[{"_id":"20456","scopus_import":"1","oa_version":"Published Version","doi":"10.1007/s00454-025-00778-7","OA_place":"publisher","file_date_updated":"2026-01-05T13:21:20Z","language":[{"iso":"eng"}],"article_type":"original","isi":1,"date_created":"2025-10-12T22:01:26Z","quality_controlled":"1","project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"external_id":{"isi":["001584166900001"],"arxiv":["2212.03121"]},"day":"01","oa":1,"type":"journal_article","PlanS_conform":"1","department":[{"_id":"HeEd"}],"OA_type":"hybrid","publication_status":"published","year":"2026","publisher":"Springer Nature","arxiv":1,"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","title":"On the size of chromatic Delaunay mosaics","abstract":[{"text":"Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications.","lang":"eng"}],"citation":{"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.","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>.","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>","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>","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>."},"has_accepted_license":"1","corr_author":"1","date_published":"2026-01-01T00:00:00Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"15090"}]},"date_updated":"2026-01-05T13:21:56Z","intvolume":"        75","publication":"Discrete and Computational Geometry","status":"public","author":[{"last_name":"Biswas","orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita"},{"orcid":"0000-0001-6249-0832","last_name":"Cultrera di Montesano","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Ondrej","last_name":"Draganov","orcid":"0000-0003-0464-3823","full_name":"Draganov, Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"last_name":"Saghafian","first_name":"Morteza","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"file":[{"date_updated":"2026-01-05T13:21:20Z","creator":"dernst","date_created":"2026-01-05T13:21:20Z","access_level":"open_access","relation":"main_file","checksum":"0addb5c1b78142f9fb453bfa04695400","file_name":"2026_DiscreteCompGeom_Biswas.pdf","success":1,"file_id":"20952","file_size":570922,"content_type":"application/pdf"}],"page":"24-47","month":"01","volume":75,"ec_funded":1,"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.","ddc":["510"]},{"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"first_name":"Matthew","last_name":"Kahle","full_name":"Kahle, Matthew"},{"first_name":"Shu","last_name":"Kanazawa","full_name":"Kanazawa, Shu"}],"status":"public","publication":"Journal of Applied and Computational Topology","month":"03","article_number":"5","ddc":["500"],"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.","volume":10,"file":[{"creator":"dernst","date_updated":"2026-03-09T11:29:30Z","access_level":"open_access","date_created":"2026-03-09T11:29:30Z","relation":"main_file","checksum":"0bf6dc430cafa40c08f260fe17d54595","success":1,"file_name":"2026_JourAppliedCompTopology_Edelsbrunner.pdf","file_id":"21416","file_size":323111,"content_type":"application/pdf"}],"date_published":"2026-03-01T00:00:00Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"ista":"Edelsbrunner H, Kahle M, Kanazawa S. 2026. Maximum persistent Betti numbers of Čech complexes. Journal of Applied and Computational Topology. 10, 5.","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>.","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>","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>","short":"H. Edelsbrunner, M. Kahle, S. Kanazawa, Journal of Applied and Computational Topology 10 (2026).","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>.","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."},"abstract":[{"lang":"eng","text":"This note proves that only a linear number of holes in a Cech complex of n points in R^d\r\ncan persist over an interval of constant length. Specifically, for any fixed dimension p <\r\nd and fixed ε > 0, the number of p-dimensional holes in the ˇ Cech complex at radius 1\r\nthat persist to radius 1+ε is bounded above by a constant times n,where n is the number\r\nof points. The proof uses a packing argument supported by relating theCˇ ech complexes\r\nwith corresponding snap complexes over the cells in a partition of space. The argument\r\nis self-contained and elementary, relying on geometric and combinatorial constructions\r\nrather than on the existing theory of sparse approximations or interleavings. The bound\r\nalso applies to Alpha complexes and Vietoris–Rips complexes. While our result can be\r\ninferred from prior work on sparse filtrations, to our knowledge, no explicit statement\r\nor direct proof of this bound appears in the literature."}],"has_accepted_license":"1","intvolume":"        10","date_updated":"2026-03-09T11:31:29Z","PlanS_conform":"1","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","OA_type":"hybrid","publication_status":"published","year":"2026","oa":1,"external_id":{"arxiv":["2409.05241"]},"day":"01","type":"journal_article","title":"Maximum persistent Betti numbers of Čech complexes","article_processing_charge":"Yes (in subscription journal)","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"language":[{"iso":"eng"}],"OA_place":"publisher","file_date_updated":"2026-03-09T11:29:30Z","article_type":"original","oa_version":"Published Version","scopus_import":"1","_id":"21407","doi":"10.1007/s41468-026-00233-3","quality_controlled":"1","project":[{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"date_created":"2026-03-08T23:01:45Z"},{"quality_controlled":"1","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"}],"date_created":"2026-03-08T23:01:45Z","language":[{"iso":"eng"}],"OA_place":"repository","oa_version":"Preprint","scopus_import":"1","_id":"21410","doi":"10.1007/978-981-95-7127-7_26","title":"On the MST-ratio: Theoretical bounds and complexity of finding the maximum","article_processing_charge":"No","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["9789819571260"]},"department":[{"_id":"HeEd"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.11079","open_access":"1"}],"publisher":"Springer Nature","publication_status":"published","year":"2026","OA_type":"green","oa":1,"external_id":{"arxiv":["2409.11079"]},"day":"14","type":"conference","intvolume":"     16444","date_updated":"2026-03-09T10:25:41Z","date_published":"2026-02-14T00:00:00Z","conference":{"location":"Perugia, Italy","name":"WALCOM: International Conference and Workshops on Algorithms and Computation","end_date":"2026-03-06","start_date":"2026-03-04"},"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"}],"citation":{"ista":"Jabal Ameli A, Motiei F, Saghafian M. 2026. On the MST-ratio: Theoretical bounds and complexity of finding the maximum. 20th International Conference and Workshops on Algorithms and Computation. WALCOM: International Conference and Workshops on Algorithms and Computation, LNCS, vol. 16444, 386–401.","chicago":"Jabal Ameli, Afrouz, Faezeh Motiei, and Morteza Saghafian. “On the MST-Ratio: Theoretical Bounds and Complexity of Finding the Maximum.” In <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>.","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>","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>","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>.","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.","short":"A. Jabal Ameli, F. Motiei, M. Saghafian, in:, 20th International Conference and Workshops on Algorithms and Computation, Springer Nature, 2026, pp. 386–401."