry. 69, 156–191."},"isi":1,"scopus_import":"1","day":"01","title":"Local criteria for triangulating general manifolds","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"status":"public","department":[{"_id":"HeEd"}],"date_published":"2023-01-01T00:00:00Z","file_date_updated":"2023-02-02T11:01:10Z","has_accepted_license":"1","acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). Arijit Ghosh is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015). Part of this work was done when Arijit Ghosh was a Researcher at Max-Planck-Institute for Informatics, Germany, supported by the IndoGerman Max Planck Center for Computer Science (IMPECS). Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Austrian Science Fund (FWF): M-3073. A part of the results described in this paper were presented at SoCG 2018 and in [3]. \r\nOpen access funding provided by the Austrian Science Fund (FWF).","_id":"12287","abstract":[{"lang":"eng","text":"We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use."}],"year":"2023","volume":69,"page":"156-191","external_id":{"isi":["000862193600001"]},"file":[{"date_updated":"2023-02-02T11:01:10Z","success":1,"checksum":"46352e0ee71e460848f88685ca852681","file_id":"12488","file_size":582850,"file_name":"2023_DiscreteCompGeometry_Boissonnat.pdf","creator":"dernst","relation":"main_file","content_type":"application/pdf","access_level":"open_access","date_created":"2023-02-02T11:01:10Z"}],"oa_version":"Published Version","date_updated":"2025-04-14T07:44:00Z","quality_controlled":"1","publisher":"Springer Nature","publication":"Discrete & Computational Geometry","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"article_processing_charge":"No","corr_author":"1","fulldoi":"https://doi.org/10.1007/s00454-022-00431-7","doi":"10.1007/s00454-022-00431-7","intvolume":"        69","publication_status":"published","ddc":["510"],"month":"01","article_type":"original","language":[{"iso":"eng"}],"ec_funded":1,"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"author":[{"full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel","last_name":"Boissonnat"},{"first_name":"Ramsay","last_name":"Dyer","full_name":"Dyer, Ramsay"},{"last_name":"Ghosh","first_name":"Arijit","full_name":"Ghosh, Arijit"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}]},{"doi":"10.1021/acs.jcim.2c01346","fulldoi":"https://doi.org/10.1021/acs.jcim.2c01346","corr_author":"1","article_processing_charge":"No","pmid":1,"publication_identifier":{"eissn":["1549-960X"],"issn":["1549-9596"]},"oa":1,"author":[{"first_name":"Patrice","last_name":"Koehl","full_name":"Koehl, Patrice"},{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"ec_funded":1,"language":[{"iso":"eng"}],"article_type":"original","publication_status":"published","month":"02","intvolume":"        63","ddc":["510","540"],"volume":63,"external_id":{"pmid":["36638318"],"isi":["000920370700001"]},"file":[{"success":1,"checksum":"7d20562269edff1e31b9d6019d4983b0","file_id":"14070","file_size":8069223,"date_updated":"2023-08-16T12:21:13Z","date_created":"2023-08-16T12:21:13Z","file_name":"2023_JCIM_Koehl.pdf","content_type":"application/pdf","creator":"dernst","relation":"main_file","access_level":"open_access"}],"page":"973-985","year":"2023","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"publication":"Journal of Chemical Information and Modeling","publisher":"American Chemical Society","date_updated":"2025-04-15T07:16:52Z","quality_controlled":"1","oa_version":"Published Version","date_published":"2023-02-13T00:00:00Z","department":[{"_id":"HeEd"}],"status":"public","abstract":[{"lang":"eng","text":"Geometry is crucial in our efforts to comprehend the structures and dynamics of biomolecules. For example, volume, surface area, and integrated mean and Gaussian curvature of the union of balls representing a molecule are used to quantify its interactions with the water surrounding it in the morphometric implicit solvent models. The Alpha Shape theory provides an accurate and reliable method for computing these geometric measures. In this paper, we derive homogeneous formulas for the expressions of these measures and their derivatives with respect to the atomic coordinates, and we provide algorithms that implement them into a new software package, AlphaMol. The only variables in these formulas are the interatomic distances, making them insensitive to translations and rotations. AlphaMol includes a sequential algorithm and a parallel algorithm. In the parallel version, we partition the atoms of the molecule of interest into 3D rectangular blocks, using a kd-tree algorithm. We then apply the sequential algorithm of AlphaMol to each block, augmented by a buffer zone to account for atoms whose ball representations may partially cover the block. The current parallel version of AlphaMol leads to a 20-fold speed-up compared to an independent serial implementation when using 32 processors. For instance, it takes 31 s to compute the geometric measures and derivatives of each atom in a viral capsid with more than 26 million atoms on 32 Intel processors running at 2.7 GHz. The presence of the buffer zones, however, leads to redundant computations, which ultimately limit the impact of using multiple processors. AlphaMol is available as an OpenSource software."}],"_id":"12544","acknowledgement":"P.K. acknowledges support from the University of California Multicampus Research Programs and Initiatives (Grant No. M21PR3267) and from the NSF (Grant No.1760485). H.E. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program, 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.