[{"abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n                  <jats:p>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.</jats:p>","lang":"eng"}],"license":"https://creativecommons.org/licenses/by/4.0/","year":"2026","has_accepted_license":"1","title":"Towards stratified space learning: 2-complexes","intvolume":"         5","publication":"La Matematica","file":[{"file_id":"21347","access_level":"open_access","date_updated":"2026-02-23T10:18:52Z","file_name":"2026_LaMatematica_Bleile.pdf","success":1,"relation":"main_file","creator":"dernst","content_type":"application/pdf","checksum":"6cae2efb47b025af22a8539c606a4e09","file_size":15051582,"date_created":"2026-02-23T10:18:52Z"}],"month":"02","arxiv":1,"date_updated":"2026-06-11T11:51:14Z","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.","article_number":"17","type":"journal_article","article_processing_charge":"Yes (via OA deal)","OA_type":"hybrid","PlanS_conform":"1","article_type":"original","date_published":"2026-02-08T00:00:00Z","external_id":{"arxiv":["2305.02724"]},"publication_identifier":{"issn":["2730-9657"]},"doi":"10.1007/s44007-025-00183-9","file_date_updated":"2026-02-23T10:18:52Z","department":[{"_id":"HeEd"}],"quality_controlled":"1","citation":{"apa":"Bokor Bleile, Y. (2026). Towards stratified space learning: 2-complexes. <i>La Matematica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s44007-025-00183-9\">https://doi.org/10.1007/s44007-025-00183-9</a>","chicago":"Bokor Bleile, Yossi. “Towards Stratified Space Learning: 2-Complexes.” <i>La Matematica</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s44007-025-00183-9\">https://doi.org/10.1007/s44007-025-00183-9</a>.","short":"Y. Bokor Bleile, La Matematica 5 (2026).","ieee":"Y. Bokor Bleile, “Towards stratified space learning: 2-complexes,” <i>La Matematica</i>, vol. 5. Springer Nature, 2026.","ista":"Bokor Bleile Y. 2026. Towards stratified space learning: 2-complexes. La Matematica. 5, 17.","mla":"Bokor Bleile, Yossi. “Towards Stratified Space Learning: 2-Complexes.” <i>La Matematica</i>, vol. 5, 17, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s44007-025-00183-9\">10.1007/s44007-025-00183-9</a>.","ama":"Bokor Bleile Y. Towards stratified space learning: 2-complexes. <i>La Matematica</i>. 2026;5. doi:<a href=\"https://doi.org/10.1007/s44007-025-00183-9\">10.1007/s44007-025-00183-9</a>"},"author":[{"orcid":"0000-0002-4861-9174","last_name":"Bleile","id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2","full_name":"Bleile, Yossi","first_name":"Yossi"}],"OA_place":"publisher","status":"public","publisher":"Springer Nature","date_created":"2026-02-16T10:44:44Z","day":"08","ddc":["510"],"_id":"21232","scopus_import":"1","oa_version":"Published Version","corr_author":"1","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1007/s44007-025-00183-9","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publication_status":"published","volume":5,"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"title":"Edge-constrained Hamiltonian paths on a point set","intvolume":"     16448","year":"2026","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"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2511.22526","open_access":"1"}],"month":"02","date_updated":"2026-03-02T08:49:20Z","alternative_title":["LNCS"],"arxiv":1,"publication":"51st International Conference on Current Trends in Theory and Practice of Computer Science","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.","OA_type":"green","article_processing_charge":"No","type":"conference","doi":"10.1007/978-3-032-17801-5_39","department":[{"_id":"HeEd"}],"date_published":"2026-02-13T00:00:00Z","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783032178008"]},"external_id":{"arxiv":["2511.22526"]},"publisher":"Springer Nature","status":"public","OA_place":"repository","author":[{"last_name":"Antić","first_name":"Todor","full_name":"Antić, Todor"},{"full_name":"Džuklevski, Aleksa","first_name":"Aleksa","last_name":"Džuklevski"},{"last_name":"Fiala","full_name":"Fiala, Jiří","first_name":"Jiří"},{"full_name":"Kratochvíl, Jan","first_name":"Jan","last_name":"Kratochvíl"},{"first_name":"Giuseppe","full_name":"Liotta, Giuseppe","last_name":"Liotta"},{"first_name":"Morteza","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian"},{"last_name":"Saumell","first_name":"Maria","full_name":"Saumell, Maria"},{"last_name":"Zink","first_name":"Johannes","full_name":"Zink, Johannes"}],"page":"532-546","quality_controlled":"1","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.","ieee":"T. Antić <i>et al.</i>, “Edge-constrained Hamiltonian paths on a point set,” in <i>51st International Conference on Current Trends in Theory and Practice of Computer Science</i>, Krakow, Poland, 2026, vol. 16448, pp. 532–546.","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 <i>51st International Conference on Current Trends in Theory and Practice of Computer Science</i> (Vol. 16448, pp. 532–546). Krakow, Poland: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-032-17801-5_39\">https://doi.org/10.1007/978-3-032-17801-5_39</a>","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 <i>51st International Conference on Current Trends in Theory and Practice of Computer Science</i>, 16448:532–46. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/978-3-032-17801-5_39\">https://doi.org/10.1007/978-3-032-17801-5_39</a>.","ama":"Antić T, Džuklevski A, Fiala J, et al. Edge-constrained Hamiltonian paths on a point set. In: <i>51st International Conference on Current Trends in Theory and Practice of Computer Science</i>. Vol 16448. Springer Nature; 2026:532-546. doi:<a href=\"https://doi.org/10.1007/978-3-032-17801-5_39\">10.1007/978-3-032-17801-5_39</a>","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.","mla":"Antić, Todor, et al. “Edge-Constrained Hamiltonian Paths on a Point Set.” <i>51st International Conference on Current Trends in Theory and Practice of Computer Science</i>, vol. 16448, Springer Nature, 2026, pp. 532–46, doi:<a href=\"https://doi.org/10.1007/978-3-032-17801-5_39\">10.1007/978-3-032-17801-5_39</a>."},"scopus_import":"1","oa_version":"Preprint","language":[{"iso":"eng"}],"_id":"21374","date_created":"2026-03-01T23:01:40Z","day":"13","conference":{"start_date":"2026-02-09","name":"SOFSEM: Conference on Current Trends in Theory and Practice of Computer Science","end_date":"2026-02-13","location":"Krakow, Poland"},"volume":16448,"oa":1,"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.1007/978-3-032-17801-5_39"},{"article_number":"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.","OA_type":"hybrid","article_processing_charge":"Yes (in subscription journal)","type":"journal_article","intvolume":"        10","title":"Maximum persistent Betti numbers of Čech complexes","has_accepted_license":"1","year":"2026","abstract":[{"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.","lang":"eng"}],"date_updated":"2026-03-09T11:31:29Z","arxiv":1,"month":"03","file":[{"file_name":"2026_JourAppliedCompTopology_Edelsbrunner.pdf","date_updated":"2026-03-09T11:29:30Z","access_level":"open_access","file_id":"21416","content_type":"application/pdf","checksum":"0bf6dc430cafa40c08f260fe17d54595","date_created":"2026-03-09T11:29:30Z","file_size":323111,"success":1,"relation":"main_file","creator":"dernst"}],"publication":"Journal of Applied and Computational Topology","oa_version":"Published Version","language":[{"iso":"eng"}],"scopus_import":"1","_id":"21407","ddc":["500"],"day":"01","date_created":"2026-03-08T23:01:45Z","project":[{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"volume":10,"oa":1,"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.1007/s41468-026-00233-3","department":[{"_id":"HeEd"}],"doi":"10.1007/s41468-026-00233-3","file_date_updated":"2026-03-09T11:29:30Z","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"external_id":{"arxiv":["2409.05241"]},"date_published":"2026-03-01T00:00:00Z","article_type":"original","PlanS_conform":"1","publisher":"Springer Nature","status":"public","author":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"last_name":"Kahle","full_name":"Kahle, Matthew","first_name":"Matthew"},{"last_name":"Kanazawa","first_name":"Shu","full_name":"Kanazawa, Shu"}],"OA_place":"publisher","citation":{"ama":"Edelsbrunner H, Kahle M, Kanazawa S. Maximum persistent Betti numbers of Čech complexes. <i>Journal of Applied and Computational Topology</i>. 2026;10. doi:<a href=\"https://doi.org/10.1007/s41468-026-00233-3\">10.1007/s41468-026-00233-3</a>","mla":"Edelsbrunner, Herbert, et al. “Maximum Persistent Betti Numbers of Čech Complexes.” <i>Journal of Applied and Computational Topology</i>, vol. 10, 5, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s41468-026-00233-3\">10.1007/s41468-026-00233-3</a>.","ista":"Edelsbrunner H, Kahle M, Kanazawa S. 2026. Maximum persistent Betti numbers of Čech complexes. Journal of Applied and Computational Topology. 10, 5.","ieee":"H. Edelsbrunner, M. Kahle, and S. Kanazawa, “Maximum persistent Betti numbers of Čech complexes,” <i>Journal of Applied and Computational Topology</i>, 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.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s41468-026-00233-3\">https://doi.org/10.1007/s41468-026-00233-3</a>.","apa":"Edelsbrunner, H., Kahle, M., &#38; Kanazawa, S. (2026). Maximum persistent Betti numbers of Čech complexes. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-026-00233-3\">https://doi.org/10.1007/s41468-026-00233-3</a>"},"quality_controlled":"1"},{"doi":"10.1007/978-981-95-7127-7_26","department":[{"_id":"HeEd"}],"date_published":"2026-02-14T00:00:00Z","external_id":{"arxiv":["2409.11079"]},"publication_identifier":{"isbn":["9789819571260"],"issn":["0302-9743"],"eissn":["1611-3349"]},"status":"public","publisher":"Springer Nature","quality_controlled":"1","citation":{"ama":"Jabal Ameli A, Motiei F, Saghafian M. On the MST-ratio: Theoretical bounds and complexity of finding the maximum. In: <i>20th International Conference and Workshops on Algorithms and Computation</i>. Vol 16444. Springer Nature; 2026:386-401. doi:<a href=\"https://doi.org/10.1007/978-981-95-7127-7_26\">10.1007/978-981-95-7127-7_26</a>","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.","mla":"Jabal Ameli, Afrouz, et al. “On the MST-Ratio: Theoretical Bounds and Complexity of Finding the Maximum.” <i>20th International Conference and Workshops on Algorithms and Computation</i>, vol. 16444, Springer Nature, 2026, pp. 386–401, doi:<a href=\"https://doi.org/10.1007/978-981-95-7127-7_26\">10.1007/978-981-95-7127-7_26</a>.","short":"A. Jabal Ameli, F. Motiei, M. Saghafian, in:, 20th International Conference and Workshops on Algorithms and Computation, Springer Nature, 2026, pp. 386–401.","ieee":"A. Jabal Ameli, F. Motiei, and M. Saghafian, “On the MST-ratio: Theoretical bounds and complexity of finding the maximum,” in <i>20th International Conference and Workshops on Algorithms and Computation</i>, Perugia, Italy, 2026, vol. 16444, pp. 386–401.","apa":"Jabal Ameli, A., Motiei, F., &#38; Saghafian, M. (2026). On the MST-ratio: Theoretical bounds and complexity of finding the maximum. In <i>20th International Conference and Workshops on Algorithms and Computation</i> (Vol. 16444, pp. 386–401). Perugia, Italy: Springer Nature. <a href=\"https://doi.org/10.1007/978-981-95-7127-7_26\">https://doi.org/10.1007/978-981-95-7127-7_26</a>","chicago":"Jabal Ameli, Afrouz, Faezeh Motiei, and Morteza Saghafian. “On the MST-Ratio: Theoretical Bounds and Complexity of Finding the Maximum.” In <i>20th International Conference and Workshops on Algorithms and Computation</i>, 16444:386–401. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/978-981-95-7127-7_26\">https://doi.org/10.1007/978-981-95-7127-7_26</a>."},"OA_place":"repository","author":[{"last_name":"Jabal Ameli","full_name":"Jabal Ameli, Afrouz","first_name":"Afrouz"},{"last_name":"Motiei","full_name":"Motiei, Faezeh","first_name":"Faezeh"},{"first_name":"Morteza","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian"}],"page":"386-401","_id":"21410","scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"Preprint","date_created":"2026-03-08T23:01:45Z","day":"14","ec_funded":1,"publication_status":"published","oa":1,"conference":{"name":"WALCOM: International Conference and Workshops on Algorithms and Computation","start_date":"2026-03-04","location":"Perugia, Italy","end_date":"2026-03-06"},"volume":16444,"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342"}],"fulldoi":"https://doi.org/10.1007/978-981-95-7127-7_26","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"On the MST-ratio: Theoretical bounds and complexity of finding the maximum","intvolume":"     16444","abstract":[{"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.","lang":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.11079","open_access":"1"}],"year":"2026","publication":"20th International Conference and Workshops on Algorithms and Computation","month":"02","alternative_title":["LNCS"],"arxiv":1,"date_updated":"2026-03-09T10:25:41Z","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.","article_processing_charge":"No","OA_type":"green","type":"conference"},{"OA_type":"green","article_processing_charge":"No","type":"journal_article","issue":"1","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.","month":"04","arxiv":1,"date_updated":"2026-05-07T07:45:24Z","publication":"Combinatorics and Number Theory","title":"Covering complete geometric graphs by monotone paths","intvolume":"        15","year":"2026","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."}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2507.10840","open_access":"1"}],"volume":15,"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342"}],"publication_status":"published","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.2140/cnt.2026.15.73","scopus_import":"1","oa_version":"Preprint","language":[{"iso":"eng"}],"_id":"21781","ec_funded":1,"day":"17","date_created":"2026-05-03T22:01:37Z","publisher":"Mathematical Sciences Publishers","status":"public","page":"73-82","OA_place":"repository","author":[{"last_name":"Dumitrescu","full_name":"Dumitrescu, Adrian","first_name":"Adrian"},{"full_name":"Pach, János","first_name":"János","last_name":"Pach"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824"},{"last_name":"Scott","first_name":"Alex","full_name":"Scott, Alex"}],"quality_controlled":"1","citation":{"chicago":"Dumitrescu, Adrian, János Pach, Morteza Saghafian, and Alex Scott. “Covering Complete Geometric Graphs by Monotone Paths.” <i>Combinatorics and Number Theory</i>. Mathematical Sciences Publishers, 2026. <a href=\"https://doi.org/10.2140/cnt.2026.15.73\">https://doi.org/10.2140/cnt.2026.15.73</a>.","apa":"Dumitrescu, A., Pach, J., Saghafian, M., &#38; Scott, A. (2026). Covering complete geometric graphs by monotone paths. <i>Combinatorics and Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/cnt.2026.15.73\">https://doi.org/10.2140/cnt.2026.15.73</a>","ieee":"A. Dumitrescu, J. Pach, M. Saghafian, and A. Scott, “Covering complete geometric graphs by monotone paths,” <i>Combinatorics and Number Theory</i>, vol. 15, no. 1. Mathematical Sciences Publishers, pp. 73–82, 2026.","short":"A. Dumitrescu, J. Pach, M. Saghafian, A. Scott, Combinatorics and Number Theory 15 (2026) 73–82.","mla":"Dumitrescu, Adrian, et al. “Covering Complete Geometric Graphs by Monotone Paths.” <i>Combinatorics and Number Theory</i>, vol. 15, no. 1, Mathematical Sciences Publishers, 2026, pp. 73–82, doi:<a href=\"https://doi.org/10.2140/cnt.2026.15.73\">10.2140/cnt.2026.15.73</a>.","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.","ama":"Dumitrescu A, Pach J, Saghafian M, Scott A. Covering complete geometric graphs by monotone paths. <i>Combinatorics and Number Theory</i>. 2026;15(1):73-82. doi:<a href=\"https://doi.org/10.2140/cnt.2026.15.73\">10.2140/cnt.2026.15.73</a>"},"doi":"10.2140/cnt.2026.15.73","department":[{"_id":"HeEd"}],"date_published":"2026-04-17T00:00:00Z","external_id":{"arxiv":["2507.10840"]},"publication_identifier":{"eissn":["2996-220X"],"issn":["2996-2196"]},"article_type":"original"},{"day":"15","date_created":"2026-06-09T19:19:13Z","_id":"21971","corr_author":"1","type":"software","fulldoi":"https://doi.org/10.15479/AT-ISTA-21971","user_id":"68b8ca59-c5b3-11ee-8790-cd641c68093d","oa":1,"tmp":{"legal_code_url":"https://opensource.org/licenses/MIT","short":"MIT","name":"The MIT License"},"project":[{"grant_number":"ESP 9584724","name":"Quantitative Unbiased Shape Analysis with Geometry & Topology","_id":"9106a876-16d5-11f0-9cad-bbf11c9952f9"}],"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"}],"license":"https://opensource.org/licenses/MIT","date_published":"2026-06-15T00:00:00Z","year":"2026","has_accepted_license":"1","title":"Quadrix","keyword":["quadratics","mathematics","dendrites","geometry","topology"],"file_date_updated":"2026-06-15T08:14:24Z","doi":"10.15479/AT-ISTA-21971","department":[{"_id":"HeEd"}],"citation":{"short":"Y. Bokor Bleile, E. Cortinovis, (2026).","ieee":"Y. Bokor Bleile and E. Cortinovis, “Quadrix.” Institute of Science and Technology Austria, 2026.","apa":"Bokor Bleile, Y., &#38; Cortinovis, E. (2026). Quadrix. 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Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-21971\">10.15479/AT-ISTA-21971</a>."},"month":"06","file":[{"file_name":"LICENSE","date_updated":"2026-06-09T19:16:02Z","access_level":"open_access","file_id":"21974","date_created":"2026-06-09T19:16:02Z","file_size":1081,"content_type":"application/octet-stream","checksum":"48f633b6767c4b15dd6220ca2b4dc175","creator":"ybleile","success":1,"relation":"main_file"},{"file_name":"quadrix-x64.exe","date_updated":"2026-06-09T19:16:27Z","access_level":"open_access","file_id":"21975","date_created":"2026-06-09T19:16:27Z","file_size":11308032,"checksum":"de25d0b224acbde3d38f837fdd8f97d5","content_type":"application/octet-stream","creator":"ybleile","success":1,"relation":"main_file"},{"content_type":"application/octet-stream","checksum":"a7b94a7380dc178e76ebdba9f1fa45c2","file_size":10655744,"date_created":"2026-06-09T19:16:28Z","success":1,"relation":"main_file","creator":"ybleile","date_updated":"2026-06-09T19:16:28Z","file_name":"quadrix-arm64.exe","file_id":"21976","access_level":"open_access"},{"date_updated":"2026-06-09T19:16:27Z","file_name":"Quadrix Desktop.app.zip","file_id":"21977","access_level":"open_access","file_size":2032,"date_created":"2026-06-09T19:16:27Z","content_type":"application/zip","checksum":"2404aa8619a56668bd95032791ee1250","creator":"ybleile","success":1,"relation":"main_file"},{"file_id":"21978","access_level":"open_access","date_updated":"2026-06-09T19:16:40Z","file_name":"quadrix-arm64","relation":"main_file","success":1,"creator":"ybleile","content_type":"application/octet-stream","checksum":"106930f81563c5c719a5f4030b5ca5ed","file_size":12187896,"date_created":"2026-06-09T19:16:40Z"},{"creator":"ybleile","success":1,"relation":"main_file","file_size":20587592,"date_created":"2026-06-09T19:16:52Z","content_type":"application/octet-stream","checksum":"0e6ba129318446676f220087e7e6ff41","file_id":"21979","access_level":"open_access","date_updated":"2026-06-09T19:16:52Z","file_name":"quadrix-x64"},{"content_type":"application/gzip","checksum":"f0b03385d17df049219465ab7403fe09","date_created":"2026-06-09T19:19:12Z","file_size":1914198,"relation":"main_file","creator":"pub-gitlab-bot","file_name":"Quadrix.zip","date_updated":"2026-06-09T19:19:12Z","access_level":"open_access","file_id":"21972"},{"creator":"ybleile","relation":"supplementary_material","date_created":"2026-06-10T19:09:38Z","file_size":37557,"checksum":"ede0bbb24bf41ab4009cf1b6a9009671","content_type":"application/zip","access_level":"open_access","file_id":"21993","file_name":"THIRD_PARTY_LICENSES.zip","date_updated":"2026-06-10T19:09:38Z"},{"file_name":"README.md","date_updated":"2026-06-15T08:13:32Z","access_level":"open_access","file_id":"22009","content_type":"text/markdown","checksum":"f3c5fcc62c88e449ab5c660244df5aef","date_created":"2026-06-15T08:13:32Z","file_size":3839,"relation":"main_file","success":1,"creator":"ybleile"},{"access_level":"open_access","file_id":"22008","file_name":"Quadrix.zip","date_updated":"2026-06-15T08:14:24Z","creator":"pub-gitlab-bot","relation":"main_file","date_created":"2026-06-15T08:14:24Z","file_size":1912923,"checksum":"aa74828c3165aafcdee4ddcc9ecd37ac","content_type":"application/gzip"}],"date_updated":"2026-06-15T23:00:03Z","author":[{"first_name":"Yossi","full_name":"Bleile, Yossi","orcid":"0000-0002-4861-9174","id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2","last_name":"Bleile"},{"full_name":"Cortinovis, Emanuele","first_name":"Emanuele","last_name":"Cortinovis"}],"status":"public","publisher":"Institute of Science and Technology Austria"},{"article_processing_charge":"Yes (via OA deal)","OA_type":"hybrid","type":"journal_article","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.","publication":"Discrete and Computational Geometry","arxiv":1,"date_updated":"2026-01-05T13:21:56Z","month":"01","file":[{"relation":"main_file","success":1,"creator":"dernst","checksum":"0addb5c1b78142f9fb453bfa04695400","content_type":"application/pdf","file_size":570922,"date_created":"2026-01-05T13:21:20Z","file_id":"20952","access_level":"open_access","date_updated":"2026-01-05T13:21:20Z","file_name":"2026_DiscreteCompGeom_Biswas.pdf"}],"title":"On the size of chromatic Delaunay mosaics","intvolume":"        75","has_accepted_license":"1","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"15090"}]},"abstract":[{"lang":"eng","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."