},"month":"02","ec_funded":1,"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.","volume":16444,"page":"386-401","author":[{"last_name":"Jabal Ameli","first_name":"Afrouz","full_name":"Jabal Ameli, Afrouz"},{"full_name":"Motiei, Faezeh","last_name":"Motiei","first_name":"Faezeh"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian"}],"status":"public","publication":"20th International Conference and Workshops on Algorithms and Computation","alternative_title":["LNCS"]},{"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["2996-220X"],"issn":["2996-2196"]},"title":"Covering complete geometric graphs by monotone paths","article_processing_charge":"No","oa":1,"external_id":{"arxiv":["2507.10840"]},"day":"17","type":"journal_article","department":[{"_id":"HeEd"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2507.10840"}],"publisher":"Mathematical Sciences Publishers","publication_status":"published","OA_type":"green","year":"2026","date_created":"2026-05-03T22:01:37Z","quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF"}],"scopus_import":"1","oa_version":"Preprint","_id":"21781","doi":"10.2140/cnt.2026.15.73","OA_place":"repository","language":[{"iso":"eng"}],"article_type":"original","page":"73-82","month":"04","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.","volume":15,"ec_funded":1,"issue":"1","publication":"Combinatorics and Number Theory","author":[{"full_name":"Dumitrescu, Adrian","last_name":"Dumitrescu","first_name":"Adrian"},{"first_name":"János","last_name":"Pach","full_name":"Pach, János"},{"first_name":"Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza"},{"full_name":"Scott, Alex","last_name":"Scott","first_name":"Alex"}],"status":"public","date_updated":"2026-05-07T07:45:24Z","intvolume":"        15","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."}],"citation":{"short":"A. Dumitrescu, J. Pach, M. Saghafian, A. Scott, Combinatorics and Number Theory 15 (2026) 73–82.","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.","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>.","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>","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>","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>.","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."},"date_published":"2026-04-17T00:00:00Z"},{"intvolume":"       461","date_updated":"2025-04-15T07:16:53Z","date_published":"2025-02-01T00:00:00Z","corr_author":"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"}],"citation":{"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>","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>.","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>.","ieee":"H. Edelsbrunner, A. Garber, and M. Saghafian, “Order-2 Delaunay triangulations optimize angles,” <i>Advances in Mathematics</i>, vol. 461. Elsevier, 2025.","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>"},"ec_funded":1,"volume":461,"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.","article_number":"110055","month":"02","status":"public","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"full_name":"Garber, Alexey","last_name":"Garber","first_name":"Alexey"},{"first_name":"Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza"}],"publication":"Advances in Mathematics","project":[{"grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","date_created":"2024-12-08T23:01:54Z","isi":1,"article_type":"original","language":[{"iso":"eng"}],"OA_place":"repository","doi":"10.1016/j.aim.2024.110055","_id":"18626","scopus_import":"1","oa_version":"Preprint","article_processing_charge":"No","title":"Order-2 Delaunay triangulations optimize angles","publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"year":"2025","publication_status":"published","OA_type":"green","publisher":"Elsevier","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2310.18238","open_access":"1"}],"department":[{"_id":"HeEd"}],"type":"journal_article","day":"01","external_id":{"arxiv":["2310.18238"],"isi":["001370682500001"]},"oa":1},{"date_created":"2025-06-30T08:48:48Z","isi":1,"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"quality_controlled":"1","doi":"10.1016/j.ins.2025.122425","oa_version":"None","scopus_import":"1","_id":"19937","article_type":"original","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0020-0255"]},"title":"Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality","article_processing_charge":"No","type":"journal_article","day":"01","external_id":{"isi":["001516170500002"]},"publisher":"Elsevier","OA_type":"closed access","year":"2025","publication_status":"published","department":[{"_id":"HeEd"}],"date_updated":"2025-12-30T09:05:32Z","intvolume":"       719","corr_author":"1","abstract":[{"text":"Simplets are elementary units within simplicial complexes and are fundamental for analyzing the structure of simplicial complexes. Previous efforts have mainly focused on accurately counting or approximating the number of simplets rather than studying their frequencies. However, analyzing simplet frequencies is more practical for large-scale simplicial complexes. This paper introduces the Simplet Frequency Distribution (SFD) vector, which enables the analysis of simplet frequencies in simplicial complexes. Additionally, we provide a bound on the sample complexity required to approximate the SFD vector using any uniform sampling-based algorithm accurately. We extend the definition of simplet frequency distribution to encompass simplices, allowing for the analysis of simplet frequencies within simplices of simplicial complexes. This paper introduces the Simplet Degree Vector (SDV) and the Simplet Degree Centrality (SDC), facilitating this analysis for each simplex. Furthermore, we present a bound on the sample complexity required for accurately approximating the SDV and SDC for a set of simplices using any uniform sampling-based algorithm. We also introduce algorithms for approximating SFD, geometric SFD, SDV, and SDC. We also validate the theoretical bounds with experiments on random simplicial complexes and demonstrate the practical application through a case study.","lang":"eng"}],"citation":{"ista":"Mahini M, Beigy H, Qadami S, Saghafian M. 2025. Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. Information Sciences. 719(11), 122425.","ieee":"M. Mahini, H. Beigy, S. Qadami, and M. Saghafian, “Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality,” <i>Information Sciences</i>, vol. 719, no. 11. Elsevier, 2025.","short":"M. Mahini, H. Beigy, S. Qadami, M. Saghafian, Information Sciences 719 (2025).","mla":"Mahini, Mohammad, et al. “Simplet-Based Signatures and Approximation in Simplicial Complexes: Frequency, Degree, and Centrality.” <i>Information Sciences</i>, vol. 719, no. 11, 122425, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ins.2025.122425\">10.1016/j.ins.2025.122425</a>.","apa":"Mahini, M., Beigy, H., Qadami, S., &#38; Saghafian, M. (2025). Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. <i>Information Sciences</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ins.2025.122425\">https://doi.org/10.1016/j.ins.2025.122425</a>","ama":"Mahini M, Beigy H, Qadami S, Saghafian M. Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. <i>Information Sciences</i>. 2025;719(11). doi:<a href=\"https://doi.org/10.1016/j.ins.2025.122425\">10.1016/j.ins.2025.122425</a>","chicago":"Mahini, Mohammad, Hamid Beigy, Salman Qadami, and Morteza Saghafian. “Simplet-Based Signatures and Approximation in Simplicial Complexes: Frequency, Degree, and Centrality.” <i>Information Sciences</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.ins.2025.122425\">https://doi.org/10.1016/j.ins.2025.122425</a>."},"date_published":"2025-11-01T00:00:00Z","article_number":"122425","ec_funded":1,"volume":719,"acknowledgement":"The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which improved this paper.\r\nWork by the first and fourth authors is partially supported by the European Research Council (ERC), grant no. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35.","month":"11","issue":"11","publication":"Information Sciences","author":[{"full_name":"Mahini, Mohammad","last_name":"Mahini","first_name":"Mohammad"},{"last_name":"Beigy","first_name":"Hamid","full_name":"Beigy, Hamid"},{"first_name":"Salman","last_name":"Qadami","full_name":"Qadami, Salman"},{"last_name":"Saghafian","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza"}],"status":"public"},{"oa_version":"Published Version","scopus_import":"1","_id":"20005","doi":"10.4230/LIPIcs.SoCG.2025.43","file_date_updated":"2025-07-14T07:24:22Z","language":[{"iso":"eng"}],"OA_place":"publisher","date_created":"2025-07-13T22:01:22Z","quality_controlled":"1","project":[{"grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"oa":1,"external_id":{"arxiv":["2410.21204"]},"day":"20","type":"conference","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2025","publication_status":"published","OA_type":"gold","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959773706"]},"title":"On spheres with k points inside","article_processing_charge":"Yes","conference":{"start_date":"2025-06-23","end_date":"2025-06-27","location":"Kanazawa, Japan","name":"SoCG: Symposium on Computational Geometry"},"citation":{"ama":"Edelsbrunner H, Garber A, Saghafian M. On spheres with k points inside. In: <i>41st International Symposium on Computational Geometry</i>. Vol 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.43\">10.4230/LIPIcs.SoCG.2025.43</a>","chicago":"Edelsbrunner, Herbert, Alexey Garber, and Morteza Saghafian. “On Spheres with k Points Inside.” In <i>41st International Symposium on Computational Geometry</i>, Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.43\">https://doi.org/10.4230/LIPIcs.SoCG.2025.43</a>.","ieee":"H. Edelsbrunner, A. Garber, and M. Saghafian, “On spheres with k points inside,” in <i>41st International Symposium on Computational Geometry</i>, Kanazawa, Japan, 2025, vol. 332.","mla":"Edelsbrunner, Herbert, et al. “On Spheres with k Points Inside.” <i>41st International Symposium on Computational Geometry</i>, vol. 332, 43, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.43\">10.4230/LIPIcs.SoCG.2025.43</a>.","short":"H. Edelsbrunner, A. Garber, M. Saghafian, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","apa":"Edelsbrunner, H., Garber, A., &#38; Saghafian, M. (2025). On spheres with k points inside. In <i>41st International Symposium on Computational Geometry</i> (Vol. 332). Kanazawa, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.43\">https://doi.org/10.4230/LIPIcs.SoCG.2025.43</a>","ista":"Edelsbrunner H, Garber A, Saghafian M. 2025. On spheres with k points inside. 41st International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 332, 43."},"abstract":[{"text":"We generalize a classical result by Boris Delaunay that introduced Delaunay triangulations. In particular, we prove that for a locally finite and coarsely dense generic point set A in ℝ^d, every generic point of ℝ^d belongs to exactly binom(d+k,d) simplices whose vertices belong to A and whose circumspheres enclose exactly k points of A. We extend this result to the cases in which the points are weighted, and when A contains only finitely many points in ℝ^d or in 𝕊^d. Furthermore, we use the result to give a new geometric proof for the fact that volumes of hypersimplices are Eulerian numbers.","lang":"eng"}],"corr_author":"1","has_accepted_license":"1","date_published":"2025-06-20T00:00:00Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2025-07-14T07:26:14Z","intvolume":"       332","publication":"41st International Symposium on Computational Geometry","alternative_title":["LIPIcs"],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"full_name":"Garber, Alexey","first_name":"Alexey","last_name":"Garber"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"status":"public","file":[{"file_size":661893,"content_type":"application/pdf","success":1,"file_name":"2025_LIPIcs.SoCG_Edelsbrunner.pdf","file_id":"20016","relation":"main_file","checksum":"b5313ed8575ea87913c71a6e3c7513c8","creator":"dernst","date_updated":"2025-07-14T07:24:22Z","date_created":"2025-07-14T07:24:22Z","access_level":"open_access"}],"month":"06","ddc":["510"],"article_number":"43","acknowledgement":"Herbert Edelsbrunner: partially supported by the Wittgenstein Prize, Austrian Science\r\nFund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109,\r\nAustrian Science Fund (FWF), grant no. I 02979-N35.\r\nAlexey Garber: partially supported by the Simons Foundation.\r\nMorteza Saghafian: partially supported by the Wittgenstein Prize, Austrian Science Fund (FWF),\r\ngrant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science\r\nFund (FWF), grant no. I 02979-N35","volume":332},{"intvolume":"       332","date_updated":"2025-12-30T11:04:33Z","date_published":"2025-06-20T00:00:00Z","related_material":{"link":[{"url":"https://github.com/laraost/BananaPersist","relation":"software"}]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"start_date":"2025-06-23","end_date":"2025-06-27","name":"SoCG: Symposium on Computational Geometry","location":"Kanazawa, Japan"},"citation":{"ista":"Ost L, Cultrera di Montesano S, Edelsbrunner H. 2025. Banana trees for the persistence in time series experimentally. 