[{"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"name":"Persistent Homology, Algorithms and Stochastic Geometry","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"}],"quality_controlled":"1","type":"conference","citation":{"ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells of order-k voronoi tessellations in ℝ<sup>3</sup> with morse theory. In: <i>Leibniz International Proceedings in Informatics</i>. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.16\">10.4230/LIPIcs.SoCG.2021.16</a>","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting cells of order-k voronoi tessellations in ℝ<sup>3</sup> with morse theory. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 16.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ<sup>3</sup> with Morse Theory.” In <i>Leibniz International Proceedings in Informatics</i>, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.16\">https://doi.org/10.4230/LIPIcs.SoCG.2021.16</a>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2021). Counting cells of order-k voronoi tessellations in ℝ<sup>3</sup> with morse theory. In <i>Leibniz International Proceedings in Informatics</i> (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.16\">https://doi.org/10.4230/LIPIcs.SoCG.2021.16</a>","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting cells of order-k voronoi tessellations in ℝ<sup>3</sup> with morse theory,” in <i>Leibniz International Proceedings in Informatics</i>, Online, 2021, vol. 189.","mla":"Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in ℝ<sup>3</sup> with Morse Theory.” <i>Leibniz International Proceedings in Informatics</i>, vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.16\">10.4230/LIPIcs.SoCG.2021.16</a>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"16","has_accepted_license":"1","publication_identifier":{"isbn":["9783959771849"],"issn":["1868-8969"]},"conference":{"end_date":"2021-06-11","location":"Online","start_date":"2021-06-07","name":"SoCG: International Symposium on Computational Geometry"},"status":"public","ec_funded":1,"file":[{"creator":"asandaue","success":1,"file_name":"2021_LIPIcs_Biswas.pdf","content_type":"application/pdf","checksum":"22b11a719018b22ecba2471b51f2eb40","relation":"main_file","file_id":"9611","date_updated":"2021-06-28T13:11:39Z","access_level":"open_access","file_size":727817,"date_created":"2021-06-28T13:11:39Z"}],"file_date_updated":"2021-06-28T13:11:39Z","volume":189,"alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","_id":"9604","author":[{"full_name":"Biswas, Ranita","last_name":"Biswas","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890"},{"orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Morteza","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"date_published":"2021-06-02T00:00:00Z","year":"2021","day":"02","oa":1,"intvolume":"       189","month":"06","ddc":["516"],"date_created":"2021-06-27T22:01:48Z","publication":"Leibniz International Proceedings in Informatics","doi":"10.4230/LIPIcs.SoCG.2021.16","abstract":[{"text":"Generalizing Lee’s inductive argument for counting the cells of higher order Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse theoretic quantities for piecewise constant functions on planar arrangements. Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for 1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s first k-1 sublevel sets. We get similar expressions for the vertices, edges, and polygons of the order-k Voronoi tessellation.","lang":"eng"}],"title":"Counting cells of order-k voronoi tessellations in ℝ<sup>3</sup> with morse theory","scopus_import":"1","publication_status":"published","date_updated":"2025-07-10T12:01:56Z","language":[{"iso":"eng"}],"oa_version":"Published Version"},{"has_accepted_license":"1","publication_identifier":{"isbn":["9783959771849"],"issn":["1868-8969"]},"related_material":{"link":[{"url":"https://arxiv.org/abs/2103.07823","relation":"extended_version"}],"record":[{"id":"12709","status":"public","relation":"later_version"}]},"article_number":"27","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"citation":{"chicago":"Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” In <i>Leibniz International Proceedings in Informatics</i>, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.27\">https://doi.org/10.4230/LIPIcs.SoCG.2021.27</a>.","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","ieee":"R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” in <i>Leibniz International Proceedings in Informatics</i>, Online, 2021, vol. 189.","apa":"Corbet, R., Kerber, M., Lesnick, M., &#38; Osang, G. F. (2021). Computing the multicover bifiltration. In <i>Leibniz International Proceedings in Informatics</i> (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.27\">https://doi.org/10.4230/LIPIcs.SoCG.2021.27</a>","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2021. Computing the multicover bifiltration. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 27.","ama":"Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. In: <i>Leibniz International Proceedings in Informatics</i>. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.27\">10.4230/LIPIcs.SoCG.2021.27</a>","mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” <i>Leibniz International Proceedings in Informatics</i>, vol. 189, 27, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.27\">10.4230/LIPIcs.SoCG.2021.27</a>."},"quality_controlled":"1","type":"conference","date_published":"2021-06-02T00:00:00Z","day":"02","year":"2021","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"René","last_name":"Corbet","full_name":"Corbet, René"},{"first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"},{"full_name":"Lesnick, Michael","last_name":"Lesnick","first_name":"Michael"},{"last_name":"Osang","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"_id":"9605","article_processing_charge":"No","alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","file_date_updated":"2021-06-28T12:40:47Z","volume":189,"status":"public","file":[{"checksum":"0de217501e7ba8b267d58deed0d51761","content_type":"application/pdf","file_name":"2021_LIPIcs_Corbet.pdf","creator":"cziletti","success":1,"file_id":"9610","relation":"main_file","access_level":"open_access","date_updated":"2021-06-28T12:40:47Z","file_size":"1367983","date_created":"2021-06-28T12:40:47Z"}],"conference":{"location":"Online","end_date":"2021-06-11","start_date":"2021-06-07","name":"SoCG: International Symposium on Computational Geometry"},"arxiv":1,"acknowledgement":"The authors want to thank the reviewers for many helpful comments and suggestions.","date_created":"2021-06-27T22:01:49Z","publication":"Leibniz International Proceedings in Informatics","month":"06","ddc":["516"],"intvolume":"       189","oa":1,"language":[{"iso":"eng"}],"oa_version":"Published Version","publication_status":"published","date_updated":"2025-07-10T12:01:57Z","scopus_import":"1","external_id":{"arxiv":["2103.07823"]},"abstract":[{"lang":"eng","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. "}],"title":"Computing the multicover bifiltration","doi":"10.4230/LIPIcs.SoCG.2021.27"},{"month":"07","ddc":["006"],"isi":1,"date_created":"2021-08-08T22:01:28Z","publication":"PLoS ONE","oa":1,"intvolume":"        16","scopus_import":"1","date_updated":"2026-04-02T13:56:42Z","publication_status":"published","language":[{"iso":"eng"}],"oa_version":"Published Version","doi":"10.1371/journal.pone.0253851","abstract":[{"text":"Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent homology is a novel data analysis tool developed in the recent decades that is rooted at algebraic topology. The Topological Data Analysis (TDA) approach focuses on examining the shape of the data in terms of connectedness and holes, and has recently proved to be very effective in various fields of research. In this paper we propose the use of persistent homology to the hrv analysis. We recall selected topological descriptors used in the literature and we introduce some new topological