[{"external_id":{"pmid":["40870326"],"isi":["001557476000001"]},"quality_controlled":"1","date_updated":"2025-09-30T14:32:31Z","license":"https://creativecommons.org/licenses/by/4.0/","month":"08","volume":27,"title":"Tight bounds between the Jensen–Shannon divergence and the minmax divergence","PlanS_conform":"1","isi":1,"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.","date_published":"2025-08-01T00:00:00Z","article_processing_charge":"Yes","OA_type":"gold","publication_identifier":{"eissn":["1099-4300"]},"type":"journal_article","status":"public","oa_version":"Published Version","citation":{"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.","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>","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>","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>.","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.","short":"A. Akopyan, H. Edelsbrunner, Z. Virk, H. Wagner, Entropy 27 (2025)."},"article_number":"854","scopus_import":"1","abstract":[{"lang":"eng","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."}],"publisher":"MDPI","file_date_updated":"2025-09-08T07:55:48Z","author":[{"first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert","first_name":"Hubert","last_name":"Wagner"}],"ddc":["500"],"language":[{"iso":"eng"}],"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Mathematics, Computer Science","call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"file":[{"file_size":379340,"content_type":"application/pdf","relation":"main_file","date_updated":"2025-09-08T07:55:48Z","creator":"dernst","checksum":"65c5399c4015d9c8abb8c7a96f3d7836","access_level":"open_access","file_name":"2025_Entropy_Akopyan.pdf","date_created":"2025-09-08T07:55:48Z","file_id":"20309","success":1}],"doi":"10.3390/e27080854","oa":1,"publication_status":"published","intvolume":"        27","year":"2025","DOAJ_listed":"1","date_created":"2025-09-07T22:01:33Z","article_type":"original","day":"01","corr_author":"1","OA_place":"publisher","publication":"Entropy","ec_funded":1,"issue":"8","department":[{"_id":"HeEd"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"20293","pmid":1,"has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"intvolume":"       229","oa":1,"publication_status":"published","file":[{"relation":"main_file","content_type":"application/pdf","date_updated":"2025-12-30T07:55:08Z","file_size":3090836,"success":1,"file_id":"20886","date_created":"2025-12-30T07:55:08Z","file_name":"2025_JourPureAppliedAlgebra_Brown.pdf","access_level":"open_access","checksum":"39bcad462278c9322ef810af7db67f56","creator":"dernst"}],"doi":"10.1016/j.jpaa.2025.108068","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"ddc":["510"],"language":[{"iso":"eng"}],"author":[{"first_name":"Adam","last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425","full_name":"Brown, Adam"},{"id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej","last_name":"Draganov","first_name":"Ondrej","orcid":"0000-0003-0464-3823"}],"file_date_updated":"2025-12-30T07:55:08Z","article_type":"original","date_created":"2025-09-10T05:40:09Z","year":"2025","publication":"Journal of Pure and Applied Algebra","corr_author":"1","OA_place":"publisher","day":"01","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"20323","issue":"10","ec_funded":1,"department":[{"_id":"HeEd"}],"month":"10","quality_controlled":"1","date_updated":"2025-12-30T07:55:21Z","external_id":{"arxiv":["2209.14993"]},"date_published":"2025-10-01T00:00:00Z","arxiv":1,"article_processing_charge":"Yes (via OA deal)","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","PlanS_conform":"1","title":"Discrete microlocal Morse theory","volume":229,"status":"public","type":"journal_article","publication_identifier":{"issn":["0022-4049"]},"related_material":{"record":[{"id":"18981","relation":"earlier_version","status":"public"}]},"OA_type":"hybrid","publisher":"Elsevier","citation":{"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>.","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>","ista":"Brown A, Draganov O. 2025. Discrete microlocal Morse theory. Journal of Pure and Applied Algebra. 229(10), 108068.","short":"A. Brown, O. Draganov, Journal of Pure and Applied Algebra 229 (2025).","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>.","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>"},"article_number":"108068","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."}],"scopus_import":"1","oa_version":"Published Version"},{"month":"11","external_id":{"arxiv":["2504.14743"]},"date_updated":"2025-11-24T10:05:11Z","quality_controlled":"1","title":"The mid-sphere cousin of the medial axis transform","article_processing_charge":"No","arxiv":1,"date_published":"2025-11-01T00:00:00Z","volume":16296,"type":"conference","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783032095435"]},"status":"public","OA_type":"green","publisher":"Springer Nature","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2504.14743"}],"citation":{"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>.","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>","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.","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.","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>.","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.","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>"},"scopus_import":"1","abstract":[{"lang":"eng","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."}],"oa_version":"Preprint","publication_status":"published","oa":1,"doi":"10.1007/978-3-032-09544-2_10","intvolume":"     16296","language":[{"iso":"eng"}],"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","full_name":"Stephenson, Elizabeth R","first_name":"Elizabeth R","last_name":"Stephenson","orcid":"0000-0002-6862-208X"},{"full_name":"Thoresen, Martin H","id":"47CB1472-F248-11E8-B48F-1D18A9856A87","first_name":"Martin H","last_name":"Thoresen"}],"date_created":"2025-11-23T23:01:37Z","alternative_title":["LNCS"],"year":"2025","OA_place":"repository","publication":"4th International Joint Conference on Discrete Geometry and Mathematical Morphology","day":"01","page":"133-147","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"20658","department":[{"_id":"HeEd"}],"conference":{"location":"Groningen, The Netherlands","end_date":"2025-11-06","name":"DGMM: Discrete Geometry and Mathematical Morphology","start_date":"2025-11-03"}},{"OA_place":"publisher","corr_author":"1","publication":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","day":"10","page":"188-196","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"location":"Guanajuato, Mexico","start_date":"2025-07-28","end_date":"2025-08-01","name":"ISSAC: International Symposium on Symbolic and Algebraic Computation"},"department":[{"_id":"HeEd"}],"_id":"20729","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1145/3747199.3747561","file":[{"file_size":761617,"content_type":"application/pdf","date_updated":"2025-12-09T13:43:17Z","relation":"main_file","creator":"dernst","checksum":"1c299cca165a20e2518afe4fda63dbf1","access_level":"open_access","file_name":"2025_ISSAC_GonzalezDiaz.pdf","date_created":"2025-12-09T13:43:17Z","file_id":"20751","success":1}],"publication_status":"published","oa":1,"file_date_updated":"2025-12-09T13:43:17Z","author":[{"full_name":"Gonzalez-Diaz, Rocio","last_name":"Gonzalez-Diaz","first_name":"Rocio"},{"id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","full_name":"Soriano