41st International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 332, 71.","mla":"Ost, Lara, et al. “Banana Trees for the Persistence in Time Series Experimentally.” <i>41st International Symposium on Computational Geometry</i>, vol. 332, 71, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.71\">10.4230/LIPIcs.SoCG.2025.71</a>.","ieee":"L. Ost, S. Cultrera di Montesano, and H. Edelsbrunner, “Banana trees for the persistence in time series experimentally,” in <i>41st International Symposium on Computational Geometry</i>, Kanazawa, Japan, 2025, vol. 332.","short":"L. Ost, S. Cultrera di Montesano, H. Edelsbrunner, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","apa":"Ost, L., Cultrera di Montesano, S., &#38; Edelsbrunner, H. (2025). Banana trees for the persistence in time series experimentally. In <i>41st International Symposium on Computational Geometry</i> (Vol. 332). Kanazawa, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.71\">https://doi.org/10.4230/LIPIcs.SoCG.2025.71</a>","ama":"Ost L, Cultrera di Montesano S, Edelsbrunner H. Banana trees for the persistence in time series experimentally. In: <i>41st International Symposium on Computational Geometry</i>. Vol 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.71\">10.4230/LIPIcs.SoCG.2025.71</a>","chicago":"Ost, Lara, Sebastiano Cultrera di Montesano, and Herbert Edelsbrunner. “Banana Trees for the Persistence in Time Series Experimentally.” In <i>41st International Symposium on Computational Geometry</i>, Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.71\">https://doi.org/10.4230/LIPIcs.SoCG.2025.71</a>."},"abstract":[{"lang":"eng","text":"In numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tree data structure, specifically designed to efficiently maintain the multi-scale topological descriptor commonly known as persistent homology for dynamically changing time series data. We implement this data structure and conduct an experimental study to assess its properties and runtime for update operations. Our findings indicate that banana trees are highly effective with unbiased random data, outperforming state-of-the-art static algorithms in these scenarios. Additionally, our results show that real-world time series share structural properties with unbiased random walks, suggesting potential practical utility for our implementation."}],"has_accepted_license":"1","corr_author":"1","month":"06","article_number":"71","ddc":["000"],"acknowledgement":"Lara Ost: Supported by the Vienna Graduate School on Computational Optimization\r\n(VGSCO), FWF project no. W1260-N35.\r\nSebastiano Cultrera di Montesano: Supported by the Eric and Wendy Schmidt Center at the Broad Institute of MIT and Harvard.\r\nHerbert Edelsbrunner: Partially supported by the Wittgenstein Prize, FWF grant no. Z 342-N31,\r\nand by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.","volume":332,"file":[{"relation":"main_file","checksum":"3a4a7a707a56e0cfdf51428782dee55a","date_updated":"2025-07-14T08:23:38Z","creator":"dernst","date_created":"2025-07-14T08:23:38Z","access_level":"open_access","file_size":834623,"content_type":"application/pdf","file_name":"2025_LIPIcs.SoCG_Ost.pdf","success":1,"file_id":"20017"}],"author":[{"last_name":"Ost","first_name":"Lara","full_name":"Ost, Lara"},{"full_name":"Cultrera di Montesano, Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","last_name":"Cultrera di Montesano","first_name":"Sebastiano"},{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"status":"public","publication":"41st International Symposium on Computational Geometry","alternative_title":["LIPIcs"],"quality_controlled":"1","project":[{"grant_number":"W1260-N35","name":"Vienna Graduate School on Computational Optimization","_id":"9B9290DE-BA93-11EA-9121-9846C619BF3A"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"date_created":"2025-07-13T22:01:22Z","language":[{"iso":"eng"}],"file_date_updated":"2025-07-14T08:23:38Z","OA_place":"publisher","scopus_import":"1","oa_version":"Published Version","_id":"20006","doi":"10.4230/LIPIcs.SoCG.2025.71","title":"Banana trees for the persistence in time series experimentally","article_processing_charge":"Yes","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959773706"]},"department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","OA_type":"gold","publication_status":"published","year":"2025","oa":1,"external_id":{"arxiv":["2405.17920"]},"day":"20","type":"conference"},{"date_published":"2025-08-01T00:00:00Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"abstract":[{"text":"Motivated by questions arising at the intersection of information theory and geometry, we compare two dissimilarity measures between finite categorical distributions. One is the well-known Jensen–Shannon divergence, which is easy to compute and whose square root is a proper metric. The other is what we call the minmax divergence, which is harder to compute. Just like the Jensen–Shannon divergence, it arises naturally from the Kullback–Leibler divergence. The main contribution of this paper is a proof showing that the minmax divergence can be tightly approximated by the Jensen–Shannon divergence. The bounds suggest that the square root of the minmax divergence is a metric, and we prove that this is indeed true in the one-dimensional case. The general case remains open. Finally, we consider analogous questions in the context of another Bregman divergence and the corresponding Burbea–Rao (Jensen–Bregman) divergence.","lang":"eng"}],"citation":{"ista":"Akopyan A, Edelsbrunner H, Virk Z, Wagner H. 2025. Tight bounds between the Jensen–Shannon divergence and the minmax divergence. Entropy. 27(8), 854.","short":"A. Akopyan, H. Edelsbrunner, Z. Virk, H. Wagner, Entropy 27 (2025).","mla":"Akopyan, Arseniy, et al. “Tight Bounds between the Jensen–Shannon Divergence and the Minmax Divergence.” <i>Entropy</i>, vol. 27, no. 8, 854, MDPI, 2025, doi:<a href=\"https://doi.org/10.3390/e27080854\">10.3390/e27080854</a>.","ieee":"A. Akopyan, H. Edelsbrunner, Z. Virk, and H. Wagner, “Tight bounds between the Jensen–Shannon divergence and the minmax divergence,” <i>Entropy</i>, vol. 27, no. 8. MDPI, 2025.","apa":"Akopyan, A., Edelsbrunner, H., Virk, Z., &#38; Wagner, H. (2025). Tight bounds between the Jensen–Shannon divergence and the minmax divergence. <i>Entropy</i>. MDPI. <a href=\"https://doi.org/10.3390/e27080854\">https://doi.org/10.3390/e27080854</a>","ama":"Akopyan A, Edelsbrunner H, Virk Z, Wagner H. Tight bounds between the Jensen–Shannon divergence and the minmax divergence. <i>Entropy</i>. 2025;27(8). doi:<a href=\"https://doi.org/10.3390/e27080854\">10.3390/e27080854</a>","chicago":"Akopyan, Arseniy, Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner. “Tight Bounds between the Jensen–Shannon Divergence and the Minmax Divergence.” <i>Entropy</i>. MDPI, 2025. <a href=\"https://doi.org/10.3390/e27080854\">https://doi.org/10.3390/e27080854</a>."