[{"title":"Braiding Vineyards","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"21051"}]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2504.11203"}],"abstract":[{"text":"In this work, we introduce and study what we believe is an intriguing, and, to the best of our knowledge, previously unknown connection between two fundamental areas in computational topology, namely topological data analysis (TDA) and knot theory. Given a function from a topological space to ℝ, TDA provides tools to simplify and study the importance of topological features: in particular, the 𝑙^𝑡ℎ-dimensional persistence diagram encodes the topological changes (or 𝑙-homology) in the sublevel set as the function value increases into a set of points in the plane. Given a continuous one parameter family of such functions, we can combine the persistence diagrams into an object known as a vineyard, which tracks the evolution of points in the persistence diagram as the function changes. If we further restrict that family of functions to be periodic, we identify the two ends of the vineyard, yielding a closed vineyard. This allows the study of monodromy, which in this context means that following the family of functions for a period permutes the set of points in a non-trivial way. Recent work has studied monodromy in the directional persistent homology transform, demonstrating some interesting connections between an input shape and monodromy in the persistent homology transform for 0-dimensional homology embedded in ℝ^2.\r\nIn this work, given a link and a value 𝑙, we construct a topological space (based on the given link) and periodic family of functions on this space (based on the Euclidean distance function), such that the closed 𝑙-vineyard contains this link. This shows that vineyards are topologically as rich as one could possibly hope, suggesting many future directions of work. Importantly, it has at least two immediate consequences we explicitly point out:\r\n1.\tMonodromy of any periodicity can occur in a 𝑙-vineyard for any 𝑙. This answers a variant of a question by Arya and collaborators. To exhibit this as a consequence of our first main result we also reformulate monodromy in a more geometric way, which may be of interest in itself.\r\n2.\tTopologically distinguishing closed vineyards is likely to be difficult (from a complexity theory as well as from a practical perspective) because of the difficulty of knot and link recognition, which have strong connections to many NP-hard problems.","lang":"eng"}],"day":"07","date_created":"2026-01-28T12:58:16Z","type":"book_chapter","publication":"Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms","place":"Philadelphia, PA, United States","citation":{"mla":"Chambers, Erin W., et al. “Braiding Vineyards.” Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, edited by Kasper Green Larsen and Barna Saha, Society for Industrial and Applied Mathematics, 2026, pp. 6240–63, doi:10.1137/1.9781611978971.225.","ieee":"E. W. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “Braiding Vineyards,” in Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, K. Green Larsen and B. Saha, Eds. Philadelphia, PA, United States: Society for Industrial and Applied Mathematics, 2026, pp. 6240–6263.","apa":"Chambers, E. W., Fillmore, C. D., Stephenson, E. R., & Wintraecken, M. (2026). Braiding Vineyards. In K. Green Larsen & B. Saha (Eds.), Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 6240–6263). Philadelphia, PA, United States: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611978971.225","ama":"Chambers EW, Fillmore CD, Stephenson ER, Wintraecken M. Braiding Vineyards. In: Green Larsen K, Saha B, eds. Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA, United States: Society for Industrial and Applied Mathematics; 2026:6240-6263. doi:10.1137/1.9781611978971.225","ista":"Chambers EW, Fillmore CD, Stephenson ER, Wintraecken M. 2026.Braiding Vineyards. In: Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms. , 6240–6263.","chicago":"Chambers, Erin W., Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs Wintraecken. “Braiding Vineyards.” In Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, edited by Kasper Green Larsen and Barna Saha, 6240–63. Philadelphia, PA, United States: Society for Industrial and Applied Mathematics, 2026. https://doi.org/10.1137/1.9781611978971.225.","short":"E.W. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, K. Green Larsen, B. Saha (Eds.), Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, United States, 2026, pp. 6240–6263."},"acknowledgement":"We thank the reviewers for both SODA and ATMCS for their comments, whichimproved the exposition. We thank Kate Turner for discussion and Clément Maria for pointing out thatAlexander’s theorem was already (well) known. Mathijs Wintraecken would like to express his gratitude tothe administrative support he received from University of Notre Dame during his visit and from Sophie Honnoratand Stephanie Verdonck at Inria in general.This work has been supported by the ANR grant StratMesh, ANR-24-CE48-1899, by NSF award 2444309, andthe welcome package from IDEX of the Université Côte d’Azur, ANR-15-IDEX-01.","external_id":{"arxiv":["2504.11203"]},"arxiv":1,"quality_controlled":"1","author":[{"last_name":"Chambers","first_name":"Erin W.","full_name":"Chambers, Erin W."},{"last_name":"Fillmore","full_name":"Fillmore, Christopher D","first_name":"Christopher D","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425"},{"orcid":"0000-0002-6862-208X","last_name":"Stephenson","first_name":"Elizabeth R","full_name":"Stephenson, Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-7472-2220","last_name":"Wintraecken","first_name":"Mathijs","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"page":"6240-6263","doi":"10.1137/1.9781611978971.225","_id":"21056","date_published":"2026-01-07T00:00:00Z","month":"01","publication_status":"published","date_updated":"2026-02-16T08:06:23Z","publisher":"Society for Industrial and Applied Mathematics","oa":1,"article_processing_charge":"No","department":[{"_id":"HeEd"}],"OA_place":"repository","publication_identifier":{"eisbn":["9781611978971"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","OA_type":"green","year":"2026","status":"public","editor":[{"last_name":"Green Larsen","first_name":"Kasper","full_name":"Green Larsen, Kasper"},{"first_name":"Barna","full_name":"Saha, Barna","last_name":"Saha"}]},{"publisher":"Public Library of Science","PlanS_conform":"1","date_updated":"2026-06-11T11:51:13Z","publication_status":"published","article_type":"original","date_published":"2026-01-28T00:00:00Z","month":"01","article_number":"e1013890","department":[{"_id":"HeEd"}],"article_processing_charge":"Yes","oa":1,"OA_type":"gold","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":8908746,"access_level":"open_access","checksum":"3899d929ee9be0453c95524e49992d72","creator":"dernst","success":1,"date_updated":"2026-02-10T07:13:06Z","date_created":"2026-02-10T07:13:06Z","file_name":"2026_PloSCompBio_Bleile.pdf","relation":"main_file","file_id":"21204"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["1553-7358"]},"OA_place":"publisher","has_accepted_license":"1","corr_author":"1","status":"public","year":"2026","pmid":1,"scopus_import":"1","date_created":"2026-01-30T10:36:32Z","abstract":[{"lang":"eng","text":"Quantifying cell morphology is central to understanding cellular regulation, fate, and heterogeneity, yet conventional image-based analyses often struggle with diverse or irregular shapes. We present a computational framework that uses topological data analysis to characterise and compare single-cell morphologies from fluorescence microscopy. Each cell is represented by its contour together with the position of its nucleus, from which we construct a filtration based on a radial distance function and derive a persistence diagram encoding the shape’s topological evolution. The similarity between two cells is quantified using the 2-Wasserstein distance between their diagrams, yielding a shape distance we call the PH distance. We apply this method to two representative experimental systems—primary human mesenchymal stem cells (hMSCs) and HeLa cells—and show that PH distances enable the detection of outliers in those systems, the identification of sub-populations, and the quantification of shape heterogeneity. We benchmark PH against three established contour-based distances (aspect ratio, Fourier descriptors, and elastic shape analysis) and show that PH offers better separation between cell types and greater robustness when clustering heterogeneous populations. Together, these results demonstrate that persistent-homology-based signatures provide a principled and sensitive approach for analysing cell morphology in settings where traditional geometric or image-based descriptors are insufficient."}],"day":"28","volume":22,"file_date_updated":"2026-02-10T07:13:06Z","language":[{"iso":"eng"}],"related_material":{"link":[{"url":"https://github.com/yossibokorbleile/correa","relation":"software"}]},"title":"Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population","DOAJ_listed":"1","intvolume":" 22","external_id":{"pmid":["41604421"]},"ddc":["000"],"citation":{"ama":"Bokor Bleile Y, Yadav P, Koehl P, Rehfeldt F. Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population. PLoS Computational Biology. 2026;22. doi:10.1371/journal.pcbi.1013890","apa":"Bokor Bleile, Y., Yadav, P., Koehl, P., & Rehfeldt, F. (2026). Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population. PLoS Computational Biology. Public Library of Science. https://doi.org/10.1371/journal.pcbi.1013890","ieee":"Y. Bokor Bleile, P. Yadav, P. Koehl, and F. Rehfeldt, “Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population,” PLoS Computational Biology, vol. 22. Public Library of Science, 2026.","mla":"Bokor Bleile, Yossi, et al. “Persistence Diagrams as Morphological Signatures of Cells: A Method to Measure and Compare Cells within a Population.” PLoS Computational Biology, vol. 22, e1013890, Public Library of Science, 2026, doi:10.1371/journal.pcbi.1013890.","short":"Y. Bokor Bleile, P. Yadav, P. Koehl, F. Rehfeldt, PLoS Computational Biology 22 (2026).","chicago":"Bokor Bleile, Yossi, Pooja Yadav, Patrice Koehl, and Florian Rehfeldt. “Persistence Diagrams as Morphological Signatures of Cells: A Method to Measure and Compare Cells within a Population.” PLoS Computational Biology. Public Library of Science, 2026. https://doi.org/10.1371/journal.pcbi.1013890.","ista":"Bokor Bleile Y, Yadav P, Koehl P, Rehfeldt F. 2026. Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population. PLoS Computational Biology. 22, e1013890."},"acknowledgement":"We thank Stephan Huckemann, Katharine Turner, Benjamin Eltzner, Stephan Tillmann, Fariza Rashid, Vanessa Robins, and Lamiae Azizi for many useful discussions at various stages of this project. FR and PY gratefully acknowledge Matthias Weiss (Experimental Physics I, University of Bayreuth, Germany) for granting access to cell culture and laboratories, as well as funding consumables and the fruitful discussion that contributed to this work. For open access purposes, the author has applied a CC BY public copyright license to any author-accepted manuscript version arising from this submission.","type":"journal_article","publication":"PLoS Computational Biology","_id":"21115","doi":"10.1371/journal.pcbi.1013890","author":[{"id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2","full_name":"Bleile, Yossi","first_name":"Yossi","last_name":"Bleile","orcid":"0000-0002-4861-9174"},{"last_name":"Yadav","full_name":"Yadav, Pooja","first_name":"Pooja"},{"last_name":"Koehl","full_name":"Koehl, Patrice","first_name":"Patrice"},{"first_name":"Florian","full_name":"Rehfeldt, Florian","last_name":"Rehfeldt"}],"quality_controlled":"1"},{"abstract":[{"lang":"eng","text":"Abstract\r\n In this paper, we consider a simple class of stratified spaces – 2-complexes. We present an algorithm that learns the abstract structure of an embedded 2-complex from a point cloud sampled from it. We use tools and inspiration from computational geometry, algebraic topology, and topological data analysis and prove the correctness of the identified abstract structure under assumptions on the embedding."}],"day":"08","date_created":"2026-02-16T10:44:44Z","title":"Towards stratified space learning: 2-complexes","language":[{"iso":"eng"}],"file_date_updated":"2026-02-23T10:18:52Z","volume":5,"scopus_import":"1","doi":"10.1007/s44007-025-00183-9","_id":"21232","quality_controlled":"1","author":[{"id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2","first_name":"Yossi","full_name":"Bleile, Yossi","last_name":"Bleile","orcid":"0000-0002-4861-9174"}],"acknowledgement":"The author would like to thank Kate Turner, Chris Williams, Jonathan Spreer, Stephan Tillmann, Vanessa Robins, Vigleik Angeltveit, Martin Helmer, and James Morgan for very helpful discussions; and thanks Sara Kališnik Hintz and Paul Bendich for comments on an earlier version. Additonally, the author would like to thank both reviewers for their very insightful and helpful comments, without which the paper would be infinitely less coherent than it currently is. Open access funding provided by Institute of Science and Technology (IST Austria). The work in this paper was supported by an Australian Federal Government Grant, 2019-2022, Stratified Space Learning.","citation":{"ista":"Bokor Bleile Y. 2026. Towards stratified space learning: 2-complexes. La Matematica. 5, 17.","chicago":"Bokor Bleile, Yossi. “Towards Stratified Space Learning: 2-Complexes.” La Matematica. Springer Nature, 2026. https://doi.org/10.1007/s44007-025-00183-9.","short":"Y. Bokor Bleile, La Matematica 5 (2026).","mla":"Bokor Bleile, Yossi. “Towards Stratified Space Learning: 2-Complexes.” La Matematica, vol. 5, 17, Springer Nature, 2026, doi:10.1007/s44007-025-00183-9.","ieee":"Y. Bokor Bleile, “Towards stratified space learning: 2-complexes,” La Matematica, vol. 5. Springer Nature, 2026.","apa":"Bokor Bleile, Y. (2026). Towards stratified space learning: 2-complexes. La Matematica. Springer Nature. https://doi.org/10.1007/s44007-025-00183-9","ama":"Bokor Bleile Y. Towards stratified space learning: 2-complexes. La Matematica. 2026;5. doi:10.1007/s44007-025-00183-9"},"ddc":["510"],"external_id":{"arxiv":["2305.02724"]},"arxiv":1,"intvolume":" 5","publication":"La Matematica","type":"journal_article","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"HeEd"}],"article_number":"17","oa":1,"publisher":"Springer Nature","month":"02","article_type":"original","date_published":"2026-02-08T00:00:00Z","publication_status":"published","date_updated":"2026-06-11T11:51:14Z","PlanS_conform":"1","has_accepted_license":"1","corr_author":"1","year":"2026","status":"public","file":[{"date_updated":"2026-02-23T10:18:52Z","content_type":"application/pdf","file_size":15051582,"access_level":"open_access","checksum":"6cae2efb47b025af22a8539c606a4e09","creator":"dernst","success":1,"file_id":"21347","date_created":"2026-02-23T10:18:52Z","file_name":"2026_LaMatematica_Bleile.pdf","relation":"main_file"}],"oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"OA_type":"hybrid","OA_place":"publisher","publication_identifier":{"issn":["2730-9657"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"department":[{"_id":"HeEd"}],"conference":{"end_date":"2026-02-13","location":"Krakow, Poland","start_date":"2026-02-09","name":"SOFSEM: Conference on Current Trends in Theory and Practice of Computer Science"},"article_processing_charge":"No","oa":1,"publisher":"Springer Nature","date_updated":"2026-03-02T08:49:20Z","publication_status":"published","date_published":"2026-02-13T00:00:00Z","month":"02","year":"2026","status":"public","OA_type":"green","oa_version":"Preprint","alternative_title":["LNCS"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["9783032178008"]},"OA_place":"repository","date_created":"2026-03-01T23:01:40Z","day":"13","abstract":[{"text":"Let . S be a set of distinct points in general position in the\r\nEuclidean plane. A plane Hamiltonian path on . S is a crossing-free geometric path such that every point of .S is a vertex of the path. It is\r\nknown that, if. S is sufficiently large, there exist three edge-disjoint plane\r\nHamiltonian paths on . S. In this paper we study an edge-constrained\r\nversion of the problem of finding Hamiltonian paths on a point set. We\r\nfirst consider the problem of finding a single plane Hamiltonian path . π\r\nwith endpoints .s, t ∈ S and constraints given by a segment . ab, where\r\n.a, b ∈ S. We consider the following scenarios: (i) .ab ∈ π; (ii) .ab π. We\r\ncharacterize those quintuples . S, a, b, s, t for which . π exists. Secondly,\r\nwe consider the problem of finding two plane Hamiltonian paths . π1, π2\r\non a set . S with constraints given by a segment . ab, where .a, b ∈ S. We\r\nconsider the following scenarios: (i) .π1 and .π2 share no edges and .ab is\r\nan edge of . π1; (ii) .π1 and .π2 share no edges and none of them includes\r\n.ab as an edge; (iii) both .π1 and .π2 include .ab as an edge and share no\r\nother edges. In all cases, we characterize those triples . S, a, b for which\r\n.π1 and .π2 exist.","lang":"eng"}],"volume":16448,"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2511.22526"}],"title":"Edge-constrained Hamiltonian paths on a point set","scopus_import":"1","_id":"21374","doi":"10.1007/978-3-032-17801-5_39","page":"532-546","author":[{"last_name":"Antić","first_name":"Todor","full_name":"Antić, Todor"},{"full_name":"Džuklevski, Aleksa","first_name":"Aleksa","last_name":"Džuklevski"},{"last_name":"Fiala","first_name":"Jiří","full_name":"Fiala, Jiří"},{"last_name":"Kratochvíl","first_name":"Jan","full_name":"Kratochvíl, Jan"},{"last_name":"Liotta","full_name":"Liotta, Giuseppe","first_name":"Giuseppe"},{"last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","full_name":"Saghafian, Morteza"},{"last_name":"Saumell","full_name":"Saumell, Maria","first_name":"Maria"},{"last_name":"Zink","first_name":"Johannes","full_name":"Zink, Johannes"}],"quality_controlled":"1","intvolume":" 16448","arxiv":1,"external_id":{"arxiv":["2511.22526"]},"citation":{"short":"T. Antić, A. Džuklevski, J. Fiala, J. Kratochvíl, G. Liotta, M. Saghafian, M. Saumell, J. Zink, in:, 51st International Conference on Current Trends in Theory and Practice of Computer Science, Springer Nature, 2026, pp. 532–546.","chicago":"Antić, Todor, Aleksa Džuklevski, Jiří Fiala, Jan Kratochvíl, Giuseppe Liotta, Morteza Saghafian, Maria Saumell, and Johannes Zink. “Edge-Constrained Hamiltonian Paths on a Point Set.” In 51st International Conference on Current Trends in Theory and Practice of Computer Science, 16448:532–46. Springer Nature, 2026. https://doi.org/10.1007/978-3-032-17801-5_39.","ista":"Antić T, Džuklevski A, Fiala J, Kratochvíl J, Liotta G, Saghafian M, Saumell M, Zink J. 2026. Edge-constrained Hamiltonian paths on a point set. 51st International Conference on Current Trends in Theory and Practice of Computer Science. SOFSEM: Conference on Current Trends in Theory and Practice of Computer Science, LNCS, vol. 16448, 532–546.","ama":"Antić T, Džuklevski A, Fiala J, et al. Edge-constrained Hamiltonian paths on a point set. In: 51st International Conference on Current Trends in Theory and Practice of Computer Science. Vol 16448. Springer Nature; 2026:532-546. doi:10.1007/978-3-032-17801-5_39","apa":"Antić, T., Džuklevski, A., Fiala, J., Kratochvíl, J., Liotta, G., Saghafian, M., … Zink, J. (2026). Edge-constrained Hamiltonian paths on a point set. In 51st International Conference on Current Trends in Theory and Practice of Computer Science (Vol. 16448, pp. 532–546). Krakow, Poland: Springer Nature. https://doi.org/10.1007/978-3-032-17801-5_39","mla":"Antić, Todor, et al. “Edge-Constrained Hamiltonian Paths on a Point Set.” 51st International Conference on Current Trends in Theory and Practice of Computer Science, vol. 16448, Springer Nature, 2026, pp. 532–46, doi:10.1007/978-3-032-17801-5_39.","ieee":"T. Antić et al., “Edge-constrained Hamiltonian paths on a point set,” in 51st International Conference on Current Trends in Theory and Practice of Computer Science, Krakow, Poland, 2026, vol. 16448, pp. 532–546."},"acknowledgement":"We thank the organizers of the HOMONOLO 2024 workshop in Nová Louka, Czech Republic, for the fruitful atmosphere where the research on this project was initiated.