Trigueros, Manuel","first_name":"Manuel","last_name":"Soriano Trigueros","orcid":"0000-0003-2449-1433"},{"first_name":"Alvaro","last_name":"Torras-Casas","full_name":"Torras-Casas, Alvaro"}],"ddc":["510"],"language":[{"iso":"eng"}],"date_created":"2025-12-07T23:02:01Z","year":"2025","publication_identifier":{"isbn":["9798400720758"]},"type":"conference","status":"public","OA_type":"hybrid","publisher":"Association for Computing Machinery","oa_version":"Published Version","scopus_import":"1","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"}],"citation":{"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>","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>.","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.","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.","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>"},"month":"11","date_updated":"2025-12-09T13:46:42Z","quality_controlled":"1","title":"Additive partial matchings for persistent homology","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).","article_processing_charge":"Yes (in subscription journal)","date_published":"2025-11-10T00:00:00Z"},{"OA_place":"repository","publication":"arXiv","day":"23","ec_funded":1,"department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"21016","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"}],"doi":"10.48550/arXiv.2505.17858","oa":1,"publication_status":"submitted","author":[{"last_name":"Bleile","first_name":"Yossi","orcid":"0000-0002-4861-9174","id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2","full_name":"Bleile, Yossi"},{"full_name":"Fajstrup, Lisbeth","first_name":"Lisbeth","last_name":"Fajstrup"},{"first_name":"Teresa","last_name":"Heiss","orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","full_name":"Heiss, Teresa"},{"full_name":"Svane, Anne Marie","first_name":"Anne Marie","last_name":"Svane"},{"last_name":"Sørensen","first_name":"Søren Strandskov","full_name":"Sørensen, Søren Strandskov"}],"language":[{"iso":"eng"}],"date_created":"2026-01-20T10:12:21Z","year":"2025","type":"preprint","status":"public","OA_type":"green","das_tickbox":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2505.17858","open_access":"1"}],"oa_version":"Preprint","citation":{"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>.","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>","short":"Y. Bokor Bleile, L. Fajstrup, T. Heiss, A.M. Svane, S.S. Sørensen, ArXiv (n.d.).","ista":"Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms using kernel persistence. arXiv, 2505.17858.","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>.","ieee":"Y. Bokor Bleile, L. Fajstrup, T. Heiss, A. M. Svane, and S. S. Sørensen, “Identifying cobordisms using kernel persistence,” <i>arXiv</i>. .","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>"},"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"}],"article_number":"2505.17858","month":"05","external_id":{"arxiv":["2505.17858"]},"date_updated":"2026-07-22T06:33:07Z","title":"Identifying cobordisms using kernel persistence","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.","arxiv":1,"date_published":"2025-05-23T00:00:00Z","article_processing_charge":"No"},{"title":"Counting equilibria of the electrostatic potential","article_processing_charge":"No","date_published":"2025-03-20T00:00:00Z","arxiv":1,"external_id":{"arxiv":["2501.05315"]},"date_updated":"2026-07-22T06:33:55Z","month":"03","oa_version":"Preprint","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>","ieee":"H. Edelsbrunner, C. D. Fillmore, and G. Olivera, “Counting equilibria of the electrostatic potential,” <i>arXiv</i>. .","ista":"Edelsbrunner H, Fillmore CD, Olivera G. Counting equilibria of the electrostatic potential. arXiv, 2501.05315.","short":"H. Edelsbrunner, C.D. Fillmore, G. Olivera, ArXiv (n.d.).","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>.","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>.","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>"},"article_number":"2501.05315","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."}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2501.05315"}],"das_tickbox":"1","OA_type":"green","related_material":{"record":[{"relation":"dissertation_contains","id":"21021","status":"public"},{"status":"public","id":"21931","relation":"later_version"}]},"type":"preprint","status":"public","year":"2025","date_created":"2026-01-27T14:29:27Z","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"last_name":"Fillmore","first_name":"Christopher D","full_name":"Fillmore, Christopher D","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425"},{"last_name":"Olivera","first_name":"Gonçalo","full_name":"Olivera, Gonçalo"}],"language":[{"iso":"eng"}],"doi":"10.48550/ARXIV.2501.05315","publication_status":"draft","oa":1,"department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"21050","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"20","OA_place":"repository","corr_author":"1","publication":"arXiv"},{"publication":"Journal of Applied and Computational Topology","OA_place":"publisher","corr_author":"1","day":"01","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"page":"1101-1119","pmid":1,"department":[{"_id":"HeEd"}],"ec_funded":1,"_id":"13182","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"         8","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"name":"Persistent Homology, Algorithms and Stochastic Geometry","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"name":"Mathematics, Computer Science","call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"doi":"10.1007/s41468-023-00126-9","file":[{"access_level":"open_access","file_name":"2024_JourApplCompTopo_Biswas.pdf","checksum":"d493df5088c222b88d9ca46b623ad0ee","creator":"dernst","file_id":"18783","success":1,"date_created":"2025-01-09T07:39:41Z","relation":"main_file","date_updated":"2025-01-09T07:39:41Z","content_type":"application/pdf","file_size":476896}],"oa":1,"publication_status":"published","author":[{"orcid":"0000-0002-5372-7890","last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera Di Montesano, Sebastiano","last_name":"Cultrera Di Montesano","first_name":"Sebastiano","orcid":"0000-0001-6249-0832"},{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian"}],"ddc":["000"],"language":[{"iso":"eng"}],"file_date_updated":"2025-01-09T07:39:41Z","article_type":"original","date_created":"2023-07-02T22:00:44Z","year":"2024","status":"public","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"type":"journal_article","OA_type":"hybrid","related_material":{"record":[{"status":"public","id":"15094","relation":"dissertation_contains"}]},"publisher":"Springer Nature","oa_version":"Published Version","scopus_import":"1","citation":{"ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization of the persistence of 1D maps. <i>Journal of Applied and Computational Topology</i>. 2024;8:1101-1119. doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric characterization of the persistence of 1D maps,” <i>Journal of Applied and Computational Topology</i>, vol. 8. Springer Nature, pp. 1101–1119, 2024.","mla":"Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>, vol. 8, Springer Nature, 2024, pp. 1101–19, doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. 8, 1101–1119.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). Geometric characterization of the persistence of 1D maps. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>."