},"corr_author":"1","has_accepted_license":"1","intvolume":"        27","date_updated":"2025-09-30T14:32:31Z","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","first_name":"Arseniy","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Virk","first_name":"Ziga","full_name":"Virk, Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"status":"public","publication":"Entropy","issue":"8","month":"08","article_number":"854","ddc":["500"],"acknowledgement":"This research received partial funding from the European Research Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme, grant no. 788183, the\r\nWittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, the DFG Collaborative\r\nResearch Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35, and the 2022 Google Research Scholar Award for project ‘Algorithms for Topological Analysis of Neural Networks’. The APC was waived.","ec_funded":1,"volume":27,"file":[{"file_name":"2025_Entropy_Akopyan.pdf","success":1,"file_id":"20309","file_size":379340,"content_type":"application/pdf","date_updated":"2025-09-08T07:55:48Z","creator":"dernst","access_level":"open_access","date_created":"2025-09-08T07:55:48Z","relation":"main_file","checksum":"65c5399c4015d9c8abb8c7a96f3d7836"}],"language":[{"iso":"eng"}],"OA_place":"publisher","file_date_updated":"2025-09-08T07:55:48Z","article_type":"original","DOAJ_listed":"1","oa_version":"Published Version","scopus_import":"1","_id":"20293","doi":"10.3390/e27080854","quality_controlled":"1","project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF","grant_number":"Z00342"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"isi":1,"date_created":"2025-09-07T22:01:33Z","department":[{"_id":"HeEd"}],"PlanS_conform":"1","publisher":"MDPI","OA_type":"gold","publication_status":"published","year":"2025","oa":1,"external_id":{"isi":["001557476000001"],"pmid":["40870326"]},"pmid":1,"day":"01","type":"journal_article","title":"Tight bounds between the Jensen–Shannon divergence and the minmax divergence","article_processing_charge":"Yes","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_identifier":{"eissn":["1099-4300"]}},{"issue":"10","publication":"Journal of Pure and Applied Algebra","status":"public","author":[{"full_name":"Brown, Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","first_name":"Adam"},{"first_name":"Ondrej","orcid":"0000-0003-0464-3823","last_name":"Draganov","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej"}],"file":[{"relation":"main_file","checksum":"39bcad462278c9322ef810af7db67f56","date_updated":"2025-12-30T07:55:08Z","creator":"dernst","date_created":"2025-12-30T07:55:08Z","access_level":"open_access","file_size":3090836,"content_type":"application/pdf","file_name":"2025_JourPureAppliedAlgebra_Brown.pdf","success":1,"file_id":"20886"}],"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35","ec_funded":1,"volume":229,"ddc":["510"],"article_number":"108068","month":"10","has_accepted_license":"1","corr_author":"1","citation":{"ista":"Brown A, Draganov O. 2025. Discrete microlocal Morse theory. Journal of Pure and Applied Algebra. 229(10), 108068.","chicago":"Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” <i>Journal of Pure and Applied Algebra</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">https://doi.org/10.1016/j.jpaa.2025.108068</a>.","ama":"Brown A, Draganov O. Discrete microlocal Morse theory. <i>Journal of Pure and Applied Algebra</i>. 2025;229(10). doi:<a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">10.1016/j.jpaa.2025.108068</a>","apa":"Brown, A., &#38; Draganov, O. (2025). Discrete microlocal Morse theory. <i>Journal of Pure and Applied Algebra</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">https://doi.org/10.1016/j.jpaa.2025.108068</a>","ieee":"A. Brown and O. Draganov, “Discrete microlocal Morse theory,” <i>Journal of Pure and Applied Algebra</i>, vol. 229, no. 10. Elsevier, 2025.","short":"A. Brown, O. Draganov, Journal of Pure and Applied Algebra 229 (2025).","mla":"Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” <i>Journal of Pure and Applied Algebra</i>, vol. 229, no. 10, 108068, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">10.1016/j.jpaa.2025.108068</a>."},"abstract":[{"lang":"eng","text":"We establish several results combining discrete Morse theory and microlocal sheaf theory in the setting of finite posets and simplicial complexes. Our primary tool is a computationally tractable description of the bounded derived category of sheaves on a poset with the Alexandrov topology. We prove that each bounded complex of sheaves on a finite poset admits a unique (up to isomorphism of complexes) minimal injective resolution, and we provide algorithms for computing minimal injective resolution of an injective complex, as well as several useful functors between derived categories of sheaves. For the constant sheaf on a simplicial complex, we give asymptotically tight bounds on the complexity of computing the minimal injective resolution using those algorithms. Our main result is a novel definition of the discrete microsupport of a bounded complex of sheaves on a finite poset. We detail several foundational properties of the discrete microsupport, as well as a microlocal generalization of the discrete homological Morse theorem and Morse inequalities."}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"18981"}]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2025-10-01T00:00:00Z","date_updated":"2025-12-30T07:55:21Z","intvolume":"       229","type":"journal_article","external_id":{"arxiv":["2209.14993"]},"day":"01","oa":1,"year":"2025","OA_type":"hybrid","publication_status":"published","publisher":"Elsevier","PlanS_conform":"1","department":[{"_id":"HeEd"}],"publication_identifier":{"issn":["0022-4049"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"article_processing_charge":"Yes (via OA deal)","title":"Discrete microlocal Morse theory","doi":"10.1016/j.jpaa.2025.108068","_id":"20323","scopus_import":"1","oa_version":"Published Version","article_type":"original","file_date_updated":"2025-12-30T07:55:08Z","language":[{"iso":"eng"}],"OA_place":"publisher","date_created":"2025-09-10T05:40:09Z","project":[{"grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"},{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"quality_controlled":"1"},{"year":"2025","publication_status":"epub_ahead","OA_type":"green","publisher":"Elsevier","department":[{"_id":"HeEd"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2212.11380"}],"type":"journal_article","day":"10","external_id":{"isi":["001599061500002"],"arxiv":["2212.11380"]},"oa":1,"article_processing_charge":"No","title":"Flips in two-dimensional hypertriangulations","publication_identifier":{"issn":["0195-6698"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"article_type":"original","OA_place":"repository","language":[{"iso":"eng"}],"doi":"10.1016/j.ejc.2025.104248","_id":"20490","scopus_import":"1","oa_version":"Preprint","project":[{"grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF","grant_number":"Z00342"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"quality_controlled":"1","date_created":"2025-10-19T22:01:31Z","isi":1,"status":"public","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"full_name":"Garber, Alexey","first_name":"Alexey","last_name":"Garber"},{"first_name":"Mohadese","last_name":"Ghafari","full_name":"Ghafari, Mohadese"},{"orcid":"0000-0002-1780-2689","last_name":"Heiss","first_name":"Teresa","full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian"}],"publication":"European Journal of Combinatorics","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.","volume":132,"ec_funded":1,"article_number":"104248","month":"10","date_published":"2025-10-10T00:00:00Z","corr_author":"1","citation":{"short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, European Journal of Combinatorics 132 (2025).","mla":"Edelsbrunner, Herbert, et al. “Flips in Two-Dimensional Hypertriangulations.” <i>European Journal of Combinatorics</i>, vol. 132, 104248, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104248\">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, 2025.","apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., &#38; Saghafian, M. (2025). 