descriptors that reflect the specificity of hrv, and we discuss their relation to the standard hrv measures. In particular, we show that this novel approach provides a collection of indices that might be at least as useful as the classical parameters in differentiating between series of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering from a stroke episode.","lang":"eng"}],"title":"Persistent homology as a new method of the assessment of heart rate variability","external_id":{"pmid":["34292957"],"isi":["000678124900050"]},"article_number":"e0253851","issue":"7","has_accepted_license":"1","publication_identifier":{"eissn":["1932-6203"]},"quality_controlled":"1","type":"journal_article","pmid":1,"citation":{"ieee":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, and K. Narkiewicz, “Persistent homology as a new method of the assessment of heart rate variability,” <i>PLoS ONE</i>, vol. 16, no. 7. Public Library of Science, 2021.","apa":"Graff, G., Graff, B., Pilarczyk, P., Jablonski, G., Gąsecki, D., &#38; Narkiewicz, K. (2021). Persistent homology as a new method of the assessment of heart rate variability. <i>PLoS ONE</i>. Public Library of Science. <a href=\"https://doi.org/10.1371/journal.pone.0253851\">https://doi.org/10.1371/journal.pone.0253851</a>","short":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, K. Narkiewicz, PLoS ONE 16 (2021).","chicago":"Graff, Grzegorz, Beata Graff, Pawel Pilarczyk, Grzegorz Jablonski, Dariusz Gąsecki, and Krzysztof Narkiewicz. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” <i>PLoS ONE</i>. Public Library of Science, 2021. <a href=\"https://doi.org/10.1371/journal.pone.0253851\">https://doi.org/10.1371/journal.pone.0253851</a>.","ista":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. 2021. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 16(7), e0253851.","ama":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. Persistent homology as a new method of the assessment of heart rate variability. <i>PLoS ONE</i>. 2021;16(7). doi:<a href=\"https://doi.org/10.1371/journal.pone.0253851\">10.1371/journal.pone.0253851</a>","mla":"Graff, Grzegorz, et al. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” <i>PLoS ONE</i>, vol. 16, no. 7, e0253851, Public Library of Science, 2021, doi:<a href=\"https://doi.org/10.1371/journal.pone.0253851\">10.1371/journal.pone.0253851</a>."},"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publisher":"Public Library of Science","author":[{"last_name":"Graff","full_name":"Graff, Grzegorz","first_name":"Grzegorz"},{"last_name":"Graff","full_name":"Graff, Beata","first_name":"Beata"},{"first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel"},{"first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","last_name":"Jablonski"},{"full_name":"Gąsecki, Dariusz","last_name":"Gąsecki","first_name":"Dariusz"},{"last_name":"Narkiewicz","full_name":"Narkiewicz, Krzysztof","first_name":"Krzysztof"}],"_id":"9821","article_processing_charge":"Yes","department":[{"_id":"HeEd"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_published":"2021-07-01T00:00:00Z","day":"01","year":"2021","acknowledgement":"We express our gratitude to the anonymous referees who provided constructive comments that helped us improve the quality of the paper.","status":"public","file":[{"relation":"main_file","file_id":"9832","success":1,"creator":"asandaue","file_name":"2021_PLoSONE_Graff.pdf","checksum":"0277aa155d5db1febd2cb384768bba5f","content_type":"application/pdf","date_created":"2021-08-09T09:25:41Z","file_size":2706919,"date_updated":"2021-08-09T09:25:41Z","access_level":"open_access"}],"file_date_updated":"2021-08-09T09:25:41Z","volume":16},{"scopus_import":"1","publication_status":"published","date_updated":"2026-04-07T12:54:09Z","oa_version":"Published Version","language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.SoCG.2021.32","abstract":[{"lang":"eng","text":"Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction."}],"title":"The density fingerprint of a periodic point set","ddc":["004","516"],"month":"06","publication":"37th International Symposium on Computational Geometry (SoCG 2021)","page":"32:1-32:16","date_created":"2021-04-22T08:09:58Z","oa":1,"intvolume":"       189","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","alternative_title":["LIPIcs"],"_id":"9345","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","last_name":"Heiss","full_name":"Heiss, Teresa"},{"full_name":" Kurlin , Vitaliy","last_name":" Kurlin ","first_name":"Vitaliy"},{"last_name":"Smith","full_name":"Smith, Philip","first_name":"Philip"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"article_processing_charge":"No","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","department":[{"_id":"HeEd"}],"day":"02","year":"2021","date_published":"2021-06-02T00:00:00Z","conference":{"start_date":"2021-06-07","name":"SoCG: Symposium on Computational Geometry","end_date":"2021-06-11","location":"Virtual"},"acknowledgement":"The authors thank Janos Pach for insightful discussions on the topic of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.","file":[{"date_updated":"2021-04-22T08:08:14Z","access_level":"open_access","file_size":3117435,"date_created":"2021-04-22T08:08:14Z","creator":"mwintrae","success":1,"content_type":"application/pdf","file_name":"df_socg_final_version.pdf","checksum":"1787baef1523d6d93753b90d0c109a6d","relation":"main_file","file_id":"9346"}],"status":"public","ec_funded":1,"file_date_updated":"2021-04-22T08:08:14Z","volume":189,"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"18667"}]},"publication_identifier":{"issn":["1868-8969"]},"has_accepted_license":"1","type":"conference","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"name":"Persistent Homology, Algorithms and Stochastic Geometry","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"},{"_id":"25C5A090-B435-11E9-9278-68D0E5697425","name":"Synaptic communication in neuronal microcircuits","call_identifier":"FWF","grant_number":"Z00312"},{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"}],"quality_controlled":"1","citation":{"mla":"Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>, vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">10.4230/LIPIcs.SoCG.2021.32</a>.","ista":"Edelsbrunner H, Heiss T,  Kurlin  V, Smith P, Wintraecken M. 2021. The density fingerprint of a periodic point set. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol. 189, 32:1-32:16.","ama":"Edelsbrunner H, Heiss T,  Kurlin  V, Smith P, Wintraecken M. The density fingerprint of a periodic point set. In: <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">10.4230/LIPIcs.SoCG.2021.32</a>","ieee":"H. Edelsbrunner, T. Heiss, V.  Kurlin , P. Smith, and M. Wintraecken, “The density fingerprint of a periodic point set,” in <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>, Virtual, 2021, vol. 189, p. 32:1-32:16.","apa":"Edelsbrunner, H., Heiss, T.,  Kurlin , V., Smith, P., &#38; Wintraecken, M. (2021). The density fingerprint of a periodic point set. In <i>37th International Symposium on Computational Geometry (SoCG 2021)</i> (Vol. 189, p. 32:1-32:16). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">https://doi.org/10.4230/LIPIcs.SoCG.2021.32</a>","short":"H. Edelsbrunner, T. Heiss, V.  Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.","chicago":"Edelsbrunner, Herbert, Teresa Heiss, Vitaliy  Kurlin , Philip Smith, and Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>, 189:32:1-32:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">https://doi.org/10.4230/LIPIcs.SoCG.2021.32</a>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"}},{"OA_place":"publisher","doi":"10.15479/AT:ISTA:9056","abstract":[{"lang":"eng","text":"In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations. The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,\r\nand thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics. We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss the implications on persistence for periodic data sets."