[{"year":"2025","corr_author":"1","publisher":"Elsevier","publication_status":"published","title":"Order-2 Delaunay triangulations optimize angles","type":"journal_article","volume":461,"date_created":"2024-12-08T23:01:54Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2310.18238"}],"citation":{"ieee":"H. Edelsbrunner, A. Garber, and M. Saghafian, “Order-2 Delaunay triangulations optimize angles,” <i>Advances in Mathematics</i>, vol. 461. Elsevier, 2025.","short":"H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).","ama":"Edelsbrunner H, Garber A, Saghafian M. Order-2 Delaunay triangulations optimize angles. <i>Advances in Mathematics</i>. 2025;461. doi:<a href=\"https://doi.org/10.1016/j.aim.2024.110055\">10.1016/j.aim.2024.110055</a>","ista":"Edelsbrunner H, Garber A, Saghafian M. 2025. Order-2 Delaunay triangulations optimize angles. Advances in Mathematics. 461, 110055.","apa":"Edelsbrunner, H., Garber, A., &#38; Saghafian, M. (2025). Order-2 Delaunay triangulations optimize angles. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2024.110055\">https://doi.org/10.1016/j.aim.2024.110055</a>","chicago":"Edelsbrunner, Herbert, Alexey Garber, and Morteza Saghafian. “Order-2 Delaunay Triangulations Optimize Angles.” <i>Advances in Mathematics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.aim.2024.110055\">https://doi.org/10.1016/j.aim.2024.110055</a>.","mla":"Edelsbrunner, Herbert, et al. “Order-2 Delaunay Triangulations Optimize Angles.” <i>Advances in Mathematics</i>, vol. 461, 110055, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.aim.2024.110055\">10.1016/j.aim.2024.110055</a>."},"article_number":"110055","OA_type":"green","day":"01","ec_funded":1,"scopus_import":"1","external_id":{"isi":["001370682500001"],"arxiv":["2310.18238"]},"month":"02","abstract":[{"lang":"eng","text":"The local angle property of the (order-1) Delaunay triangulations of a generic set in R2\r\n asserts that the sum of two angles opposite a common edge is less than π. This paper extends this property to higher order and uses it to generalize two classic properties from order-1 to order-2: (1) among the complete level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation lexicographically maximizes the sorted angle vector; (2) among the maximal level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation is the only one that has the local angle property. We also use our method of establishing (2) to give a new short proof of the angle vector optimality for the (order-1) Delaunay triangulation. For order-1, both properties have been instrumental in numerous applications of Delaunay triangulations, and we expect that their generalization will make order-2 Delaunay triangulations more attractive to applications as well."}],"date_updated":"2025-04-15T07:16:53Z","arxiv":1,"oa_version":"Preprint","quality_controlled":"1","intvolume":"       461","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","article_type":"original","publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"publication":"Advances in Mathematics","isi":1,"_id":"18626","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Garber, Alexey","last_name":"Garber","first_name":"Alexey"},{"last_name":"Saghafian","first_name":"Morteza","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"OA_place":"repository","article_processing_charge":"No","project":[{"call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF"}],"language":[{"iso":"eng"}],"acknowledgement":"Work by the first and third authors is partially supported by the European Research Council (ERC), grant no. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35. Work by the second author is partially supported by the Alexander von Humboldt Foundation.","date_published":"2025-02-01T00:00:00Z","department":[{"_id":"HeEd"}],"doi":"10.1016/j.aim.2024.110055"},{"article_processing_charge":"No","OA_place":"publisher","file":[{"checksum":"af6567e5d35e5eb330b8925ae37f1998","file_id":"18983","content_type":"application/zip","access_level":"closed","date_created":"2025-01-31T16:58:30Z","creator":"odragano","date_updated":"2025-01-31T16:58:30Z","relation":"source_file","file_size":11899491,"file_name":"Thesis.zip"},{"relation":"main_file","date_updated":"2025-02-04T16:22:07Z","file_size":8857514,"content_type":"application/pdf","file_id":"19000","checksum":"c3fef68e35b9dc2020b2ca6006da6343","creator":"odragano","access_level":"open_access","date_created":"2025-02-04T16:22:07Z","file_name":"Thesis.pdf"}],"project":[{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF"}],"acknowledgement":"The research presented in this thesis was funded with the Wittgenstein Prize,\r\nAustrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research\r\nCenter TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF),\r\ngrant no. I 02979-N35.\r\n","language":[{"iso":"eng"}],"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"date_published":"2025-02-03T00:00:00Z","doi":"10.15479/at:ista:18979","ddc":["514","004"],"publication_identifier":{"issn":["2663-337X"]},"alternative_title":["ISTA Thesis"],"_id":"18979","author":[{"last_name":"Draganov","first_name":"Ondrej","orcid":"0000-0003-0464-3823","full_name":"Draganov, Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87"}],"has_accepted_license":"1","oa_version":"Published Version","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","oa":1,"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"15091"},{"relation":"part_of_dissertation","id":"18981","status":"public"}]},"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"degree_awarded":"PhD","month":"02","abstract":[{"text":"Topological Data Analysis (TDA) is a discipline utilizing the mathematical field of topology to study data, most prominently collections of point sets. This thesis summarizes three projects related to computations in TDA.\r\n\r\nThe first one establishes a variant of TDA for chromatic point sets, where each point is given a color. For example, we are given positions of cells within a tumor microenvironment, and color the cancerous cells red, and the immune cells blue.\r\n\r\nThe aim is then to give a quantitative description of how the two or more sets of points spatially interact. Building on image, kernel and cokernel variants of persistent homology, we suggest six-packs of persistent diagrams as such a descriptor.\r\n\r\nWe describe a construction of a chromatic alpha complex, which enables  efficient computation of several variants of the six-packs. We give topological descriptions of natural subcomplexes of the chromatic alpha complex, and show that the radii of the simplices form a discrete Morse function. Finally, we provide an implementation of the presented chromatic TDA pipeline.\r\n\r\nThe second part aims to translate a powerful tool of sheaf theory to elementary terms using labeled matrices. The goal is to enable their use in computational settings. We show that derived categories of sheaves over finite posets have, up to isomorphism, unique objects---minimal injective resolutions---and give a concrete algorithm to compute them. We further describe simple algorithms to compute derived pushforwards and pullbacks for monotonic maps, and their proper variants for inclusions, and demonstrate their tractability by providing an implementation. Finally, we suggest a discrete definition of microsupport and show desirable properties inspired by discrete Morse theory.\r\n\r\nIn the last part, we present a collection of observations about collapses. We give a characterization of collapsibility in terms of unitriangular submatrices of the boundary matrix, a cotree-tree decomposition, and the optimal solution to a variant of the Procrustes problem. We establish relation between dual collapses and relative Morse theory and pose several open questions. Finally, focusing on complexes embedded in the three-dimensional Euclidean space, we describe a relation between the collapsibility and the triviality of a polygonal knot.","lang":"eng"}],"date_updated":"2026-04-07T11:47:30Z","day":"03","date_created":"2025-01-31T17:04:40Z","citation":{"ieee":"O. Draganov, “Structures and computations in topological data analysis,” Institute of Science and Technology Austria, 2025.","mla":"Draganov, Ondrej. <i>Structures and Computations in Topological Data Analysis</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/at:ista:18979\">10.15479/at:ista:18979</a>.","chicago":"Draganov, Ondrej. “Structures and Computations in Topological Data Analysis.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/at:ista:18979\">https://doi.org/10.15479/at:ista:18979</a>.","apa":"Draganov, O. (2025). <i>Structures and computations in topological data analysis</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18979\">https://doi.org/10.15479/at:ista:18979</a>","ista":"Draganov O. 2025. Structures and computations in topological data analysis. Institute of Science and Technology Austria.","short":"O. Draganov, Structures and Computations in Topological Data Analysis, Institute of Science and Technology Austria, 2025.","ama":"Draganov O. Structures and computations in topological data analysis. 2025. doi:<a href=\"https://doi.org/10.15479/at:ista:18979\">10.15479/at:ista:18979</a>"},"supervisor":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"title":"Structures and computations in topological data analysis","file_date_updated":"2025-02-04T16:22:07Z","type":"dissertation","keyword":["topological data analysis","chromatic point set","alpha complex","persistent homology","six pack","sheaf","microlocal discrete Morse","injective resolution","collapse","knot","discrete Morse theory"],"page":"140","year":"2025","corr_author":"1","publisher":"Institute of Science and Technology Austria","publication_status":"published"},{"day":"01","ec_funded":1,"scopus_import":"1","volume":719,"date_created":"2025-06-30T08:48:48Z","article_number":"122425","citation":{"ieee":"M. Mahini, H. Beigy, S. Qadami, and M. Saghafian, “Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality,” <i>Information Sciences</i>, vol. 719, no. 11. Elsevier, 2025.","ista":"Mahini M, Beigy H, Qadami S, Saghafian M. 2025. Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. Information Sciences. 719(11), 122425.","apa":"Mahini, M., Beigy, H., Qadami, S., &#38; Saghafian, M. (2025). Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. <i>Information Sciences</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ins.2025.122425\">https://doi.org/10.1016/j.ins.2025.122425</a>","ama":"Mahini M, Beigy H, Qadami S, Saghafian M. Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. <i>Information Sciences</i>. 2025;719(11). doi:<a href=\"https://doi.org/10.1016/j.ins.2025.122425\">10.1016/j.ins.2025.122425</a>","short":"M. Mahini, H. Beigy, S. Qadami, M. Saghafian, Information Sciences 719 (2025).","mla":"Mahini, Mohammad, et al. “Simplet-Based Signatures and Approximation in Simplicial Complexes: Frequency, Degree, and Centrality.” <i>Information Sciences</i>, vol. 719, no. 11, 122425, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ins.2025.122425\">10.1016/j.ins.2025.122425</a>.","chicago":"Mahini, Mohammad, Hamid Beigy, Salman Qadami, and Morteza Saghafian. “Simplet-Based Signatures and Approximation in Simplicial Complexes: Frequency, Degree, and Centrality.” <i>Information Sciences</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.ins.2025.122425\">https://doi.org/10.1016/j.ins.2025.122425</a>."},"OA_type":"closed access","issue":"11","title":"Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality","type":"journal_article","year":"2025","corr_author":"1","publisher":"Elsevier","publication_status":"published","article_processing_charge":"No","project":[{"call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"language":[{"iso":"eng"}],"acknowledgement":"The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which improved this paper.\r\nWork by the first and fourth authors is partially supported by the European Research Council (ERC), grant no. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35.","date_published":"2025-11-01T00:00:00Z","department":[{"_id":"HeEd"}],"doi":"10.1016/j.ins.2025.122425","publication":"Information Sciences","publication_identifier":{"issn":["0020-0255"]},"isi":1,"_id":"19937","author":[{"full_name":"Mahini, Mohammad","first_name":"Mohammad","last_name":"Mahini"},{"last_name":"Beigy","first_name":"Hamid","full_name":"Beigy, Hamid"},{"first_name":"Salman","last_name":"Qadami","full_name":"Qadami, Salman"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"oa_version":"None","quality_controlled":"1","intvolume":"       719","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","article_type":"original","external_id":{"isi":["001516170500002"]},"month":"11","abstract":[{"lang":"eng","text":"Simplets are elementary units within simplicial complexes and are fundamental for analyzing the structure of simplicial complexes. Previous efforts have mainly focused on accurately counting or approximating the number of simplets rather than studying their frequencies. However, analyzing simplet frequencies is more practical for large-scale simplicial complexes. This paper introduces the Simplet Frequency Distribution (SFD) vector, which enables the analysis of simplet frequencies in simplicial complexes. Additionally, we provide a bound on the sample complexity required to approximate the SFD vector using any uniform sampling-based algorithm accurately. We extend the definition of simplet frequency distribution to encompass simplices, allowing for the analysis of simplet frequencies within simplices of simplicial complexes. This paper introduces the Simplet Degree Vector (SDV) and the Simplet Degree Centrality (SDC), facilitating this analysis for each simplex. Furthermore, we present a bound on the sample complexity required for accurately approximating the SDV and SDC for a set of simplices using any uniform sampling-based algorithm. We also introduce algorithms for approximating SFD, geometric SFD, SDV, and SDC. We also validate the theoretical bounds with experiments on random simplicial complexes and demonstrate the practical application through a case study."}],"date_updated":"2025-12-30T09:05:32Z"},{"type":"conference","file_date_updated":"2025-07-14T07:24:22Z","title":"On spheres with k points inside","corr_author":"1","year":"2025","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","conference":{"start_date":"2025-06-23","location":"Kanazawa, Japan","name":"SoCG: Symposium on Computational Geometry","end_date":"2025-06-27"},"day":"20","scopus_import":"1","date_created":"2025-07-13T22:01:22Z","volume":332,"article_number":"43","citation":{"ama":"Edelsbrunner H, Garber A, Saghafian M. On spheres with k points inside. In: <i>41st International Symposium on Computational Geometry</i>. Vol 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.43\">10.4230/LIPIcs.SoCG.2025.43</a>","short":"H. Edelsbrunner, A. Garber, M. Saghafian, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","apa":"Edelsbrunner, H., Garber, A., &#38; Saghafian, M. (2025). On spheres with k points inside. In <i>41st International Symposium on Computational Geometry</i> (Vol. 332). Kanazawa, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.43\">https://doi.org/10.4230/LIPIcs.SoCG.2025.43</a>","ista":"Edelsbrunner H, Garber A, Saghafian M. 2025. On spheres with k points inside. 41st International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 332, 43.","chicago":"Edelsbrunner, Herbert, Alexey Garber, and Morteza Saghafian. “On Spheres with k Points Inside.” In <i>41st International Symposium on Computational Geometry</i>, Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.43\">https://doi.org/10.4230/LIPIcs.SoCG.2025.43</a>.","mla":"Edelsbrunner, Herbert, et al. “On Spheres with k Points Inside.” <i>41st International Symposium on Computational Geometry</i>, vol. 332, 43, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.43\">10.4230/LIPIcs.SoCG.2025.43</a>.","ieee":"H. Edelsbrunner, A. Garber, and M. Saghafian, “On spheres with k points inside,” in <i>41st International Symposium on Computational Geometry</i>, Kanazawa, Japan, 2025, vol. 332."},"OA_type":"gold","quality_controlled":"1","oa_version":"Published Version","arxiv":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"intvolume":"       332","external_id":{"arxiv":["2410.21204"]},"date_updated":"2025-07-14T07:26:14Z","abstract":[{"lang":"eng","text":"We generalize a classical result by Boris Delaunay that introduced Delaunay triangulations. In particular, we prove that for a locally finite and coarsely dense generic point set A in ℝ^d, every generic point of ℝ^d belongs to exactly binom(d+k,d) simplices whose vertices belong to A and whose circumspheres enclose exactly k points of A. We extend this result to the cases in which the points are weighted, and when A contains only finitely many points in ℝ^d or in 𝕊^d. Furthermore, we use the result to give a new geometric proof for the fact that volumes of hypersimplices are Eulerian numbers."}],"month":"06","project":[{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"},{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"file":[{"checksum":"b5313ed8575ea87913c71a6e3c7513c8","file_id":"20016","content_type":"application/pdf","creator":"dernst","date_created":"2025-07-14T07:24:22Z","access_level":"open_access","relation":"main_file","date_updated":"2025-07-14T07:24:22Z","file_size":661893,"success":1,"file_name":"2025_LIPIcs.SoCG_Edelsbrunner.pdf"}],"OA_place":"publisher","article_processing_charge":"Yes","doi":"10.4230/LIPIcs.SoCG.2025.43","date_published":"2025-06-20T00:00:00Z","department":[{"_id":"HeEd"}],"acknowledgement":"Herbert Edelsbrunner: partially supported by the Wittgenstein Prize, Austrian Science\r\nFund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109,\r\nAustrian Science Fund (FWF), grant no. I 02979-N35.\r\nAlexey Garber: partially supported by the Simons Foundation.\r\nMorteza Saghafian: partially supported by the Wittgenstein Prize, Austrian Science Fund (FWF),\r\ngrant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science\r\nFund (FWF), grant no. I 02979-N35","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783959773706"],"eissn":["1868-8969"]},"ddc":["510"],"publication":"41st International Symposium on Computational Geometry","has_accepted_license":"1","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Garber, Alexey","last_name":"Garber","first_name":"Alexey"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza","full_name":"Saghafian, Morteza"}],"_id":"20005","alternative_title":["LIPIcs"]},{"corr_author":"1","year":"2025","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","type":"conference","title":"Banana trees for the persistence in time series experimentally","file_date_updated":"2025-07-14T08:23:38Z","date_created":"2025-07-13T22:01:22Z","volume":332,"article_number":"71","citation":{"ieee":"L. Ost, S. Cultrera di Montesano, and H. Edelsbrunner, “Banana trees for the persistence in time series experimentally,” in <i>41st International Symposium on Computational Geometry</i>, Kanazawa, Japan, 2025, vol. 332.","mla":"Ost, Lara, et al. “Banana Trees for the Persistence in Time Series Experimentally.” <i>41st International Symposium on Computational Geometry</i>, vol. 332, 71, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.71\">10.4230/LIPIcs.SoCG.2025.71</a>.","chicago":"Ost, Lara, Sebastiano Cultrera di Montesano, and Herbert Edelsbrunner. “Banana Trees for the Persistence in Time Series Experimentally.” In <i>41st International Symposium on Computational Geometry</i>, Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.71\">https://doi.org/10.4230/LIPIcs.SoCG.2025.71</a>.","ista":"Ost L, Cultrera di Montesano S, Edelsbrunner H. 2025. Banana trees for the persistence in time series experimentally. 