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>","ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. Flips in two-dimensional hypertriangulations. <i>European Journal of Combinatorics</i>. 2025;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, 2025. <a href=\"https://doi.org/10.1016/j.ejc.2025.104248\">https://doi.org/10.1016/j.ejc.2025.104248</a>.","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2025. Flips in two-dimensional hypertriangulations. European Journal of Combinatorics. 132, 104248."},"abstract":[{"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","lang":"eng"}],"intvolume":"       132","date_updated":"2025-12-01T12:57:29Z"},{"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.","volume":8,"ec_funded":1,"month":"03","page":"30-62","author":[{"first_name":"Sebastiano","orcid":"0000-0001-6249-0832","last_name":"Cultrera di Montesano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano"},{"id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej","last_name":"Draganov","orcid":"0000-0003-0464-3823","first_name":"Ondrej"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"status":"public","publication":"Foundations of Data Science","intvolume":"         8","date_updated":"2025-11-04T12:25:47Z","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"15091"}]},"date_published":"2025-03-01T00:00:00Z","corr_author":"1","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."}],"citation":{"chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes.” <i>Foundations of Data Science</i>. American Institute of Mathematical Sciences, 2025. <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>. 2025;8:30-62. doi:<a href=\"https://doi.org/10.3934/fods.2025003\">10.3934/fods.2025003</a>","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (2025). Chromatic alpha complexes. <i>Foundations of Data Science</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/fods.2025003\">https://doi.org/10.3934/fods.2025003</a>","ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” <i>Foundations of Data Science</i>, vol. 8. American Institute of Mathematical Sciences, pp. 30–62, 2025.","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Foundations of Data Science 8 (2025) 30–62.","mla":"Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” <i>Foundations of Data Science</i>, vol. 8, American Institute of Mathematical Sciences, 2025, 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. 2025. Chromatic alpha complexes. Foundations of Data Science. 8, 30–62."},"title":"Chromatic alpha complexes","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["2639-8001"]},"arxiv":1,"publisher":"American Institute of Mathematical Sciences","year":"2025","publication_status":"epub_ahead","OA_type":"green","department":[{"_id":"HeEd"}],"type":"journal_article","day":"01","external_id":{"arxiv":["2212.03128"]},"project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"quality_controlled":"1","date_created":"2025-11-02T23:01:33Z","article_type":"original","language":[{"iso":"eng"}],"OA_place":"repository","doi":"10.3934/fods.2025003","scopus_import":"1","oa_version":"Preprint","_id":"20585"},{"oa":1,"external_id":{"isi":["001610592600001"],"arxiv":["2310.14801"]},"day":"10","type":"journal_article","department":[{"_id":"HeEd"}],"PlanS_conform":"1","main_file_link":[{"url":"https://doi.org/10.1007/s00454-025-00796-5","open_access":"1"}],"publisher":"Springer Nature","OA_type":"hybrid","year":"2025","publication_status":"epub_ahead","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"title":"Maximum Betti numbers of Čech complexes","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","scopus_import":"1","_id":"20657","doi":"10.1007/s00454-025-00796-5","language":[{"iso":"eng"}],"OA_place":"publisher","article_type":"original","isi":1,"date_created":"2025-11-19T09:44:58Z","quality_controlled":"1","project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"publication":"Discrete & Computational Geometry","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"first_name":"János","last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János"}],"status":"public","month":"11","ddc":["510"],"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.","ec_funded":1,"abstract":[{"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. ","lang":"eng"}],"citation":{"apa":"Edelsbrunner, H., &#38; Pach, J. (2025). 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>","ieee":"H. Edelsbrunner and J. Pach, “Maximum Betti numbers of Čech complexes,” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2025.","short":"H. Edelsbrunner, J. Pach, Discrete &#38; Computational Geometry (2025).","mla":"Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” <i>Discrete &#38; Computational Geometry</i>, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00454-025-00796-5\">10.1007/s00454-025-00796-5</a>.","chicago":"Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2025. <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>. 2025. doi:<a href=\"https://doi.org/10.1007/s00454-025-00796-5\">10.1007/s00454-025-00796-5</a>","ista":"Edelsbrunner H, Pach J. 2025. Maximum Betti numbers of Čech complexes. Discrete &#38; Computational Geometry."},"has_accepted_license":"1","corr_author":"1","date_published":"2025-11-10T00:00:00Z","related_material":{"record":[{"id":"17146","status":"public","relation":"earlier_version"}]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2025-12-01T15:19:21Z"},{"article_processing_charge":"Yes (via OA deal)","title":"Average and expected distortion of Voronoi paths and scapes","arxiv":1,"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"publication_status":"published","OA_type":"hybrid","year":"2025","publisher":"Springer Nature","day":"01","external_id":{"isi":["001238566200004"],"pmid":["39974750"],"arxiv":["2012.03350"]},"pmid":1,"oa":1,"type":"journal_article","quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"grant_number":"Z00342","_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","call_identifier":"FWF","grant_number":"I02979-N35"}],"isi":1,"date_created":"2024-06-16T22:01:07Z","language":[{"iso":"eng"}],"file_date_updated":"2025-04-23T07:31:32Z","OA_place":"publisher","article_type":"original","_id":"17149","scopus_import":"1","oa_version":"Published Version","doi":"10.1007/s00454-024-00660-y","month":"03","volume":73,"acknowledgement":"The authors thank Ranita Biswas and Tatiana Ezubova for the collaboration on computational experiments that motivated the work reported in this paper. The authors also thank Daniel Bonnema for proofreading and noticing an issue with the original proof of Lemma 4.3.