}],"year":"2026","publication_status":"published","oa":1,"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"volume":75,"fulldoi":"https://doi.org/10.1007/s00454-025-00778-7","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"20456","language":[{"iso":"eng"}],"corr_author":"1","oa_version":"Published Version","scopus_import":"1","date_created":"2025-10-12T22:01:26Z","day":"01","ddc":["510"],"ec_funded":1,"status":"public","publisher":"Springer Nature","isi":1,"citation":{"ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. <i>Discrete and Computational Geometry</i>. 2026;75:24-47. doi:<a href=\"https://doi.org/10.1007/s00454-025-00778-7\">10.1007/s00454-025-00778-7</a>","mla":"Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” <i>Discrete and Computational Geometry</i>, vol. 75, Springer Nature, 2026, pp. 24–47, doi:<a href=\"https://doi.org/10.1007/s00454-025-00778-7\">10.1007/s00454-025-00778-7</a>.","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.","ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” <i>Discrete and Computational Geometry</i>, vol. 75. Springer Nature, pp. 24–47, 2026.","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.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00454-025-00778-7\">https://doi.org/10.1007/s00454-025-00778-7</a>.","apa":"Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (2026). On the size of chromatic Delaunay mosaics. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-025-00778-7\">https://doi.org/10.1007/s00454-025-00778-7</a>"},"quality_controlled":"1","author":[{"full_name":"Biswas, Ranita","first_name":"Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano"},{"orcid":"0000-0003-0464-3823","last_name":"Draganov","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej","first_name":"Ondrej"},{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","first_name":"Morteza"}],"page":"24-47","OA_place":"publisher","department":[{"_id":"HeEd"}],"doi":"10.1007/s00454-025-00778-7","file_date_updated":"2026-01-05T13:21:20Z","article_type":"original","PlanS_conform":"1","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"external_id":{"isi":["001584166900001"],"arxiv":["2212.03121"]},"date_published":"2026-01-01T00:00:00Z"},{"doi":"10.1016/j.jsc.2026.102598","department":[{"_id":"HeEd"}],"keyword":["Persistence module","Persistence map","Persistent homology"],"date_published":"2026-06-23T00:00:00Z","publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"external_id":{"arxiv":["2006.11100"]},"PlanS_conform":"1","article_type":"original","publisher":"Elsevier","status":"public","OA_place":"publisher","author":[{"first_name":"Rocio","full_name":"Gonzalez-Diaz, Rocio","last_name":"Gonzalez-Diaz"},{"first_name":"Manuel","full_name":"Soriano Trigueros, Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","last_name":"Soriano Trigueros","orcid":"0000-0003-2449-1433"},{"last_name":"Torras-Casas","first_name":"Alvaro","full_name":"Torras-Casas, Alvaro"}],"quality_controlled":"1","citation":{"mla":"Gonzalez-Diaz, Rocio, et al. “Additive Partial Matchings Induced by Persistence Maps.” <i>Journal of Symbolic Computation</i>, vol. 138, 102598, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">10.1016/j.jsc.2026.102598</a>.","ista":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. 2026. Additive partial matchings induced by persistence maps. Journal of Symbolic Computation. 138, 102598.","ama":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. Additive partial matchings induced by persistence maps. <i>Journal of Symbolic Computation</i>. 2026;138. doi:<a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">10.1016/j.jsc.2026.102598</a>","chicago":"Gonzalez-Diaz, Rocio, Manuel Soriano Trigueros, and Alvaro Torras-Casas. “Additive Partial Matchings Induced by Persistence Maps.” <i>Journal of Symbolic Computation</i>. Elsevier, 2026. <a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">https://doi.org/10.1016/j.jsc.2026.102598</a>.","apa":"Gonzalez-Diaz, R., Soriano Trigueros, M., &#38; Torras-Casas, A. (2026). Additive partial matchings induced by persistence maps. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">https://doi.org/10.1016/j.jsc.2026.102598</a>","ieee":"R. Gonzalez-Diaz, M. Soriano Trigueros, and A. Torras-Casas, “Additive partial matchings induced by persistence maps,” <i>Journal of Symbolic Computation</i>, vol. 138. Elsevier, 2026.","short":"R. Gonzalez-Diaz, M. Soriano Trigueros, A. Torras-Casas, Journal of Symbolic Computation 138 (2026)."},"scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","corr_author":"1","_id":"22291","ddc":["500"],"day":"23","date_created":"2026-07-13T09:43:38Z","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"volume":138,"dataavailabilitystatement":"The code used for the computational experiments is available in https://github.com/Cimagroup/IBloFunMatch","publication_status":"epub_ahead","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.1016/j.jsc.2026.102598","mathsc":["55N31","16G20"],"has_accepted_license":"1","intvolume":"       138","title":"Additive partial matchings induced by persistence maps","year":"2026","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jsc.2026.102598"}],"abstract":[{"lang":"eng","text":"Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and fast-to-compute invariant known as the persistence diagram. However, this is no longer the case for maps between persistence modules (i.e. persistence maps). We propose a new invariant for persistence maps, consisting of a partial matching between the persistence diagrams of the domain and codomain modules. We show that this invariant is additive with respect to the direct sum decomposition of persistence maps, is more discriminative than the image module, and is computable in cubic time. Furthermore, we provide an implementation and demonstrate its efficiency by integrating it with edge collapse techniques for flag complexes (e.g., Vietoris–Rips complexes). As a key technical contribution, we describe how to induce a persistence map between two flag complexes that have been independently simplified via edge collapses, even when a direct simplicial map between them is no longer available."}],"month":"06","researchdata_availability":"yes","arxiv":1,"date_updated":"2026-07-13T12:00:07Z","publication":"Journal of Symbolic Computation","supplementarymaterial":"no","das_tickbox":"1","article_number":"102598","acknowledgement":"This project was partially funded by MCIN/AEI and the NextGenerationEU/PRTR, under project TED2021-129438B-I00. The authors thank IMUS-Maria de Maeztu grant CEX2024-001517-M - Apoyo a Unidades de Excelencia María de Maeztu for supporting this research, funded by MICIU/AEI/ 10.13039/501100011033. The authors would also like to thank Lars M Salbu for fruitful discussions regarding the operators from Definition 4.1 and their relation with the order relations introduced in Definition 3.2.","OA_type":"hybrid","article_processing_charge":"No","type":"journal_article"},{"type":"conference","OA_type":"gold","article_processing_charge":"No","issue":"-4/W8-2025","acknowledgement":"We sincerely thank the Iranian Airports and Air Navigation\r\nCompany for sharing statistical data on flights from Iranian\r\nairports, separated by origin and destination, for this research.","supplementarymaterial":"no","das_tickbox":"0","date_updated":"2026-07-14T05:56:30Z","researchdata_availability":"no","file":[{"date_updated":"2026-07-14T05:55:34Z","file_name":"2026_ISPRS_EghbaliMardekheh.pdf","file_id":"22328","access_level":"open_access","content_type":"application/pdf","checksum":"7c088dd179cfee6074a350c95671dbe3","file_size":2697680,"date_created":"2026-07-14T05:55:34Z","success":1,"relation":"main_file","creator":"dernst"}],"month":"05","publication":"8th ISPRS Geospatial Conference","year":"2026","abstract":[{"lang":"eng","text":"Air traffic management is a critical component of aviation, aiming to balance safety, capacity and demand within controlled airspace. This research analyses Iran's domestic air transport network (2018-2021) by developing annual Origin-Destination (OD) impedance matrices based on flight frequency. The methodology quantifies network connectivity, revealing a highly centralized structure dominated by core corridors like Tehran-Mashhad, which carried over 10,500 flights in 2019. The COVID-19 pandemic caused a severe disruption in 2020, with traffic on major routes falling by nearly half, followed by a partial recovery in 2021. Analysis shows core hubs rebounded faster than peripheral airports, widening accessibility gaps. Through origin-destination matrix processing, the system identifies high density air routes and analyses historical trends in airspace utilization. The impedance matrix, validated against data (R²=0.87), successfully maps the intense service on hub links and the high impedance of sparse peripheral routes. Then an interactive Web GIS platform was implemented for spatiotemporal analysis of air traffic density."