41st International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 332, 71.","apa":"Ost, L., Cultrera di Montesano, S., &#38; Edelsbrunner, H. (2025). Banana trees for the persistence in time series experimentally. In <i>41st International Symposium on Computational Geometry</i> (Vol. 332). Kanazawa, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.71\">https://doi.org/10.4230/LIPIcs.SoCG.2025.71</a>","short":"L. Ost, S. Cultrera di Montesano, H. Edelsbrunner, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","ama":"Ost L, Cultrera di Montesano S, Edelsbrunner H. Banana trees for the persistence in time series experimentally. In: <i>41st International Symposium on Computational Geometry</i>. Vol 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.71\">10.4230/LIPIcs.SoCG.2025.71</a>"},"OA_type":"gold","conference":{"location":"Kanazawa, Japan","start_date":"2025-06-23","name":"SoCG: Symposium on Computational Geometry","end_date":"2025-06-27"},"day":"20","scopus_import":"1","external_id":{"arxiv":["2405.17920"]},"date_updated":"2025-12-30T11:04:33Z","abstract":[{"lang":"eng","text":"In numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tree data structure, specifically designed to efficiently maintain the multi-scale topological descriptor commonly known as persistent homology for dynamically changing time series data. We implement this data structure and conduct an experimental study to assess its properties and runtime for update operations. Our findings indicate that banana trees are highly effective with unbiased random data, outperforming state-of-the-art static algorithms in these scenarios. Additionally, our results show that real-world time series share structural properties with unbiased random walks, suggesting potential practical utility for our implementation."}],"month":"06","quality_controlled":"1","oa_version":"Published Version","arxiv":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"status":"public","related_material":{"link":[{"url":"https://github.com/laraost/BananaPersist","relation":"software"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"intvolume":"       332","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959773706"]},"publication":"41st International Symposium on Computational Geometry","ddc":["000"],"has_accepted_license":"1","author":[{"full_name":"Ost, Lara","last_name":"Ost","first_name":"Lara"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"}],"_id":"20006","alternative_title":["LIPIcs"],"project":[{"name":"Vienna Graduate School on Computational Optimization","_id":"9B9290DE-BA93-11EA-9121-9846C619BF3A","grant_number":"W1260-N35"},{"grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"file":[{"success":1,"file_name":"2025_LIPIcs.SoCG_Ost.pdf","file_id":"20017","checksum":"3a4a7a707a56e0cfdf51428782dee55a","content_type":"application/pdf","creator":"dernst","date_created":"2025-07-14T08:23:38Z","access_level":"open_access","date_updated":"2025-07-14T08:23:38Z","relation":"main_file","file_size":834623}],"article_processing_charge":"Yes","OA_place":"publisher","doi":"10.4230/LIPIcs.SoCG.2025.71","date_published":"2025-06-20T00:00:00Z","department":[{"_id":"HeEd"}],"acknowledgement":"Lara Ost: Supported by the Vienna Graduate School on Computational Optimization\r\n(VGSCO), FWF project no. W1260-N35.\r\nSebastiano Cultrera di Montesano: Supported by the Eric and Wendy Schmidt Center at the Broad Institute of MIT and Harvard.\r\nHerbert Edelsbrunner: Partially supported by the Wittgenstein Prize, FWF grant no. Z 342-N31,\r\nand by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.","language":[{"iso":"eng"}]},{"volume":4,"date_created":"2025-08-31T22:01:33Z","citation":{"ieee":"E. W. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “Burning or collapsing the medial axis is unstable,” <i>La Matematica</i>, vol. 4. Springer Nature, pp. 811–828, 2025.","short":"E.W. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, La Matematica 4 (2025) 811–828.","ama":"Chambers EW, Fillmore CD, Stephenson ER, Wintraecken M. Burning or collapsing the medial axis is unstable. <i>La Matematica</i>. 2025;4:811-828. doi:<a href=\"https://doi.org/10.1007/s44007-025-00170-0\">10.1007/s44007-025-00170-0</a>","ista":"Chambers EW, Fillmore CD, Stephenson ER, Wintraecken M. 2025. Burning or collapsing the medial axis is unstable. La Matematica. 4, 811–828.","apa":"Chambers, E. W., Fillmore, C. D., Stephenson, E. R., &#38; Wintraecken, M. (2025). Burning or collapsing the medial axis is unstable. <i>La Matematica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s44007-025-00170-0\">https://doi.org/10.1007/s44007-025-00170-0</a>","chicago":"Chambers, Erin Wolf, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs Wintraecken. “Burning or Collapsing the Medial Axis Is Unstable.” <i>La Matematica</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s44007-025-00170-0\">https://doi.org/10.1007/s44007-025-00170-0</a>.","mla":"Chambers, Erin Wolf, et al. “Burning or Collapsing the Medial Axis Is Unstable.” <i>La Matematica</i>, vol. 4, Springer Nature, 2025, pp. 811–28, doi:<a href=\"https://doi.org/10.1007/s44007-025-00170-0\">10.1007/s44007-025-00170-0</a>."},"OA_type":"hybrid","day":"01","ec_funded":1,"scopus_import":"1","year":"2025","page":"811-828","corr_author":"1","publication_status":"published","publisher":"Springer Nature","file_date_updated":"2025-12-30T07:52:58Z","title":"Burning or collapsing the medial axis is unstable","type":"journal_article","ddc":["510"],"publication_identifier":{"eissn":["2730-9657"]},"publication":"La Matematica","author":[{"first_name":"Erin Wolf","last_name":"Chambers","full_name":"Chambers, Erin Wolf"},{"first_name":"Christopher D","last_name":"Fillmore","full_name":"Fillmore, Christopher D","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425"},{"first_name":"Elizabeth R","last_name":"Stephenson","orcid":"0000-0002-6862-208X","full_name":"Stephenson, Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"has_accepted_license":"1","_id":"20260","OA_place":"publisher","article_processing_charge":"Yes (via OA deal)","project":[{"call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses","grant_number":"M03073"}],"file":[{"file_name":"2025_LaMatematica_Chambers.pdf","success":1,"file_size":2678640,"relation":"main_file","date_updated":"2025-12-30T07:52:58Z","date_created":"2025-12-30T07:52:58Z","access_level":"open_access","creator":"dernst","content_type":"application/pdf","checksum":"e2043259194bfcdf3d74c4da8a5a853f","file_id":"20885"}],"department":[{"_id":"HeEd"}],"date_published":"2025-12-01T00:00:00Z","doi":"10.1007/s44007-025-00170-0","acknowledgement":"We thank André Lieutier, David Letscher, Ellen Gasparovic, Kathryn Leonard, and Tao Ju for early discussions on this work. We also thank Lu Liu, Yajie Yan, and Tao Ju for sharing code to generate the examples. We further thank Abigail Thompson for discussion on the conjecture and James Damon for sharing his insight in singularity theory. We thank the reviewers for their detailed reviews, which helped to improve the exposition.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). Partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’ and the European Research Council (ERC), grant no. 788183, ‘Alpha Shape Theory Extended’. The first author was supported in part by the National Science Foundation through grants DBI-1759807, CCF-1907612, and CCF-2444309. The fourth author was supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) M-3073, ANR grant StratMesh, ANR-24-CE48-1899, and the welcome package from IDEX of the Université Côte d’Azur, ANR-15-IDEX-01.","language":[{"iso":"eng"}],"date_updated":"2026-04-07T11:42:48Z","abstract":[{"lang":"eng","text":"The medial axis of a set consists of the points in the ambient space without a unique closest point in the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a skeleton topologically equivalent to the original set. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities, various prunings of the medial axis have been proposed in the computational geometry community. Here, we examine one type of pruning, called burning. Because of the good experimental results it was hoped that the burning method of simplifying the medial axis would be stable. In this work, we show a simple example that dashes such hopes. Based on Bing’s house with two rooms, we demonstrate an isotopy of a shape where the medial axis goes from collapsible to non-collapsible. More precisely, we consider the standard deformation retract from the closed ball to Bing’s house with two rooms, but stop just short of the point where Bing’s house becomes two dimensional. This way we obtain an isotopy from the 3-ball to a thickened version of Bing’s house. Under this isotopy, the medial axis goes from collapsible to non-collapsible. We stress that this isotopy can be made generic, in the sense of singularity theory, as developed by Arnol’d and Thom."}],"month":"12","oa_version":"Published Version","quality_controlled":"1","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"PlanS_conform":"1","article_type":"original","intvolume":"         4","related_material":{"record":[{"id":"21021","status":"public","relation":"dissertation_contains"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1},{"date_updated":"2025-09-30T14:32:31Z","abstract":[{"text":"Motivated by questions arising at the intersection of information theory and geometry, we compare two dissimilarity measures between finite categorical distributions. One is the well-known Jensen–Shannon divergence, which is easy to compute and whose square root is a proper metric. The other is what we call the minmax divergence, which is harder to compute. Just like the Jensen–Shannon divergence, it arises naturally from the Kullback–Leibler divergence. The main contribution of this paper is a proof showing that the minmax divergence can be tightly approximated by the Jensen–Shannon divergence. The bounds suggest that the square root of the minmax divergence is a metric, and we prove that this is indeed true in the one-dimensional case. The general case remains open. Finally, we consider analogous questions in the context of another Bregman divergence and the corresponding Burbea–Rao (Jensen–Bregman) divergence.","lang":"eng"}],"month":"08","external_id":{"isi":["001557476000001"],"pmid":["40870326"]},"PlanS_conform":"1","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"pmid":1,"intvolume":"        27","quality_controlled":"1","oa_version":"Published Version","has_accepted_license":"1","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","full_name":"Virk, Ziga","first_name":"Ziga","last_name":"Virk"},{"first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"_id":"20293","isi":1,"ddc":["500"],"DOAJ_listed":"1","publication":"Entropy","publication_identifier":{"eissn":["1099-4300"]},"doi":"10.3390/e27080854","department":[{"_id":"HeEd"}],"date_published":"2025-08-01T00:00:00Z","language":[{"iso":"eng"}],"acknowledgement":"This research received partial funding from the European Research Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme, grant no. 