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.","ec_funded":1,"ddc":["510"],"file":[{"checksum":"ffb0c818222138f9f113f4bbea41e834","relation":"main_file","date_created":"2025-04-23T07:31:32Z","access_level":"open_access","date_updated":"2025-04-23T07:31:32Z","creator":"dernst","content_type":"application/pdf","file_size":283443,"file_id":"19610","file_name":"2025_DiscreteComputGeom_EdelsbrunnerHe.pdf","success":1}],"page":"490-499","status":"public","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton","last_name":"Nikitenko","orcid":"0000-0002-0659-3201","first_name":"Anton"}],"publication":"Discrete & Computational Geometry","intvolume":"        73","date_updated":"2026-02-16T12:18:50Z","date_published":"2025-03-01T00:00:00Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"abstract":[{"lang":"eng","text":"The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about 4/Pi. We prove that this factor is the same on average (in the ergodic sense) for approximations of any rectifiable curve by the edges of any non-exotic Delaunay mosaic (known as Voronoi path), and extend the results to all dimensions, generalizing Voronoi paths to Voronoi scapes."}],"citation":{"ama":"Edelsbrunner H, Nikitenko A. Average and expected distortion of Voronoi paths and scapes. <i>Discrete &#38; Computational Geometry</i>. 2025;73:490-499. doi:<a href=\"https://doi.org/10.1007/s00454-024-00660-y\">10.1007/s00454-024-00660-y</a>","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Average and Expected Distortion of Voronoi Paths and Scapes.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00454-024-00660-y\">https://doi.org/10.1007/s00454-024-00660-y</a>.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Average and Expected Distortion of Voronoi Paths and Scapes.” <i>Discrete &#38; Computational Geometry</i>, vol. 73, Springer Nature, 2025, pp. 490–99, doi:<a href=\"https://doi.org/10.1007/s00454-024-00660-y\">10.1007/s00454-024-00660-y</a>.","ieee":"H. Edelsbrunner and A. Nikitenko, “Average and expected distortion of Voronoi paths and scapes,” <i>Discrete &#38; Computational Geometry</i>, vol. 73. Springer Nature, pp. 490–499, 2025.","short":"H. Edelsbrunner, A. Nikitenko, Discrete &#38; Computational Geometry 73 (2025) 490–499.","apa":"Edelsbrunner, H., &#38; Nikitenko, A. (2025). Average and expected distortion of Voronoi paths and scapes. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-024-00660-y\">https://doi.org/10.1007/s00454-024-00660-y</a>","ista":"Edelsbrunner H, Nikitenko A. 2025. Average and expected distortion of Voronoi paths and scapes. Discrete &#38; Computational Geometry. 73, 490–499."},"corr_author":"1","has_accepted_license":"1"},{"keyword":["topological data analysis","chromatic point set","alpha complex","persistent homology","six pack","sheaf","microlocal discrete Morse","injective resolution","collapse","knot","discrete Morse theory"],"date_updated":"2026-04-07T11:47:30Z","date_published":"2025-02-03T00:00:00Z","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"15091"},{"id":"18981","relation":"part_of_dissertation","status":"public"}]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"abstract":[{"lang":"eng","text":"Topological Data Analysis (TDA) is a discipline utilizing the mathematical field of topology to study data, most prominently collections of point sets. This thesis summarizes three projects related to computations in TDA.\r\n\r\nThe first one establishes a variant of TDA for chromatic point sets, where each point is given a color. For example, we are given positions of cells within a tumor microenvironment, and color the cancerous cells red, and the immune cells blue.\r\n\r\nThe aim is then to give a quantitative description of how the two or more sets of points spatially interact. Building on image, kernel and cokernel variants of persistent homology, we suggest six-packs of persistent diagrams as such a descriptor.\r\n\r\nWe describe a construction of a chromatic alpha complex, which enables  efficient computation of several variants of the six-packs. We give topological descriptions of natural subcomplexes of the chromatic alpha complex, and show that the radii of the simplices form a discrete Morse function. Finally, we provide an implementation of the presented chromatic TDA pipeline.\r\n\r\nThe second part aims to translate a powerful tool of sheaf theory to elementary terms using labeled matrices. The goal is to enable their use in computational settings. We show that derived categories of sheaves over finite posets have, up to isomorphism, unique objects---minimal injective resolutions---and give a concrete algorithm to compute them. We further describe simple algorithms to compute derived pushforwards and pullbacks for monotonic maps, and their proper variants for inclusions, and demonstrate their tractability by providing an implementation. Finally, we suggest a discrete definition of microsupport and show desirable properties inspired by discrete Morse theory.\r\n\r\nIn the last part, we present a collection of observations about collapses. We give a characterization of collapsibility in terms of unitriangular submatrices of the boundary matrix, a cotree-tree decomposition, and the optimal solution to a variant of the Procrustes problem. We establish relation between dual collapses and relative Morse theory and pose several open questions. Finally, focusing on complexes embedded in the three-dimensional Euclidean space, we describe a relation between the collapsibility and the triviality of a polygonal knot."}],"citation":{"ista":"Draganov O. 2025. Structures and computations in topological data analysis. Institute of Science and Technology Austria.","chicago":"Draganov, Ondrej. “Structures and Computations in Topological Data Analysis.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/at:ista:18979\">https://doi.org/10.15479/at:ista:18979</a>.","ama":"Draganov O. Structures and computations in topological data analysis. 2025. doi:<a href=\"https://doi.org/10.15479/at:ista:18979\">10.15479/at:ista:18979</a>","apa":"Draganov, O. (2025). <i>Structures and computations in topological data analysis</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18979\">https://doi.org/10.15479/at:ista:18979</a>","ieee":"O. Draganov, “Structures and computations in topological data analysis,” Institute of Science and Technology Austria, 2025.","mla":"Draganov, Ondrej. <i>Structures and Computations in Topological Data Analysis</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/at:ista:18979\">10.15479/at:ista:18979</a>.","short":"O. Draganov, Structures and Computations in Topological Data Analysis, Institute of Science and Technology Austria, 2025."},"supervisor":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"has_accepted_license":"1","corr_author":"1","month":"02","acknowledgement":"The research presented in this thesis was funded with the Wittgenstein Prize,\r\nAustrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research\r\nCenter TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF),\r\ngrant no. I 02979-N35.