}],"title":"Real time interactive web GIS based modelling of high traffic air corridors in Iran using origin destination matrix analysis","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.5194/isprs-annals-x-4-w8-2025-493-2026","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"location":"Tehran, Iran","end_date":"2025-12-17","name":"ISPRS: Conference on Photogrammetry, Remote Sensing and Spatial Information Sciences,","start_date":"2025-12-15"},"volume":"X","publication_status":"published","oa":1,"ddc":["500"],"date_created":"2026-07-13T09:51:29Z","day":"29","oa_version":"Published Version","language":[{"iso":"eng"}],"scopus_import":"1","_id":"22298","author":[{"full_name":"Eghbali Mardekheh, Masoumeh","first_name":"Masoumeh","last_name":"Eghbali Mardekheh"},{"first_name":"Meysam","full_name":"Argany, Meysam","last_name":"Argany"},{"orcid":"0000-0001-6746-4174","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","last_name":"Karimipour","first_name":"Farid","full_name":"Karimipour, Farid"},{"last_name":"Sedghitabar","full_name":"Sedghitabar, Seyed Mohammad","first_name":"Seyed Mohammad"}],"page":"493-500","OA_place":"publisher","citation":{"apa":"Eghbali Mardekheh, M., Argany, M., Karimipour, F., &#38; Sedghitabar, S. M. (2026). Real time interactive web GIS based modelling of high traffic air corridors in Iran using origin destination matrix analysis. In <i>8th ISPRS Geospatial Conference</i> (Vol. X, pp. 493–500). Tehran, Iran: Copernicus Publications. <a href=\"https://doi.org/10.5194/isprs-annals-x-4-w8-2025-493-2026\">https://doi.org/10.5194/isprs-annals-x-4-w8-2025-493-2026</a>","chicago":"Eghbali Mardekheh, Masoumeh, Meysam Argany, Farid Karimipour, and Seyed Mohammad Sedghitabar. “Real Time Interactive Web GIS Based Modelling of High Traffic Air Corridors in Iran Using Origin Destination Matrix Analysis.” In <i>8th ISPRS Geospatial Conference</i>, X:493–500. Copernicus Publications, 2026. <a href=\"https://doi.org/10.5194/isprs-annals-x-4-w8-2025-493-2026\">https://doi.org/10.5194/isprs-annals-x-4-w8-2025-493-2026</a>.","short":"M. Eghbali Mardekheh, M. Argany, F. Karimipour, S.M. Sedghitabar, in:, 8th ISPRS Geospatial Conference, Copernicus Publications, 2026, pp. 493–500.","ieee":"M. Eghbali Mardekheh, M. Argany, F. Karimipour, and S. M. Sedghitabar, “Real time interactive web GIS based modelling of high traffic air corridors in Iran using origin destination matrix analysis,” in <i>8th ISPRS Geospatial Conference</i>, Tehran, Iran, 2026, vol. X, no. 4/W8-2025, pp. 493–500.","ista":"Eghbali Mardekheh M, Argany M, Karimipour F, Sedghitabar SM. 2026. Real time interactive web GIS based modelling of high traffic air corridors in Iran using origin destination matrix analysis. 8th ISPRS Geospatial Conference. ISPRS: Conference on Photogrammetry, Remote Sensing and Spatial Information Sciences, vol. X, 493–500.","mla":"Eghbali Mardekheh, Masoumeh, et al. “Real Time Interactive Web GIS Based Modelling of High Traffic Air Corridors in Iran Using Origin Destination Matrix Analysis.” <i>8th ISPRS Geospatial Conference</i>, vol. X, no. 4/W8-2025, Copernicus Publications, 2026, pp. 493–500, doi:<a href=\"https://doi.org/10.5194/isprs-annals-x-4-w8-2025-493-2026\">10.5194/isprs-annals-x-4-w8-2025-493-2026</a>.","ama":"Eghbali Mardekheh M, Argany M, Karimipour F, Sedghitabar SM. Real time interactive web GIS based modelling of high traffic air corridors in Iran using origin destination matrix analysis. In: <i>8th ISPRS Geospatial Conference</i>. Vol X. Copernicus Publications; 2026:493-500. doi:<a href=\"https://doi.org/10.5194/isprs-annals-x-4-w8-2025-493-2026\">10.5194/isprs-annals-x-4-w8-2025-493-2026</a>"},"quality_controlled":"1","publisher":"Copernicus Publications","status":"public","publication_identifier":{"issn":["2194-9050"]},"date_published":"2026-05-29T00:00:00Z","department":[{"_id":"HeEd"}],"file_date_updated":"2026-07-14T05:55:34Z","doi":"10.5194/isprs-annals-x-4-w8-2025-493-2026","keyword":["Air Traffic simulation","Dynamic Air Traffic Corridors","Origin Destination matrix","Interactive Web GIS","Iran Aviation Network","Spatiotemporal Modelling"]},{"publisher":"Institute of Science and Technology Austria","status":"public","author":[{"last_name":"Fillmore","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","full_name":"Fillmore, Christopher D","first_name":"Christopher D"}],"OA_place":"publisher","page":"122","degree_awarded":"PhD","citation":{"short":"C.D. Fillmore, Braiding Geometry and Topology to Study Shapes and Data, Institute of Science and Technology Austria, 2026.","ieee":"C. D. Fillmore, “Braiding geometry and topology to study shapes and data,” Institute of Science and Technology Austria, 2026.","apa":"Fillmore, C. D. (2026). <i>Braiding geometry and topology to study shapes and data</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-21021\">https://doi.org/10.15479/AT-ISTA-21021</a>","chicago":"Fillmore, Christopher D. “Braiding Geometry and Topology to Study Shapes and Data.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-21021\">https://doi.org/10.15479/AT-ISTA-21021</a>.","ama":"Fillmore CD. Braiding geometry and topology to study shapes and data. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-21021\">10.15479/AT-ISTA-21021</a>","ista":"Fillmore CD. 2026. Braiding geometry and topology to study shapes and data. Institute of Science and Technology Austria.","mla":"Fillmore, Christopher D. <i>Braiding Geometry and Topology to Study Shapes and Data</i>. Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-21021\">10.15479/AT-ISTA-21021</a>."},"department":[{"_id":"GradSch"},{"_id":"HeEd"},{"_id":"UlWa"}],"file_date_updated":"2026-01-30T11:40:09Z","doi":"10.15479/AT-ISTA-21021","publication_identifier":{"issn":["2663-337X"]},"date_published":"2026-01-21T00:00:00Z","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","oa":1,"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","fulldoi":"https://doi.org/10.15479/AT-ISTA-21021","language":[{"iso":"eng"}],"corr_author":"1","oa_version":"Published Version","_id":"21021","acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"ScienComp"}],"ddc":["514","516"],"date_created":"2026-01-20T21:38:40Z","day":"21","alternative_title":["ISTA Thesis"],"date_updated":"2026-07-22T06:33:54Z","file":[{"content_type":"application/pdf","checksum":"4c0889130095c31d4e5088c5b8dfd607","date_created":"2026-01-26T19:44:46Z","file_size":55954297,"relation":"main_file","creator":"cfillmor","file_name":"2025_Fillmore_Christopher_Thesis.pdf","date_updated":"2026-01-30T11:40:09Z","access_level":"open_access","file_id":"21046"},{"date_updated":"2026-01-26T19:46:20Z","file_name":"Thesis.zip","file_id":"21047","access_level":"closed","file_size":166080788,"date_created":"2026-01-26T19:46:20Z","checksum":"d69afb71d82ab98f856886126ee7303a","content_type":"application/x-zip-compressed","creator":"cfillmor","relation":"source_file"}],"month":"01","related_material":{"record":[{"id":"20260","status":"public","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"21051"},{"id":"21050","status":"public","relation":"part_of_dissertation"}]},"title":"Braiding geometry and topology to study shapes and data","has_accepted_license":"1","year":"2026","abstract":[{"text":"This thesis examines how geometry and topology intersect in the representation, transformation, and analysis of complex shapes. It considers how continuous manifolds relate to their discrete analogues, how topological structures evolve in persistence vineyards, and how tools from topological data analysis can illuminate problems in mathematical physics. Central to this exploration is the question of how structure, both geometric and topological, persists or changes under approximation, sampling, or deformation. The work develops new approaches to skeletal and grid-based representations of surfaces, reveals the full expressive capacity of persistence vineyards, and applies topological methods to the longstanding problem of equilibria in electrostatic fields. These threads braid together into a broader understanding of how topology and geometry inform one another across theory, computation, and application.","lang":"eng"}],"article_processing_charge":"No","type":"dissertation","supervisor":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"full_name":"Wagner, Uli","first_name":"Uli","orcid":"0000-0002-1494-0568","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"acknowledgement":"The research presented in this thesis was funded by the DFG Collaborative Research\r\nCenter TRR 109, ‘Discretization in Geometry and Dynamics’.\r\n"},{"publication":"Proceedings of the London Mathematical Society","month":"05","date_updated":"2026-07-22T06:33:54Z","arxiv":1,"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"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2501.05315","open_access":"1"}],"year":"2026","title":"Counting equilibria of the electrostatic potential","intvolume":"       132","related_material":{"record":[{"id":"21050","status":"public","relation":"earlier_version"}]},"type":"journal_article","article_processing_charge":"No","OA_type":"green","issue":"5","article_number":"e70163","quality_controlled":"1","citation":{"ama":"Edelsbrunner H, Fillmore CD, Oliveira G. Counting equilibria of the electrostatic potential. <i>Proceedings of the London Mathematical Society</i>. 2026;132(5). doi:<a href=\"https://doi.org/10.1112/plms.70163\">10.1112/plms.70163</a>","ista":"Edelsbrunner H, Fillmore CD, Oliveira G. 2026. Counting equilibria of the electrostatic potential. Proceedings of the London Mathematical Society. 132(5), e70163.","mla":"Edelsbrunner, Herbert, et al. “Counting Equilibria of the Electrostatic Potential.” <i>Proceedings of the London Mathematical Society</i>, vol. 132, no. 5, e70163, Wiley, 2026, doi:<a href=\"https://doi.org/10.1112/plms.70163\">10.1112/plms.70163</a>.","short":"H. Edelsbrunner, C.D. Fillmore, G. Oliveira, Proceedings of the London Mathematical Society 132 (2026).","ieee":"H. Edelsbrunner, C. D. Fillmore, and G. Oliveira, “Counting equilibria of the electrostatic potential,” <i>Proceedings of the London Mathematical Society</i>, vol. 132, no. 5. Wiley, 2026.","apa":"Edelsbrunner, H., Fillmore, C. D., &#38; Oliveira, G. (2026). Counting equilibria of the electrostatic potential. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.70163\">https://doi.org/10.1112/plms.70163</a>","chicago":"Edelsbrunner, Herbert, Christopher D Fillmore, and Goncalo Oliveira. “Counting Equilibria of the Electrostatic Potential.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2026. <a href=\"https://doi.org/10.1112/plms.70163\">https://doi.org/10.1112/plms.70163</a>."},"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Fillmore, Christopher D","first_name":"Christopher D","last_name":"Fillmore","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425"},{"id":"58abbde8-f455-11eb-a497-98c8fd71b905","last_name":"Oliveira","first_name":"Goncalo","full_name":"Oliveira, Goncalo"}],"OA_place":"repository","status":"public","publisher":"Wiley","article_type":"original","date_published":"2026-05-01T00:00:00Z","external_id":{"arxiv":["2501.05315"]},"publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]},"doi":"10.1112/plms.70163","department":[{"_id":"HeEd"},{"_id":"TaHa"}],"fulldoi":"https://doi.org/10.1112/plms.70163","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publication_status":"published","volume":132,"date_created":"2026-05-31T22:02:13Z","day":"01","_id":"21931","scopus_import":"1","corr_author":"1","oa_version":"Preprint","language":[{"iso":"eng"}]},{"month":"02","date_updated":"2026-07-23T11:58:37Z","arxiv":1,"publication":"European Journal of Combinatorics","intvolume":"       132","title":"Flips in two-dimensional hypertriangulations","year":"2026","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2212.11380","open_access":"1"}],"abstract":[{"lang":"eng","text":"We study flips in hypertriangulations of planar points sets. Here a level-k hypertriangulation of n\r\n points in the plane is a subdivision induced by the projection of a k-hypersimplex, which is the convex hull of the barycenters of the (k-1)-dimensional faces of the standard (n-1)-simplex. In particular, we introduce four types of flips and prove that the level-2 hypertriangulations are connected by these flips.\r\n"}],"OA_type":"green","article_processing_charge":"No","type":"journal_article","das_tickbox":"0","article_number":"104248","acknowledgement":"Work by all authors but the second is supported by the European Research Council (ERC), grant no. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35. Work by the second author is partially supported by the Alexander von Humboldt Foundation and by the Simons Foundation . The second author thanks Jesús A. De Loera for useful discussions on flips and non-flips and Pavel Galashin and Alexey Balitskiy for useful discussions on plabic graphs.","publisher":"Elsevier","status":"public","OA_place":"repository","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"last_name":"Garber","full_name":"Garber, Alexey","first_name":"Alexey"},{"last_name":"Ghafari","full_name":"Ghafari, Mohadese","first_name":"Mohadese"},{"last_name":"Heiss","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","first_name":"Teresa"},{"first_name":"Morteza","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian"}],"quality_controlled":"1","isi":1,"citation":{"mla":"Edelsbrunner, Herbert, et al. “Flips in Two-Dimensional Hypertriangulations.” <i>European Journal of Combinatorics</i>, vol. 132, 104248, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104248\">10.1016/j.ejc.2025.104248</a>.","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2026. Flips in two-dimensional hypertriangulations. European Journal of Combinatorics. 132, 104248.","ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. Flips in two-dimensional hypertriangulations. <i>European Journal of Combinatorics</i>. 2026;132. doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104248\">10.1016/j.ejc.2025.104248</a>","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “Flips in Two-Dimensional Hypertriangulations.” <i>European Journal of Combinatorics</i>. Elsevier, 2026. <a href=\"https://doi.org/10.1016/j.ejc.2025.104248\">https://doi.org/10.1016/j.ejc.2025.104248</a>.","apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., &#38; Saghafian, M. (2026). Flips in two-dimensional hypertriangulations. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2025.104248\">https://doi.org/10.1016/j.ejc.2025.104248</a>","ieee":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “Flips in two-dimensional hypertriangulations,” <i>European Journal of Combinatorics</i>, vol. 132. Elsevier, 2026.","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, European Journal of Combinatorics 132 (2026)."},"doi":"10.1016/j.ejc.2025.104248","department":[{"_id":"HeEd"}],"date_published":"2026-02-01T00:00:00Z","external_id":{"isi":["001599061500002"],"arxiv":["2212.11380"]},"publication_identifier":{"issn":["0195-6698"]},"article_type":"original","project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"volume":132,"publication_status":"published","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.1016/j.ejc.2025.104248","scopus_import":"1","language":[{"iso":"eng"}],"corr_author":"1","oa_version":"Preprint","_id":"20490","ec_funded":1,"date_created":"2025-10-19T22:01:31Z","day":"01"},{"doi":"10.1007/s10208-026-09766-6","department":[{"_id":"HeEd"}],"keyword":["Multivector field","Conley index","Morse decomposition","Bifurcation","Continuation","Zigzag persistence","Persistence barcode","Gentle algebra"],"date_published":"2026-08-04T00:00:00Z","publication_identifier":{"issn":["1615-3375"],"eissn":["1615-3383"]},"external_id":{"arxiv":["2504.17105"]},"PlanS_conform":"1","article_type":"original","publisher":"Springer","status":"public","OA_place":"publisher","author":[{"first_name":"Tamal K.","full_name":"Dey, Tamal K.","last_name":"Dey"},{"orcid":"0000-0001-9789-9750","id":"dfffb474-4317-11ee-8f5c-fe3fc95a425e","last_name":"Lipiński","first_name":"Michał","full_name":"Lipiński, Michał"},{"orcid":"0000-0003-2449-1433","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","last_name":"Soriano Trigueros","first_name":"Manuel","full_name":"Soriano Trigueros, Manuel"}],"quality_controlled":"1","citation":{"ista":"Dey TK, Lipiński M, Soriano Trigueros M. 2026. Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations. Foundations of Computational Mathematics.","mla":"Dey, Tamal K., et al. “Conley-Morse Persistence Barcode: A Homological Signature of Combinatorial Bifurcations.” <i>Foundations of Computational Mathematics</i>, Springer, 2026, doi:<a href=\"https://doi.org/10.1007/s10208-026-09766-6\">10.1007/s10208-026-09766-6</a>.","ama":"Dey TK, Lipiński M, Soriano Trigueros M. Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations. <i>Foundations of Computational Mathematics</i>. 2026. doi:<a href=\"https://doi.org/10.1007/s10208-026-09766-6\">10.1007/s10208-026-09766-6</a>","apa":"Dey, T. K., Lipiński, M., &#38; Soriano Trigueros, M. (2026). Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-026-09766-6\">https://doi.org/10.1007/s10208-026-09766-6</a>","chicago":"Dey, Tamal K., Michał Lipiński, and Manuel Soriano Trigueros. “Conley-Morse Persistence Barcode: A Homological Signature of Combinatorial Bifurcations.” <i>Foundations of Computational Mathematics</i>. Springer, 2026. <a href=\"https://doi.org/10.1007/s10208-026-09766-6\">https://doi.org/10.1007/s10208-026-09766-6</a>.","short":"T.K. Dey, M. Lipiński, M. Soriano Trigueros, Foundations of Computational Mathematics (2026).","ieee":"T. K. Dey, M. Lipiński, and M. Soriano Trigueros, “Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations,” <i>Foundations of Computational Mathematics</i>. Springer, 2026."},"scopus_import":"1","oa_version":"Published Version","corr_author":"1","language":[{"iso":"eng"}],"_id":"22648","ddc":["500"],"ec_funded":1,"date_created":"2026-08-05T06:11:30Z","day":"04","project":[{"grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa":1,"publication_status":"epub_ahead","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.1007/s10208-026-09766-6","has_accepted_license":"1","title":"Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations","year":"2026","abstract":[{"text":"Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations within the framework of combinatorial dynamical systems—a young but already well-established theory. We introduce the Conley–Morse persistence barcode, a compact algebraic descriptor of combinatorial bifurcations. This barcode captures structural changes in a dynamical system at the level of Morse decompositions and provides a characterization of the nature of observed transitions in terms of the Conley index. The construction of the Conley–Morse persistence barcode builds upon ideas from topological persistence. Specifically, we consider a persistence module obtained from the Conley index of invariant sets indexed over a poset. Using gentle algebras, we prove that this module decomposes into simple intervals (bars) and compute them by adapting the zigzag persistence algorithm to our purpose.","lang":"eng"}],"main_file_link":[{"url":"https://doi.org/10.1007/s10208-026-09766-6","open_access":"1"}],"month":"08","researchdata_availability":"no","date_updated":"2026-08-11T06:13:33Z","arxiv":1,"publication":"Foundations of Computational Mathematics","das_tickbox":"0","supplementarymaterial":"yes","acknowledgement":"M.L. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. T.D. acknowledges the support of NSF funds CCF-2437030 and DMS-2301360. The authors would like to thank the anonymous reviewers for their careful reading of the paper. Their feedback significantly improved the quality of the article. T.D. and M.L. would like to acknowledge many thought-provoking discussions with Marian Mrozek on combinatorial dynamical systems and their continuations. M.S.T. would like to thank Álvaro Sánchez for insightful discussions about representation theory. Open access funding provided by Institute of Science and Technology (IST Austria).","OA_type":"hybrid","article_processing_charge":"Yes (via OA deal)","type":"journal_article"},{"day":"01","date_created":"2026-01-12T11:17:06Z","ec_funded":1,"ddc":["510"],"_id":"20980","oa_version":"Preprint","language":[{"iso":"eng"}],"scopus_import":"1","fulldoi":"https://doi.org/10.1137/25m1739406","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","oa":1,"volume":25,"project":[{"grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program"}],"article_type":"original","external_id":{"arxiv":["2502.19369"]},"publication_identifier":{"issn":["1536-0040"]},"date_published":"2026-01-01T00:00:00Z","department":[{"_id":"HeEd"}],"doi":"10.1137/25m1739406","citation":{"mla":"Dey, Tamal K., et al. “Computing a Connection Matrix and Persistence Efficiently from a Morse Decomposition.