\r\n\r\nT. Antić, A. Džuklevski, J. Kratochvíl and M. Saumell received funding from GAČR grant 23–04949X, T.A and A.Dž were additionally supported by GAUK grant SVV–2025–260822. G. Liotta was supported in part by MUR of Italy, PRIN Project no. 2022TS4Y3N – EXPAND and PON Project ARS01_00540. J. Fiala was in part supported by GAČR grant 25-16847S.","type":"conference","publication":"51st International Conference on Current Trends in Theory and Practice of Computer Science"},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"OA_type":"hybrid","file":[{"file_id":"21416","relation":"main_file","file_name":"2026_JourAppliedCompTopology_Edelsbrunner.pdf","date_created":"2026-03-09T11:29:30Z","date_updated":"2026-03-09T11:29:30Z","success":1,"creator":"dernst","file_size":323111,"access_level":"open_access","checksum":"0bf6dc430cafa40c08f260fe17d54595","content_type":"application/pdf"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"publisher","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"has_accepted_license":"1","status":"public","year":"2026","publisher":"Springer Nature","PlanS_conform":"1","article_type":"original","month":"03","date_published":"2026-03-01T00:00:00Z","date_updated":"2026-03-09T11:31:29Z","publication_status":"published","department":[{"_id":"HeEd"}],"article_number":"5","article_processing_charge":"Yes (in subscription journal)","oa":1,"arxiv":1,"intvolume":" 10","citation":{"ama":"Edelsbrunner H, Kahle M, Kanazawa S. Maximum persistent Betti numbers of Čech complexes. Journal of Applied and Computational Topology. 2026;10. doi:10.1007/s41468-026-00233-3","apa":"Edelsbrunner, H., Kahle, M., & Kanazawa, S. (2026). Maximum persistent Betti numbers of Čech complexes. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-026-00233-3","mla":"Edelsbrunner, Herbert, et al. “Maximum Persistent Betti Numbers of Čech Complexes.” Journal of Applied and Computational Topology, vol. 10, 5, Springer Nature, 2026, doi:10.1007/s41468-026-00233-3.","ieee":"H. Edelsbrunner, M. Kahle, and S. Kanazawa, “Maximum persistent Betti numbers of Čech complexes,” Journal of Applied and Computational Topology, vol. 10. Springer Nature, 2026.","short":"H. Edelsbrunner, M. Kahle, S. Kanazawa, Journal of Applied and Computational Topology 10 (2026).","chicago":"Edelsbrunner, Herbert, Matthew Kahle, and Shu Kanazawa. “Maximum Persistent Betti Numbers of Čech Complexes.” Journal of Applied and Computational Topology. Springer Nature, 2026. https://doi.org/10.1007/s41468-026-00233-3.","ista":"Edelsbrunner H, Kahle M, Kanazawa S. 2026. Maximum persistent Betti numbers of Čech complexes. Journal of Applied and Computational Topology. 10, 5."},"acknowledgement":"The authors would like to thank Michael Lesnick and Primoz Skraba for their helpful comments regarding sparse approximations of filtrations. We are also grateful to the anonymous referees for their careful reading and constructive suggestions. The three authors are supported by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35, the U.S. National Science Foundation (NSF-DMS), grant no. 2005630, and a JSPS Grant-in-Aid for Transformative Research Areas (A) (22H05107, Y.H.), EPSRC Research Grant EP/Y008642/1.","external_id":{"arxiv":["2409.05241"]},"ddc":["500"],"type":"journal_article","publication":"Journal of Applied and Computational Topology","project":[{"name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"doi":"10.1007/s41468-026-00233-3","_id":"21407","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"last_name":"Kahle","full_name":"Kahle, Matthew","first_name":"Matthew"},{"full_name":"Kanazawa, Shu","first_name":"Shu","last_name":"Kanazawa"}],"quality_controlled":"1","scopus_import":"1","day":"01","abstract":[{"lang":"eng","text":"This note proves that only a linear number of holes in a Cech complex of n points in R^d\r\ncan persist over an interval of constant length. Specifically, for any fixed dimension p <\r\nd and fixed ε > 0, the number of p-dimensional holes in the ˇ Cech complex at radius 1\r\nthat persist to radius 1+ε is bounded above by a constant times n,where n is the number\r\nof points. The proof uses a packing argument supported by relating theCˇ ech complexes\r\nwith corresponding snap complexes over the cells in a partition of space. The argument\r\nis self-contained and elementary, relying on geometric and combinatorial constructions\r\nrather than on the existing theory of sparse approximations or interleavings. The bound\r\nalso applies to Alpha complexes and Vietoris–Rips complexes. While our result can be\r\ninferred from prior work on sparse filtrations, to our knowledge, no explicit statement\r\nor direct proof of this bound appears in the literature."}],"date_created":"2026-03-08T23:01:45Z","file_date_updated":"2026-03-09T11:29:30Z","volume":10,"title":"Maximum persistent Betti numbers of Čech complexes","language":[{"iso":"eng"}]},{"oa":1,"department":[{"_id":"HeEd"}],"conference":{"name":"WALCOM: International Conference and Workshops on Algorithms and Computation","start_date":"2026-03-04","location":"Perugia, Italy","end_date":"2026-03-06"},"article_processing_charge":"No","publication_status":"published","date_updated":"2026-03-09T10:25:41Z","month":"02","date_published":"2026-02-14T00:00:00Z","ec_funded":1,"publisher":"Springer Nature","year":"2026","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"isbn":["9789819571260"],"issn":["0302-9743"],"eissn":["1611-3349"]},"OA_place":"repository","OA_type":"green","oa_version":"Preprint","alternative_title":["LNCS"],"volume":16444,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2409.11079"}],"language":[{"iso":"eng"}],"title":"On the MST-ratio: Theoretical bounds and complexity of finding the maximum","date_created":"2026-03-08T23:01:45Z","day":"14","abstract":[{"lang":"eng","text":"Given a finite set of red and blue points in R^d, the MST-ratio is defined as the total length of the Euclidean minimum spanning trees of the red points and the blue points, divided by the length of the Euclidean minimum spanning tree of their union. The MST-ratio has recently gained attention due to its direct interpretation in topological models for studying point sets with applications in spatial biology. The maximum MST-ratio of a point set is the maximum MST-ratio over all proper colorings of its points by red and blue. We prove that finding the maximum MST-ratio of a given point set is NP-hard when the dimension is part of the input. Moreover, we present a quadratic-time 3-approximation algorithm for this problem. As part of the proof, we show that in any metric space, the maximum MST-ratio is smaller than 3. Furthermore, we study the average MST-ratio over all colorings of a set of n points. We show that this average is always at least n-2/n-1, and for n random points uniformly distributed in a d-dimensional unit cube, the average tends to (math formular) in expectation as n approaches infinity."}],"scopus_import":"1","page":"386-401","author":[{"last_name":"Jabal Ameli","full_name":"Jabal Ameli, Afrouz","first_name":"Afrouz"},{"last_name":"Motiei","full_name":"Motiei, Faezeh","first_name":"Faezeh"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"_id":"21410","doi":"10.1007/978-981-95-7127-7_26","publication":"20th International Conference and Workshops on Algorithms and Computation","type":"conference","intvolume":" 16444","arxiv":1,"external_id":{"arxiv":["2409.11079"]},"acknowledgement":"A. J. Ameli—Supported by the project COALESCE (ERC grant no. 853234).\r\nM. Saghafian—Partially supported by the European Research Council (ERC), grant no. 788183, and by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","citation":{"mla":"Jabal Ameli, Afrouz, et al. “On the MST-Ratio: Theoretical Bounds and Complexity of Finding the Maximum.” 20th International Conference and Workshops on Algorithms and Computation, vol. 16444, Springer Nature, 2026, pp. 386–401, doi:10.1007/978-981-95-7127-7_26.","ieee":"A. Jabal Ameli, F. Motiei, and M. Saghafian, “On the MST-ratio: Theoretical bounds and complexity of finding the maximum,” in 20th International Conference and Workshops on Algorithms and Computation, Perugia, Italy, 2026, vol. 16444, pp. 386–401.","apa":"Jabal Ameli, A., Motiei, F., & Saghafian, M. (2026). On the MST-ratio: Theoretical bounds and complexity of finding the maximum. In 20th International Conference and Workshops on Algorithms and Computation (Vol. 16444, pp. 386–401). Perugia, Italy: Springer Nature. https://doi.org/10.1007/978-981-95-7127-7_26","ama":"Jabal Ameli A, Motiei F, Saghafian M. On the MST-ratio: Theoretical bounds and complexity of finding the maximum. In: 20th International Conference and Workshops on Algorithms and Computation. Vol 16444. Springer Nature; 2026:386-401. doi:10.1007/978-981-95-7127-7_26","ista":"Jabal Ameli A, Motiei F, Saghafian M. 2026. On the MST-ratio: Theoretical bounds and complexity of finding the maximum. 20th International Conference and Workshops on Algorithms and Computation. WALCOM: International Conference and Workshops on Algorithms and Computation, LNCS, vol. 16444, 386–401.","chicago":"Jabal Ameli, Afrouz, Faezeh Motiei, and Morteza Saghafian. “On the MST-Ratio: Theoretical Bounds and Complexity of Finding the Maximum.” In 20th International Conference and Workshops on Algorithms and Computation, 16444:386–401. Springer Nature, 2026. https://doi.org/10.1007/978-981-95-7127-7_26.","short":"A. Jabal Ameli, F. Motiei, M. Saghafian, in:, 20th International Conference and Workshops on Algorithms and Computation, Springer Nature, 2026, pp. 386–401."}},{"publication_status":"published","date_updated":"2026-05-07T07:45:24Z","date_published":"2026-04-17T00:00:00Z","article_type":"original","month":"04","publisher":"Mathematical Sciences Publishers","ec_funded":1,"oa":1,"article_processing_charge":"No","department":[{"_id":"HeEd"}],"publication_identifier":{"issn":["2996-2196"],"eissn":["2996-220X"]},"OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","OA_type":"green","issue":"1","year":"2026","status":"public","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2507.10840","open_access":"1"}],"language":[{"iso":"eng"}],"title":"Covering complete geometric graphs by monotone paths","volume":15,"date_created":"2026-05-03T22:01:37Z","abstract":[{"lang":"eng","text":"Given a set A of n points (vertices) in general position in the plane, the complete geometric graph \r\nKn[A] consists of all (n2) segments (edges) between the elements of A. It is known that the edge set of every complete geometric graph on n vertices can be partitioned into O(n3∕2) crossing-free paths (or matchings). We strengthen this result under various additional assumptions on the point set. In particular, we prove that for a set A of n randomly selected points, uniformly distributed in [0,1]2, with probability tending to 1 as n→∞, the edge set of Kn[A] can be covered by O(nlogn) crossing-free paths and by O(n√logn) crossing-free matchings. On the other hand, we construct n-element point sets such that covering the edge set of Kn[A] requires a quadratic number of monotone paths."