},"abstract":[{"text":"We characterize critical points of 1-dimensional maps paired in persistent homology\r\ngeometrically and this way get elementary proofs of theorems about the symmetry\r\nof persistence diagrams and the variation of such maps. In particular, we identify\r\nbranching points and endpoints of networks as the sole source of asymmetry and\r\nrelate the cycle basis in persistent homology with a version of the stable marriage\r\nproblem. Our analysis provides the foundations of fast algorithms for maintaining a\r\ncollection of sorted lists together with its persistence diagram.","lang":"eng"}],"month":"10","date_updated":"2026-04-07T12:58:47Z","quality_controlled":"1","external_id":{"pmid":["39678706"]},"acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of this paper thank anonymous reviewers for their constructive criticism and Monika Henzinger for detailed comments on an earlier version of this paper.","article_processing_charge":"Yes (via OA deal)","date_published":"2024-10-01T00:00:00Z","title":"Geometric characterization of the persistence of 1D maps","volume":8},{"status":"public","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"type":"journal_article","publisher":"Springer Nature","oa_version":"Published Version","scopus_import":"1","citation":{"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>.","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.","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.","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>","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>.","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>","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."},"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"}],"month":"07","quality_controlled":"1","date_updated":"2025-04-23T08:41:59Z","external_id":{"pmid":["39610762"],"arxiv":["2204.01076"],"isi":["001060727600004"]},"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.","isi":1,"date_published":"2024-07-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","arxiv":1,"title":"On angles in higher order Brillouin tessellations and related tilings in the plane","volume":72,"publication":"Discrete and Computational Geometry","corr_author":"1","day":"01","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"page":"29-48","pmid":1,"ec_funded":1,"department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14345","intvolume":"        72","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"file":[{"file_size":892019,"content_type":"application/pdf","date_updated":"2024-07-22T09:43:19Z","relation":"main_file","date_created":"2024-07-22T09:43:19Z","file_id":"17301","success":1,"checksum":"b207b4e00f904e8ea8a30e24f0251f79","creator":"dernst","access_level":"open_access","file_name":"2024_DiscreteComputGeom_Edelsbrunner.pdf"}],"doi":"10.1007/s00454-023-00566-1","oa":1,"publication_status":"published","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Garber","first_name":"Alexey","full_name":"Garber, Alexey"},{"full_name":"Ghafari, Mohadese","last_name":"Ghafari","first_name":"Mohadese"},{"full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","first_name":"Teresa","last_name":"Heiss"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian"}],"ddc":["510"],"language":[{"iso":"eng"}],"file_date_updated":"2024-07-22T09:43:19Z","article_type":"original","date_created":"2023-09-17T22:01:10Z","year":"2024"},{"status":"public","publication_identifier":{"isbn":["9783031492747"],"eissn":["1611-3349"],"issn":["0302-9743"]},"type":"conference","oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"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.","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>","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>","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>.","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>.","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.","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."},"scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2202.12175","open_access":"1"}],"publisher":"Springer Nature","date_updated":"2025-09-04T11:52:35Z","quality_controlled":"1","external_id":{"arxiv":["2202.12175"],"isi":["001207942000002"]},"month":"01","volume":14466,"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].","isi":1,"date_published":"2024-01-06T00:00:00Z","article_processing_charge":"No","arxiv":1,"title":"Removing popular faces in curve arrangements","day":"06","publication":"31st International Symposium on Graph Drawing and Network Visualization","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"conference":{"start_date":"2023-09-20","name":"GD: Graph Drawing and Network Visualization","end_date":"2023-09-22","location":"Isola delle Femmine, Palermo, Italy"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"14888","page":"18-33","author":[{"last_name":"De Nooijer","first_name":"Phoebe","full_name":"De Nooijer, Phoebe"},{"full_name":"Terziadis, Soeren","last_name":"Terziadis","first_name":"Soeren"},{"full_name":"Weinberger, Alexandra","first_name":"Alexandra","last_name":"Weinberger"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana","first_name":"Zuzana","last_name":"Masárová","orcid":"0000-0002-6660-1322"},{"full_name":"Mchedlidze, Tamara","first_name":"Tamara","last_name":"Mchedlidze"},{"full_name":"Löffler, Maarten","last_name":"Löffler","first_name":"Maarten"},{"full_name":"Rote, Günter","last_name":"Rote","first_name":"Günter"}],"language":[{"iso":"eng"}],"intvolume":"     14466","doi":"10.1007/978-3-031-49275-4_2","oa":1,"publication_status":"published","year":"2024","alternative_title":["LNCS"],"date_created":"2024-01-28T23:01:43Z"},{"oa_version":"Preprint","citation":{"short":"J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, 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.","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>.","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>","ama":"Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests. In: <i>31st International Symposium on Graph Drawing and Network Visualization</i>. Vol 14465. Springer Nature; 2024:339-346. doi:<a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">10.1007/978-3-031-49272-3_23</a>","ieee":"J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs into star-forests,” in <i>31st International Symposium on Graph Drawing and Network Visualization</i>, Isola delle Femmine, Palermo, Italy, 2024, vol. 14465, pp. 339–346."},"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."