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 25, no. 1, SIAM, 2026, pp. 108–30, doi:<a href=\"https://doi.org/10.1137/25m1739406\">10.1137/25m1739406</a>.","ista":"Dey TK, Haas A, Lipiński M. 2026. Computing a connection matrix and persistence efficiently from a morse decomposition. SIAM Journal on Applied Dynamical Systems. 25(1), 108–130.","ama":"Dey TK, Haas A, Lipiński M. Computing a connection matrix and persistence efficiently from a morse decomposition. <i>SIAM Journal on Applied Dynamical Systems</i>. 2026;25(1):108-130. doi:<a href=\"https://doi.org/10.1137/25m1739406\">10.1137/25m1739406</a>","chicago":"Dey, Tamal K., Andrew Haas, and Michał Lipiński. “Computing a Connection Matrix and Persistence Efficiently from a Morse Decomposition.” <i>SIAM Journal on Applied Dynamical Systems</i>. SIAM, 2026. <a href=\"https://doi.org/10.1137/25m1739406\">https://doi.org/10.1137/25m1739406</a>.","apa":"Dey, T. K., Haas, A., &#38; Lipiński, M. (2026). Computing a connection matrix and persistence efficiently from a morse decomposition. <i>SIAM Journal on Applied Dynamical Systems</i>. SIAM. <a href=\"https://doi.org/10.1137/25m1739406\">https://doi.org/10.1137/25m1739406</a>","ieee":"T. K. Dey, A. Haas, and M. Lipiński, “Computing a connection matrix and persistence efficiently from a morse decomposition,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 25, no. 1. SIAM, pp. 108–130, 2026.","short":"T.K. Dey, A. Haas, M. Lipiński, SIAM Journal on Applied Dynamical Systems 25 (2026) 108–130."},"quality_controlled":"1","author":[{"first_name":"Tamal K.","full_name":"Dey, Tamal K.","last_name":"Dey"},{"last_name":"Haas","full_name":"Haas, Andrew","first_name":"Andrew"},{"first_name":"Michał","full_name":"Lipiński, Michał","orcid":"0000-0001-9789-9750","id":"dfffb474-4317-11ee-8f5c-fe3fc95a425e","last_name":"Lipiński"}],"OA_place":"repository","page":"108-130","status":"public","publisher":"SIAM","acknowledgement":"This research was supported by NSF grants DMS-2301360 and CCF-2437030 as well as from the European Union's Horizon 2020 research and innovation programme under Marie Sk\\lodowska-Curie grant 101034413.\r\n","issue":"1","type":"journal_article","article_processing_charge":"No","OA_type":"green","abstract":[{"lang":"eng","text":"Morse decompositions partition the flows in a vector field into equivalent structures. Given such a decomposition, one can define a further summary of its flow structure by what is called a connection matrix. These matrices, a generalization of Morse boundary operators from classical Morse theory, capture the connections made by the flows among the critical structures—such as attractors, repellers, and orbits—in a vector field. Recently, in the context of combinatorial dynamics, an efficient persistence-like algorithm to compute connection matrices has been proposed in Dey, Lipiński, Mrozek, and Slechta [SIAM J. Appl. Dyn. Syst., 23 (2024), pp. 81–97]. We show that, actually, the classical persistence algorithm with exhaustive reduction retrieves connection matrices, both simplifying the algorithm of Dey et al. and bringing the theory of persistence closer to combinatorial dynamical systems. We supplement this main result with an observation: the concept of persistence as defined for scalar fields naturally adapts to Morse decompositions whose Morse sets are filtered with a Lyapunov function. We conclude by presenting preliminary experimental results."}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.19369","open_access":"1"}],"year":"2026","title":"Computing a connection matrix and persistence efficiently from a morse decomposition","intvolume":"        25","publication":"SIAM Journal on Applied Dynamical Systems","arxiv":1,"date_updated":"2026-08-12T06:23:46Z","month":"01"},{"article_processing_charge":"Yes","OA_type":"gold","type":"conference","article_number":"41:1-41:18","supplementarymaterial":"no","das_tickbox":"0","acknowledgement":"The authors thank Jakub Leśkiewicz and Bartosz Furmanek for discussions\r\nthat helped improve the paper. Herbert Edelsbrunner: DFG Collaborative Research Center TRR 109, Austrian Science\r\nFund (FWF), grant no. I 02979-N35\r\nMichał Lipiński: European Union’s Horizon 2020 research and innovation programme under the\r\nMarie Skłodowska-Curie Grant Agreement No. 101034413\r\nMarian Mrozek: Polish National Science Center under Opus Grant 2019/35/B/ST1/00874 and Opus\r\nGrant 2025/57/B/ST1/00550","publication":"42nd International Symposium on Computational Geometry","month":"05","file":[{"access_level":"open_access","file_id":"22329","file_name":"2026_LIPIcSSoCG_Edelsbrunner.pdf","date_updated":"2026-07-14T06:08:05Z","creator":"dernst","success":1,"relation":"main_file","date_created":"2026-07-14T06:08:05Z","file_size":2902144,"content_type":"application/pdf","checksum":"9dfb96ee66985c724b499b0e5888dc8e"}],"date_updated":"2026-08-12T09:02:56Z","arxiv":1,"researchdata_availability":"no","alternative_title":["LIPIcs"],"has_accepted_license":"1","intvolume":"       367","title":"The depth poset under transpositions in the filter","abstract":[{"text":"The depth poset of a filtered Lefschetz complex reflects the dependencies between the cancellations of different shallow birth-death pairs. Using the fast algorithms for computing the depth poset in [Edelsbrunner et al., 2026] and for updating the persistence diagram under transpositions in [Cohen-Steiner et al., 2006], we give a complete case analysis of how transpositions of cells in the filter affect the depth poset. In addition, we present statistics on the depth poset for random point data and its sensitivity to the transpositions that occur in random straight-line homotopies.","lang":"eng"}],"year":"2026","publication_status":"published","oa":1,"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"end_date":"2026-06-05","location":"New Brunswick, NJ, United States","start_date":"2026-06-02","name":"SoCG: Symposium on Computational Geometry"},"volume":367,"project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"},{"grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"fulldoi":"https://doi.org/10.4230/LIPICS.SOCG.2026.41","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"22299","scopus_import":"1","oa_version":"Published Version","language":[{"iso":"eng"}],"corr_author":"1","date_created":"2026-07-13T09:56:38Z","day":"27","ec_funded":1,"ddc":["500"],"status":"public","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","citation":{"ama":"Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. The depth poset under transpositions in the filter. In: <i>42nd International Symposium on Computational Geometry</i>. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href=\"https://doi.org/10.4230/LIPICS.SOCG.2026.41\">10.4230/LIPICS.SOCG.2026.41</a>","mla":"Edelsbrunner, Herbert, et al. “The Depth Poset under Transpositions in the Filter.” <i>42nd International Symposium on Computational Geometry</i>, vol. 367, 41:1-41:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href=\"https://doi.org/10.4230/LIPICS.SOCG.2026.41\">10.4230/LIPICS.SOCG.2026.41</a>.","ista":"Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. 2026. The depth poset under transpositions in the filter. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 367, 41:1-41:18.","ieee":"H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, and F. Zimin, “The depth poset under transpositions in the filter,” in <i>42nd International Symposium on Computational Geometry</i>, New Brunswick, NJ, United States, 2026, vol. 367.","short":"H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, F. Zimin, in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","chicago":"Edelsbrunner, Herbert, Michał Lipiński, Marian Mrozek, Manuel Soriano Trigueros, and Fedor Zimin. “The Depth Poset under Transpositions in the Filter.” In <i>42nd International Symposium on Computational Geometry</i>, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href=\"https://doi.org/10.4230/LIPICS.SOCG.2026.41\">https://doi.org/10.4230/LIPICS.SOCG.2026.41</a>.","apa":"Edelsbrunner, H., Lipiński, M., Mrozek, M., Soriano Trigueros, M., &#38; Zimin, F. (2026). The depth poset under transpositions in the filter. In <i>42nd International Symposium on Computational Geometry</i> (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.SOCG.2026.41\">https://doi.org/10.4230/LIPICS.SOCG.2026.41</a>"},"OA_place":"publisher","author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"orcid":"0000-0001-9789-9750","id":"dfffb474-4317-11ee-8f5c-fe3fc95a425e","last_name":"Lipiński","first_name":"Michał","full_name":"Lipiński, Michał"},{"last_name":"Mrozek","orcid":"0000-0002-0619-6417","first_name":"Marian","full_name":"Mrozek, Marian"},{"first_name":"Manuel","full_name":"Soriano Trigueros, Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","last_name":"Soriano Trigueros","orcid":"0000-0003-2449-1433"},{"last_name":"Zimin","id":"afd27eda-91c1-11f0-aad8-c6edbec24c04","full_name":"Zimin, Fedor","first_name":"Fedor"}],"keyword":["Algebraic topology","Lefschetz complexes","persistent homology","vines and vineyards","birth-death pairs","shallow pairs","relations","partial orders","transpositions","Theory of computation → Computational geometry"],"file_date_updated":"2026-07-14T06:08:05Z","doi":"10.4230/LIPICS.SOCG.2026.41","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"date_published":"2026-05-27T00:00:00Z","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959774185"]},"external_id":{"arxiv":["2511.21961"]}},{"das_tickbox":"0","supplementarymaterial":"no","acknowledgement":"The first author is supported by the European Research Council (ERC), grant no. 788183, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35. The second author is supported by the European Research Council (ERC), grant “GeoScape” and by the Hungarian Science Foundation (NKFIH), grant K-131529. Both authors are supported by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. Open access funding provided by Institute of Science and Technology (IST Austria).","OA_type":"hybrid","article_processing_charge":"Yes (via OA deal)","type":"journal_article","related_material":{"record":[{"id":"17146","status":"public","relation":"earlier_version"}]},"title":"Maximum Betti numbers of Čech complexes","intvolume":"        75","has_accepted_license":"1","year":"2026","abstract":[{"lang":"eng","text":"The Upper Bound Theorem for convex polytopes implies that the p-th Betti number of the Čech complex of any set of N points in ℝ^d and any radius satisfies β_p = O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions, which prove that this upper bound is asymptotically tight. For example, we describe a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of the Čech complex at the other radius is n². "}],"researchdata_availability":"no","date_updated":"2026-10-02T11:48:00Z","arxiv":1,"month":"03","file":[{"access_level":"open_access","file_id":"22410","file_name":"2026_DiscreteCompGeom_Edelsbrunner.pdf","date_updated":"2026-07-27T08:11:05Z","relation":"main_file","success":1,"creator":"dernst","content_type":"application/pdf","checksum":"c17c014dbbf5be702195c737890251c8","date_created":"2026-07-27T08:11:05Z","file_size":546483}],"publication":"Discrete & Computational Geometry","oa_version":"Published Version","corr_author":"1","language":[{"iso":"eng"}],"scopus_import":"1","_id":"20657","ddc":["510"],"ec_funded":1,"day":"01","date_created":"2025-11-19T09:44:58Z","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF","grant_number":"Z00342"}],"volume":75,"oa":1,"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.1007/s00454-025-00796-5","department":[{"_id":"HeEd"}],"file_date_updated":"2026-07-27T08:11:05Z","doi":"10.1007/s00454-025-00796-5","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"external_id":{"arxiv":["2310.14801"],"isi":["001610592600001"]},"date_published":"2026-03-01T00:00:00Z","article_type":"original","PlanS_conform":"1","publisher":"Springer Nature","status":"public","page":"597-624","OA_place":"publisher","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"first_name":"János","full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach"}],"isi":1,"citation":{"ieee":"H. Edelsbrunner and J. Pach, “Maximum Betti numbers of Čech complexes,” <i>Discrete &#38; Computational Geometry</i>, vol. 75. Springer Nature, pp. 597–624, 2026.","short":"H. Edelsbrunner, J. Pach, Discrete &#38; Computational Geometry 75 (2026) 597–624.","chicago":"Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00454-025-00796-5\">https://doi.org/10.1007/s00454-025-00796-5</a>.","apa":"Edelsbrunner, H., &#38; Pach, J. (2026). Maximum Betti numbers of Čech complexes. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-025-00796-5\">https://doi.org/10.1007/s00454-025-00796-5</a>","ama":"Edelsbrunner H, Pach J. Maximum Betti numbers of Čech complexes. <i>Discrete &#38; Computational Geometry</i>. 2026;75:597-624. doi:<a href=\"https://doi.org/10.1007/s00454-025-00796-5\">10.1007/s00454-025-00796-5</a>","mla":"Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” <i>Discrete &#38; Computational Geometry</i>, vol. 75, Springer Nature, 2026, pp. 597–624, doi:<a href=\"https://doi.org/10.1007/s00454-025-00796-5\">10.1007/s00454-025-00796-5</a>.","ista":"Edelsbrunner H, Pach J. 2026. Maximum Betti numbers of Čech complexes. Discrete &#38; Computational Geometry. 75, 597–624."},"quality_controlled":"1"},{"acknowledgement":"This project has received funding from the European Research\r\nCouncil (ERC) under the European Union’s Horizon 2020 research and innovation\r\nprogramme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund\r\n(FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR\r\n109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF),\r\ngrant no. I 02979-N35.","OA_type":"green","article_processing_charge":"No","type":"journal_article","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"15091"}]},"intvolume":"         8","title":"Chromatic alpha complexes","has_accepted_license":"1","year":"2026","abstract":[{"lang":"eng","text":"Motivated by applications in medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay and alpha complexes, and code that does these computations is provided."}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2212.03128","open_access":"1"}],"date_updated":"2026-10-02T11:56:12Z","arxiv":1,"month":"03","publication":"Foundations of Data Science","corr_author":"1","language":[{"iso":"eng"}],"oa_version":"Preprint","scopus_import":"1","_id":"20585","ec_funded":1,"ddc":["510"],"date_created":"2025-11-02T23:01:33Z","day":"01","volume":8,"project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342"},{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"oa":1,"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","mathsc":["62R40","55N31","68T09","57Q70"],"fulldoi":"https://doi.org/10.3934/fods.2025003","department":[{"_id":"HeEd"}],"doi":"10.3934/fods.2025003","keyword":["Topological data analysis","Delaunay mosaic","alpha complex","chromatic sets","persistent homology","kernel/image/cokernel persistent homology","radius function","discrete Morse theory","exact sequences"],"external_id":{"arxiv":["2212.03128"]},"publication_identifier":{"eissn":["2639-8001"]},"date_published":"2026-03-01T00:00:00Z","article_type":"original","publisher":"AIMS","status":"public","OA_place":"repository","author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano"},{"full_name":"Draganov, Ondrej","first_name":"Ondrej","orcid":"0000-0003-0464-3823","last_name":"Draganov","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","first_name":"Morteza"}],"page":"30-62","citation":{"ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” <i>Foundations of Data Science</i>, vol. 8. AIMS, pp. 30–62, 2026.","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Foundations of Data Science 8 (2026) 30–62.","chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes.” <i>Foundations of Data Science</i>. AIMS, 2026. <a href=\"https://doi.org/10.3934/fods.2025003\">https://doi.org/10.3934/fods.2025003</a>.","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (2026). Chromatic alpha complexes. <i>Foundations of Data Science</i>. AIMS. <a href=\"https://doi.org/10.3934/fods.2025003\">https://doi.org/10.3934/fods.2025003</a>","ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. <i>Foundations of Data Science</i>. 2026;8:30-62. doi:<a href=\"https://doi.org/10.3934/fods.2025003\">10.3934/fods.2025003</a>","mla":"Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” <i>Foundations of Data Science</i>, vol. 8, AIMS, 2026, pp. 30–62, doi:<a href=\"https://doi.org/10.3934/fods.2025003\">10.3934/fods.2025003</a>.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2026. Chromatic alpha complexes. Foundations of Data Science. 8, 30–62."},"quality_controlled":"1"},{"publication":"Nature Communications","file":[{"creator":"dernst","success":1,"relation":"main_file","date_created":"2026-10-12T09:00:06Z","file_size":1889857,"checksum":"eba760f5982a89f59664957e00c5d2d6","content_type":"application/pdf","access_level":"open_access","file_id":"23104","file_name":"2026_NatureComm_Pegoraro.pdf","date_updated":"2026-10-12T09:00:06Z"}],"month":"09","researchdata_availability":"yes","date_updated":"2026-10-12T09:03:58Z","abstract":[{"text":"Disordered materials such as glasses are promising candidates as solid-state electrolytes for batteries, but they tend to exhibit low ionic conductivity and current methods for investigating and predicting the ionic conductivity of electrolyte materials are inefficient. Here, we propose a framework that summarizes the topological properties of the electrolyte material’s atomic structure with a weighted graph based on periodic boundary conditions. We then compute a variation of the max-flow algorithm, a commonly used model in continuum models of transportation and liquid flow, on this summary and show that it is compatible with the simulated periodic atomic structures. Using molecular dynamics simulations of various glassy solid-state electrolyte families including both mobile lithium and sodium ions, we validate the approach by showing a positive correlation between the area-normalized maximum flow predicted from the static glass structures and the ionic conductivity as obtained from the simulations, especially in the case of high-conductivity sulfide glass electrolytes. We envision that the developed methodology, which only relies on static atomic structure, will accelerate the discovery of highly conductive sulfide glassy electrolytes for high-performance all-solid-state batteries.","lang":"eng"}],"year":"2026","has_accepted_license":"1","title":"Predicting ionic conductivity of sulfide glass solid-state electrolytes using max-flow methodology","intvolume":"        17","type":"journal_article","pmid":1,"article_processing_charge":"Yes","OA_type":"gold","acknowledgement":"We thank the Danish e-Infrastructure Cooperation (DeiC) for access to computational resources at Sophia and LUMI-C (DeiC-AAU-N5-202200005). This work was supported by the Independent Research Fund Denmark (1026-00037), European Union (ERC, NewGLASS, 101044664), and Danish Data Science Academy, which in turn is funded by the Novo Nordisk Foundation (NNF21SA0069429) and VILLUM FONDEN (40516). Y.B.B. acknowledges support from the Austrian Science Fund (FWF) 10.55776/ESP9584724.","article_number":"10343","das_tickbox":"1","supplementarymaterial":"yes","quality_controlled":"1","citation":{"ista":"Pegoraro M, Christensen R, Sørensen SS, Lindbjerg AR, Du T, Bokor Bleile Y, Svane AM, Biscio CAN, Fajstrup L, Smedskjaer MM. 2026. Predicting ionic conductivity of sulfide glass solid-state electrolytes using max-flow methodology. Nature Communications. 17, 10343.","mla":"Pegoraro, Matteo, et al. “Predicting Ionic Conductivity of Sulfide Glass Solid-State Electrolytes Using Max-Flow Methodology.” <i>Nature Communications</i>, vol. 17, 10343, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1038/s41467-026-77363-w\">10.1038/s41467-026-77363-w</a>.","ama":"Pegoraro M, Christensen R, Sørensen SS, et al. Predicting ionic conductivity of sulfide glass solid-state electrolytes using max-flow methodology. <i>Nature Communications</i>. 