}],"day":"17","type":"journal_article","publication":"Combinatorics and Number Theory","external_id":{"arxiv":["2507.10840"]},"acknowledgement":"Research partially supported by ERC Advanced Grant \"GeoScape\", no. 882971 and\r\nHungarian NKFIH grant no. K-131529. Work by the third author is supported by EPSRC grant\r\nEP/X013642/1. Work by the third author is partially supported by the European Research Council (ERC), grant no. 788183, and by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","citation":{"chicago":"Dumitrescu, Adrian, János Pach, Morteza Saghafian, and Alex Scott. “Covering Complete Geometric Graphs by Monotone Paths.” Combinatorics and Number Theory. Mathematical Sciences Publishers, 2026. https://doi.org/10.2140/cnt.2026.15.73.","short":"A. Dumitrescu, J. Pach, M. Saghafian, A. Scott, Combinatorics and Number Theory 15 (2026) 73–82.","ista":"Dumitrescu A, Pach J, Saghafian M, Scott A. 2026. Covering complete geometric graphs by monotone paths. Combinatorics and Number Theory. 15(1), 73–82.","apa":"Dumitrescu, A., Pach, J., Saghafian, M., & Scott, A. (2026). Covering complete geometric graphs by monotone paths. Combinatorics and Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/cnt.2026.15.73","ama":"Dumitrescu A, Pach J, Saghafian M, Scott A. Covering complete geometric graphs by monotone paths. Combinatorics and Number Theory. 2026;15(1):73-82. doi:10.2140/cnt.2026.15.73","ieee":"A. Dumitrescu, J. Pach, M. Saghafian, and A. Scott, “Covering complete geometric graphs by monotone paths,” Combinatorics and Number Theory, vol. 15, no. 1. Mathematical Sciences Publishers, pp. 73–82, 2026.","mla":"Dumitrescu, Adrian, et al. “Covering Complete Geometric Graphs by Monotone Paths.” Combinatorics and Number Theory, vol. 15, no. 1, Mathematical Sciences Publishers, 2026, pp. 73–82, doi:10.2140/cnt.2026.15.73."},"intvolume":" 15","arxiv":1,"quality_controlled":"1","page":"73-82","author":[{"last_name":"Dumitrescu","first_name":"Adrian","full_name":"Dumitrescu, Adrian"},{"last_name":"Pach","full_name":"Pach, János","first_name":"János"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","first_name":"Morteza","last_name":"Saghafian"},{"first_name":"Alex","full_name":"Scott, Alex","last_name":"Scott"}],"_id":"21781","doi":"10.2140/cnt.2026.15.73","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183"},{"grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"}]},{"volume":132,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2501.05315","open_access":"1"}],"related_material":{"record":[{"status":"public","id":"21050","relation":"earlier_version"}]},"language":[{"iso":"eng"}],"title":"Counting equilibria of the electrostatic potential","date_created":"2026-05-31T22:02:13Z","abstract":[{"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 (nonoptimal) upper bound was only obtained in 2007 by Gabrielov, Novikov, and Shapiro, who also posed two additional interesting conjectures. 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 Conjecture 1.8 by Gabrielov, Novikov, and Shapiro that the number of equilibria cannot exceed those of the distance function defined by the unit point charges. Finally, we note that it is quite possible that Maxwell's quadratic upper bound is not tight, so it is prudent to find lower 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.","lang":"eng"}],"day":"01","scopus_import":"1","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Fillmore","first_name":"Christopher D","full_name":"Fillmore, Christopher D","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425"},{"last_name":"Oliveira","id":"58abbde8-f455-11eb-a497-98c8fd71b905","first_name":"Goncalo","full_name":"Oliveira, Goncalo"}],"quality_controlled":"1","_id":"21931","doi":"10.1112/plms.70163","publication":"Proceedings of the London Mathematical Society","type":"journal_article","intvolume":" 132","arxiv":1,"external_id":{"arxiv":["2501.05315"]},"citation":{"mla":"Edelsbrunner, Herbert, et al. “Counting Equilibria of the Electrostatic Potential.” Proceedings of the London Mathematical Society, vol. 132, no. 5, e70163, Wiley, 2026, doi:10.1112/plms.70163.","ieee":"H. Edelsbrunner, C. D. Fillmore, and G. Oliveira, “Counting equilibria of the electrostatic potential,” Proceedings of the London Mathematical Society, vol. 132, no. 5. Wiley, 2026.","apa":"Edelsbrunner, H., Fillmore, C. D., & Oliveira, G. (2026). Counting equilibria of the electrostatic potential. Proceedings of the London Mathematical Society. Wiley. https://doi.org/10.1112/plms.70163","ama":"Edelsbrunner H, Fillmore CD, Oliveira G. Counting equilibria of the electrostatic potential. Proceedings of the London Mathematical Society. 2026;132(5). doi:10.1112/plms.70163","ista":"Edelsbrunner H, Fillmore CD, Oliveira G. 2026. Counting equilibria of the electrostatic potential. Proceedings of the London Mathematical Society. 132(5), e70163.","chicago":"Edelsbrunner, Herbert, Christopher D Fillmore, and Goncalo Oliveira. “Counting Equilibria of the Electrostatic Potential.” Proceedings of the London Mathematical Society. Wiley, 2026. https://doi.org/10.1112/plms.70163.","short":"H. Edelsbrunner, C.D. Fillmore, G. Oliveira, Proceedings of the London Mathematical Society 132 (2026)."},"oa":1,"article_number":"e70163","department":[{"_id":"HeEd"},{"_id":"TaHa"}],"article_processing_charge":"No","date_updated":"2026-06-02T09:24:18Z","publication_status":"published","date_published":"2026-05-01T00:00:00Z","article_type":"original","month":"05","publisher":"Wiley","year":"2026","issue":"5","status":"public","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]},"OA_place":"repository","OA_type":"green","oa_version":"Preprint"},{"publisher":"Institute of Science and Technology Austria","date_updated":"2026-06-15T23:00:03Z","month":"06","date_published":"2026-06-15T00:00:00Z","department":[{"_id":"HeEd"}],"date_created":"2026-06-09T19:19:13Z","abstract":[{"text":"A Rust library for analyzing dendritic structures using quadric matrices. This project provides efficient tools for representing dendritic trees, computing quadric error metrics, and visualizing eigenvalue distributions on hexagonal plots.\r\n\r\nThis library implements quadric-based geometric analysis of dendritic structures, commonly found in neuroscience applications. Key features include:\r\n\r\nTree data structures: Hierarchical vertex and edge representations for dendritic trees\r\nQuadric matrices: Computation of quadric error metrics for edges and vertices\r\nVisualisation: Hexagonal plot generation using NormPolar transformations\r\nInteractive tools: Desktop application with plotting capabilities","lang":"eng"}],"day":"15","keyword":["quadratics","mathematics","dendrites","geometry","topology"],"file_date_updated":"2026-06-15T08:14:24Z","oa":1,"title":"Quadrix","license":"https://opensource.org/licenses/MIT","tmp":{"legal_code_url":"https://opensource.org/licenses/MIT","short":"MIT","name":"The MIT License"},"file":[{"relation":"main_file","date_created":"2026-06-09T19:16:02Z","file_name":"LICENSE","file_id":"21974","success":1,"content_type":"application/octet-stream","checksum":"48f633b6767c4b15dd6220ca2b4dc175","access_level":"open_access","file_size":1081,"creator":"ybleile","date_updated":"2026-06-09T19:16:02Z"},{"relation":"main_file","date_created":"2026-06-09T19:16:27Z","file_name":"quadrix-x64.exe","file_id":"21975","success":1,"checksum":"de25d0b224acbde3d38f837fdd8f97d5","file_size":11308032,"access_level":"open_access","content_type":"application/octet-stream","creator":"ybleile","date_updated":"2026-06-09T19:16:27Z"},{"date_updated":"2026-06-09T19:16:28Z","content_type":"application/octet-stream","file_size":10655744,"checksum":"a7b94a7380dc178e76ebdba9f1fa45c2","access_level":"open_access","creator":"ybleile","success":1,"file_id":"21976","date_created":"2026-06-09T19:16:28Z","file_name":"quadrix-arm64.exe","relation":"main_file"},{"date_updated":"2026-06-09T19:16:27Z","success":1,"access_level":"open_access","file_size":2032,"checksum":"2404aa8619a56668bd95032791ee1250","content_type":"application/zip","creator":"ybleile","file_id":"21977","relation":"main_file","date_created":"2026-06-09T19:16:27Z","file_name":"Quadrix Desktop.app.zip"},{"date_updated":"2026-06-09T19:16:40Z","success":1,"creator":"ybleile","content_type":"application/octet-stream","checksum":"106930f81563c5c719a5f4030b5ca5ed","file_size":12187896,"access_level":"open_access","file_id":"21978","relation":"main_file","file_name":"quadrix-arm64","date_created":"2026-06-09T19:16:40Z"},{"date_created":"2026-06-09T19:16:52Z","file_name":"quadrix-x64","relation":"main_file","file_id":"21979","file_size":20587592,"content_type":"application/octet-stream","checksum":"0e6ba129318446676f220087e7e6ff41","access_level":"open_access","creator":"ybleile","success":1,"date_updated":"2026-06-09T19:16:52Z"},{"date_updated":"2026-06-09T19:19:12Z","content_type":"application/gzip","checksum":"f0b03385d17df049219465ab7403fe09","access_level":"open_access","file_size":1914198,"creator":"pub-gitlab-bot","file_id":"21972","date_created":"2026-06-09T19:19:12Z","file_name":"Quadrix.zip","relation":"main_file"},{"date_created":"2026-06-10T19:09:38Z","file_name":"THIRD_PARTY_LICENSES.zip","relation":"supplementary_material","file_id":"21993","checksum":"ede0bbb24bf41ab4009cf1b6a9009671","access_level":"open_access","file_size":37557,"content_type":"application/zip","creator":"ybleile","date_updated":"2026-06-10T19:09:38Z"},{"success":1,"checksum":"f3c5fcc62c88e449ab5c660244df5aef","content_type":"text/markdown","access_level":"open_access","file_size":3839,"creator":"ybleile","date_updated":"2026-06-15T08:13:32Z","relation":"main_file","date_created":"2026-06-15T08:13:32Z","file_name":"README.md","file_id":"22009"},{"file_name":"Quadrix.zip","date_created":"2026-06-15T08:14:24Z","relation":"main_file","file_id":"22008","creator":"pub-gitlab-bot","checksum":"aa74828c3165aafcdee4ddcc9ecd37ac","access_level":"open_access","file_size":1912923,"content_type":"application/gzip","date_updated":"2026-06-15T08:14:24Z"}],"citation":{"ista":"Bokor Bleile Y, Cortinovis E. 2026. Quadrix, Institute of Science and Technology Austria, 10.15479/AT-ISTA-21971.","chicago":"Bokor Bleile, Yossi, and Emanuele Cortinovis. “Quadrix.” Institute of Science and Technology Austria, 2026. https://doi.org/10.15479/AT-ISTA-21971.","short":"Y. Bokor Bleile, E. Cortinovis, (2026).","mla":"Bokor Bleile, Yossi, and Emanuele Cortinovis. Quadrix. Institute of Science and Technology Austria, 2026, doi:10.15479/AT-ISTA-21971.","ieee":"Y. Bokor Bleile and E. Cortinovis, “Quadrix.” Institute of Science and Technology Austria, 2026.","apa":"Bokor Bleile, Y., & Cortinovis, E. (2026). Quadrix. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-21971","ama":"Bokor Bleile Y, Cortinovis E. Quadrix. 2026. doi:10.15479/AT-ISTA-21971"},"user_id":"68b8ca59-c5b3-11ee-8790-cd641c68093d","type":"software","project":[{"_id":"9106a876-16d5-11f0-9cad-bbf11c9952f9","grant_number":"ESP 9584724","name":"Quantitative Unbiased Shape Analysis with Geometry & Topology"}],"corr_author":"1","has_accepted_license":"1","_id":"21971","doi":"10.15479/AT-ISTA-21971","author":[{"id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2","first_name":"Yossi","full_name":"Bleile, Yossi","last_name":"Bleile","orcid":"0000-0002-4861-9174"},{"last_name":"Cortinovis","full_name":"Cortinovis, Emanuele","first_name":"Emanuele"}],"year":"2026","status":"public"},{"isi":1,"scopus_import":"1","abstract":[{"text":"Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications.","lang":"eng"}],"day":"01","date_created":"2025-10-12T22:01:26Z","file_date_updated":"2026-01-05T13:21:20Z","volume":75,"title":"On the size of chromatic Delaunay mosaics","related_material":{"record":[{"status":"public","id":"15090","relation":"earlier_version"}]},"language":[{"iso":"eng"}],"arxiv":1,"intvolume":" 75","citation":{"ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” Discrete and Computational Geometry, vol. 75. Springer Nature, pp. 24–47, 2026.","mla":"Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” Discrete and Computational Geometry, vol. 75, Springer Nature, 2026, pp. 24–47, doi:10.1007/s00454-025-00778-7.","ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. Discrete and Computational Geometry. 2026;75:24-47. doi:10.1007/s00454-025-00778-7","apa":"Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (2026). On the size of chromatic Delaunay mosaics. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-025-00778-7","ista":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2026. On the size of chromatic Delaunay mosaics. Discrete and Computational Geometry. 75, 24–47.","short":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 75 (2026) 24–47.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.” Discrete and Computational Geometry. Springer Nature, 2026. https://doi.org/10.1007/s00454-025-00778-7."},"acknowledgement":"The fourth author thanks Boris Aronov for insightful discussions on the size of the overlay of Voronoi tessellations. Open 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.","external_id":{"isi":["001584166900001"],"arxiv":["2212.03121"]},"ddc":["510"],"type":"journal_article","publication":"Discrete and Computational Geometry","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF"}],"doi":"10.1007/s00454-025-00778-7","_id":"20456","page":"24-47","author":[{"first_name":"Ranita","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","last_name":"Biswas"},{"orcid":"0000-0001-6249-0832","last_name":"Cultrera di Montesano","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Ondrej","full_name":"Draganov, Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0464-3823","last_name":"Draganov"},{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"first_name":"Morteza","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian"}],"quality_controlled":"1","ec_funded":1,"publisher":"Springer Nature","PlanS_conform":"1","article_type":"original","month":"01","date_published":"2026-01-01T00:00:00Z","publication_status":"published","date_updated":"2026-01-05T13:21:56Z","department":[{"_id":"HeEd"}],"article_processing_charge":"Yes (via OA deal)","oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"OA_type":"hybrid","file":[{"date_updated":"2026-01-05T13:21:20Z","checksum":"0addb5c1b78142f9fb453bfa04695400","content_type":"application/pdf","access_level":"open_access","file_size":570922,"creator":"dernst","success":1,"file_id":"20952","date_created":"2026-01-05T13:21:20Z","file_name":"2026_DiscreteCompGeom_Biswas.pdf","relation":"main_file"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"publisher","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"corr_author":"1","has_accepted_license":"1","status":"public","year":"2026"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"publisher","publication_identifier":{"issn":["1472-2747"],"eissn":["1472-2739"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"OA_type":"diamond","file":[{"creator":"dernst","checksum":"1e05b4f17a44500ae1ae1e21bc636f6a","access_level":"open_access","file_size":574389,"content_type":"application/pdf","success":1,"date_updated":"2026-01-05T12:16:38Z","file_name":"2025_AlgebraicGeomTopology_Zava.pdf","date_created":"2026-01-05T12:16:38Z","relation":"main_file","file_id":"20943"}],"oa_version":"Published Version","status":"public","year":"2025","issue":"8","corr_author":"1","has_accepted_license":"1","PlanS_conform":"1","date_published":"2025-11-20T00:00:00Z","article_type":"original","month":"11","date_updated":"2026-01-05T12:19:09Z","publication_status":"published","publisher":"Mathematical Sciences Publishers","oa":1,"department":[{"_id":"HeEd"}],"article_processing_charge":"No","publication":"Algebraic & Geometric Topology","type":"journal_article","arxiv":1,"intvolume":" 25","acknowledgement":"The author was supported by the FWF Grant, Project number I4245-N35. The author would like to thank Thomas Weighill for the helpful discussions around Theorem 3.10, and Takamitsu Yamauchi for bringing to my attention the fundamental reference [35]. Furthermore, the author\r\nis thankful for the detailed and helpful comments of the reviewer of this manuscript.","citation":{"chicago":"Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the Gromov–Hausdorff Space into Hilbert Spaces.” Algebraic & Geometric Topology. Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/agt.2025.25.5153.","short":"N. Zava, Algebraic & Geometric Topology 25 (2025) 5153–5174.","ista":"Zava N. 2025. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces. Algebraic & Geometric Topology. 25(8), 5153–5174.","apa":"Zava, N. (2025). Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces. Algebraic & Geometric Topology. Mathematical Sciences Publishers. https://doi.org/10.2140/agt.2025.25.5153","ama":"Zava N. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces. Algebraic & Geometric Topology. 2025;25(8):5153-5174. doi:10.2140/agt.2025.25.5153","mla":"Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the Gromov–Hausdorff Space into Hilbert Spaces.” Algebraic & Geometric Topology, vol. 25, no. 8, Mathematical Sciences Publishers, 2025, pp. 5153–74, doi:10.2140/agt.2025.25.5153.","ieee":"N. Zava, “Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces,” Algebraic & Geometric Topology, vol. 25, no. 8. Mathematical Sciences Publishers, pp. 5153–5174, 2025."},"ddc":["500"],"external_id":{"arxiv":["2303.04730"]},"author":[{"last_name":"Zava","orcid":"0000-0001-8686-1888","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","first_name":"Nicolò","full_name":"Zava, Nicolò"}],"page":"5153-5174","quality_controlled":"1","project":[{"call_identifier":"FWF","grant_number":"I04245","name":"Algebraic Footprints of Geometric Features in Homology","_id":"26AD5D90-B435-11E9-9278-68D0E5697425"}],"doi":"10.2140/agt.2025.25.5153","_id":"20867","scopus_import":"1","file_date_updated":"2026-01-05T12:16:38Z","volume":25,"title":"Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We discuss the embeddability of subspaces of the Gromov–Hausdorff space, which consists of isometry classes of compact metric spaces endowed with the Gromov–Hausdorff distance, into Hilbert spaces. These embeddings are particularly valuable for applications to topological data analysis. We prove that its subspace consisting of metric spaces with at most n points has asymptotic dimension n(n−1)∕2. Thus, there exists a coarse embedding of that space into a Hilbert space. On the contrary, if the number of points is not bounded, then the subspace cannot be coarsely embedded into any uniformly convex Banach space and so, in particular, into any Hilbert space. Furthermore, we prove that, even if we restrict to finite metric spaces whose diameter is bounded by some constant, the subspace still cannot be bi-Lipschitz embedded into any finite-dimensional Hilbert space. We obtain both nonembeddability results by finding obstructions to coarse and bi-Lipschitz embeddings in families of isometry classes of finite subsets of the real line endowed with the Euclidean–Hausdorff distance."}],"day":"20","date_created":"2025-12-29T12:09:09Z"},{"ec_funded":1,"date_published":"2025-05-23T00:00:00Z","month":"05","date_updated":"2026-06-11T11:51:13Z","publication_status":"submitted","department":[{"_id":"HeEd"}],"article_number":"2505.17858","article_processing_charge":"No","abstract":[{"lang":"eng","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."}],"day":"23","date_created":"2026-01-20T10:12:21Z","title":"Identifying cobordisms using kernel persistence","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2505.17858","open_access":"1"}],"language":[{"iso":"eng"}],"arxiv":1,"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.","citation":{"chicago":"Bokor Bleile, Yossi, Lisbeth Fajstrup, Teresa Heiss, Anne Marie Svane, and Søren Strandskov Sørensen. “Identifying Cobordisms Using Kernel Persistence.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2505.17858.","short":"Y. Bokor Bleile, L. Fajstrup, T. Heiss, A.M. Svane, S.S. 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Sørensen, “Identifying cobordisms using kernel persistence,” arXiv. ."