}],"scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.13201","open_access":"1"}],"publisher":"Springer Nature","related_material":{"record":[{"relation":"later_version","id":"21253","status":"public"}]},"status":"public","publication_identifier":{"eissn":["1611-3349"],"issn":["0302-9743"],"eisbn":["9783031492723"],"isbn":["9783031492716"]},"type":"conference","volume":14465,"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.","isi":1,"arxiv":1,"date_published":"2024-01-01T00:00:00Z","article_processing_charge":"No","title":"Decomposition of geometric graphs into star-forests","quality_controlled":"1","date_updated":"2026-04-16T09:12:37Z","external_id":{"isi":["001207939600023"],"arxiv":["2306.13201"]},"month":"01","department":[{"_id":"HeEd"}],"ec_funded":1,"conference":{"location":"Isola delle Femmine, Palermo, Italy","start_date":"2023-09-20","end_date":"2023-09-22","name":"GD: Graph Drawing and Network Visualization"},"_id":"15012","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","page":"339-346","day":"01","publication":"31st International Symposium on Graph Drawing and Network Visualization","year":"2024","alternative_title":["LNCS"],"date_created":"2024-02-18T23:01:03Z","author":[{"last_name":"Pach","first_name":"János","full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"last_name":"Saghafian","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza"},{"last_name":"Schnider","first_name":"Patrick","full_name":"Schnider, Patrick"}],"language":[{"iso":"eng"}],"intvolume":"     14465","doi":"10.1007/978-3-031-49272-3_23","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Mathematics, Computer Science"}],"publication_status":"published","oa":1},{"year":"2024","date_created":"2024-03-08T10:27:39Z","author":[{"first_name":"Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","last_name":"Henzinger","first_name":"Monika H"},{"full_name":"Ost, Lara","first_name":"Lara","last_name":"Ost"}],"language":[{"iso":"eng"}],"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"Mathematics, Computer Science","call_identifier":"FWF"},{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures"},{"grant_number":"Z00422","_id":"34def286-11ca-11ed-8bc3-da5948e1613c","name":"Efficient algorithms"},{"name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"doi":"10.1137/1.9781611977912.11","publication_status":"published","oa":1,"conference":{"location":"Alexandria, VA, USA","name":"SODA: Symposium on Discrete Algorithms","end_date":"2024-01-10","start_date":"2024-01-07"},"department":[{"_id":"HeEd"},{"_id":"MoHe"}],"ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"15093","page":"243 - 295","day":"04","corr_author":"1","publication":"Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)","title":"Dynamically maintaining the persistent homology of time series","editor":[{"full_name":"Woodruff, David P.","last_name":"Woodruff","first_name":"David P."}],"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.","arxiv":1,"article_processing_charge":"No","date_published":"2024-01-04T00:00:00Z","external_id":{"arxiv":["2311.01115"]},"date_updated":"2026-04-07T12:58:47Z","quality_controlled":"1","month":"01","oa_version":"Preprint","scopus_import":"1","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."}],"citation":{"ama":"Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. Dynamically maintaining the persistent homology of time series. In: Woodruff DP, ed. <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>. Society for Industrial and Applied Mathematics; 2024:243-295. doi:<a href=\"https://doi.org/10.1137/1.9781611977912.11\">10.1137/1.9781611977912.11</a>","ieee":"S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, and L. Ost, “Dynamically maintaining the persistent homology of time series,” in <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, Alexandria, VA, USA, 2024, pp. 243–295.","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.","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.","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>.","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>.","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>"},"publisher":"Society for Industrial and Applied Mathematics","main_file_link":[{"url":"https://arxiv.org/abs/2311.01115","open_access":"1"}],"related_material":{"record":[{"id":"15094","relation":"dissertation_contains","status":"public"}]},"publication_identifier":{"eisbn":["9781611977912"]},"type":"conference","status":"public"},{"status":"public","publication_identifier":{"issn":["2663-337X"]},"type":"dissertation","related_material":{"record":[{"relation":"part_of_dissertation","id":"15091","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"11660"},{"status":"public","id":"15090","relation":"part_of_dissertation"},{"status":"public","id":"15093","relation":"part_of_dissertation"},{"status":"public","id":"13182","relation":"part_of_dissertation"},{"status":"public","id":"11658","relation":"part_of_dissertation"}]},"publisher":"Institute of Science and Technology Austria","oa_version":"Published Version","abstract":[{"text":"Point sets, geometric networks, and arrangements of hyperplanes are fundamental objects in\r\ndiscrete geometry that have captivated mathematicians for centuries, if not millennia. This\r\nthesis seeks to cast new light on these structures by illustrating specific instances where a\r\ntopological perspective, specifically through discrete Morse theory and persistent homology,\r\nprovides valuable insights.\r\n\r\nAt first glance, the topology of these geometric objects might seem uneventful: point sets\r\nessentially lack of topology, arrangements of hyperplanes are a decomposition of Rd, which\r\nis a contractible space, and the topology of a network primarily involves the enumeration\r\nof connected components and cycles within the network. However, beneath this apparent\r\nsimplicity, there lies an array of intriguing structures, a small subset of which will be uncovered\r\nin this thesis.\r\n\r\nFocused on three case studies, each addressing one of the mentioned objects, this work\r\nwill showcase connections that intertwine topology with diverse fields such as combinatorial\r\ngeometry, algorithms and data structures, and emerging applications like spatial biology.\r\n\r\n","lang":"eng"}],"citation":{"ama":"Cultrera di Montesano S. Persistence and Morse theory for discrete geometric structures. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:15094\">10.15479/at:ista:15094</a>","ieee":"S. Cultrera di Montesano, “Persistence and Morse theory for discrete geometric structures,” Institute of Science and Technology Austria, 2024.","short":"S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024.","ista":"Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria.","mla":"Cultrera di Montesano, Sebastiano. <i>Persistence and Morse Theory for Discrete Geometric Structures</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:15094\">10.15479/at:ista:15094</a>.","chicago":"Cultrera di Montesano, Sebastiano. “Persistence and Morse Theory for Discrete Geometric Structures.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:15094\">https://doi.org/10.15479/at:ista:15094</a>.","apa":"Cultrera di Montesano, S. (2024). <i>Persistence and Morse theory for discrete geometric structures</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:15094\">https://doi.org/10.15479/at:ista:15094</a>"},"month":"03","date_updated":"2026-04-07T12:58:48Z","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","article_processing_charge":"No","date_published":"2024-03-08T00:00:00Z","title":"Persistence and Morse theory for discrete geometric structures","OA_place":"publisher","corr_author":"1","day":"08","has_accepted_license":"1","supervisor":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"page":"108","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"ec_funded":1,"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","_id":"15094","doi":"10.15479/at:ista:15094","file":[{"file_size":4106872,"date_updated":"2024-03-14T08:55:07Z","content_type":"application/pdf","relation":"main_file","date_created":"2024-03-14T08:55:07Z","success":1,"file_id":"15112","checksum":"1e468bfa42a7dcf04d89f4dadc621c87","creator":"scultrer","file_name":"Thesis Sebastiano.pdf","access_level":"open_access"},{"file_id":"15113","date_created":"2024-03-14T08:56:24Z","file_name":"Thesis (1).zip","access_level":"closed","checksum":"bcbd213490f5a7e68855a092bbce93f1","creator":"scultrer","date_updated":"2024-03-14T14:14:35Z","content_type":"application/zip","relation":"source_file","file_size":4746234}],"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Persistent Homology, Algorithms and Stochastic Geometry"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"publication_status":"published","oa":1,"author":[{"first_name":"Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano"}],"language":[{"iso":"eng"}],"ddc":["514","500","516"],"degree_awarded":"PhD","file_date_updated":"2024-03-14T14:14:35Z","alternative_title":["ISTA Thesis"],"date_created":"2024-03-08T15:28:10Z","year":"2024"},{"file_date_updated":"2025-01-09T08:37:20Z","author":[{"full_name":"Frankl, Peter","last_name":"Frankl","first_name":"Peter"},{"full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","last_name":"Pach"},{"full_name":"Pálvölgyi, Dömötör","last_name":"Pálvölgyi","first_name":"Dömötör"}],"ddc":["510"],"language":[{"iso":"eng"}],"file":[{"relation":"main_file","content_type":"application/pdf","date_updated":"2025-01-09T08:37:20Z","file_size":366029,"access_level":"open_access","file_name":"2024_JourCombiTheoryA_Frankl.pdf","checksum":"ffc29d65e712849f0d31009271e06a63","creator":"dernst","file_id":"18791","success":1,"date_created":"2025-01-09T08:37:20Z"}],"doi":"10.1016/j.jcta.2024.105889","publication_status":"published","oa":1,"intvolume":"       206","year":"2024","date_created":"2024-03-31T22:01:11Z","article_type":"original","day":"01","corr_author":"1","OA_place":"publisher","publication":"Journal of Combinatorial Theory, Series A","department":[{"_id":"HeEd"}],"issue":"8","_id":"15247","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","image":"/images/cc_by_nc.png","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","short":"CC BY-NC (4.0)"},"external_id":{"arxiv":["2310.16701"],"isi":["001217739200001"]},"date_updated":"2025-09-04T13:20:39Z","quality_controlled":"1","license":"https://creativecommons.org/licenses/by-nc/4.0/","month":"08","volume":206,"title":"Odd-sunflowers","isi":1,"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.","date_published":"2024-08-01T00:00:00Z","arxiv":1,"article_processing_charge":"No","OA_type":"hybrid","publication_identifier":{"issn":["0097-3165"],"eissn":["1096-0899"]},"type":"journal_article","status":"public","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant <2 such that every family of subsets of an n-element set that contains no odd-sunflower consists of at most n sets. We construct such families of size at least 1.5021n. We also characterize minimal odd-sunflowers of triples."}],"article_number":"105889","scopus_import":"1","citation":{"apa":"Frankl, P., Pach, J., &#38; Pálvölgyi, D. (2024). Odd-sunflowers. <i>Journal of Combinatorial Theory, Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">https://doi.org/10.1016/j.jcta.2024.105889</a>","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>.","ista":"Frankl P, Pach J, Pálvölgyi D. 2024. Odd-sunflowers. Journal of Combinatorial Theory, Series A. 206(8), 105889.","short":"P. Frankl, J. Pach, D. Pálvölgyi, Journal of Combinatorial Theory, Series A 206 (2024).","ieee":"P. Frankl, J. Pach, and D. Pálvölgyi, “Odd-sunflowers,” <i>Journal of Combinatorial Theory, Series A</i>, vol. 206, no. 8. Elsevier, 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>"},"publisher":"Elsevier"},{"volume":8,"title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","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.","article_processing_charge":"Yes (via OA deal)","date_published":"2024-09-01T00:00:00Z","external_id":{"pmid":["39308789"]},"quality_controlled":"1","date_updated":"2025-05-14T09:27:57Z","month":"09","oa_version":"Published Version","citation":{"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.","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>.","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.","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>","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>."},"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"}],"scopus_import":"1","publisher":"Springer Nature","related_material":{"record":[{"relation":"earlier_version","id":"11658","status":"public"}]},"OA_type":"hybrid","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"type":"journal_article","status":"public","year":"2024","date_created":"2024-05-12T22:01:03Z","article_type":"original","file_date_updated":"2025-04-23T08:01:36Z","author":[{"orcid":"0000-0002-5372-7890","first_name":"Ranita","last_name":"Biswas","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Cultrera Di Montesano","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera Di Montesano, Sebastiano"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"last_name":"Saghafian","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza"}],"ddc":["510"],"language":[{"iso":"eng"}],"file":[{"file_id":"19612","success":1,"date_created":"2025-04-23T08:01:36Z","access_level":"open_access","file_name":"2024_JourApplCompTopo_BiswasRa.pdf","checksum":"0ee15c1493a6413cf356ab2f32c81a9e","creator":"dernst","date_updated":"2025-04-23T08:01:36Z","relation":"main_file","content_type":"application/pdf","file_size":522831}],"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"doi":"10.1007/s41468-024-00173-w","publication_status":"published","oa":1,"intvolume":"         8","department":[{"_id":"HeEd"}],"ec_funded":1,"_id":"15380","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","pmid":1,"page":"557-578","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"01","corr_author":"1","OA_place":"publisher","publication":"Journal of Applied and Computational Topology"},{"year":"2024","alternative_title":["LIPIcs"],"date_created":"2024-06-16T22:01:06Z","language":[{"iso":"eng"}],"ddc":["510"],"author":[{"last_name":"Kourimska","first_name":"Hana","orcid":"0000-0001-7841-0091","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","full_name":"Kourimska, Hana"},{"full_name":"Lieutier, André","first_name":"André","last_name":"Lieutier"},{"full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken"}],"file_date_updated":"2024-06-17T08:33:40Z","intvolume":"       293","oa":1,"publication_status":"published","file":[{"file_size":1612558,"date_updated":"2024-06-17T08:33:40Z","content_type":"application/pdf","relation":"main_file","date_created":"2024-06-17T08:33:40Z","success":1,"file_id":"17150","checksum":"b40ff456c19294adb5d9613fcfd751c6","creator":"dernst","file_name":"2024_LIPICS_Kourimska.pdf","access_level":"open_access"}],"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"name":"Mathematics, Computer Science","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"},{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"name":"Learning and triangulating manifolds via collapses","grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"doi":"10.4230/LIPIcs.SoCG.2024.69","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"17144","department":[{"_id":"HeEd"}],"ec_funded":1,"conference":{"location":"Athens, Greece","end_date":"2024-06-14","name":"SoCG: Symposium on Computational Geometry"},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","day":"01","publication":"40th International Symposium on Computational Geometry","volume":293,"article_processing_charge":"No","date_published":"2024-06-01T00:00:00Z","arxiv":1,"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.","title":"The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms","quality_controlled":"1","date_updated":"2025-04-15T07:16:58Z","external_id":{"arxiv":["2212.01118"]},"month":"06","scopus_import":"1","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.","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>","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>","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>.","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.","short":"H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024."