2026;17. doi:<a href=\"https://doi.org/10.1038/s41467-026-77363-w\">10.1038/s41467-026-77363-w</a>","apa":"Pegoraro, M., Christensen, R., Sørensen, S. S., Lindbjerg, A. R., Du, T., Bokor Bleile, Y., … Smedskjaer, M. M. (2026). Predicting ionic conductivity of sulfide glass solid-state electrolytes using max-flow methodology. <i>Nature Communications</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41467-026-77363-w\">https://doi.org/10.1038/s41467-026-77363-w</a>","chicago":"Pegoraro, Matteo, Rasmus Christensen, Søren S. Sørensen, Anders R. Lindbjerg, Tao Du, Yossi Bokor Bleile, Anne Marie Svane, Christophe A.N. Biscio, Lisbeth Fajstrup, and Morten M. Smedskjaer. “Predicting Ionic Conductivity of Sulfide Glass Solid-State Electrolytes Using Max-Flow Methodology.” <i>Nature Communications</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1038/s41467-026-77363-w\">https://doi.org/10.1038/s41467-026-77363-w</a>.","short":"M. Pegoraro, R. Christensen, S.S. Sørensen, A.R. Lindbjerg, T. Du, Y. Bokor Bleile, A.M. Svane, C.A.N. Biscio, L. Fajstrup, M.M. Smedskjaer, Nature Communications 17 (2026).","ieee":"M. Pegoraro <i>et al.</i>, “Predicting ionic conductivity of sulfide glass solid-state electrolytes using max-flow methodology,” <i>Nature Communications</i>, vol. 17. Springer Nature, 2026."},"OA_place":"publisher","author":[{"last_name":"Pegoraro","first_name":"Matteo","full_name":"Pegoraro, Matteo"},{"full_name":"Christensen, Rasmus","first_name":"Rasmus","last_name":"Christensen"},{"last_name":"Sørensen","first_name":"Søren S.","full_name":"Sørensen, Søren S."},{"full_name":"Lindbjerg, Anders R.","first_name":"Anders R.","last_name":"Lindbjerg"},{"last_name":"Du","full_name":"Du, Tao","first_name":"Tao"},{"orcid":"0000-0002-4861-9174","id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2","last_name":"Bleile","first_name":"Yossi","full_name":"Bleile, Yossi"},{"first_name":"Anne Marie","full_name":"Svane, Anne Marie","last_name":"Svane"},{"last_name":"Biscio","first_name":"Christophe A.N.","full_name":"Biscio, Christophe A.N."},{"first_name":"Lisbeth","full_name":"Fajstrup, Lisbeth","last_name":"Fajstrup"},{"full_name":"Smedskjaer, Morten M.","first_name":"Morten M.","last_name":"Smedskjaer"}],"status":"public","publisher":"Springer Nature","PlanS_conform":"1","DOAJ_listed":"1","article_type":"original","date_published":"2026-09-30T00:00:00Z","external_id":{"pmid":["42811056"]},"publication_identifier":{"eissn":["2041-1723"]},"file_date_updated":"2026-10-12T09:00:06Z","doi":"10.1038/s41467-026-77363-w","department":[{"_id":"HeEd"}],"fulldoi":"https://doi.org/10.1038/s41467-026-77363-w","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publication_status":"published","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"volume":17,"project":[{"name":"Quantitative Unbiased Shape Analysis with Geometry &amp; Topology","_id":"9106a876-16d5-11f0-9cad-bbf11c9952f9","grant_number":"ESP 9584724"}],"dataavailabilitystatement":"All data supporting the findings of this study are available within the article and Supplementary Information files. Source data are provided with this paper. The developed code to perform the max-flow calculations is available as part of the Topological Materials Analysis (ToMA) library, which is available at Zenodo (https://doi.org/10.5281/zenodo.10781424) and Github (https://github.com/yossibokorbleile/TopologicalMaterialAnalysis), with documentation available at https://yossi.eu/toma/. To enhance usability, we have included a brief documentation on how to compile ToMA as well as a minimal working example of the code together with an example trajectory directly in the ToMA repository. LAMMPS is an open-source code available at https://lammps.sandia.gov.","day":"30","date_created":"2026-10-11T22:02:03Z","ddc":["500"],"_id":"23087","scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"Published Version"},{"fulldoi":"https://doi.org/10.2140/agt.2025.25.5153","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publication_status":"published","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"call_identifier":"FWF","_id":"26AD5D90-B435-11E9-9278-68D0E5697425","name":"Algebraic Footprints of Geometric Features in Homology","grant_number":"I04245"}],"volume":25,"day":"20","date_created":"2025-12-29T12:09:09Z","ddc":["500"],"_id":"20867","language":[{"iso":"eng"}],"oa_version":"Published Version","corr_author":"1","scopus_import":"1","citation":{"ista":"Zava N. 2025. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces. Algebraic &#38; Geometric Topology. 25(8), 5153–5174.","mla":"Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the Gromov–Hausdorff Space into Hilbert Spaces.” <i>Algebraic &#38; Geometric Topology</i>, vol. 25, no. 8, Mathematical Sciences Publishers, 2025, pp. 5153–74, doi:<a href=\"https://doi.org/10.2140/agt.2025.25.5153\">10.2140/agt.2025.25.5153</a>.","ama":"Zava N. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces. <i>Algebraic &#38; Geometric Topology</i>. 2025;25(8):5153-5174. doi:<a href=\"https://doi.org/10.2140/agt.2025.25.5153\">10.2140/agt.2025.25.5153</a>","apa":"Zava, N. (2025). Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces. <i>Algebraic &#38; Geometric Topology</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/agt.2025.25.5153\">https://doi.org/10.2140/agt.2025.25.5153</a>","chicago":"Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the Gromov–Hausdorff Space into Hilbert Spaces.” <i>Algebraic &#38; Geometric Topology</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/agt.2025.25.5153\">https://doi.org/10.2140/agt.2025.25.5153</a>.","short":"N. Zava, Algebraic &#38; Geometric Topology 25 (2025) 5153–5174.","ieee":"N. Zava, “Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces,” <i>Algebraic &#38; Geometric Topology</i>, vol. 25, no. 8. Mathematical Sciences Publishers, pp. 5153–5174, 2025."},"quality_controlled":"1","author":[{"full_name":"Zava, Nicolò","first_name":"Nicolò","last_name":"Zava","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","orcid":"0000-0001-8686-1888"}],"OA_place":"publisher","page":"5153-5174","status":"public","publisher":"Mathematical Sciences Publishers","article_type":"original","PlanS_conform":"1","publication_identifier":{"issn":["1472-2747"],"eissn":["1472-2739"]},"external_id":{"arxiv":["2303.04730"]},"date_published":"2025-11-20T00:00:00Z","department":[{"_id":"HeEd"}],"doi":"10.2140/agt.2025.25.5153","file_date_updated":"2026-01-05T12:16:38Z","type":"journal_article","article_processing_charge":"No","OA_type":"diamond","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.","issue":"8","publication":"Algebraic & Geometric Topology","arxiv":1,"date_updated":"2026-01-05T12:19:09Z","file":[{"content_type":"application/pdf","checksum":"1e05b4f17a44500ae1ae1e21bc636f6a","date_created":"2026-01-05T12:16:38Z","file_size":574389,"success":1,"relation":"main_file","creator":"dernst","file_name":"2025_AlgebraicGeomTopology_Zava.pdf","date_updated":"2026-01-05T12:16:38Z","access_level":"open_access","file_id":"20943"}],"month":"11","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."}],"year":"2025","intvolume":"        25","title":"Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces","has_accepted_license":"1"},{"publication_status":"published","oa":1,"volume":461,"project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"fulldoi":"https://doi.org/10.1016/j.aim.2024.110055","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"18626","oa_version":"Preprint","language":[{"iso":"eng"}],"corr_author":"1","scopus_import":"1","date_created":"2024-12-08T23:01:54Z","day":"01","ec_funded":1,"status":"public","publisher":"Elsevier","isi":1,"citation":{"chicago":"Edelsbrunner, Herbert, Alexey Garber, and Morteza Saghafian. “Order-2 Delaunay Triangulations Optimize Angles.” <i>Advances in Mathematics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.aim.2024.110055\">https://doi.org/10.1016/j.aim.2024.110055</a>.","apa":"Edelsbrunner, H., Garber, A., &#38; Saghafian, M. (2025). Order-2 Delaunay triangulations optimize angles. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2024.110055\">https://doi.org/10.1016/j.aim.2024.110055</a>","ieee":"H. Edelsbrunner, A. Garber, and M. Saghafian, “Order-2 Delaunay triangulations optimize angles,” <i>Advances in Mathematics</i>, vol. 461. Elsevier, 2025.","short":"H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).","mla":"Edelsbrunner, Herbert, et al. “Order-2 Delaunay Triangulations Optimize Angles.” <i>Advances in Mathematics</i>, vol. 461, 110055, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.aim.2024.110055\">10.1016/j.aim.2024.110055</a>.","ista":"Edelsbrunner H, Garber A, Saghafian M. 2025. Order-2 Delaunay triangulations optimize angles. Advances in Mathematics. 461, 110055.","ama":"Edelsbrunner H, Garber A, Saghafian M. Order-2 Delaunay triangulations optimize angles. <i>Advances in Mathematics</i>. 2025;461. doi:<a href=\"https://doi.org/10.1016/j.aim.2024.110055\">10.1016/j.aim.2024.110055</a>"},"quality_controlled":"1","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Garber, Alexey","first_name":"Alexey","last_name":"Garber"},{"last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","first_name":"Morteza"}],"OA_place":"repository","department":[{"_id":"HeEd"}],"doi":"10.1016/j.aim.2024.110055","article_type":"original","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"external_id":{"arxiv":["2310.18238"],"isi":["001370682500001"]},"date_published":"2025-02-01T00:00:00Z","article_processing_charge":"No","OA_type":"green","type":"journal_article","article_number":"110055","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.","publication":"Advances in Mathematics","arxiv":1,"date_updated":"2025-04-15T07:16:53Z","month":"02","intvolume":"       461","title":"Order-2 Delaunay triangulations optimize angles","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2310.18238","open_access":"1"}],"abstract":[{"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.","lang":"eng"}],"year":"2025"}]