},"external_id":{"arxiv":["2505.17858"]},"oa_version":"Preprint","type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"arXiv","OA_place":"repository","project":[{"call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"doi":"10.48550/arXiv.2505.17858","_id":"21016","author":[{"id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2","first_name":"Yossi","full_name":"Bleile, Yossi","last_name":"Bleile","orcid":"0000-0002-4861-9174"},{"full_name":"Fajstrup, Lisbeth","first_name":"Lisbeth","last_name":"Fajstrup"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","full_name":"Heiss, Teresa","first_name":"Teresa","last_name":"Heiss","orcid":"0000-0002-1780-2689"},{"last_name":"Svane","first_name":"Anne Marie","full_name":"Svane, Anne Marie"},{"first_name":"Søren Strandskov","full_name":"Sørensen, Søren Strandskov","last_name":"Sørensen"}],"status":"public","year":"2025"},{"language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2501.05315","open_access":"1"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"21021"},{"status":"public","relation":"later_version","id":"21931"}]},"title":"Counting equilibria of the electrostatic potential","date_created":"2026-01-27T14:29:27Z","abstract":[{"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.","lang":"eng"}],"article_processing_charge":"No","day":"20","department":[{"_id":"HeEd"}],"date_updated":"2026-06-02T09:24:17Z","publication_status":"draft","date_published":"2025-03-20T00:00:00Z","month":"03","status":"public","author":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","first_name":"Christopher D","full_name":"Fillmore, Christopher D","last_name":"Fillmore"},{"full_name":"Olivera, Gonçalo","first_name":"Gonçalo","last_name":"Olivera"}],"year":"2025","_id":"21050","doi":"10.48550/ARXIV.2501.05315","corr_author":"1","OA_place":"repository","publication":"arXiv","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","type":"preprint","oa_version":"Preprint","external_id":{"arxiv":["2501.05315"]},"citation":{"mla":"Edelsbrunner, Herbert, et al. “Counting Equilibria of the Electrostatic Potential.” ArXiv, doi:10.48550/ARXIV.2501.05315.","ieee":"H. Edelsbrunner, C. D. Fillmore, and G. Olivera, “Counting equilibria of the electrostatic potential,” arXiv. .","ama":"Edelsbrunner H, Fillmore CD, Olivera G. Counting equilibria of the electrostatic potential. arXiv. doi:10.48550/ARXIV.2501.05315","apa":"Edelsbrunner, H., Fillmore, C. D., & Olivera, G. (n.d.). Counting equilibria of the electrostatic potential. arXiv. https://doi.org/10.48550/ARXIV.2501.05315","ista":"Edelsbrunner H, Fillmore CD, Olivera G. Counting equilibria of the electrostatic potential. arXiv, 10.48550/ARXIV.2501.05315.","short":"H. Edelsbrunner, C.D. Fillmore, G. Olivera, ArXiv (n.d.).","chicago":"Edelsbrunner, Herbert, Christopher D Fillmore, and Gonçalo Olivera. “Counting Equilibria of the Electrostatic Potential.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2501.05315."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"arxiv":1},{"publication":"Computational Geometry","type":"journal_article","citation":{"mla":"Pach, János, et al. “Decomposition of Geometric Graphs into Star-Forests.” Computational Geometry, vol. 129, 102186, Elsevier, 2025, doi:10.1016/j.comgeo.2025.102186.","ieee":"J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs into star-forests,” Computational Geometry, vol. 129. Elsevier, 2025.","ama":"Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests. Computational Geometry. 2025;129. doi:10.1016/j.comgeo.2025.102186","apa":"Pach, J., Saghafian, M., & Schnider, P. (2025). Decomposition of geometric graphs into star-forests. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2025.102186","ista":"Pach J, Saghafian M, Schnider P. 2025. Decomposition of geometric graphs into star-forests. Computational Geometry. 129, 102186.","short":"J. Pach, M. Saghafian, P. Schnider, Computational Geometry 129 (2025).","chicago":"Pach, János, Morteza Saghafian, and Patrick Schnider. “Decomposition of Geometric Graphs into Star-Forests.” Computational Geometry. Elsevier, 2025. https://doi.org/10.1016/j.comgeo.2025.102186."},"acknowledgement":"A preliminary version of this note has been published in the proceedings of the 31st International Symposium on Graph Drawing and Network Visualization, Palermo, 2023. The authors would like to thank the anonymous referees for their valuable comments.","external_id":{"arxiv":["2306.13201"]},"arxiv":1,"intvolume":" 129","quality_controlled":"1","author":[{"last_name":"Pach","full_name":"Pach, János","first_name":"János"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"},{"full_name":"Schnider, Patrick","first_name":"Patrick","last_name":"Schnider"}],"doi":"10.1016/j.comgeo.2025.102186","_id":"21253","title":"Decomposition of geometric graphs into star-forests","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"15012"}]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.13201","open_access":"1"}],"volume":129,"day":"01","abstract":[{"text":"We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than n - 1 star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs.","lang":"eng"}],"date_created":"2026-02-16T15:48:42Z","OA_place":"repository","publication_identifier":{"issn":["0925-7721"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","OA_type":"green","year":"2025","status":"public","corr_author":"1","article_type":"original","month":"12","date_published":"2025-12-01T00:00:00Z","publication_status":"published","date_updated":"2026-04-16T09:12:36Z","publisher":"Elsevier","oa":1,"article_processing_charge":"No","article_number":"102186","department":[{"_id":"HeEd"}]},{"has_accepted_license":"1","corr_author":"1","year":"2025","status":"public","OA_type":"hybrid","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"oa_version":"Published Version","file":[{"file_id":"19610","relation":"main_file","file_name":"2025_DiscreteComputGeom_EdelsbrunnerHe.pdf","date_created":"2025-04-23T07:31:32Z","date_updated":"2025-04-23T07:31:32Z","success":1,"creator":"dernst","content_type":"application/pdf","access_level":"open_access","checksum":"ffb0c818222138f9f113f4bbea41e834","file_size":283443}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"OA_place":"publisher","department":[{"_id":"HeEd"}],"article_processing_charge":"Yes (via OA deal)","oa":1,"ec_funded":1,"publisher":"Springer Nature","publication_status":"published","date_updated":"2026-02-16T12:18:50Z","date_published":"2025-03-01T00:00:00Z","month":"03","article_type":"original","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"_id":"17149","doi":"10.1007/s00454-024-00660-y","page":"490-499","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"last_name":"Nikitenko","orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","full_name":"Nikitenko, Anton"}],"quality_controlled":"1","intvolume":" 73","arxiv":1,"ddc":["510"],"external_id":{"isi":["001238566200004"],"arxiv":["2012.03350"],"pmid":["39974750"]},"acknowledgement":"The authors thank Ranita Biswas and Tatiana Ezubova for the collaboration on computational experiments that motivated the work reported in this paper. The authors also thank Daniel Bonnema for proofreading and noticing an issue with the original proof of Lemma 4.3.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nThis 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.","citation":{"ama":"Edelsbrunner H, Nikitenko A. Average and expected distortion of Voronoi paths and scapes. Discrete & Computational Geometry. 2025;73:490-499. doi:10.1007/s00454-024-00660-y","apa":"Edelsbrunner, H., & Nikitenko, A. (2025). Average and expected distortion of Voronoi paths and scapes. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-024-00660-y","ieee":"H. Edelsbrunner and A. Nikitenko, “Average and expected distortion of Voronoi paths and scapes,” Discrete & Computational Geometry, vol. 73. Springer Nature, pp. 490–499, 2025.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Average and Expected Distortion of Voronoi Paths and Scapes.” Discrete & Computational Geometry, vol. 73, Springer Nature, 2025, pp. 490–99, doi:10.1007/s00454-024-00660-y.","short":"H. Edelsbrunner, A. Nikitenko, Discrete & Computational Geometry 73 (2025) 490–499.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Average and Expected Distortion of Voronoi Paths and Scapes.” Discrete & Computational Geometry. Springer Nature, 2025. https://doi.org/10.1007/s00454-024-00660-y.","ista":"Edelsbrunner H, Nikitenko A. 2025. Average and expected distortion of Voronoi paths and scapes. Discrete & Computational Geometry. 73, 490–499."},"type":"journal_article","publication":"Discrete & Computational Geometry","date_created":"2024-06-16T22:01:07Z","day":"01","abstract":[{"text":"The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about 4/Pi. We prove that this factor is the same on average (in the ergodic sense) for approximations of any rectifiable curve by the edges of any non-exotic Delaunay mosaic (known as Voronoi path), and extend the results to all dimensions, generalizing Voronoi paths to Voronoi scapes.","lang":"eng"}],"volume":73,"file_date_updated":"2025-04-23T07:31:32Z","language":[{"iso":"eng"}],"title":"Average and expected distortion of Voronoi paths and scapes","pmid":1,"isi":1,"scopus_import":"1"},{"scopus_import":"1","isi":1,"date_created":"2024-12-08T23:01:54Z","abstract":[{"lang":"eng","text":"The local angle property of the (order-1) Delaunay triangulations of a generic set in R2\r\n asserts that the sum of two angles opposite a common edge is less than π. This paper extends this property to higher order and uses it to generalize two classic properties from order-1 to order-2: (1) among the complete level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation lexicographically maximizes the sorted angle vector; (2) among the maximal level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation is the only one that has the local angle property. We also use our method of establishing (2) to give a new short proof of the angle vector optimality for the (order-1) Delaunay triangulation. For order-1, both properties have been instrumental in numerous applications of Delaunay triangulations, and we expect that their generalization will make order-2 Delaunay triangulations more attractive to applications as well."}],"day":"01","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2310.18238"}],"title":"Order-2 Delaunay triangulations optimize angles","volume":461,"external_id":{"isi":["001370682500001"],"arxiv":["2310.18238"]},"acknowledgement":"Work by the first and third authors is partially supported by the European Research Council (ERC), grant no. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35. Work by the second author is partially supported by the Alexander von Humboldt Foundation.","citation":{"ista":"Edelsbrunner H, Garber A, Saghafian M. 2025. Order-2 Delaunay triangulations optimize angles. Advances in Mathematics. 