\r\nOpen Access is funded by the Austrian Science Fund (FWF).","file_date_updated":"2023-08-16T12:21:13Z","has_accepted_license":"1","citation":{"mla":"Koehl, Patrice, et al. “Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.” <i>Journal of Chemical Information and Modeling</i>, vol. 63, no. 3, American Chemical Society, 2023, pp. 973–85, doi:<a href=\"https://doi.org/10.1021/acs.jcim.2c01346\">10.1021/acs.jcim.2c01346</a>.","short":"P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and Modeling 63 (2023) 973–985.","ieee":"P. Koehl, A. Akopyan, and H. Edelsbrunner, “Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives,” <i>Journal of Chemical Information and Modeling</i>, vol. 63, no. 3. American Chemical Society, pp. 973–985, 2023.","apa":"Koehl, P., Akopyan, A., &#38; Edelsbrunner, H. (2023). Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. <i>Journal of Chemical Information and Modeling</i>. American Chemical Society. <a href=\"https://doi.org/10.1021/acs.jcim.2c01346\">https://doi.org/10.1021/acs.jcim.2c01346</a>","chicago":"Koehl, Patrice, Arseniy Akopyan, and Herbert Edelsbrunner. “Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.” <i>Journal of Chemical Information and Modeling</i>. American Chemical Society, 2023. <a href=\"https://doi.org/10.1021/acs.jcim.2c01346\">https://doi.org/10.1021/acs.jcim.2c01346</a>.","ama":"Koehl P, Akopyan A, Edelsbrunner H. Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. <i>Journal of Chemical Information and Modeling</i>. 2023;63(3):973-985. doi:<a href=\"https://doi.org/10.1021/acs.jcim.2c01346\">10.1021/acs.jcim.2c01346</a>","ista":"Koehl P, Akopyan A, Edelsbrunner H. 2023. Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical Information and Modeling. 63(3), 973–985."},"date_created":"2023-02-12T23:00:59Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives","day":"13","issue":"3","scopus_import":"1","isi":1},{"publisher":"Springer Nature","publication":"Discrete and Computational Geometry","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9605"}]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa_version":"Published Version","quality_controlled":"1","date_updated":"2025-07-10T12:01:57Z","volume":70,"page":"376-405","file":[{"date_updated":"2023-03-07T14:40:14Z","checksum":"71ce7e59f7ee4620acc704fecca620c2","file_id":"12715","success":1,"file_size":1359323,"file_name":"2023_DisCompGeo_Corbet.pdf","access_level":"open_access","relation":"main_file","creator":"cchlebak","content_type":"application/pdf","date_created":"2023-03-07T14:40:14Z"}],"external_id":{"arxiv":["2103.07823"],"pmid":["37581017"],"isi":["000936496800001"]},"year":"2023","language":[{"iso":"eng"}],"author":[{"last_name":"Corbet","first_name":"René","full_name":"Corbet, René"},{"full_name":"Kerber, Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","last_name":"Kerber","orcid":"0000-0002-8030-9299"},{"first_name":"Michael","last_name":"Lesnick","full_name":"Lesnick, Michael"},{"full_name":"Osang, Georg F","last_name":"Osang","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"month":"09","ddc":["000"],"intvolume":"        70","publication_status":"published","article_type":"original","doi":"10.1007/s00454-022-00476-8","oa":1,"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"pmid":1,"article_processing_charge":"Yes (via OA deal)","arxiv":1,"fulldoi":"https://doi.org/10.1007/s00454-022-00476-8","day":"01","title":"Computing the multicover bifiltration","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"scopus_import":"1","citation":{"mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” <i>Discrete and Computational Geometry</i>, vol. 70, Springer Nature, 2023, pp. 376–405, doi:<a href=\"https://doi.org/10.1007/s00454-022-00476-8\">10.1007/s00454-022-00476-8</a>.","ieee":"R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” <i>Discrete and Computational Geometry</i>, vol. 70. Springer Nature, pp. 376–405, 2023.","apa":"Corbet, R., Kerber, M., Lesnick, M., &#38; Osang, G. F. (2023). Computing the multicover bifiltration. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00476-8\">https://doi.org/10.1007/s00454-022-00476-8</a>","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, Discrete and Computational Geometry 70 (2023) 376–405.","ama":"Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. <i>Discrete and Computational Geometry</i>. 2023;70:376-405. doi:<a href=\"https://doi.org/10.1007/s00454-022-00476-8\">10.1007/s00454-022-00476-8</a>","chicago":"Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-022-00476-8\">https://doi.org/10.1007/s00454-022-00476-8</a>.","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2023. Computing the multicover bifiltration. Discrete and Computational Geometry. 70, 376–405."},"date_created":"2023-03-05T23:01:06Z","type":"journal_article","_id":"12709","abstract":[{"text":"Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness.","lang":"eng"}],"has_accepted_license":"1","file_date_updated":"2023-03-07T14:40:14Z","acknowledgement":"We thank the anonymous reviewers for many helpful comments and suggestions, which led to substantial improvements of the paper. The first two authors were supported by the Austrian Science Fund (FWF) grant number P 29984-N35 and W1230. The first author was partly supported by an Austrian Marshall Plan Scholarship, and by the Brummer & Partners MathDataLab. A conference version of this paper was presented at the 37th International Symposium on Computational Geometry (SoCG 2021). Open access funding provided by the Royal Institute of Technology.","department":[{"_id":"HeEd"}],"date_published":"2023-09-01T00:00:00Z","status":"public"}]