788183, the\r\nWittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, the DFG Collaborative\r\nResearch Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35, and the 2022 Google Research Scholar Award for project ‘Algorithms for Topological Analysis of Neural Networks’. The APC was waived.","project":[{"grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF"}],"file":[{"success":1,"file_name":"2025_Entropy_Akopyan.pdf","creator":"dernst","access_level":"open_access","date_created":"2025-09-08T07:55:48Z","file_id":"20309","checksum":"65c5399c4015d9c8abb8c7a96f3d7836","content_type":"application/pdf","date_updated":"2025-09-08T07:55:48Z","relation":"main_file","file_size":379340}],"OA_place":"publisher","article_processing_charge":"Yes","publication_status":"published","publisher":"MDPI","corr_author":"1","year":"2025","type":"journal_article","file_date_updated":"2025-09-08T07:55:48Z","title":"Tight bounds between the Jensen–Shannon divergence and the minmax divergence","issue":"8","citation":{"chicago":"Akopyan, Arseniy, Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner. “Tight Bounds between the Jensen–Shannon Divergence and the Minmax Divergence.” <i>Entropy</i>. MDPI, 2025. <a href=\"https://doi.org/10.3390/e27080854\">https://doi.org/10.3390/e27080854</a>.","mla":"Akopyan, Arseniy, et al. “Tight Bounds between the Jensen–Shannon Divergence and the Minmax Divergence.” <i>Entropy</i>, vol. 27, no. 8, 854, MDPI, 2025, doi:<a href=\"https://doi.org/10.3390/e27080854\">10.3390/e27080854</a>.","ama":"Akopyan A, Edelsbrunner H, Virk Z, Wagner H. Tight bounds between the Jensen–Shannon divergence and the minmax divergence. <i>Entropy</i>. 2025;27(8). doi:<a href=\"https://doi.org/10.3390/e27080854\">10.3390/e27080854</a>","short":"A. Akopyan, H. Edelsbrunner, Z. Virk, H. Wagner, Entropy 27 (2025).","ista":"Akopyan A, Edelsbrunner H, Virk Z, Wagner H. 2025. Tight bounds between the Jensen–Shannon divergence and the minmax divergence. Entropy. 27(8), 854.","apa":"Akopyan, A., Edelsbrunner, H., Virk, Z., &#38; Wagner, H. (2025). Tight bounds between the Jensen–Shannon divergence and the minmax divergence. <i>Entropy</i>. MDPI. <a href=\"https://doi.org/10.3390/e27080854\">https://doi.org/10.3390/e27080854</a>","ieee":"A. Akopyan, H. Edelsbrunner, Z. Virk, and H. Wagner, “Tight bounds between the Jensen–Shannon divergence and the minmax divergence,” <i>Entropy</i>, vol. 27, no. 8. MDPI, 2025."},"OA_type":"gold","article_number":"854","date_created":"2025-09-07T22:01:33Z","volume":27,"ec_funded":1,"scopus_import":"1","day":"01"},{"author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","first_name":"Adam","full_name":"Brown, Adam"},{"id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej","orcid":"0000-0003-0464-3823","last_name":"Draganov","first_name":"Ondrej"}],"has_accepted_license":"1","_id":"20323","publication_identifier":{"issn":["0022-4049"]},"ddc":["510"],"publication":"Journal of Pure and Applied Algebra","date_published":"2025-10-01T00:00:00Z","department":[{"_id":"HeEd"}],"doi":"10.1016/j.jpaa.2025.108068","language":[{"iso":"eng"}],"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35","article_processing_charge":"Yes (via OA deal)","OA_place":"publisher","file":[{"creator":"dernst","date_created":"2025-12-30T07:55:08Z","access_level":"open_access","content_type":"application/pdf","checksum":"39bcad462278c9322ef810af7db67f56","file_id":"20886","date_updated":"2025-12-30T07:55:08Z","relation":"main_file","file_size":3090836,"success":1,"file_name":"2025_JourPureAppliedAlgebra_Brown.pdf"}],"project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF"}],"date_updated":"2025-12-30T07:55:21Z","abstract":[{"lang":"eng","text":"We establish several results combining discrete Morse theory and microlocal sheaf theory in the setting of finite posets and simplicial complexes. Our primary tool is a computationally tractable description of the bounded derived category of sheaves on a poset with the Alexandrov topology. We prove that each bounded complex of sheaves on a finite poset admits a unique (up to isomorphism of complexes) minimal injective resolution, and we provide algorithms for computing minimal injective resolution of an injective complex, as well as several useful functors between derived categories of sheaves. For the constant sheaf on a simplicial complex, we give asymptotically tight bounds on the complexity of computing the minimal injective resolution using those algorithms. Our main result is a novel definition of the discrete microsupport of a bounded complex of sheaves on a finite poset. We detail several foundational properties of the discrete microsupport, as well as a microlocal generalization of the discrete homological Morse theorem and Morse inequalities."}],"month":"10","external_id":{"arxiv":["2209.14993"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"status":"public","PlanS_conform":"1","article_type":"original","intvolume":"       229","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"18981"}]},"oa_version":"Published Version","quality_controlled":"1","arxiv":1,"article_number":"108068","citation":{"ieee":"A. Brown and O. Draganov, “Discrete microlocal Morse theory,” <i>Journal of Pure and Applied Algebra</i>, vol. 229, no. 10. Elsevier, 2025.","ama":"Brown A, Draganov O. Discrete microlocal Morse theory. <i>Journal of Pure and Applied Algebra</i>. 2025;229(10). doi:<a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">10.1016/j.jpaa.2025.108068</a>","short":"A. Brown, O. Draganov, Journal of Pure and Applied Algebra 229 (2025).","ista":"Brown A, Draganov O. 2025. Discrete microlocal Morse theory. Journal of Pure and Applied Algebra. 229(10), 108068.","apa":"Brown, A., &#38; Draganov, O. (2025). Discrete microlocal Morse theory. <i>Journal of Pure and Applied Algebra</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">https://doi.org/10.1016/j.jpaa.2025.108068</a>","chicago":"Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” <i>Journal of Pure and Applied Algebra</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">https://doi.org/10.1016/j.jpaa.2025.108068</a>.","mla":"Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” <i>Journal of Pure and Applied Algebra</i>, vol. 229, no. 10, 108068, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">10.1016/j.jpaa.2025.108068</a>."},"OA_type":"hybrid","volume":229,"date_created":"2025-09-10T05:40:09Z","scopus_import":"1","ec_funded":1,"day":"01","publication_status":"published","publisher":"Elsevier","year":"2025","corr_author":"1","file_date_updated":"2025-12-30T07:55:08Z","title":"Discrete microlocal Morse theory","type":"journal_article","issue":"10"},{"article_processing_charge":"No","OA_place":"repository","language":[{"iso":"eng"}],"doi":"10.1007/978-3-032-09544-2_10","date_published":"2025-11-01T00:00:00Z","department":[{"_id":"HeEd"}],"publication":"4th International Joint Conference on Discrete Geometry and Mathematical Morphology","publication_identifier":{"issn":["0302-9743"],"isbn":["9783032095435"],"eissn":["1611-3349"]},"_id":"20658","alternative_title":["LNCS"],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X","first_name":"Elizabeth R","last_name":"Stephenson"},{"last_name":"Thoresen","first_name":"Martin H","full_name":"Thoresen, Martin H","id":"47CB1472-F248-11E8-B48F-1D18A9856A87"}],"arxiv":1,"quality_controlled":"1","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"intvolume":"     16296","status":"public","external_id":{"arxiv":["2504.14743"]},"month":"11","abstract":[{"text":"The medial axis of a smoothly embedded surface in R^3 consists of all points for which the Euclidean distance function on the surface has at least two global minima. We generalize this notion to the mid-sphere axis, which consists of all points for which the Euclidean distance function has two interchanging saddles that swap their partners in the pairing by persistent homology. It offers a discrete-algebraic multi-scale approach to computing ridge-like structures on the surface. As a proof of concept, an algorithm that computes stair-case approximations of the mid-sphere axis is provided.","lang":"eng"}],"date_updated":"2025-11-24T10:05:11Z","day":"01","conference":{"name":"DGMM: Discrete Geometry and Mathematical Morphology","start_date":"2025-11-03","location":"Groningen, The Netherlands","end_date":"2025-11-06"},"scopus_import":"1","date_created":"2025-11-23T23:01:37Z","volume":16296,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2504.14743"}],"citation":{"ieee":"H. Edelsbrunner, E. R. Stephenson, and M. H. Thoresen, “The mid-sphere cousin of the medial axis transform,” in <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i>, Groningen, The Netherlands, 2025, vol. 16296, pp. 133–147.","chicago":"Edelsbrunner, Herbert, Elizabeth R Stephenson, and Martin H Thoresen. “The Mid-Sphere Cousin of the Medial Axis Transform.” In <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i>, 16296:133–47. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/978-3-032-09544-2_10\">https://doi.org/10.1007/978-3-032-09544-2_10</a>.","mla":"Edelsbrunner, Herbert, et al. “The Mid-Sphere Cousin of the Medial Axis Transform.” <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i>, vol. 16296, Springer Nature, 2025, pp. 133–47, doi:<a href=\"https://doi.org/10.1007/978-3-032-09544-2_10\">10.1007/978-3-032-09544-2_10</a>.","ama":"Edelsbrunner H, Stephenson ER, Thoresen MH. The mid-sphere cousin of the medial axis transform. In: <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i>. Vol 16296. Springer Nature; 2025:133-147. doi:<a href=\"https://doi.org/10.1007/978-3-032-09544-2_10\">10.1007/978-3-032-09544-2_10</a>","short":"H. Edelsbrunner, E.R. Stephenson, M.H. Thoresen, in:, 4th International Joint Conference on Discrete Geometry and Mathematical Morphology, Springer Nature, 2025, pp. 133–147.","ista":"Edelsbrunner H, Stephenson ER, Thoresen MH. 2025. The mid-sphere cousin of the medial axis transform. 