461, 110055.","short":"H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).","chicago":"Edelsbrunner, Herbert, Alexey Garber, and Morteza Saghafian. “Order-2 Delaunay Triangulations Optimize Angles.” Advances in Mathematics. Elsevier, 2025. https://doi.org/10.1016/j.aim.2024.110055.","mla":"Edelsbrunner, Herbert, et al. “Order-2 Delaunay Triangulations Optimize Angles.” Advances in Mathematics, vol. 461, 110055, Elsevier, 2025, doi:10.1016/j.aim.2024.110055.","ieee":"H. Edelsbrunner, A. Garber, and M. Saghafian, “Order-2 Delaunay triangulations optimize angles,” Advances in Mathematics, vol. 461. Elsevier, 2025.","ama":"Edelsbrunner H, Garber A, Saghafian M. Order-2 Delaunay triangulations optimize angles. Advances in Mathematics. 2025;461. doi:10.1016/j.aim.2024.110055","apa":"Edelsbrunner, H., Garber, A., & Saghafian, M. (2025). Order-2 Delaunay triangulations optimize angles. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2024.110055"},"intvolume":" 461","arxiv":1,"type":"journal_article","publication":"Advances in Mathematics","_id":"18626","doi":"10.1016/j.aim.2024.110055","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"quality_controlled":"1","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Garber","full_name":"Garber, Alexey","first_name":"Alexey"},{"last_name":"Saghafian","first_name":"Morteza","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"publisher":"Elsevier","ec_funded":1,"date_updated":"2025-04-15T07:16:53Z","publication_status":"published","month":"02","article_type":"original","date_published":"2025-02-01T00:00:00Z","article_processing_charge":"No","department":[{"_id":"HeEd"}],"article_number":"110055","oa":1,"oa_version":"Preprint","OA_type":"green","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","year":"2025","status":"public"},{"oa":1,"article_processing_charge":"No","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"date_published":"2025-02-03T00:00:00Z","month":"02","date_updated":"2026-04-07T11:47:30Z","publication_status":"published","publisher":"Institute of Science and Technology Austria","degree_awarded":"PhD","status":"public","year":"2025","corr_author":"1","has_accepted_license":"1","OA_place":"publisher","publication_identifier":{"issn":["2663-337X"]},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","file":[{"creator":"odragano","file_size":11899491,"access_level":"closed","content_type":"application/zip","checksum":"af6567e5d35e5eb330b8925ae37f1998","date_updated":"2025-01-31T16:58:30Z","relation":"source_file","file_name":"Thesis.zip","date_created":"2025-01-31T16:58:30Z","file_id":"18983"},{"creator":"odragano","content_type":"application/pdf","file_size":8857514,"access_level":"open_access","checksum":"c3fef68e35b9dc2020b2ca6006da6343","date_updated":"2025-02-04T16:22:07Z","file_name":"Thesis.pdf","date_created":"2025-02-04T16:22:07Z","relation":"main_file","file_id":"19000"}],"alternative_title":["ISTA Thesis"],"oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"title":"Structures and computations in topological data analysis","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"15091"},{"status":"public","relation":"part_of_dissertation","id":"18981"}]},"file_date_updated":"2025-02-04T16:22:07Z","keyword":["topological data analysis","chromatic point set","alpha complex","persistent homology","six pack","sheaf","microlocal discrete Morse","injective resolution","collapse","knot","discrete Morse theory"],"day":"03","abstract":[{"text":"Topological Data Analysis (TDA) is a discipline utilizing the mathematical field of topology to study data, most prominently collections of point sets. This thesis summarizes three projects related to computations in TDA.\r\n\r\nThe first one establishes a variant of TDA for chromatic point sets, where each point is given a color. For example, we are given positions of cells within a tumor microenvironment, and color the cancerous cells red, and the immune cells blue.\r\n\r\nThe aim is then to give a quantitative description of how the two or more sets of points spatially interact. Building on image, kernel and cokernel variants of persistent homology, we suggest six-packs of persistent diagrams as such a descriptor.\r\n\r\nWe describe a construction of a chromatic alpha complex, which enables efficient computation of several variants of the six-packs. We give topological descriptions of natural subcomplexes of the chromatic alpha complex, and show that the radii of the simplices form a discrete Morse function. Finally, we provide an implementation of the presented chromatic TDA pipeline.\r\n\r\nThe second part aims to translate a powerful tool of sheaf theory to elementary terms using labeled matrices. The goal is to enable their use in computational settings. We show that derived categories of sheaves over finite posets have, up to isomorphism, unique objects---minimal injective resolutions---and give a concrete algorithm to compute them. We further describe simple algorithms to compute derived pushforwards and pullbacks for monotonic maps, and their proper variants for inclusions, and demonstrate their tractability by providing an implementation. Finally, we suggest a discrete definition of microsupport and show desirable properties inspired by discrete Morse theory.\r\n\r\nIn the last part, we present a collection of observations about collapses. We give a characterization of collapsibility in terms of unitriangular submatrices of the boundary matrix, a cotree-tree decomposition, and the optimal solution to a variant of the Procrustes problem. We establish relation between dual collapses and relative Morse theory and pose several open questions. Finally, focusing on complexes embedded in the three-dimensional Euclidean space, we describe a relation between the collapsibility and the triviality of a polygonal knot.","lang":"eng"}],"date_created":"2025-01-31T17:04:40Z","supervisor":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"page":"140","author":[{"last_name":"Draganov","orcid":"0000-0003-0464-3823","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","first_name":"Ondrej","full_name":"Draganov, Ondrej"}],"doi":"10.15479/at:ista:18979","_id":"18979","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF"}],"type":"dissertation","citation":{"short":"O. Draganov, Structures and Computations in Topological Data Analysis, Institute of Science and Technology Austria, 2025.","chicago":"Draganov, Ondrej. “Structures and Computations in Topological Data Analysis.” Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/at:ista:18979.","ista":"Draganov O. 2025. Structures and computations in topological data analysis. Institute of Science and Technology Austria.","ama":"Draganov O. Structures and computations in topological data analysis. 2025. doi:10.15479/at:ista:18979","apa":"Draganov, O. (2025). Structures and computations in topological data analysis. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18979","mla":"Draganov, Ondrej. Structures and Computations in Topological Data Analysis. Institute of Science and Technology Austria, 2025, doi:10.15479/at:ista:18979.","ieee":"O. Draganov, “Structures and computations in topological data analysis,” Institute of Science and Technology Austria, 2025."},"acknowledgement":"The research presented in this thesis was funded with the Wittgenstein Prize,\r\nAustrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research\r\nCenter TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF),\r\ngrant no. I 02979-N35.\r\n","ddc":["514","004"]},{"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"doi":"10.1016/j.ins.2025.122425","_id":"19937","author":[{"full_name":"Mahini, Mohammad","first_name":"Mohammad","last_name":"Mahini"},{"full_name":"Beigy, Hamid","first_name":"Hamid","last_name":"Beigy"},{"full_name":"Qadami, Salman","first_name":"Salman","last_name":"Qadami"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"quality_controlled":"1","intvolume":" 719","acknowledgement":"The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which improved this paper.\r\nWork by the first and fourth authors is partially supported by the European Research Council (ERC), grant no. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35.","citation":{"short":"M. Mahini, H. Beigy, S. Qadami, M. Saghafian, Information Sciences 719 (2025).","chicago":"Mahini, Mohammad, Hamid Beigy, Salman Qadami, and Morteza Saghafian. “Simplet-Based Signatures and Approximation in Simplicial Complexes: Frequency, Degree, and Centrality.” Information Sciences. Elsevier, 2025. https://doi.org/10.1016/j.ins.2025.122425.","ista":"Mahini M, Beigy H, Qadami S, Saghafian M. 2025. Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. Information Sciences. 719(11), 122425.","ama":"Mahini M, Beigy H, Qadami S, Saghafian M. Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. Information Sciences. 2025;719(11). doi:10.1016/j.ins.2025.122425","apa":"Mahini, M., Beigy, H., Qadami, S., & Saghafian, M. (2025). Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. Information Sciences. Elsevier. https://doi.org/10.1016/j.ins.2025.122425","mla":"Mahini, Mohammad, et al. “Simplet-Based Signatures and Approximation in Simplicial Complexes: Frequency, Degree, and Centrality.” Information Sciences, vol. 719, no. 11, 122425, Elsevier, 2025, doi:10.1016/j.ins.2025.122425.","ieee":"M. Mahini, H. Beigy, S. Qadami, and M. Saghafian, “Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality,” Information Sciences, vol. 719, no. 11. Elsevier, 2025."