}],"title":"Multi-cover persistence and Delaunay mosaics","degree_awarded":"PhD","date_updated":"2026-04-08T07:01:30Z","publication_status":"published","language":[{"iso":"eng"}],"oa_version":"Published Version","oa":1,"supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"corr_author":"1","month":"02","ddc":["006","514","516"],"date_created":"2021-02-02T14:11:06Z","page":"134","file_date_updated":"2021-02-03T10:37:28Z","status":"public","file":[{"content_type":"application/zip","file_name":"thesis_source.zip","checksum":"bcf27986147cab0533b6abadd74e7629","creator":"patrickd","file_id":"9063","relation":"source_file","access_level":"closed","date_updated":"2021-02-03T10:37:28Z","file_size":13446994,"date_created":"2021-02-02T14:09:25Z"},{"file_id":"9064","relation":"main_file","content_type":"application/pdf","checksum":"9cc8af266579a464385bbe2aff6af606","file_name":"thesis_pdfA2b.pdf","creator":"patrickd","success":1,"date_created":"2021-02-02T14:09:18Z","file_size":5210329,"access_level":"open_access","date_updated":"2021-02-02T14:09:18Z"}],"_id":"9056","author":[{"full_name":"Osang, Georg F","last_name":"Osang","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116"}],"article_processing_charge":"No","alternative_title":["ISTA Thesis"],"publisher":"Institute of Science and Technology Austria","date_published":"2021-02-01T00:00:00Z","day":"01","year":"2021","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"place":"Klosterneuburg","type":"dissertation","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"citation":{"apa":"Osang, G. F. (2021). <i>Multi-cover persistence and Delaunay mosaics</i>. Institute of Science and Technology Austria, Klosterneuburg. <a href=\"https://doi.org/10.15479/AT:ISTA:9056\">https://doi.org/10.15479/AT:ISTA:9056</a>","ieee":"G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of Science and Technology Austria, Klosterneuburg, 2021.","short":"G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science and Technology Austria, 2021.","chicago":"Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/AT:ISTA:9056\">https://doi.org/10.15479/AT:ISTA:9056</a>.","ista":"Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg: Institute of Science and Technology Austria.","ama":"Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:9056\">10.15479/AT:ISTA:9056</a>","mla":"Osang, Georg F. <i>Multi-Cover Persistence and Delaunay Mosaics</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:9056\">10.15479/AT:ISTA:9056</a>."},"related_material":{"record":[{"id":"187","status":"public","relation":"part_of_dissertation"},{"id":"8703","relation":"part_of_dissertation","status":"public"}]},"has_accepted_license":"1","publication_identifier":{"issn":["2663-337X"]}},{"doi":"10.1016/j.comgeo.2020.101700","title":"Folding polyominoes with holes into a cube","abstract":[{"text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.","lang":"eng"}],"external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"scopus_import":"1","date_updated":"2026-04-16T09:14:31Z","publication_status":"published","language":[{"iso":"eng"}],"oa_version":"Preprint","oa":1,"intvolume":"        93","month":"02","isi":1,"corr_author":"1","date_created":"2020-08-30T22:01:09Z","publication":"Computational Geometry: Theory and Applications","arxiv":1,"acknowledgement":"This research was performed in part at the 33rd Bellairs Winter Workshop on Computational Geometry. We thank all other participants for a fruitful atmosphere. H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","status":"public","volume":93,"publisher":"Elsevier","article_processing_charge":"No","_id":"8317","author":[{"first_name":"Oswin","full_name":"Aichholzer, Oswin","last_name":"Aichholzer"},{"first_name":"Hugo A.","full_name":"Akitaya, Hugo A.","last_name":"Akitaya"},{"first_name":"Kenneth C.","last_name":"Cheung","full_name":"Cheung, Kenneth C."},{"full_name":"Demaine, Erik D.","last_name":"Demaine","first_name":"Erik D."},{"last_name":"Demaine","full_name":"Demaine, Martin L.","first_name":"Martin L."},{"first_name":"Sándor P.","last_name":"Fekete","full_name":"Fekete, Sándor P."},{"first_name":"Linda","last_name":"Kleist","full_name":"Kleist, Linda"},{"first_name":"Irina","full_name":"Kostitsyna, Irina","last_name":"Kostitsyna"},{"first_name":"Maarten","full_name":"Löffler, Maarten","last_name":"Löffler"},{"orcid":"0000-0002-6660-1322","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","full_name":"Masárová, Zuzana"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"first_name":"Christiane","full_name":"Schmidt, Christiane","last_name":"Schmidt"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"HeEd"}],"date_published":"2021-02-01T00:00:00Z","day":"01","year":"2021","quality_controlled":"1","project":[{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"type":"journal_article","citation":{"mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” <i>Computational Geometry: Theory and Applications</i>, vol. 93, 101700, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">10.1016/j.comgeo.2020.101700</a>.","ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2021. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 93, 101700.","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. <i>Computational Geometry: Theory and Applications</i>. 2021;93. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">10.1016/j.comgeo.2020.101700</a>","ieee":"O. Aichholzer <i>et al.</i>, “Folding polyominoes with holes into a cube,” <i>Computational Geometry: Theory and Applications</i>, vol. 93. Elsevier, 2021.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a cube. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">https://doi.org/10.1016/j.comgeo.2020.101700</a>","chicago":"Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">https://doi.org/10.1016/j.comgeo.2020.101700</a>.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, Computational Geometry: Theory and Applications 93 (2021)."},"article_type":"original","article_number":"101700","main_file_link":[{"url":"https://arxiv.org/abs/1910.09917v3","open_access":"1"}],"related_material":{"record":[{"id":"6989","status":"public","relation":"shorter_version"}]},"publication_identifier":{"issn":["0925-7721"],"eissn":["1879-081X"]}},{"language":[{"iso":"eng"}],"oa_version":"Preprint","publication_status":"published","date_updated":"2026-04-16T09:18:21Z","scopus_import":"1","external_id":{"arxiv":["2101.03928"],"isi":["001435069600018"]},"title":"On compatible matchings","abstract":[{"text":" matching is compatible to two or more labeled point sets of size n with labels   {1,…,n}  if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with   ⌊2n−−√⌋  edges. More generally, for any   ℓ  labeled point sets we construct compatible matchings of size   Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any   ℓ  given sets of n points there exists a labeling of each set such that the largest compatible matching has   O(n2/(ℓ+1))  edges. Finally, we show that   Θ(logn)  copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge.","lang":"eng"}],"doi":"10.1007/978-3-030-68211-8_18","date_created":"2021-03-28T22:01:41Z","publication":"15th International Conference on Algorithms and Computation","page":"221-233","month":"02","isi":1,"intvolume":"     12635","oa":1,"date_published":"2021-02-16T00:00:00Z","day":"16","year":"2021","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"article_processing_charge":"No","_id":"9296","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"full_name":"Arroyo Guevara, Alan M","last_name":"Arroyo Guevara","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","first_name":"Alan M","orcid":"0000-0003-2401-8670"},{"last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana"},{"full_name":"Parada, Irene","last_name":"Parada","first_name":"Irene"},{"last_name":"Perz","full_name":"Perz, Daniel","first_name":"Daniel"},{"full_name":"Pilz, Alexander","last_name":"Pilz","first_name":"Alexander"},{"full_name":"Tkadlec, Josef","last_name":"Tkadlec","first_name":"Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684"},{"last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit","first_name":"Birgit"}],"alternative_title":["LNCS"],"publisher":"Springer