},"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."}],"article_number":"69","oa_version":"Published Version","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","status":"public","type":"conference","publication_identifier":{"isbn":["9783959773164"],"issn":["1868-8969"]}},{"day":"01","publication":"40th International Symposium on Computational Geometry","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"17145","department":[{"_id":"HeEd"}],"conference":{"location":"Athens, Greece","end_date":"2024-06-14","name":"SoCG: Symposium on Computational Geometry","start_date":"2024-06-11"},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","file_date_updated":"2024-06-17T08:40:04Z","ddc":["510"],"language":[{"iso":"eng"}],"author":[{"full_name":"Rote, Günter","first_name":"Günter","last_name":"Rote"},{"first_name":"Moritz","last_name":"Rüber","full_name":"Rüber, Moritz"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza"}],"oa":1,"publication_status":"published","file":[{"relation":"main_file","content_type":"application/pdf","date_updated":"2024-06-17T08:40:04Z","file_size":1430896,"success":1,"file_id":"17151","date_created":"2024-06-17T08:40:04Z","file_name":"2024_LIPICS_Rote.pdf","access_level":"open_access","creator":"dernst","checksum":"fbad1de06383a6b7e8a1cb3e8c7205ce"}],"doi":"10.4230/LIPIcs.SoCG.2024.76","intvolume":"       293","year":"2024","date_created":"2024-06-16T22:01:06Z","alternative_title":["LIPIcs"],"type":"conference","publication_identifier":{"isbn":["9783959773164"],"issn":["1868-8969"]},"status":"public","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>","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.","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.","short":"G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","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>.","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>.","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>"},"article_number":"76","scopus_import":"1","abstract":[{"text":"Grid peeling is the process of repeatedly removing the convex hull vertices of the grid points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes.","lang":"eng"}],"oa_version":"Published Version","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","external_id":{"arxiv":["2402.15787"]},"date_updated":"2024-06-17T08:41:56Z","quality_controlled":"1","month":"06","volume":293,"title":"Grid peeling of parabolas","article_processing_charge":"No","arxiv":1,"date_published":"2024-06-01T00:00:00Z","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."},{"alternative_title":["LIPIcs"],"date_created":"2024-06-25T11:45:58Z","year":"2024","intvolume":"       293","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"name":"Mathematics, Computer Science","call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"},{"name":"Learning and triangulating manifolds via collapses","grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"doi":"10.4230/LIPIcs.SoCG.2024.11","file":[{"relation":"main_file","date_updated":"2024-06-25T11:47:26Z","content_type":"application/pdf","file_size":20886142,"success":1,"file_id":"17171","date_created":"2024-06-25T11:47:26Z","file_name":"LIPIcs.SoCG.2024.11.pdf","access_level":"open_access","creator":"cfillmor","checksum":"6a2ddc8b51aa58f197a8b294750f1f8d"}],"oa":1,"publication_status":"published","author":[{"first_name":"Dominique","last_name":"Attali","full_name":"Attali, Dominique"},{"first_name":"Hana","last_name":"Kourimska","orcid":"0000-0001-7841-0091","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","full_name":"Kourimska, Hana"},{"id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","full_name":"Fillmore, Christopher D","first_name":"Christopher D","last_name":"Fillmore"},{"first_name":"Ishika","last_name":"Ghosh","id":"ee449b28-344d-11ef-a6d5-9ca430e9e9ff","full_name":"Ghosh, Ishika"},{"full_name":"Lieutier, André","last_name":"Lieutier","first_name":"André"},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","full_name":"Stephenson, Elizabeth R","first_name":"Elizabeth R","last_name":"Stephenson","orcid":"0000-0002-6862-208X"},{"first_name":"Mathijs","last_name":"Wintraecken","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs"}],"ddc":["516"],"language":[{"iso":"eng"}],"file_date_updated":"2024-06-25T11:47:26Z","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"page":"11:1-11:19","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"ec_funded":1,"conference":{"location":"Athens, Greece","start_date":"2024-06-11","end_date":"2024-06-14","name":"SoCG: Symposium on Computational Geometry"},"_id":"17170","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"40th International Symposium on Computational Geometry","day":"06","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\nWintraecken, Mathijs: Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant No. M-3073, and the welcome package from IDEX of the Université Côte d'Azur.","article_processing_charge":"No","date_published":"2024-06-06T00:00:00Z","arxiv":1,"title":"Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds","volume":293,"month":"06","quality_controlled":"1","date_updated":"2025-04-15T07:16:57Z","external_id":{"arxiv":["2206.10485"]},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa_version":"Published Version","abstract":[{"lang":"eng","text":"In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger on the learning of the homotopy type from a sample of an underlying space. In their work, Niyogi, Smale, and Weinberger studied samples of C² manifolds with positive reach embedded in ℝ^d. We extend their results in the following ways: - As the ambient space we consider both ℝ^d and Riemannian manifolds with lower bounded sectional curvature. - In both types of ambient spaces, we study sets of positive reach - a significantly more general setting than C² manifolds - as well as general manifolds of positive reach. - The sample P of a set (or a manifold) 𝒮 of positive reach may be noisy. We work with two one-sided Hausdorff distances - ε and δ - between P and 𝒮. We provide tight bounds in terms of ε and δ, that guarantee that there exists a parameter r such that the union of balls of radius r centred at the sample P deformation-retracts to 𝒮. We exhibit their tightness by an explicit construction. We carefully distinguish the roles of δ and ε. This is not only essential to achieve tight bounds, but also sensible in practical situations, since it allows one to adapt the bound according to sample density and the amount of noise present in the sample separately."}],"citation":{"apa":"Attali, D., Kourimska, H., Fillmore, C. D., Ghosh, I., Lieutier, A., Stephenson, E. R., &#38; Wintraecken, M. (2024). Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds. In <i>40th International Symposium on Computational Geometry</i> (Vol. 293, p. 11:1-11:19). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.11\">https://doi.org/10.4230/LIPIcs.SoCG.2024.11</a>","chicago":"Attali, Dominique, Hana Kourimska, Christopher D Fillmore, Ishika Ghosh, André Lieutier, Elizabeth R Stephenson, and Mathijs Wintraecken. “Tight Bounds for the Learning of Homotopy à La Niyogi, Smale, and Weinberger for Subsets of Euclidean Spaces and of Riemannian Manifolds.” In <i>40th International Symposium on Computational Geometry</i>, 293:11:1-11:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.11\">https://doi.org/10.4230/LIPIcs.SoCG.2024.11</a>.","mla":"Attali, Dominique, et al. “Tight Bounds for the Learning of Homotopy à La Niyogi, Smale, and Weinberger for Subsets of Euclidean Spaces and of Riemannian Manifolds.” <i>40th International Symposium on Computational Geometry</i>, vol. 293, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, p. 11:1-11:19, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.11\">10.4230/LIPIcs.SoCG.2024.11</a>.","short":"D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, p. 11:1-11:19.","ista":"Attali D, Kourimska H, Fillmore CD, Ghosh I, Lieutier A, Stephenson ER, Wintraecken M. 2024. Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 11:1-11:19.","ieee":"D. Attali <i>et al.</i>, “Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds,” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293, p. 11:1-11:19.","ama":"Attali D, Kourimska H, Fillmore CD, et al. Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds. In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024:11:1-11:19. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.11\">10.4230/LIPIcs.SoCG.2024.11</a>"},"scopus_import":"1","status":"public","publication_identifier":{"isbn":["9783959773164"],"eissn":["1868-8969"]},"type":"conference"},{"page":"1784-1807","ec_funded":1,"issue":"2","department":[{"_id":"HeEd"}],"_id":"17190","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","publication":"SIAM Journal on Discrete Mathematics","day":"07","date_created":"2024-06-30T22:01:05Z","article_type":"original","year":"2024","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"},{"name":"Mathematics, Computer Science","call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"doi":"10.1137/22M1489071","publication_status":"published","oa":1,"intvolume":"        38","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Garber","first_name":"Alexey","full_name":"Garber, Alexey"},{"full_name":"Ghafaris, Mohadese","first_name":"Mohadese","last_name":"Ghafaris"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","full_name":"Heiss, Teresa","last_name":"Heiss","first_name":"Teresa","orcid":"0000-0002-1780-2689"},{"full_name":"Saghafiant, Morteza","first_name":"Morteza","last_name":"Saghafiant"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220"}],"language":[{"iso":"eng"}],"publisher":"Society for Industrial and Applied Mathematics","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2204.01077"}],"oa_version":"Preprint","citation":{"chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafaris, Teresa Heiss, Morteza Saghafiant, and Mathijs Wintraecken. “Brillouin Zones of Integer Lattices and Their Perturbations.” <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/22M1489071\">https://doi.org/10.1137/22M1489071</a>.","apa":"Edelsbrunner, H., Garber, A., Ghafaris, M., Heiss, T., Saghafiant, M., &#38; Wintraecken, M. (2024). Brillouin zones of integer lattices and their perturbations. <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/22M1489071\">https://doi.org/10.1137/22M1489071</a>","ista":"Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. 2024. Brillouin zones of integer lattices and their perturbations. SIAM Journal on Discrete Mathematics. 38(2), 1784–1807.","short":"H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, M. Wintraecken, SIAM Journal on Discrete Mathematics 38 (2024) 1784–1807.","mla":"Edelsbrunner, Herbert, et al. “Brillouin Zones of Integer Lattices and Their Perturbations.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 38, no. 2, Society for Industrial and Applied Mathematics, 2024, pp. 1784–807, doi:<a href=\"https://doi.org/10.1137/22M1489071\">10.1137/22M1489071</a>.","ieee":"H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, and M. Wintraecken, “Brillouin zones of integer lattices and their perturbations,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 38, no. 2. Society for Industrial and Applied Mathematics, pp. 1784–1807, 2024.","ama":"Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. Brillouin zones of integer lattices and their perturbations. <i>SIAM Journal on Discrete Mathematics</i>. 2024;38(2):1784-1807. doi:<a href=\"https://doi.org/10.1137/22M1489071\">10.1137/22M1489071</a>"},"abstract":[{"text":"For a locally finite set, 𝐴⊆ℝ𝑑\r\n, the 𝑘\r\nth Brillouin zone of 𝑎∈𝐴\r\n is the region of points 𝑥∈ℝ𝑑\r\n for which ‖𝑥−𝑎‖\r\n is the 𝑘\r\nth smallest among the Euclidean distances between 𝑥\r\n and the points in 𝐴\r\n. If 𝐴\r\n is a lattice, the 𝑘\r\nth Brillouin zones of the points in 𝐴\r\n are translates of each other, and together they tile space. Depending on the value of 𝑘\r\n, they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our results include the stability of a Brillouin zone under perturbations, a linear upper bound on the number of chambers in a zone for lattices in ℝ2\r\n, and the convergence of the maximum volume of a chamber to zero for the integer lattice.","lang":"eng"}],"scopus_import":"1","publication_identifier":{"issn":["0895-4801"]},"type":"journal_article","status":"public","title":"Brillouin zones of integer lattices and their perturbations","isi":1,"acknowledgement":"The second author is partially supported by the Alexander von Humboldt Foundation. The sixth author is supported by the European Union's Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement 754411, and by Austrian Science Fund(FWF) grant M-3073. All other authors are supported by European Research Council (ERC) grant 788183, by the Wittgenstein Prize, by Austrian Science Fund (FWF) grant Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF) grant I 02979-N35.","date_published":"2024-06-07T00:00:00Z","article_processing_charge":"No","arxiv":1,"volume":38,"month":"06","external_id":{"isi":["001292728600001"],"arxiv":["2204.01077"]},"quality_controlled":"1","date_updated":"2025-09-08T08:06:04Z"},{"month":"10","date_updated":"2025-12-02T13:50:50Z","quality_controlled":"1","external_id":{"arxiv":["2403.10204"],"isi":["001540278400001"]},"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, \"Discretization in Geometry and Dynamics\", Austrian Science Fund (FWF), grant no. I 02979-N35.","isi":1,"date_published":"2024-10-28T00:00:00Z","arxiv":1,"article_processing_charge":"Yes","title":"The Euclidean MST-ratio for bi-colored lattices","volume":320,"status":"public","publication_identifier":{"isbn":["9783959773430"],"issn":["1868-8969"]},"type":"conference","OA_type":"gold","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Given a finite set, A ⊆ ℝ², and a subset, B ⊆ A, the MST-ratio is the combined length of the minimum spanning trees of B and A⧵B divided by the length of the minimum spanning tree of A. The question of the supremum, over all sets A, of the maximum, over all subsets B, is related to the Steiner ratio, and we prove this sup-max is between 2.154 and 2.427. Restricting ourselves to 2-dimensional lattices, we prove that the sup-max is 2, while the inf-max is 1.25. By some margin the most difficult of these results is the upper bound for the inf-max, which we prove by showing that the hexagonal lattice cannot have MST-ratio larger than 1.25."