},"external_id":{"isi":["001516170500002"]},"type":"journal_article","publication":"Information Sciences","abstract":[{"text":"Simplets are elementary units within simplicial complexes and are fundamental for analyzing the structure of simplicial complexes. Previous efforts have mainly focused on accurately counting or approximating the number of simplets rather than studying their frequencies. However, analyzing simplet frequencies is more practical for large-scale simplicial complexes. This paper introduces the Simplet Frequency Distribution (SFD) vector, which enables the analysis of simplet frequencies in simplicial complexes. Additionally, we provide a bound on the sample complexity required to approximate the SFD vector using any uniform sampling-based algorithm accurately. We extend the definition of simplet frequency distribution to encompass simplices, allowing for the analysis of simplet frequencies within simplices of simplicial complexes. This paper introduces the Simplet Degree Vector (SDV) and the Simplet Degree Centrality (SDC), facilitating this analysis for each simplex. Furthermore, we present a bound on the sample complexity required for accurately approximating the SDV and SDC for a set of simplices using any uniform sampling-based algorithm. We also introduce algorithms for approximating SFD, geometric SFD, SDV, and SDC. We also validate the theoretical bounds with experiments on random simplicial complexes and demonstrate the practical application through a case study.","lang":"eng"}],"day":"01","date_created":"2025-06-30T08:48:48Z","volume":719,"title":"Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality","language":[{"iso":"eng"}],"isi":1,"scopus_import":"1","corr_author":"1","year":"2025","status":"public","issue":"11","OA_type":"closed access","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0020-0255"]},"department":[{"_id":"HeEd"}],"article_number":"122425","article_processing_charge":"No","ec_funded":1,"publisher":"Elsevier","month":"11","date_published":"2025-11-01T00:00:00Z","article_type":"original","date_updated":"2025-12-30T09:05:32Z","publication_status":"published"},{"day":"20","abstract":[{"text":"We generalize a classical result by Boris Delaunay that introduced Delaunay triangulations. In particular, we prove that for a locally finite and coarsely dense generic point set A in ℝ^d, every generic point of ℝ^d belongs to exactly binom(d+k,d) simplices whose vertices belong to A and whose circumspheres enclose exactly k points of A. We extend this result to the cases in which the points are weighted, and when A contains only finitely many points in ℝ^d or in 𝕊^d. Furthermore, we use the result to give a new geometric proof for the fact that volumes of hypersimplices are Eulerian numbers.","lang":"eng"}],"date_created":"2025-07-13T22:01:22Z","title":"On spheres with k points inside","language":[{"iso":"eng"}],"file_date_updated":"2025-07-14T07:24:22Z","volume":332,"scopus_import":"1","doi":"10.4230/LIPIcs.SoCG.2025.43","_id":"20005","project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"Mathematics, Computer Science"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"quality_controlled":"1","author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alexey","full_name":"Garber, Alexey","last_name":"Garber"},{"last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","full_name":"Saghafian, Morteza"}],"citation":{"ista":"Edelsbrunner H, Garber A, Saghafian M. 2025. On spheres with k points inside. 41st International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 332, 43.","chicago":"Edelsbrunner, Herbert, Alexey Garber, and Morteza Saghafian. “On Spheres with k Points Inside.” In 41st International Symposium on Computational Geometry, Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/LIPIcs.SoCG.2025.43.","short":"H. Edelsbrunner, A. Garber, M. Saghafian, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","mla":"Edelsbrunner, Herbert, et al. “On Spheres with k Points Inside.” 41st International Symposium on Computational Geometry, vol. 332, 43, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.SoCG.2025.43.","ieee":"H. Edelsbrunner, A. Garber, and M. Saghafian, “On spheres with k points inside,” in 41st International Symposium on Computational Geometry, Kanazawa, Japan, 2025, vol. 332.","apa":"Edelsbrunner, H., Garber, A., & Saghafian, M. (2025). On spheres with k points inside. In 41st International Symposium on Computational Geometry (Vol. 332). Kanazawa, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2025.43","ama":"Edelsbrunner H, Garber A, Saghafian M. On spheres with k points inside. In: 41st International Symposium on Computational Geometry. Vol 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:10.4230/LIPIcs.SoCG.2025.43"},"acknowledgement":"Herbert Edelsbrunner: partially supported by the Wittgenstein Prize, Austrian Science\r\nFund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109,\r\nAustrian Science Fund (FWF), grant no. I 02979-N35.\r\nAlexey Garber: partially supported by the Simons Foundation.\r\nMorteza Saghafian: partially supported by the Wittgenstein Prize, Austrian Science Fund (FWF),\r\ngrant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science\r\nFund (FWF), grant no. I 02979-N35","ddc":["510"],"external_id":{"arxiv":["2410.21204"]},"arxiv":1,"intvolume":" 332","type":"conference","publication":"41st International Symposium on Computational Geometry","article_processing_charge":"Yes","article_number":"43","conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2025-06-23","location":"Kanazawa, Japan","end_date":"2025-06-27"},"department":[{"_id":"HeEd"}],"oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","month":"06","date_published":"2025-06-20T00:00:00Z","date_updated":"2025-07-14T07:26:14Z","publication_status":"published","corr_author":"1","has_accepted_license":"1","year":"2025","status":"public","file":[{"content_type":"application/pdf","access_level":"open_access","checksum":"b5313ed8575ea87913c71a6e3c7513c8","file_size":661893,"creator":"dernst","success":1,"date_updated":"2025-07-14T07:24:22Z","date_created":"2025-07-14T07:24:22Z","file_name":"2025_LIPIcs.SoCG_Edelsbrunner.pdf","relation":"main_file","file_id":"20016"}],"alternative_title":["LIPIcs"],"oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"OA_type":"gold","OA_place":"publisher","publication_identifier":{"isbn":["9783959773706"],"eissn":["1868-8969"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"OA_type":"gold","alternative_title":["LIPIcs"],"file":[{"date_updated":"2025-07-14T08:23:38Z","content_type":"application/pdf","access_level":"open_access","file_size":834623,"checksum":"3a4a7a707a56e0cfdf51428782dee55a","creator":"dernst","success":1,"file_id":"20017","date_created":"2025-07-14T08:23:38Z","file_name":"2025_LIPIcs.SoCG_Ost.pdf","relation":"main_file"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"publisher","publication_identifier":{"isbn":["9783959773706"],"eissn":["1868-8969"]},"corr_author":"1","has_accepted_license":"1","status":"public","year":"2025","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","date_published":"2025-06-20T00:00:00Z","month":"06","publication_status":"published","date_updated":"2025-12-30T11:04:33Z","department":[{"_id":"HeEd"}],"conference":{"location":"Kanazawa, Japan","end_date":"2025-06-27","name":"SoCG: Symposium on Computational Geometry","start_date":"2025-06-23"},"article_number":"71","article_processing_charge":"Yes","oa":1,"arxiv":1,"intvolume":" 332","acknowledgement":"Lara Ost: Supported by the Vienna Graduate School on Computational Optimization\r\n(VGSCO), FWF project no. W1260-N35.\r\nSebastiano Cultrera di Montesano: Supported by the Eric and Wendy Schmidt Center at the Broad Institute of MIT and Harvard.\r\nHerbert Edelsbrunner: Partially supported by the Wittgenstein Prize, FWF grant no. Z 342-N31,\r\nand by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.","citation":{"ista":"Ost L, Cultrera di Montesano S, Edelsbrunner H. 2025. Banana trees for the persistence in time series experimentally. 41st International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 332, 71.","short":"L. Ost, S. Cultrera di Montesano, H. Edelsbrunner, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","chicago":"Ost, Lara, Sebastiano Cultrera di Montesano, and Herbert Edelsbrunner. “Banana Trees for the Persistence in Time Series Experimentally.” In 41st International Symposium on Computational Geometry, Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/LIPIcs.SoCG.2025.71.","ieee":"L. Ost, S. Cultrera di Montesano, and H. Edelsbrunner, “Banana trees for the persistence in time series experimentally,” in 41st International Symposium on Computational Geometry, Kanazawa, Japan, 2025, vol. 332.","mla":"Ost, Lara, et al. “Banana Trees for the Persistence in Time Series Experimentally.” 41st International Symposium on Computational Geometry, vol. 332, 71, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.SoCG.2025.71.","ama":"Ost L, Cultrera di Montesano S, Edelsbrunner H. Banana trees for the persistence in time series experimentally. In: 41st International Symposium on Computational Geometry. Vol 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:10.4230/LIPIcs.SoCG.2025.71","apa":"Ost, L., Cultrera di Montesano, S., & Edelsbrunner, H. (2025). Banana trees for the persistence in time series experimentally. In 41st International Symposium on Computational Geometry (Vol. 332). Kanazawa, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2025.71"},"ddc":["000"],"external_id":{"arxiv":["2405.17920"]},"type":"conference","publication":"41st International Symposium on Computational Geometry","project":[{"name":"Vienna Graduate School on Computational Optimization","grant_number":"W1260-N35","_id":"9B9290DE-BA93-11EA-9121-9846C619BF3A"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science"}],"doi":"10.4230/LIPIcs.SoCG.2025.71","_id":"20006","author":[{"first_name":"Lara","full_name":"Ost, Lara","last_name":"Ost"},{"orcid":"0000-0001-6249-0832","last_name":"Cultrera di Montesano","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","scopus_import":"1","abstract":[{"text":"In numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tree data structure, specifically designed to efficiently maintain the multi-scale topological descriptor commonly known as persistent homology for dynamically changing time series data. We implement this data structure and conduct an experimental study to assess its properties and runtime for update operations. Our findings indicate that banana trees are highly effective with unbiased random data, outperforming state-of-the-art static algorithms in these scenarios. Additionally, our results show that real-world time series share structural properties with unbiased random walks, suggesting potential practical utility for our implementation.","lang":"eng"}],"day":"20","date_created":"2025-07-13T22:01:22Z","file_date_updated":"2025-07-14T08:23:38Z","volume":332,"title":"Banana trees for the persistence in time series experimentally","related_material":{"link":[{"relation":"software","url":"https://github.com/laraost/BananaPersist"}]},"language":[{"iso":"eng"}]}]