Nature","volume":12635,"status":"public","ec_funded":1,"conference":{"end_date":"2021-03-02","location":"Yangon, Myanmar","start_date":"2021-02-28","name":"WALCOM: Algorithms and Computation"},"arxiv":1,"acknowledgement":"A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783030682101"],"eisbn":["9783030682118"],"issn":["0302-9743"]},"related_material":{"record":[{"id":"11938","relation":"later_version","status":"public"}]},"main_file_link":[{"url":"https://arxiv.org/abs/2101.03928","open_access":"1"}],"citation":{"mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” <i>15th International Conference on Algorithms and Computation</i>, vol. 12635, Springer Nature, 2021, pp. 221–33, doi:<a href=\"https://doi.org/10.1007/978-3-030-68211-8_18\">10.1007/978-3-030-68211-8_18</a>.","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. In: <i>15th International Conference on Algorithms and Computation</i>. Vol 12635. Springer Nature; 2021:221-233. doi:<a href=\"https://doi.org/10.1007/978-3-030-68211-8_18\">10.1007/978-3-030-68211-8_18</a>","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol. 12635, 221–233.","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and Computation, Springer Nature, 2021, pp. 221–233.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” In <i>15th International Conference on Algorithms and Computation</i>, 12635:221–33. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/978-3-030-68211-8_18\">https://doi.org/10.1007/978-3-030-68211-8_18</a>.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In <i>15th International Conference on Algorithms and Computation</i> (Vol. 12635, pp. 221–233). Yangon, Myanmar: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-68211-8_18\">https://doi.org/10.1007/978-3-030-68211-8_18</a>","ieee":"O. Aichholzer <i>et al.</i>, “On compatible matchings,” in <i>15th International Conference on Algorithms and Computation</i>, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233."},"quality_controlled":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"},{"grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7"},{"call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23"},{"grant_number":"S11407","call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory"}],"type":"conference"},{"isi":1,"month":"05","publication":"Discrete Geometry and Mathematical Morphology","page":"152-163","date_created":"2021-08-08T22:01:29Z","intvolume":"     12708","scopus_import":"1","date_updated":"2026-04-16T09:26:30Z","publication_status":"published","oa_version":"None","language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-76657-3_10","abstract":[{"text":"We define a new compact coordinate system in which each integer triplet addresses a voxel in the BCC grid, and we investigate some of its properties. We propose a characterization of 3D discrete analytical planes with their topological features (in the Cartesian and in the new coordinate system) such as the interrelation between the thickness of the plane and the separability constraint we aim to obtain.","lang":"eng"}],"title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","external_id":{"isi":["001286400400010"]},"publication_identifier":{"isbn":["9783030766566"],"issn":["0302-9743"],"eissn":["1611-3349"]},"type":"conference","quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35"}],"citation":{"ista":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered cubic grid - coordinate system and discrete analytical plane definition. Discrete Geometry and Mathematical Morphology. DGMM: International Conference on Discrete Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163.","ama":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic grid - coordinate system and discrete analytical plane definition. In: <i>Discrete Geometry and Mathematical Morphology</i>. Vol 12708. Springer Nature; 2021:152-163. doi:<a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">10.1007/978-3-030-76657-3_10</a>","chicago":"Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” In <i>Discrete Geometry and Mathematical Morphology</i>, 12708:152–63. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">https://doi.org/10.1007/978-3-030-76657-3_10</a>.","short":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.","apa":"Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., &#38; Andres, E. (2021). Body centered cubic grid - coordinate system and discrete analytical plane definition. In <i>Discrete Geometry and Mathematical Morphology</i> (Vol. 12708, pp. 152–163). Uppsala, Sweden: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">https://doi.org/10.1007/978-3-030-76657-3_10</a>","ieee":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered cubic grid - coordinate system and discrete analytical plane definition,” in <i>Discrete Geometry and Mathematical Morphology</i>, Uppsala, Sweden, 2021, vol. 12708, pp. 152–163.","mla":"Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” <i>Discrete Geometry and Mathematical Morphology</i>, vol. 12708, Springer Nature, 2021, pp. 152–63, doi:<a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">10.1007/978-3-030-76657-3_10</a>."},"publisher":"Springer Nature","alternative_title":["LNCS"],"_id":"9824","author":[{"last_name":"Čomić","full_name":"Čomić, Lidija","first_name":"Lidija"},{"last_name":"Zrour","full_name":"Zrour, Rita","first_name":"Rita"},{"first_name":"Gaëlle","full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin"},{"full_name":"Biswas, Ranita","last_name":"Biswas","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890"},{"first_name":"Eric","full_name":"Andres, Eric","last_name":"Andres"}],"article_processing_charge":"No","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"HeEd"}],"year":"2021","day":"16","date_published":"2021-05-16T00:00:00Z","acknowledgement":"This work has been partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia through the project no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35 (RB).","conference":{"end_date":"2021-05-27","location":"Uppsala, Sweden","name":"DGMM: International Conference on Discrete Geometry and Mathematical Morphology","start_date":"2021-05-24"},"status":"public","ec_funded":1,"volume":12708},{"has_accepted_license":"1","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"issue":"4","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"citation":{"ieee":"U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient flow and homology inference for self-maps,” <i>Journal of Applied and Computational Topology</i>, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.","apa":"Bauer, U., Edelsbrunner, H., Jablonski, G., &#38; Mrozek, M. (2020). Čech-Delaunay gradient flow and homology inference for self-maps. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-020-00058-8\">https://doi.org/10.1007/s41468-020-00058-8</a>","chicago":"Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s41468-020-00058-8\">https://doi.org/10.1007/s41468-020-00058-8</a>.","short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480.","ista":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 4(4), 455–480.","ama":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. <i>Journal of Applied and Computational Topology</i>. 2020;4(4):455-480. doi:<a href=\"https://doi.org/10.1007/s41468-020-00058-8\">10.1007/s41468-020-00058-8</a>","mla":"Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” <i>Journal of Applied and Computational Topology</i>, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:<a href=\"https://doi.org/10.1007/s41468-020-00058-8\">10.1007/s41468-020-00058-8</a>."},"quality_controlled":"1","type":"journal_article","date_published":"2020-12-01T00:00:00Z","day":"01","year":"2020","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"15064","article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Bauer","full_name":"Bauer, U.","first_name":"U."