4th International Joint Conference on Discrete Geometry and Mathematical Morphology. DGMM: Discrete Geometry and Mathematical Morphology, LNCS, vol. 16296, 133–147.","apa":"Edelsbrunner, H., Stephenson, E. R., &#38; Thoresen, M. H. (2025). The mid-sphere cousin of the medial axis transform. In <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i> (Vol. 16296, pp. 133–147). Groningen, The Netherlands: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-032-09544-2_10\">https://doi.org/10.1007/978-3-032-09544-2_10</a>"},"OA_type":"green","type":"conference","title":"The mid-sphere cousin of the medial axis transform","page":"133-147","year":"2025","publisher":"Springer Nature","publication_status":"published"},{"language":[{"iso":"eng"}],"acknowledgement":"Álvaro Torras-Casas contract is funded by the French Agence Nationale de la Recherche through the project reference ANR-22-CPJ1-0047-01. Rocio Gonzalez-Diaz is partially funded by the European Union under grant agreement no. 101070028-2 (REXASI-PRO).","date_published":"2025-11-10T00:00:00Z","department":[{"_id":"HeEd"}],"doi":"10.1145/3747199.3747561","OA_place":"publisher","article_processing_charge":"Yes (in subscription journal)","file":[{"success":1,"file_name":"2025_ISSAC_GonzalezDiaz.pdf","creator":"dernst","date_created":"2025-12-09T13:43:17Z","access_level":"open_access","file_id":"20751","checksum":"1c299cca165a20e2518afe4fda63dbf1","content_type":"application/pdf","file_size":761617,"date_updated":"2025-12-09T13:43:17Z","relation":"main_file"}],"_id":"20729","author":[{"last_name":"Gonzalez-Diaz","first_name":"Rocio","full_name":"Gonzalez-Diaz, Rocio"},{"id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","last_name":"Soriano Trigueros","first_name":"Manuel","full_name":"Soriano Trigueros, Manuel","orcid":"0000-0003-2449-1433"},{"full_name":"Torras-Casas, Alvaro","first_name":"Alvaro","last_name":"Torras-Casas"}],"has_accepted_license":"1","ddc":["510"],"publication_identifier":{"isbn":["9798400720758"]},"publication":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"oa_version":"Published Version","quality_controlled":"1","month":"11","date_updated":"2025-12-09T13:46:42Z","abstract":[{"text":"Persistence modules (defined as a sequence of vector spaces and linear maps between them) are a key tool in topological data analysis. They are easy to interpret and fast to compute. However, when considering persistence maps (i.e. maps between persistence modules), these properties are lost. We propose a new invariant for persistence maps consisting of a partial matching such that: it is easy to interpret, it is more discriminative than the image of the persistence map, and can be calculated with cubical complexity.","lang":"eng"}],"scopus_import":"1","day":"10","conference":{"location":"Guanajuato, Mexico","name":"ISSAC: International Symposium on Symbolic and Algebraic Computation","start_date":"2025-07-28","end_date":"2025-08-01"},"citation":{"ieee":"R. Gonzalez-Diaz, M. Soriano Trigueros, and A. Torras-Casas, “Additive partial matchings for persistent homology,” in <i>Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation</i>, Guanajuato, Mexico, 2025, pp. 188–196.","ama":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. Additive partial matchings for persistent homology. In: <i>Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation</i>. Association for Computing Machinery; 2025:188-196. doi:<a href=\"https://doi.org/10.1145/3747199.3747561\">10.1145/3747199.3747561</a>","short":"R. Gonzalez-Diaz, M. Soriano Trigueros, A. Torras-Casas, in:, Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation, Association for Computing Machinery, 2025, pp. 188–196.","apa":"Gonzalez-Diaz, R., Soriano Trigueros, M., &#38; Torras-Casas, A. (2025). Additive partial matchings for persistent homology. In <i>Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation</i> (pp. 188–196). Guanajuato, Mexico: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3747199.3747561\">https://doi.org/10.1145/3747199.3747561</a>","ista":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. 2025. Additive partial matchings for persistent homology. Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation. ISSAC: International Symposium on Symbolic and Algebraic Computation, 188–196.","chicago":"Gonzalez-Diaz, Rocio, Manuel Soriano Trigueros, and Alvaro Torras-Casas. “Additive Partial Matchings for Persistent Homology.” In <i>Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation</i>, 188–96. Association for Computing Machinery, 2025. <a href=\"https://doi.org/10.1145/3747199.3747561\">https://doi.org/10.1145/3747199.3747561</a>.","mla":"Gonzalez-Diaz, Rocio, et al. “Additive Partial Matchings for Persistent Homology.” <i>Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation</i>, Association for Computing Machinery, 2025, pp. 188–96, doi:<a href=\"https://doi.org/10.1145/3747199.3747561\">10.1145/3747199.3747561</a>."},"OA_type":"hybrid","date_created":"2025-12-07T23:02:01Z","file_date_updated":"2025-12-09T13:43:17Z","title":"Additive partial matchings for persistent homology","type":"conference","publisher":"Association for Computing Machinery","publication_status":"published","page":"188-196","year":"2025","corr_author":"1"},{"publication_status":"submitted","year":"2025","title":"Identifying cobordisms using kernel persistence","type":"preprint","OA_type":"green","citation":{"ieee":"Y. Bokor Bleile, L. Fajstrup, T. Heiss, A. M. Svane, and S. S. Sørensen, “Identifying cobordisms using kernel persistence,” <i>arXiv</i>. .","ista":"Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms using kernel persistence. arXiv, 2505.17858.","apa":"Bokor Bleile, Y., Fajstrup, L., Heiss, T., Svane, A. M., &#38; Sørensen, S. S. (n.d.). Identifying cobordisms using kernel persistence. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2505.17858\">https://doi.org/10.48550/arXiv.2505.17858</a>","ama":"Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms using kernel persistence. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2505.17858\">10.48550/arXiv.2505.17858</a>","short":"Y. Bokor Bleile, L. Fajstrup, T. Heiss, A.M. Svane, S.S. Sørensen, ArXiv (n.d.).","mla":"Bokor Bleile, Yossi, et al. “Identifying Cobordisms Using Kernel Persistence.” <i>ArXiv</i>, 2505.17858, doi:<a href=\"https://doi.org/10.48550/arXiv.2505.17858\">10.48550/arXiv.2505.17858</a>.","chicago":"Bokor Bleile, Yossi, Lisbeth Fajstrup, Teresa Heiss, Anne Marie Svane, and Søren Strandskov Sørensen. “Identifying Cobordisms Using Kernel Persistence.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2505.17858\">https://doi.org/10.48550/arXiv.2505.17858</a>."},"article_number":"2505.17858","date_created":"2026-01-20T10:12:21Z","das_tickbox":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2505.17858","open_access":"1"}],"ec_funded":1,"day":"23","month":"05","date_updated":"2026-07-22T06:33:07Z","abstract":[{"text":"Motivated by applications in chemistry, we give a homlogical definition of tunnels, or more generally cobordisms, connecting disjoint parts of a cell complex. For a filtered complex, this defines a persistence module. We give a method for identifying birth and death times using kernel persistence and a matrix reduction algorithm for pairing birth and death times.","lang":"eng"}],"external_id":{"arxiv":["2505.17858"]},"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","arxiv":1,"oa_version":"Preprint","_id":"21016","author":[{"full_name":"Bleile, Yossi","orcid":"0000-0002-4861-9174","last_name":"Bleile","first_name":"Yossi","id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2"},{"full_name":"Fajstrup, Lisbeth","last_name":"Fajstrup","first_name":"Lisbeth"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","last_name":"Heiss","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"full_name":"Svane, Anne Marie","first_name":"Anne Marie","last_name":"Svane"},{"first_name":"Søren Strandskov","last_name":"Sørensen","full_name":"Sørensen, Søren Strandskov"}],"publication":"arXiv","acknowledgement":"Y. B. B. and L. F. were funded by the Independent Research Fund Denmark, grant\r\nnumber 1026-00037. T. H. was partially supported by the European Research Council\r\n(ERC) Horizon 2020, grant number 788183.","language":[{"iso":"eng"}],"department":[{"_id":"HeEd"}],"date_published":"2025-05-23T00:00:00Z","doi":"10.48550/arXiv.2505.17858","OA_place":"repository","article_processing_charge":"No","project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020"}]},{"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","first_name":"Christopher D","last_name":"Fillmore","full_name":"Fillmore, Christopher D"},{"full_name":"Olivera, Gonçalo","last_name":"Olivera","first_name":"Gonçalo"}],"_id":"21050","publication":"arXiv","date_published":"2025-03-20T00:00:00Z","department":[{"_id":"HeEd"}],"doi":"10.48550/ARXIV.2501.05315","language":[{"iso":"eng"}],"article_processing_charge":"No","OA_place":"repository","date_updated":"2026-07-22T06:33:55Z","abstract":[{"lang":"eng","text":"In 1873, James C. Maxwell conjectured that the electric field generated by $n$ point charges in generic position has at most $(n-1)^2$ isolated zeroes. The first (non-optimal) upper bound was only obtained in 2007 by Gabrielov, Novikov and Shapiro, who also posed two additional interesting conjectures.\r\n In this article, we give the best upper bound known to date on the number of zeroes of the electric field, and construct a counterexample to a conjecture of Gabrielov, Novikov and Shapiro that the number of equilibria cannot exceed those of the distance function defined by the unit point charges.\r\n Finally, we note that it is quite possible that Maxwell's quadratic upper bound is not tight, so it is prudent to find smaller bounds. Hence, we also explore examples and construct configurations of charges achieving the highest ratios of the number of electric field zeroes by point charges found to this day."}],"month":"03","external_id":{"arxiv":["2501.05315"]},"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"related_material":{"record":[{"status":"public","id":"21021","relation":"dissertation_contains"},{"status":"public","id":"21931","relation":"later_version"}]},"oa_version":"Preprint","arxiv":1,"article_number":"2501.05315","citation":{"ama":"Edelsbrunner H, Fillmore CD, Olivera G. Counting equilibria of the electrostatic potential. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2501.05315\">10.48550/ARXIV.2501.05315</a>","short":"H. Edelsbrunner, C.D. Fillmore, G. Olivera, ArXiv (n.d.).","apa":"Edelsbrunner, H., Fillmore, C. D., &#38; Olivera, G. (n.d.). Counting equilibria of the electrostatic potential. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2501.05315\">https://doi.org/10.48550/ARXIV.2501.05315</a>","ista":"Edelsbrunner H, Fillmore CD, Olivera G. Counting equilibria of the electrostatic potential. arXiv, 2501.05315.","chicago":"Edelsbrunner, Herbert, Christopher D Fillmore, and Gonçalo Olivera. “Counting Equilibria of the Electrostatic Potential.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2501.05315\">https://doi.org/10.48550/ARXIV.2501.05315</a>.","mla":"Edelsbrunner, Herbert, et al. “Counting Equilibria of the Electrostatic Potential.” <i>ArXiv</i>, 2501.05315, doi:<a href=\"https://doi.org/10.48550/ARXIV.2501.05315\">10.48550/ARXIV.2501.05315</a>.","ieee":"H. Edelsbrunner, C. D. Fillmore, and G. Olivera, “Counting equilibria of the electrostatic potential,” <i>arXiv</i>. ."},"OA_type":"green","das_tickbox":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2501.05315","open_access":"1"}],"date_created":"2026-01-27T14:29:27Z","day":"20","publication_status":"draft","year":"2025","corr_author":"1","title":"Counting equilibria of the electrostatic potential","type":"preprint"},{"scopus_import":"1","ec_funded":1,"day":"01","citation":{"ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. 2024;72:29-48. doi:<a href=\"https://doi.org/10.1007/s00454-023-00566-1\">10.1007/s00454-023-00566-1</a>","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.","apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., &#38; Saghafian, M. (2024). On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-023-00566-1\">https://doi.org/10.1007/s00454-023-00566-1</a>","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2024. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 72, 29–48.","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00454-023-00566-1\">https://doi.org/10.1007/s00454-023-00566-1</a>.","mla":"Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>, vol. 72, Springer Nature, 2024, pp. 29–48, doi:<a href=\"https://doi.org/10.1007/s00454-023-00566-1\">10.1007/s00454-023-00566-1</a>.","ieee":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles in higher order Brillouin tessellations and related tilings in the plane,” <i>Discrete and Computational Geometry</i>, vol. 72. Springer Nature, pp. 29–48, 2024."},"date_created":"2023-09-17T22:01:10Z","volume":72,"type":"journal_article","title":"On angles in higher order Brillouin tessellations and related tilings in the plane","file_date_updated":"2024-07-22T09:43:19Z","publication_status":"published","publisher":"Springer Nature","corr_author":"1","page":"29-48","year":"2024","doi":"10.1007/s00454-023-00566-1","department":[{"_id":"HeEd"}],"date_published":"2024-07-01T00:00:00Z","acknowledgement":"Work by all authors but A. Garber is supported by the European Research Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially supported by the Alexander von Humboldt Foundation.","language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF"},{"grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"file":[{"file_name":"2024_DiscreteComputGeom_Edelsbrunner.pdf","success":1,"file_size":892019,"date_updated":"2024-07-22T09:43:19Z","relation":"main_file","date_created":"2024-07-22T09:43:19Z","access_level":"open_access","creator":"dernst","checksum":"b207b4e00f904e8ea8a30e24f0251f79","file_id":"17301","content_type":"application/pdf"}],"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Garber, Alexey","last_name":"Garber","first_name":"Alexey"},{"last_name":"Ghafari","first_name":"Mohadese","full_name":"Ghafari, Mohadese"},{"first_name":"Teresa","last_name":"Heiss","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza","full_name":"Saghafian, Morteza"}],"_id":"14345","isi":1,"ddc":["510"],"publication":"Discrete and Computational Geometry","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"status":"public","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","pmid":1,"intvolume":"        72","quality_controlled":"1","oa_version":"Published Version","arxiv":1,"abstract":[{"text":"For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2  is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970)).","lang":"eng"}],"date_updated":"2025-04-23T08:41:59Z","month":"07","external_id":{"arxiv":["2204.01076"],"isi":["001060727600004"],"pmid":["39610762"]}},{"date_updated":"2025-09-04T11:52:35Z","abstract":[{"lang":"eng","text":"A face in a curve arrangement is called popular if it is bounded by the same curve multiple times. Motivated by the automatic generation of curved nonogram puzzles, we investigate possibilities to eliminate the popular faces in an arrangement by inserting a single additional curve. This turns out to be NP-hard; however, it becomes tractable when the number of popular faces is small: We present a probabilistic FPT-approach in the number of popular faces."}],"month":"01","external_id":{"isi":["001207942000002"],"arxiv":["2202.12175"]},"status":"public","intvolume":"     14466","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Preprint","quality_controlled":"1","arxiv":1,"author":[{"first_name":"Phoebe","last_name":"De Nooijer","full_name":"De Nooijer, Phoebe"},{"last_name":"Terziadis","first_name":"Soeren","full_name":"Terziadis, Soeren"},{"first_name":"Alexandra","last_name":"Weinberger","full_name":"Weinberger, Alexandra"},{"last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mchedlidze","first_name":"Tamara","full_name":"Mchedlidze, Tamara"},{"first_name":"Maarten","last_name":"Löffler","full_name":"Löffler, Maarten"},{"full_name":"Rote, Günter","first_name":"Günter","last_name":"Rote"}],"isi":1,"alternative_title":["LNCS"],"_id":"14888","publication":"31st International Symposium on Graph Drawing and Network Visualization","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783031492747"]},"date_published":"2024-01-06T00:00:00Z","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"doi":"10.1007/978-3-031-49275-4_2","acknowledgement":"This work was initiated at the 16th European Research Week on Geometric Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF): W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]. A preliminary version of this work has been presented at the 38th European Workshop on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper, which includes appendices but is otherwise identical, is available as a technical report [10].","language":[{"iso":"eng"}],"article_processing_charge":"No","publication_status":"published","publisher":"Springer Nature","page":"18-33","year":"2024","title":"Removing popular faces in curve arrangements","type":"conference","citation":{"ieee":"P. De Nooijer <i>et al.</i>, “Removing popular faces in curve arrangements,” in <i>31st International Symposium on Graph Drawing and Network Visualization</i>, Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33.","ista":"De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14466, 18–33.","apa":"De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T., Löffler, M., &#38; Rote, G. (2024). Removing popular faces in curve arrangements. In <i>31st International Symposium on Graph Drawing and Network Visualization</i> (Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-49275-4_2\">https://doi.org/10.1007/978-3-031-49275-4_2</a>","ama":"De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve arrangements. In: <i>31st International Symposium on Graph Drawing and Network Visualization</i>. Vol 14466. Springer Nature; 2024:18-33. doi:<a href=\"https://doi.org/10.1007/978-3-031-49275-4_2\">10.1007/978-3-031-49275-4_2</a>","short":"P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M. Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 18–33.","mla":"De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.” <i>31st International Symposium on Graph Drawing and Network Visualization</i>, vol. 14466, Springer Nature, 2024, pp. 18–33, doi:<a href=\"https://doi.org/10.1007/978-3-031-49275-4_2\">10.1007/978-3-031-49275-4_2</a>.","chicago":"De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová, Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve Arrangements.” In <i>31st International Symposium on Graph Drawing and Network Visualization</i>, 14466:18–33. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/978-3-031-49275-4_2\">https://doi.org/10.1007/978-3-031-49275-4_2</a>."},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2202.12175","open_access":"1"}],"volume":14466,"date_created":"2024-01-28T23:01:43Z","scopus_import":"1","conference":{"end_date":"2023-09-22","name":"GD: Graph Drawing and Network Visualization","location":"Isola delle Femmine, Palermo, Italy","start_date":"2023-09-20"},"day":"06"},{"title":"Decomposition of geometric graphs into star-forests","type":"conference","publication_status":"published","publisher":"Springer Nature","page":"339-346","year":"2024","scopus_import":"1","ec_funded":1,"conference":{"name":"GD: Graph Drawing and Network Visualization","location":"Isola delle Femmine, Palermo, Italy","start_date":"2023-09-20","end_date":"2023-09-22"},"day":"01","citation":{"ieee":"J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs into star-forests,” in <i>31st International Symposium on Graph Drawing and Network Visualization</i>, Isola delle Femmine, Palermo, Italy, 2024, vol. 14465, pp. 339–346.","ista":"Pach J, Saghafian M, Schnider P. 2024. Decomposition of geometric graphs into star-forests. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14465, 339–346.","apa":"Pach, J., Saghafian, M., &#38; Schnider, P. (2024). Decomposition of geometric graphs into star-forests. In <i>31st International Symposium on Graph Drawing and Network Visualization</i> (Vol. 14465, pp. 339–346). Isola delle Femmine, Palermo, Italy: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">https://doi.org/10.1007/978-3-031-49272-3_23</a>","short":"J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.","ama":"Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests. In: <i>31st International Symposium on Graph Drawing and Network Visualization</i>. Vol 14465. Springer Nature; 2024:339-346. doi:<a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">10.1007/978-3-031-49272-3_23</a>","mla":"Pach, János, et al. “Decomposition of Geometric Graphs into Star-Forests.” <i>31st International Symposium on Graph Drawing and Network Visualization</i>, vol. 14465, Springer Nature, 2024, pp. 339–46, doi:<a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">10.1007/978-3-031-49272-3_23</a>.","chicago":"Pach, János, Morteza Saghafian, and Patrick Schnider. “Decomposition of Geometric Graphs into Star-Forests.” In <i>31st International Symposium on Graph Drawing and Network Visualization</i>, 14465:339–46. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">https://doi.org/10.1007/978-3-031-49272-3_23</a>."},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.13201","open_access":"1"}],"volume":14465,"date_created":"2024-02-18T23:01:03Z","status":"public","intvolume":"     14465","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","oa":1,"related_material":{"record":[{"status":"public","id":"21253","relation":"later_version"}]},"oa_version":"Preprint","quality_controlled":"1","arxiv":1,"abstract":[{"lang":"eng","text":"We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than n-1 star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs."}],"date_updated":"2026-04-16T09:12:37Z","month":"01","external_id":{"isi":["001207939600023"],"arxiv":["2306.13201"]},"department":[{"_id":"HeEd"}],"date_published":"2024-01-01T00:00:00Z","doi":"10.1007/978-3-031-49272-3_23","language":[{"iso":"eng"}],"acknowledgement":"János Pach’s Research partially supported by European Research Council (ERC), grant “GeoScape” No. 882971 and by the Hungarian Science Foundation (NKFIH), grant K-131529. Work by Morteza Saghafian is partially supported by the European Research Council (ERC), grant No. 788183, and by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31.","article_processing_charge":"No","project":[{"call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"author":[{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János","first_name":"János","last_name":"Pach"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"},{"last_name":"Schnider","first_name":"Patrick","full_name":"Schnider, Patrick"}],"alternative_title":["LNCS"],"isi":1,"_id":"15012","publication_identifier":{"eisbn":["9783031492723"],"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783031492716"]},"publication":"31st International Symposium on Graph Drawing and Network Visualization"},{"date_updated":"2026-04-07T12:58:47Z","abstract":[{"lang":"eng","text":"We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right."}],"month":"01","external_id":{"arxiv":["2311.01115"]},"status":"public","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"id":"15094","status":"public","relation":"dissertation_contains"}]},"quality_controlled":"1","editor":[{"last_name":"Woodruff","first_name":"David P.","full_name":"Woodruff, David P."}],"oa_version":"Preprint","arxiv":1,"author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","last_name":"Cultrera di Montesano"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H","last_name":"Henzinger"},{"last_name":"Ost","first_name":"Lara","full_name":"Ost, Lara"}],"_id":"15093","publication":"Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)","publication_identifier":{"eisbn":["9781611977912"]},"doi":"10.1137/1.9781611977912.11","department":[{"_id":"HeEd"},{"_id":"MoHe"}],"date_published":"2024-01-04T00:00:00Z","acknowledgement":"The  first  and  second  authors  are  funded  by  the  European  Research  Council  under  the European Union’s Horizon 2020 research and innovation programme, ERC grant no. 788183,“Alpha Shape Theory Extended (Alpha)”, by the Wittgenstein Prize, FWF grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.The third author received funding by the European Research Council under the European Union’s Horizon 2020research  and  innovation  programme,  ERC  grant  no.  101019564,  “The  Design  of  Modern  Fully  Dynamic  DataStructures (MoDynStruct)”, and by the Austrian Science Fund through the Wittgenstein Prize with FWF grant no. Z 422-N, and also by FWF grant no. I 5982-N, and by FWF grant no. P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024.  The fourth author is funded by the Vienna Graduate School on Computational Optimization, FWF project no. W1260-N35.","language":[{"iso":"eng"}],"project":[{"grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"},{"grant_number":"101019564","call_identifier":"H2020","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","name":"The design and evaluation of modern fully dynamic data structures"},{"grant_number":"Z00422","name":"Efficient algorithms","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775"}],"article_processing_charge":"No","publication_status":"published","publisher":"Society for Industrial and Applied Mathematics","corr_author":"1","page":"243 - 295","year":"2024","type":"conference","title":"Dynamically maintaining the persistent homology of time series","citation":{"ieee":"S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, and L. Ost, “Dynamically maintaining the persistent homology of time series,” in <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, Alexandria, VA, USA, 2024, pp. 243–295.","short":"S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, L. Ost, in:, D.P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics, 2024, pp. 243–295.","ama":"Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. Dynamically maintaining the persistent homology of time series. In: Woodruff DP, ed. <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>. Society for Industrial and Applied Mathematics; 2024:243-295. doi:<a href=\"https://doi.org/10.1137/1.9781611977912.11\">10.1137/1.9781611977912.11</a>","ista":"Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. 2024. Dynamically maintaining the persistent homology of time series. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). SODA: Symposium on Discrete Algorithms, 243–295.","apa":"Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M., &#38; Ost, L. (2024). Dynamically maintaining the persistent homology of time series. In D. P. Woodruff (Ed.), <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i> (pp. 243–295). Alexandria, VA, USA: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611977912.11\">https://doi.org/10.1137/1.9781611977912.11</a>","chicago":"Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika Henzinger, and Lara Ost. “Dynamically Maintaining the Persistent Homology of Time Series.” In <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, edited by David P. Woodruff, 243–95. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/1.9781611977912.11\">https://doi.org/10.1137/1.9781611977912.11</a>.","mla":"Cultrera di Montesano, Sebastiano, et al. “Dynamically Maintaining the Persistent Homology of Time Series.” <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, edited by David P. Woodruff, Society for Industrial and Applied Mathematics, 2024, pp. 243–95, doi:<a href=\"https://doi.org/10.1137/1.9781611977912.11\">10.1137/1.9781611977912.11</a>."},"main_file_link":[{"url":"https://arxiv.org/abs/2311.01115","open_access":"1"}],"date_created":"2024-03-08T10:27:39Z","scopus_import":"1","ec_funded":1,"conference":{"end_date":"2024-01-10","start_date":"2024-01-07","name":"SODA: Symposium on Discrete Algorithms","location":"Alexandria, VA, USA"},"day":"04"},{"date_created":"2024-03-31T22:01:11Z","volume":206,"citation":{"chicago":"Frankl, Peter, János Pach, and Dömötör Pálvölgyi. “Odd-Sunflowers.” <i>Journal of Combinatorial Theory, Series A</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">https://doi.org/10.1016/j.jcta.2024.105889</a>.","mla":"Frankl, Peter, et al. “Odd-Sunflowers.” <i>Journal of Combinatorial Theory, Series A</i>, vol. 206, no. 8, 105889, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">10.1016/j.jcta.2024.105889</a>.","short":"P. Frankl, J. Pach, D. Pálvölgyi, Journal of Combinatorial Theory, Series A 206 (2024).","ama":"Frankl P, Pach J, Pálvölgyi D. Odd-sunflowers. <i>Journal of Combinatorial Theory, Series A</i>. 2024;206(8). doi:<a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">10.1016/j.jcta.2024.105889</a>","apa":"Frankl, P., Pach, J., &#38; Pálvölgyi, D. (2024). Odd-sunflowers. <i>Journal of Combinatorial Theory, Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">https://doi.org/10.1016/j.jcta.2024.105889</a>","ista":"Frankl P, Pach J, Pálvölgyi D. 2024. Odd-sunflowers. Journal of Combinatorial Theory, Series A. 206(8), 105889.","ieee":"P. Frankl, J. Pach, and D. Pálvölgyi, “Odd-sunflowers,” <i>Journal of Combinatorial Theory, Series A</i>, vol. 206, no. 8. Elsevier, 2024."},"article_number":"105889","OA_type":"hybrid","day":"01","scopus_import":"1","corr_author":"1","year":"2024","publication_status":"published","publisher":"Elsevier","issue":"8","type":"journal_article","file_date_updated":"2025-01-09T08:37:20Z","title":"Odd-sunflowers","ddc":["510"],"publication":"Journal of Combinatorial Theory, Series A","publication_identifier":{"eissn":["1096-0899"],"issn":["0097-3165"]},"has_accepted_license":"1","author":[{"last_name":"Frankl","first_name":"Peter","full_name":"Frankl, Peter"},{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","last_name":"Pach","full_name":"Pach, János"},{"full_name":"Pálvölgyi, Dömötör","first_name":"Dömötör","last_name":"Pálvölgyi"}],"_id":"15247","isi":1,"file":[{"success":1,"file_name":"2024_JourCombiTheoryA_Frankl.pdf","content_type":"application/pdf","checksum":"ffc29d65e712849f0d31009271e06a63","file_id":"18791","access_level":"open_access","creator":"dernst","date_created":"2025-01-09T08:37:20Z","file_size":366029,"relation":"main_file","date_updated":"2025-01-09T08:37:20Z"}],"OA_place":"publisher","article_processing_charge":"No","doi":"10.1016/j.jcta.2024.105889","department":[{"_id":"HeEd"}],"date_published":"2024-08-01T00:00:00Z","acknowledgement":"We are grateful to Balázs Keszegh, and to the members of the Miklós Schweitzer Competition committee of 2022 for valuable discussions, and Shira Zerbib for pointing out several important mathematical typos.","language":[{"iso":"eng"}],"external_id":{"arxiv":["2310.16701"],"isi":["001217739200001"]},"date_updated":"2025-09-04T13:20:39Z","abstract":[{"text":"Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant <2 such that every family of subsets of an n-element set that contains no odd-sunflower consists of at most n sets. We construct such families of size at least 1.5021n. We also characterize minimal odd-sunflowers of triples.","lang":"eng"}],"month":"08","quality_controlled":"1","oa_version":"Published Version","arxiv":1,"article_type":"original","status":"public","tmp":{"image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)"},"oa":1,"license":"https://creativecommons.org/licenses/by-nc/4.0/","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":"       206"},{"publisher":"Springer Nature","publication_status":"published","corr_author":"1","page":"557-578","year":"2024","type":"journal_article","file_date_updated":"2025-04-23T08:01:36Z","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","OA_type":"hybrid","citation":{"mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>, vol. 8, Springer Nature, 2024, pp. 557–78, doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Journal of Applied and Computational Topology. 