}],"citation":{"chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “The Euclidean MST-Ratio for Bi-Colored Lattices.” In <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, Vol. 320. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">https://doi.org/10.4230/LIPIcs.GD.2024.3</a>.","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (2024). The Euclidean MST-ratio for bi-colored lattices. In <i>32nd International Symposium on Graph Drawing and Network Visualization</i> (Vol. 320). Vienna, Austria: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">https://doi.org/10.4230/LIPIcs.GD.2024.3</a>","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2024. The Euclidean MST-ratio for bi-colored lattices. 32nd International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LIPIcs, vol. 320, 3.","mla":"Cultrera di Montesano, Sebastiano, et al. “The Euclidean MST-Ratio for Bi-Colored Lattices.” <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, vol. 320, 3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">10.4230/LIPIcs.GD.2024.3</a>.","ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “The Euclidean MST-ratio for bi-colored lattices,” in <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, Vienna, Austria, 2024, vol. 320.","ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. The Euclidean MST-ratio for bi-colored lattices. In: <i>32nd International Symposium on Graph Drawing and Network Visualization</i>. Vol 320. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">10.4230/LIPIcs.GD.2024.3</a>"},"article_number":"3","scopus_import":"1","intvolume":"       320","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"file":[{"relation":"main_file","date_updated":"2024-11-18T07:49:25Z","content_type":"application/pdf","file_size":908541,"file_id":"18560","success":1,"date_created":"2024-11-18T07:49:25Z","access_level":"open_access","file_name":"2024_LIPIcs_CultreradiMontesano.pdf","creator":"dernst","checksum":"5f9b35e115c3d375e99be78da9054cb4"}],"doi":"10.4230/LIPIcs.GD.2024.3","oa":1,"publication_status":"published","author":[{"first_name":"Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano"},{"id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej","last_name":"Draganov","first_name":"Ondrej","orcid":"0000-0003-0464-3823"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Saghafian","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza"}],"ddc":["510"],"language":[{"iso":"eng"}],"file_date_updated":"2024-11-18T07:49:25Z","alternative_title":["LIPIcs"],"date_created":"2024-11-17T23:01:47Z","year":"2024","publication":"32nd International Symposium on Graph Drawing and Network Visualization","OA_place":"publisher","corr_author":"1","day":"28","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ec_funded":1,"department":[{"_id":"HeEd"}],"conference":{"location":"Vienna, Austria","name":"GD: Graph Drawing and Network Visualization","end_date":"2024-09-20","start_date":"2024-09-18"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"18556"},{"file_date_updated":"2024-12-03T09:45:00Z","language":[{"iso":"eng"}],"ddc":["510"],"author":[{"full_name":"De Nooijer, Phoebe","last_name":"De Nooijer","first_name":"Phoebe"},{"last_name":"Terziadis","first_name":"Soeren","full_name":"Terziadis, Soeren"},{"full_name":"Weinberger, Alexandra","first_name":"Alexandra","last_name":"Weinberger"},{"full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","first_name":"Zuzana","last_name":"Masárová"},{"full_name":"Mchedlidze, Tamara","last_name":"Mchedlidze","first_name":"Tamara"},{"full_name":"Löffler, Maarten","first_name":"Maarten","last_name":"Löffler"},{"last_name":"Rote","first_name":"Günter","full_name":"Rote, Günter"}],"oa":1,"publication_status":"published","doi":"10.7155/jgaa.v28i2.2988","file":[{"file_size":1582493,"date_updated":"2024-12-03T09:45:00Z","content_type":"application/pdf","relation":"main_file","checksum":"be611da6f9d790dc980d6fb7283fe889","creator":"dernst","file_name":"2024_JourGraphAlgorithms_deNooijer.pdf","access_level":"open_access","date_created":"2024-12-03T09:45:00Z","success":1,"file_id":"18609"}],"intvolume":"        28","year":"2024","DOAJ_listed":"1","date_created":"2024-12-01T23:01:54Z","article_type":"original","day":"03","OA_place":"publisher","corr_author":"1","publication":"Journal of Graph Algorithms and Applications","_id":"18604","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"issue":"2","page":"47-82","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","external_id":{"arxiv":["2202.12175"]},"date_updated":"2024-12-03T09:49:18Z","quality_controlled":"1","month":"11","volume":28,"title":"Removing popular faces in curve arrangements","arxiv":1,"article_processing_charge":"No","date_published":"2024-11-03T00:00:00Z","acknowledgement":"This work was initiated at the 16th European Research Week on Geometric Graphs in Strobl in 2019. A.W. has been supported by the Austrian Science Fund (FWF): W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035] and by the NWO Gravitation project NETWORKS under grant no. 024.002.003. Part of the work was done while A.W. was emplyed at Graz University of Technology. Preliminary versions of this work have been presented at the 38th European Workshop on Computational Geometry (EuroCG\r\n2022) in Perugia [10] and at the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023) in Isola delle Femmine [11].","OA_type":"gold","type":"journal_article","publication_identifier":{"issn":["1526-1719"]},"status":"public","citation":{"mla":"De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.” <i>Journal of Graph Algorithms and Applications</i>, vol. 28, no. 2, Brown University, 2024, pp. 47–82, doi:<a href=\"https://doi.org/10.7155/jgaa.v28i2.2988\">10.7155/jgaa.v28i2.2988</a>.","short":"P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M. Löffler, G. Rote, Journal of Graph Algorithms and Applications 28 (2024) 47–82.","ista":"De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler M, Rote G. 2024. Removing popular faces in curve arrangements. Journal of Graph Algorithms and Applications. 28(2), 47–82.","apa":"De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T., Löffler, M., &#38; Rote, G. (2024). Removing popular faces in curve arrangements. <i>Journal of Graph Algorithms and Applications</i>. Brown University. <a href=\"https://doi.org/10.7155/jgaa.v28i2.2988\">https://doi.org/10.7155/jgaa.v28i2.2988</a>","chicago":"De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová, Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve Arrangements.” <i>Journal of Graph Algorithms and Applications</i>. Brown University, 2024. <a href=\"https://doi.org/10.7155/jgaa.v28i2.2988\">https://doi.org/10.7155/jgaa.v28i2.2988</a>.","ama":"De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve arrangements. <i>Journal of Graph Algorithms and Applications</i>. 2024;28(2):47-82. doi:<a href=\"https://doi.org/10.7155/jgaa.v28i2.2988\">10.7155/jgaa.v28i2.2988</a>","ieee":"P. De Nooijer <i>et al.</i>, “Removing popular faces in curve arrangements,” <i>Journal of Graph Algorithms and Applications</i>, vol. 28, no. 2. Brown University, pp. 47–82, 2024."},"scopus_import":"1","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 randomized FPT-time algorithm where the parameter is the number of popular faces."}],"oa_version":"Published Version","publisher":"Brown University"}]