},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","last_name":"Jablonski"},{"first_name":"M.","last_name":"Mrozek","full_name":"Mrozek, M."}],"publisher":"Springer Nature","volume":4,"file_date_updated":"2024-03-04T10:52:42Z","status":"public","file":[{"date_created":"2024-03-04T10:52:42Z","file_size":851190,"access_level":"open_access","date_updated":"2024-03-04T10:52:42Z","file_id":"15065","relation":"main_file","file_name":"2020_JourApplCompTopology_Bauer.pdf","content_type":"application/pdf","checksum":"eed1168b6e66cd55272c19bb7fca8a1c","creator":"dernst","success":1}],"acknowledgement":"This research has been supported by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding provided by Projekt DEAL.","date_created":"2024-03-04T10:47:49Z","publication":"Journal of Applied and Computational Topology","page":"455-480","month":"12","ddc":["500"],"intvolume":"         4","oa":1,"language":[{"iso":"eng"}],"oa_version":"Published Version","date_updated":"2024-03-04T10:54:04Z","publication_status":"published","scopus_import":"1","title":"Čech-Delaunay gradient flow and homology inference for self-maps","abstract":[{"text":"We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.","lang":"eng"}],"doi":"10.1007/s41468-020-00058-8"},{"issue":"3","main_file_link":[{"url":"https://arxiv.org/abs/1702.07513","open_access":"1"}],"publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"keyword":["General Mathematics"],"type":"journal_article","quality_controlled":"1","citation":{"mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” <i>International Mathematics Research Notices</i>, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:<a href=\"https://doi.org/10.1093/imrn/rny037\">10.1093/imrn/rny037</a>.","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” <i>International Mathematics Research Notices</i>, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020.","apa":"Akopyan, A., &#38; Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rny037\">https://doi.org/10.1093/imrn/rny037</a>","chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2020. <a href=\"https://doi.org/10.1093/imrn/rny037\">https://doi.org/10.1093/imrn/rny037</a>.","short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. <i>International Mathematics Research Notices</i>. 2020;2020(3):669-697. doi:<a href=\"https://doi.org/10.1093/imrn/rny037\">10.1093/imrn/rny037</a>"},"article_type":"original","publisher":"Oxford University Press","article_processing_charge":"No","_id":"10867","author":[{"orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"first_name":"Roman","last_name":"Karasev","full_name":"Karasev, Roman"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"day":"01","year":"2020","date_published":"2020-02-01T00:00:00Z","acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","arxiv":1,"status":"public","volume":2020,"isi":1,"month":"02","publication":"International Mathematics Research Notices","page":"669-697","date_created":"2022-03-18T11:39:30Z","oa":1,"intvolume":"      2020","scopus_import":"1","date_updated":"2023-08-24T14:19:55Z","publication_status":"published","oa_version":"Preprint","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rny037","abstract":[{"lang":"eng","text":"In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces."}],"title":"Waist of balls in hyperbolic and spherical spaces","external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]}},{"acknowledgement":"This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF).","status":"public","ec_funded":1,"file":[{"file_size":701673,"date_created":"2020-11-20T13:22:21Z","access_level":"open_access","date_updated":"2020-11-20T13:22:21Z","file_id":"8786","relation":"main_file","file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf","content_type":"application/pdf","checksum":"f8cc96e497f00c38340b5dafe0cb91d7","creator":"dernst","success":1}],"volume":64,"file_date_updated":"2020-11-20T13:22:21Z","publisher":"Springer Nature","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"last_name":"Ölsböck","full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina"}],"_id":"7666","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2020-03-20T00:00:00Z","year":"2020","day":"20","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"quality_controlled":"1","type":"journal_article","citation":{"mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” <i>Discrete and Computational Geometry</i>, vol. 64, Springer Nature, 2020, pp. 759–75, doi:<a href=\"https://doi.org/10.1007/s00454-020-00188-x\">10.1007/s00454-020-00188-x</a>.","ama":"Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. <i>Discrete and Computational Geometry</i>. 2020;64:759-775. doi:<a href=\"https://doi.org/10.1007/s00454-020-00188-x\">10.1007/s00454-020-00188-x</a>","ista":"Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775.","ieee":"H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” <i>Discrete and Computational Geometry</i>, vol. 64. Springer Nature, pp. 759–775, 2020.","apa":"Edelsbrunner, H., &#38; Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00188-x\">https://doi.org/10.1007/s00454-020-00188-x</a>","short":"H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00188-x\">https://doi.org/10.1007/s00454-020-00188-x</a>."},"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"has_accepted_license":"1","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"doi":"10.1007/s00454-020-00188-x","title":"Tri-partitions and bases of an ordered complex","abstract":[{"lang":"eng","text":"Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups."}],"external_id":{"isi":["000520918800001"]},"scopus_import":"1","publication_status":"published","date_updated":"2025-04-14T07:48:36Z","language":[{"iso":"eng"}],"oa_version":"Published Version","oa":1,"intvolume":"        64","month":"03","ddc":["510"],"isi":1,"corr_author":"1","date_created":"2020-04-19T22:00:56Z","page":"759-775","publication":"Discrete and Computational Geometry"},{"conference":{"start_date":"2020-06-22","name":"SoCG: Symposium on Computational Geometry","end_date":"2020-06-26","location":"Zürich, Switzerland"},"file":[{"file_size":1009739,"date_created":"2020-06-17T10:13:34Z","date_updated":"2020-07-14T12:48:06Z","access_level":"open_access","relation":"main_file","file_id":"7969","creator":"dernst","content_type":"application/pdf","file_name":"2020_LIPIcsSoCG_Boissonnat.pdf","checksum":"38cbfa4f5d484d267a35d44d210df044"}],"status":"public","ec_funded":1,"file_date_updated":"2020-07-14T12:48:06Z","volume":164,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","alternative_title":["LIPIcs"],"_id":"7952","author":[{"last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"year":"2020","day":"01","date_published":"2020-06-01T00:00:00Z","type":"conference","quality_controlled":"1","project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"citation":{"mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” <i>36th International Symposium on Computational Geometry</i>, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">10.4230/LIPIcs.SoCG.2020.20</a>.","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations of isomanifolds,” in <i>36th International Symposium on Computational Geometry</i>, Zürich, Switzerland, 2020, vol. 164.","apa":"Boissonnat, J.-D., &#38; Wintraecken, M. (2020). The topological correctness of PL-approximations of isomanifolds. In <i>36th International Symposium on Computational Geometry</i> (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">https://doi.org/10.4230/LIPIcs.SoCG.2020.20</a>","chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” In <i>36th International Symposium on Computational Geometry</i>, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">https://doi.org/10.4230/LIPIcs.SoCG.2020.20</a>.","short":"J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations of isomanifolds. In: <i>36th International Symposium on Computational Geometry</i>. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">10.4230/LIPIcs.SoCG.2020.20</a>","ista":"Boissonnat J-D, Wintraecken M. 2020. The topological correctness of PL-approximations of isomanifolds. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 20:1-20:18."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"20:1-20:18","related_material":{"record":[{"status":"public","relation":"later_version","id":"9649"}]},"publication_identifier":{"isbn":["978-3-95977-143-6"],"issn":["1868-8969"]},"has_accepted_license":"1","doi":"10.4230/LIPIcs.SoCG.2020.20","title":"The topological correctness of PL-approximations of isomanifolds","abstract":[{"text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine triangulation 𝒯. This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary. ","lang":"eng"}],"scopus_import":"1","publication_status":"published","date_updated":"2025-04-22T13:45:17Z","oa_version":"Published Version","language":[{"iso":"eng"}],"oa":1,"intvolume":"       164","ddc":["510"],"month":"06","corr_author":"1","publication":"36th International Symposium on Computational Geometry","date_created":"2020-06-09T07:24:11Z"},{"isi":1,"month":"06","publication":"Discrete and Computational Geometry","page":"888-917","date_created":"2020-06-14T22:00:51Z","oa":1,"intvolume":"        63","date_updated":"2025-04-15T07:16:56Z","publication_status":"published","scopus_import":"1","oa_version":"Preprint","language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00213-z","external_id":{"isi":["000538229000001"],"arxiv":["1803.06710"]},"title":"Almost all string graphs are intersection graphs of plane convex sets","abstract":[{"lang":"eng","text":"A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n→∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets."}],"issue":"4","main_file_link":[{"url":"https://arxiv.org/abs/1803.06710","open_access":"1"}],"publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"type":"journal_article","quality_controlled":"1","project":[{"grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"article_type":"original","citation":{"mla":"Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” <i>Discrete and Computational Geometry</i>, vol. 63, no. 4, Springer Nature, 2020, pp. 888–917, doi:<a href=\"https://doi.org/10.1007/s00454-020-00213-z\">10.1007/s00454-020-00213-z</a>.","short":"J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917.","chicago":"Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00213-z\">https://doi.org/10.1007/s00454-020-00213-z</a>.","apa":"Pach, J., Reed, B., &#38; Yuditsky, Y. (2020). Almost all string graphs are intersection graphs of plane convex sets. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00213-z\">https://doi.org/10.1007/s00454-020-00213-z</a>","ieee":"J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection graphs of plane convex sets,” <i>Discrete and Computational Geometry</i>, vol. 63, no. 4. Springer Nature, pp. 888–917, 2020.","ama":"Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs of plane convex sets. <i>Discrete and Computational Geometry</i>. 2020;63(4):888-917. doi:<a href=\"https://doi.org/10.1007/s00454-020-00213-z\">10.1007/s00454-020-00213-z</a>","ista":"Pach J, Reed B, Yuditsky Y. 2020. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 63(4), 888–917."},"_id":"7962","article_processing_charge":"No","author":[{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach","full_name":"Pach, János"},{"first_name":"Bruce","full_name":"Reed, Bruce","last_name":"Reed"},{"full_name":"Yuditsky, Yelena","last_name":"Yuditsky","first_name":"Yelena"}],"publisher":"Springer Nature","day":"05","year":"2020","date_published":"2020-06-05T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"arxiv":1,"volume":63,"status":"public"},{"doi":"10.1556/012.2020.57.2.1454","external_id":{"isi":["000570978400005"]},"abstract":[{"text":"Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces.","lang":"eng"}],"title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","publication_status":"published","date_updated":"2025-04-15T07:16:57Z","scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","oa":1,"intvolume":"        57","corr_author":"1","month":"07","isi":1,"ddc":["510"],"date_created":"2020-07-24T07:09:18Z","page":"193-199","publication":"Studia Scientiarum Mathematicarum Hungarica","acknowledgement":"The authors are greatly indebted to Dror Atariah, Günther Rote and John Sullivan for discussion and suggestions. The authors also thank Jean-Daniel Boissonnat, Ramsay Dyer, David de Laat and Rien van de Weijgaert for discussion. This work has been supported in part by the European Union’s Seventh Framework Programme for Research of the\r\nEuropean Commission, under FET-Open grant number 255827 (CGL Computational Geometry Learning) and ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions), the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement number 754411,and the Austrian Science Fund (FWF): Z00342 N31.","volume":57,"file_date_updated":"2020-07-24T07:09:06Z","ec_funded":1,"status":"public","file":[{"access_level":"open_access","date_updated":"2020-07-24T07:09:06Z","date_created":"2020-07-24T07:09:06Z","file_size":1476072,"file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","content_type":"application/pdf","creator":"mwintrae","file_id":"8164","relation":"main_file"}],"_id":"8163","article_processing_charge":"No","author":[{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"publisher":"Akadémiai Kiadó","date_published":"2020-07-24T00:00:00Z","year":"2020","day":"24","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF","grant_number":"Z00342"}],"quality_controlled":"1","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)"},"citation":{"apa":"Vegter, G., &#38; Wintraecken, M. (2020). Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. <i>Studia Scientiarum Mathematicarum Hungarica</i>. Akadémiai Kiadó. <a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">https://doi.org/10.1556/012.2020.57.2.1454</a>","ieee":"G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes,” <i>Studia Scientiarum Mathematicarum Hungarica</i>, vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” <i>Studia Scientiarum Mathematicarum Hungarica</i>. Akadémiai Kiadó, 2020. <a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">https://doi.org/10.1556/012.2020.57.2.1454</a>.","short":"G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199.","ista":"Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2), 193–199.","ama":"Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. <i>Studia Scientiarum Mathematicarum Hungarica</i>. 2020;57(2):193-199. doi:<a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">10.1556/012.2020.57.2.1454</a>","mla":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” <i>Studia Scientiarum Mathematicarum Hungarica</i>, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:<a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">10.1556/012.2020.57.2.1454</a>."},"issue":"2","has_accepted_license":"1","publication_identifier":{"issn":["0081-6906"],"eissn":["1588-2896"]}},{"intvolume":"        64","oa":1,"page":"571-574","publication":"Discrete and Computational Geometry","date_created":"2020-08-30T22:01:12Z","isi":1,"month":"10","corr_author":"1","title":"A farewell to Ricky Pollack","external_id":{"isi":["000561483500001"]},"doi":"10.1007/s00454-020-00237-5","oa_version":"None","language":[{"iso":"eng"}],"scopus_import":"1","date_updated":"2024-10-09T20:59:55Z","publication_status":"published","citation":{"apa":"Pach, J. (2020). A farewell to Ricky Pollack. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00237-5\">https://doi.org/10.1007/s00454-020-00237-5</a>","ieee":"J. Pach, “A farewell to Ricky Pollack,” <i>Discrete and Computational Geometry</i>, vol. 64. Springer Nature, pp. 571–574, 2020.","chicago":"Pach, János. “A Farewell to Ricky Pollack.