8, 557–578.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. 2024;8:557-578. doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” <i>Journal of Applied and Computational Topology</i>, vol. 8. Springer Nature, pp. 557–578, 2024."},"date_created":"2024-05-12T22:01:03Z","volume":8,"ec_funded":1,"scopus_import":"1","day":"01","month":"09","date_updated":"2025-05-14T09:27:57Z","abstract":[{"text":"The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements.","lang":"eng"}],"external_id":{"pmid":["39308789"]},"related_material":{"record":[{"relation":"earlier_version","id":"11658","status":"public"}]},"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","pmid":1,"intvolume":"         8","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"status":"public","quality_controlled":"1","oa_version":"Published Version","_id":"15380","has_accepted_license":"1","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","full_name":"Cultrera Di Montesano, Sebastiano","last_name":"Cultrera Di Montesano","first_name":"Sebastiano"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza","full_name":"Saghafian, Morteza"}],"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"ddc":["510"],"publication":"Journal of Applied and Computational Topology","language":[{"iso":"eng"}],"acknowledgement":"The authors thank Uli Wagner and Emo Welzl for comments on an earlier version of this paper, and for pointing out related work in the prior literature.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.","doi":"10.1007/s41468-024-00173-w","date_published":"2024-09-01T00:00:00Z","department":[{"_id":"HeEd"}],"project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"file":[{"success":1,"file_name":"2024_JourApplCompTopo_BiswasRa.pdf","file_id":"19612","checksum":"0ee15c1493a6413cf356ab2f32c81a9e","content_type":"application/pdf","access_level":"open_access","date_created":"2025-04-23T08:01:36Z","creator":"dernst","date_updated":"2025-04-23T08:01:36Z","relation":"main_file","file_size":522831}],"OA_place":"publisher","article_processing_charge":"Yes (via OA deal)"},{"scopus_import":"1","ec_funded":1,"day":"01","conference":{"end_date":"2024-06-14","location":"Athens, Greece","name":"SoCG: Symposium on Computational Geometry"},"article_number":"69","citation":{"ieee":"H. Kourimska, A. Lieutier, and M. Wintraecken, “The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms,” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","chicago":"Kourimska, Hana, André Lieutier, and Mathijs Wintraecken. “The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">https://doi.org/10.4230/LIPIcs.SoCG.2024.69</a>.","mla":"Kourimska, Hana, et al. “The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 69, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">10.4230/LIPIcs.SoCG.2024.69</a>.","short":"H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ama":"Kourimska H, Lieutier A, Wintraecken M. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">10.4230/LIPIcs.SoCG.2024.69</a>","ista":"Kourimska H, Lieutier A, Wintraecken M. 2024. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 69.","apa":"Kourimska, H., Lieutier, A., &#38; Wintraecken, M. (2024). The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">https://doi.org/10.4230/LIPIcs.SoCG.2024.69</a>"},"date_created":"2024-06-16T22:01:06Z","volume":293,"type":"conference","file_date_updated":"2024-06-17T08:33:40Z","title":"The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","year":"2024","language":[{"iso":"eng"}],"acknowledgement":"This research has been supported by the European Research Council (ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant No. I 02979-N35.\r\nSupported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant No. M-3073, and the welcome package from IDEX of the Université Cô d'Azur.\r\nWe are greatly indebted to Fred Chazal for sharing his insights. We further thank Erin Chambers, Christopher Fillmore, and Elizabeth Stephenson for early discussions and all members of the Edelsbrunner group (Institute of Science and Technology Austria) and the Datashape team (Inria) for the atmosphere in which this research was conducted.","doi":"10.4230/LIPIcs.SoCG.2024.69","department":[{"_id":"HeEd"}],"date_published":"2024-06-01T00:00:00Z","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF","grant_number":"Z00342"},{"call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"},{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020"},{"grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses"}],"file":[{"file_id":"17150","checksum":"b40ff456c19294adb5d9613fcfd751c6","content_type":"application/pdf","access_level":"open_access","creator":"dernst","date_created":"2024-06-17T08:33:40Z","file_size":1612558,"date_updated":"2024-06-17T08:33:40Z","relation":"main_file","success":1,"file_name":"2024_LIPICS_Kourimska.pdf"}],"article_processing_charge":"No","_id":"17144","alternative_title":["LIPIcs"],"has_accepted_license":"1","author":[{"orcid":"0000-0001-7841-0091","full_name":"Kourimska, Hana","first_name":"Hana","last_name":"Kourimska","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E"},{"full_name":"Lieutier, André","last_name":"Lieutier","first_name":"André"},{"last_name":"Wintraecken","first_name":"Mathijs","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"publication":"40th International Symposium on Computational Geometry","ddc":["510"],"publication_identifier":{"isbn":["9783959773164"],"issn":["1868-8969"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"intvolume":"       293","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"status":"public","arxiv":1,"quality_controlled":"1","oa_version":"Published Version","month":"06","date_updated":"2025-04-15T07:16:58Z","abstract":[{"lang":"eng","text":"We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let 𝒮 ⊆ ℝ^d be a fixed closed set that contains a bounding sphere. That is, the bounding sphere is part of the set 𝒮. Consider the space of C^{1,1} diffeomorphisms of ℝ^d to itself, which keep the bounding sphere invariant. The map from this space of diffeomorphisms (endowed with a Banach norm) to the space of closed subsets of ℝ^d (endowed with the Hausdorff distance), mapping a diffeomorphism F to the closure of the medial axis of F(𝒮), is Lipschitz. This extends a previous stability result of Chazal and Soufflet on the stability of the medial axis of C² manifolds under C² ambient diffeomorphisms."}],"external_id":{"arxiv":["2212.01118"]}},{"abstract":[{"lang":"eng","text":"Grid peeling is the process of repeatedly removing the convex hull vertices of the grid points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes."}],"date_updated":"2024-06-17T08:41:56Z","month":"06","external_id":{"arxiv":["2402.15787"]},"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"       293","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"oa_version":"Published Version","quality_controlled":"1","arxiv":1,"author":[{"first_name":"Günter","last_name":"Rote","full_name":"Rote, Günter"},{"full_name":"Rüber, Moritz","last_name":"Rüber","first_name":"Moritz"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"has_accepted_license":"1","alternative_title":["LIPIcs"],"_id":"17145","publication_identifier":{"issn":["1868-8969"],"isbn":["9783959773164"]},"publication":"40th International Symposium on Computational Geometry","ddc":["510"],"date_published":"2024-06-01T00:00:00Z","department":[{"_id":"HeEd"}],"doi":"10.4230/LIPIcs.SoCG.2024.76","acknowledgement":"Part of this work was done while G.R. enjoyed the hospitality of the Institute of Science and Technology Austria (ISTA) as a visiting professor during his sabbatical in the winter semester 2022/23.","language":[{"iso":"eng"}],"article_processing_charge":"No","file":[{"file_size":1430896,"relation":"main_file","date_updated":"2024-06-17T08:40:04Z","file_id":"17151","checksum":"fbad1de06383a6b7e8a1cb3e8c7205ce","content_type":"application/pdf","creator":"dernst","access_level":"open_access","date_created":"2024-06-17T08:40:04Z","file_name":"2024_LIPICS_Rote.pdf","success":1}],"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2024","title":"Grid peeling of parabolas","file_date_updated":"2024-06-17T08:40:04Z","type":"conference","citation":{"ama":"Rote G, Rüber M, Saghafian M. Grid peeling of parabolas. In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">10.4230/LIPIcs.SoCG.2024.76</a>","short":"G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","apa":"Rote, G., Rüber, M., &#38; Saghafian, M. (2024). Grid peeling of parabolas. In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">https://doi.org/10.4230/LIPIcs.SoCG.2024.76</a>","ista":"Rote G, Rüber M, Saghafian M. 2024. Grid peeling of parabolas. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 76.","chicago":"Rote, Günter, Moritz Rüber, and Morteza Saghafian. “Grid Peeling of Parabolas.” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">https://doi.org/10.4230/LIPIcs.SoCG.2024.76</a>.","mla":"Rote, Günter, et al. “Grid Peeling of Parabolas.” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 76, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">10.4230/LIPIcs.SoCG.2024.76</a>.","ieee":"G. Rote, M. Rüber, and M. Saghafian, “Grid peeling of parabolas,” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293."},"article_number":"76","volume":293,"date_created":"2024-06-16T22:01:06Z","scopus_import":"1","conference":{"location":"Athens, Greece","start_date":"2024-06-11","name":"SoCG: Symposium on Computational Geometry","end_date":"2024-06-14"},"day":"01"}]