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00237-5\">https://doi.org/10.1007/s00454-020-00237-5</a>.","short":"J. Pach, Discrete and Computational Geometry 64 (2020) 571–574.","ama":"Pach J. A farewell to Ricky Pollack. <i>Discrete and Computational Geometry</i>. 2020;64:571-574. doi:<a href=\"https://doi.org/10.1007/s00454-020-00237-5\">10.1007/s00454-020-00237-5</a>","ista":"Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574.","mla":"Pach, János. “A Farewell to Ricky Pollack.” <i>Discrete and Computational Geometry</i>, vol. 64, Springer Nature, 2020, pp. 571–74, doi:<a href=\"https://doi.org/10.1007/s00454-020-00237-5\">10.1007/s00454-020-00237-5</a>."},"article_type":"letter_note","type":"journal_article","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-020-00237-5"}],"status":"public","volume":64,"department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2020","day":"01","date_published":"2020-10-01T00:00:00Z","publisher":"Springer Nature","_id":"8323","author":[{"full_name":"Pach, János","last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"}],"article_processing_charge":"No"},{"publication_identifier":{"isbn":["9781728157511"]},"publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ","date_created":"2020-09-28T08:59:27Z","isi":1,"article_number":"9158054","month":"08","citation":{"apa":"Graff, G., Graff, B., Jablonski, G., &#38; Narkiewicz, K. (2020). The application of persistent homology in the analysis of heart rate variability. In <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>. Pisa, Italy: IEEE. <a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">https://doi.org/10.1109/ESGCO49734.2020.9158054</a>","ieee":"G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of persistent homology in the analysis of heart rate variability,” in <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>, Pisa, Italy, 2020.","short":"G. Graff, B. Graff, G. Jablonski, K. Narkiewicz, in:, 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , IEEE, 2020.","chicago":"Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” In <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>. IEEE, 2020. <a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">https://doi.org/10.1109/ESGCO49734.2020.9158054</a>.","ama":"Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent homology in the analysis of heart rate variability. In: <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>. IEEE; 2020. doi:<a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">10.1109/ESGCO49734.2020.9158054</a>","ista":"Graff G, Graff B, Jablonski G, Narkiewicz K. 2020. The application of persistent homology in the analysis of heart rate variability. 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . ESGCO: European Study Group on Cardiovascular Oscillations, 9158054.","mla":"Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>, 9158054, IEEE, 2020, doi:<a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">10.1109/ESGCO49734.2020.9158054</a>."},"type":"conference","quality_controlled":"1","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"None","year":"2020","day":"01","date_published":"2020-08-01T00:00:00Z","language":[{"iso":"eng"}],"publisher":"IEEE","scopus_import":"1","date_updated":"2023-08-22T09:33:34Z","_id":"8580","publication_status":"published","article_processing_charge":"No","author":[{"full_name":"Graff, Grzegorz","last_name":"Graff","first_name":"Grzegorz"},{"first_name":"Beata","last_name":"Graff","full_name":"Graff, Beata"},{"full_name":"Jablonski, Grzegorz","last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz","orcid":"0000-0002-3536-9866"},{"first_name":"Krzysztof","last_name":"Narkiewicz","full_name":"Narkiewicz, Krzysztof"}],"status":"public","title":"The application of persistent homology in the analysis of heart rate variability","abstract":[{"text":"We evaluate the usefulness of persistent homology in the analysis of heart rate variability. In our approach we extract several topological descriptors characterising datasets of RR-intervals, which are later used in classical machine learning algorithms. By this method we are able to differentiate the group of patients with the history of transient ischemic attack and the group of hypertensive patients.","lang":"eng"}],"external_id":{"isi":["000621172600045"]},"doi":"10.1109/ESGCO49734.2020.9158054","conference":{"end_date":"2020-07-15","location":"Pisa, Italy","start_date":"2020-07-15","name":"ESGCO: European Study Group on Cardiovascular Oscillations"}},{"publisher":"De Gruyter","_id":"9156","article_processing_charge":"No","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"day":"21","year":"2020","date_published":"2020-07-21T00:00:00Z","acknowledgement":"The authors of this paper thank Roland Roth for suggesting the analysis of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","arxiv":1,"file":[{"date_created":"2021-02-19T13:33:19Z","file_size":707452,"date_updated":"2021-02-19T13:33:19Z","access_level":"open_access","relation":"main_file","file_id":"9170","success":1,"creator":"dernst","file_name":"2020_CompMathBiophysics_Akopyan.pdf","checksum":"ca43a7440834eab6bbea29c59b56ef3a","content_type":"application/pdf"}],"ec_funded":1,"status":"public","file_date_updated":"2021-02-19T13:33:19Z","volume":8,"issue":"1","publication_identifier":{"issn":["2544-7297"]},"has_accepted_license":"1","type":"journal_article","quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"citation":{"chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/cmb-2020-0101\">https://doi.org/10.1515/cmb-2020-0101</a>.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative of a space-filling diagram,” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.","apa":"Akopyan, A., &#38; Edelsbrunner, H. (2020). The weighted Gaussian curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. De Gruyter. <a href=\"https://doi.org/10.1515/cmb-2020-0101\">https://doi.org/10.1515/cmb-2020-0101</a>","ama":"Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. 2020;8(1):74-88. doi:<a href=\"https://doi.org/10.1515/cmb-2020-0101\">10.1515/cmb-2020-0101</a>","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:<a href=\"https://doi.org/10.1515/cmb-2020-0101\">10.1515/cmb-2020-0101</a>."},"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"scopus_import":"1","date_updated":"2025-04-14T07:48:34Z","publication_status":"published","oa_version":"Published Version","language":[{"iso":"eng"}],"doi":"10.1515/cmb-2020-0101","title":"The weighted Gaussian curvature derivative of a space-filling diagram","abstract":[{"text":"The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.","lang":"eng"}],"external_id":{"arxiv":["1908.06777"]},"ddc":["510"],"month":"07","corr_author":"1","page":"74-88","publication":"Computational and Mathematical Biophysics","date_created":"2021-02-17T15:12:44Z","oa":1,"intvolume":"         8"},{"abstract":[{"lang":"eng","text":"Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy."}],"title":"The weighted mean curvature derivative of a space-filling diagram","doi":"10.1515/cmb-2020-0100","oa_version":"Published Version","language":[{"iso":"eng"}],"date_updated":"2025-04-14T07:48:35Z","publication_status":"published","intvolume":"         8","oa":1,"page":"51-67","publication":"Computational and Mathematical Biophysics","date_created":"2021-02-17T15:13:01Z","corr_author":"1","ddc":["510"],"month":"06","volume":8,"file_date_updated":"2021-02-19T13:56:24Z","file":[{"file_name":"2020_CompMathBiophysics_Akopyan2.pdf","checksum":"cea41de9937d07a3b927d71ee8b4e432","content_type":"application/pdf","creator":"dernst","success":1,"file_id":"9171","relation":"main_file","access_level":"open_access","date_updated":"2021-02-19T13:56:24Z","date_created":"2021-02-19T13:56:24Z","file_size":562359}],"status":"public","ec_funded":1,"acknowledgement":"The authors of this paper thank Roland Roth for suggesting the analysis of the weighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations and for his continued encouragement. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","year":"2020","day":"20","date_published":"2020-06-20T00:00:00Z","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"_id":"9157","article_processing_charge":"No","publisher":"De Gruyter","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"citation":{"mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:<a href=\"https://doi.org/10.1515/cmb-2020-0100\">10.1515/cmb-2020-0100</a>.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","ama":"Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. 2020;8(1):51-67. doi:<a href=\"https://doi.org/10.1515/cmb-2020-0100\">10.1515/cmb-2020-0100</a>","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67.","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/cmb-2020-0100\">https://doi.org/10.1515/cmb-2020-0100</a>.","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of a space-filling diagram,” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1. De Gruyter, pp. 51–67, 2020.","apa":"Akopyan, A., &#38; Edelsbrunner, H. (2020). The weighted mean curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. De Gruyter. <a href=\"https://doi.org/10.1515/cmb-2020-0100\">https://doi.org/10.1515/cmb-2020-0100</a>"},"type":"journal_article","quality_controlled":"1","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"publication_identifier":{"issn":["2544-7297"]},"has_accepted_license":"1","issue":"1"},{"acknowledgement":"This work has been partially supported by the European Research Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. ","file_date_updated":"2021-03-22T08:56:37Z","volume":4,"file":[{"relation":"main_file","file_id":"9272","creator":"dernst","success":1,"checksum":"4a1043fa0548a725d464017fe2483ce0","file_name":"2020_MathMorpholTheoryAppl_Biswas.pdf","content_type":"application/pdf","file_size":3668725,"date_created":"2021-03-22T08:56:37Z","date_updated":"2021-03-22T08:56:37Z","access_level":"open_access"}],"ec_funded":1,"status":"public","_id":"9249","author":[{"full_name":"Biswas, Ranita","last_name":"Biswas","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890"},{"full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin","first_name":"Gaëlle"},{"full_name":"Zrour, Rita","last_name":"Zrour","first_name":"Rita"},{"first_name":"Eric","last_name":"Andres","full_name":"Andres, Eric"}],"article_processing_charge":"No","publisher":"De Gruyter","year":"2020","day":"17","date_published":"2020-11-17T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"type":"journal_article","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"quality_controlled":"1","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"citation":{"ama":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic dodecahedron grid. <i>Mathematical Morphology - Theory and Applications</i>. 2020;4(1):143-158. doi:<a href=\"https://doi.org/10.1515/mathm-2020-0106\">10.1515/mathm-2020-0106</a>","ista":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 4(1), 143–158.","ieee":"R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects in rhombic dodecahedron grid,” <i>Mathematical Morphology - Theory and Applications</i>, vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.","apa":"Biswas, R., Largeteau-Skapin, G., Zrour, R., &#38; Andres, E. (2020). Digital objects in rhombic dodecahedron grid. <i>Mathematical Morphology - Theory and Applications</i>. De Gruyter. <a href=\"https://doi.org/10.1515/mathm-2020-0106\">https://doi.org/10.1515/mathm-2020-0106</a>","short":"R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.","chicago":"Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital Objects in Rhombic Dodecahedron Grid.” <i>Mathematical Morphology - Theory and Applications</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/mathm-2020-0106\">https://doi.org/10.1515/mathm-2020-0106</a>.","mla":"Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” <i>Mathematical Morphology - Theory and Applications</i>, vol. 4, no. 1, De Gruyter, 2020, pp. 143–58, doi:<a href=\"https://doi.org/10.1515/mathm-2020-0106\">10.1515/mathm-2020-0106</a>."},"issue":"1","publication_identifier":{"issn":["2353-3390"]},"has_accepted_license":"1","doi":"10.1515/mathm-2020-0106","title":"Digital objects in rhombic dodecahedron grid","abstract":[{"text":"Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system.","lang":"eng"}],"date_updated":"2025-04-14T07:48:35Z","publication_status":"published","oa_version":"Published Version","language":[{"iso":"eng"}],"oa":1,"intvolume":"         4","corr_author":"1","ddc":["510"],"month":"11","page":"143-158","publication":"Mathematical Morphology - Theory and Applications","date_created":"2021-03-16T08:55:19Z"},{"intvolume":"     12590","oa":1,"page":"359-371","publication":"28th International Symposium on Graph Drawing and Network Visualization","date_created":"2021-03-28T22:01:44Z","month":"09","title":"Crossings between non-homotopic edges","abstract":[{"text":"We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on   n>1  vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and   m>4n  edges is larger than   cm2n  for some constant   c>0 , and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and   m⟶∞ .","lang":"eng"}],"external_id":{"arxiv":["2006.14908"]},"doi":"10.1007/978-3-030-68766-3_28","oa_version":"Preprint","language":[{"iso":"eng"}],"scopus_import":"1","series_title":"LNCS","date_updated":"2025-04-15T07:16:52Z","publication_status":"published","citation":{"ista":"Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network VisualizationLNCS vol. 12590, 359–371.","ama":"Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: <i>28th International Symposium on Graph Drawing and Network Visualization</i>. Vol 12590. LNCS. Springer Nature; 2020:359-371. doi:<a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">10.1007/978-3-030-68766-3_28</a>","chicago":"Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic Edges.” In <i>28th International Symposium on Graph Drawing and Network Visualization</i>, 12590:359–71. LNCS. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">https://doi.org/10.1007/978-3-030-68766-3_28</a>.","short":"J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 359–371.","ieee":"J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,” in <i>28th International Symposium on Graph Drawing and Network Visualization</i>, Virtual, Online, 2020, vol. 12590, pp. 359–371.","apa":"Pach, J., Tardos, G., &#38; Tóth, G. (2020). Crossings between non-homotopic edges. In <i>28th International Symposium on Graph Drawing and Network Visualization</i> (Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">https://doi.org/10.1007/978-3-030-68766-3_28</a>","mla":"Pach, János, et al. “Crossings between Non-Homotopic Edges.” <i>28th International Symposium on Graph Drawing and Network Visualization</i>, vol. 12590, Springer Nature, 2020, pp. 359–71, doi:<a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">10.1007/978-3-030-68766-3_28</a>."},"type":"conference","project":[{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"}],"quality_controlled":"1","publication_identifier":{"issn":["0302-9743"],"isbn":["9783030687656"],"eissn":["1611-3349"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2006.14908"}],"status":"public","volume":12590,"conference":{"start_date":"2020-09-16","name":"GD: Graph Drawing and Network Visualization","location":"Virtual, Online","end_date":"2020-09-18"},"arxiv":1,"acknowledgement":"Supported by the National Research, Development and Innovation Office, NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full version can be found at https://arxiv.org/abs/2006.14908.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"day":"20","year":"2020","date_published":"2020-09-20T00:00:00Z","publisher":"Springer Nature","_id":"9299","author":[{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János","last_name":"Pach"},{"full_name":"Tardos, Gábor","last_name":"Tardos","first_name":"Gábor"},{"first_name":"Géza","last_name":"Tóth","full_name":"Tóth, Géza"}],"article_processing_charge":"No"}]