\r\n","ddc":["514","004"],"file":[{"content_type":"application/zip","file_size":11899491,"file_id":"18983","file_name":"Thesis.zip","checksum":"af6567e5d35e5eb330b8925ae37f1998","relation":"source_file","access_level":"closed","date_created":"2025-01-31T16:58:30Z","date_updated":"2025-01-31T16:58:30Z","creator":"odragano"},{"file_id":"19000","file_name":"Thesis.pdf","content_type":"application/pdf","file_size":8857514,"date_created":"2025-02-04T16:22:07Z","access_level":"open_access","date_updated":"2025-02-04T16:22:07Z","creator":"odragano","checksum":"c3fef68e35b9dc2020b2ca6006da6343","relation":"main_file"}],"page":"140","status":"public","author":[{"first_name":"Ondrej","orcid":"0000-0003-0464-3823","last_name":"Draganov","full_name":"Draganov, Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87"}],"degree_awarded":"PhD","alternative_title":["ISTA Thesis"],"project":[{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"},{"grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"date_created":"2025-01-31T17:04:40Z","file_date_updated":"2025-02-04T16:22:07Z","OA_place":"publisher","language":[{"iso":"eng"}],"_id":"18979","oa_version":"Published Version","doi":"10.15479/at:ista:18979","article_processing_charge":"No","title":"Structures and computations in topological data analysis","publication_identifier":{"issn":["2663-337X"]},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"year":"2025","publication_status":"published","publisher":"Institute of Science and Technology Austria","day":"03","oa":1,"type":"dissertation"},{"publication":"Discrete and Computational Geometry","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"last_name":"Garber","first_name":"Alexey","full_name":"Garber, Alexey"},{"full_name":"Ghafari, Mohadese","first_name":"Mohadese","last_name":"Ghafari"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","full_name":"Heiss, Teresa","last_name":"Heiss","orcid":"0000-0002-1780-2689","first_name":"Teresa"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza"}],"status":"public","file":[{"relation":"main_file","checksum":"b207b4e00f904e8ea8a30e24f0251f79","date_updated":"2024-07-22T09:43:19Z","creator":"dernst","access_level":"open_access","date_created":"2024-07-22T09:43:19Z","file_size":892019,"content_type":"application/pdf","file_name":"2024_DiscreteComputGeom_Edelsbrunner.pdf","success":1,"file_id":"17301"}],"page":"29-48","month":"07","ddc":["510"],"volume":72,"ec_funded":1,"acknowledgement":"Work by all authors but A. Garber is supported by the European Research Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially supported by the Alexander von Humboldt Foundation.","citation":{"apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., &#38; Saghafian, M. (2024). On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-023-00566-1\">https://doi.org/10.1007/s00454-023-00566-1</a>","mla":"Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>, vol. 72, Springer Nature, 2024, pp. 29–48, doi:<a href=\"https://doi.org/10.1007/s00454-023-00566-1\">10.1007/s00454-023-00566-1</a>.","ieee":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles in higher order Brillouin tessellations and related tilings in the plane,” <i>Discrete and Computational Geometry</i>, vol. 72. Springer Nature, pp. 29–48, 2024.","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00454-023-00566-1\">https://doi.org/10.1007/s00454-023-00566-1</a>.","ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. 2024;72:29-48. doi:<a href=\"https://doi.org/10.1007/s00454-023-00566-1\">10.1007/s00454-023-00566-1</a>","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2024. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 72, 29–48."},"abstract":[{"lang":"eng","text":"For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2  is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970))."}],"has_accepted_license":"1","corr_author":"1","date_published":"2024-07-01T00:00:00Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2025-04-23T08:41:59Z","intvolume":"        72","oa":1,"external_id":{"isi":["001060727600004"],"arxiv":["2204.01076"],"pmid":["39610762"]},"pmid":1,"day":"01","type":"journal_article","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","year":"2024","publication_status":"published","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"title":"On angles in higher order Brillouin tessellations and related tilings in the plane","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","oa_version":"Published Version","_id":"14345","doi":"10.1007/s00454-023-00566-1","file_date_updated":"2024-07-22T09:43:19Z","language":[{"iso":"eng"}],"article_type":"original","isi":1,"date_created":"2023-09-17T22:01:10Z","quality_controlled":"1","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}]},{"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2024-06-06T00:00:00Z","has_accepted_license":"1","corr_author":"1","conference":{"end_date":"2024-06-14","start_date":"2024-06-11","name":"SoCG: Symposium on Computational Geometry","location":"Athens, Greece"},"citation":{"ista":"Attali D, Kourimska H, Fillmore CD, Ghosh I, Lieutier A, Stephenson ER, Wintraecken M. 2024. The ultimate frontier: An optimality construction for homotopy inference (media exposition). 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 87.","apa":"Attali, D., Kourimska, H., Fillmore, C. D., Ghosh, I., Lieutier, A., Stephenson, E. R., &#38; Wintraecken, M. (2024). The ultimate frontier: An optimality construction for homotopy inference (media exposition). In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">https://doi.org/10.4230/LIPIcs.SoCG.2024.87</a>","short":"D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ieee":"D. Attali <i>et al.</i>, “The ultimate frontier: An optimality construction for homotopy inference (media exposition),” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","mla":"Attali, Dominique, et al. “The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition).” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 87, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">10.4230/LIPIcs.SoCG.2024.87</a>.","chicago":"Attali, Dominique, Hana Kourimska, Christopher D Fillmore, Ishika Ghosh, Andre Lieutier, Elizabeth R Stephenson, and Mathijs Wintraecken. “The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition).” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">https://doi.org/10.4230/LIPIcs.SoCG.2024.87</a>.","ama":"Attali D, Kourimska H, Fillmore CD, et al. The ultimate frontier: An optimality construction for homotopy inference (media exposition). In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">10.4230/LIPIcs.SoCG.2024.87</a>"},"abstract":[{"lang":"eng","text":"In our companion paper \"Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds\" we gave optimal bounds (in terms of the two one-sided Hausdorff distances) on a sample P of an input shape 𝒮 (either manifold or general set with positive reach) such that one can infer the homotopy of 𝒮 from the union of balls with some radius centred at P, both in Euclidean space and in a Riemannian manifold of bounded curvature. The construction showing the optimality of the bounds is not straightforward. The purpose of this video is to visualize and thus elucidate said construction in the Euclidean setting."}],"intvolume":"       293","date_updated":"2025-04-15T07:16:58Z","author":[{"last_name":"Attali","first_name":"Dominique","full_name":"Attali, Dominique"},{"full_name":"Kourimska, Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","first_name":"Hana","last_name":"Kourimska","orcid":"0000-0001-7841-0091"},{"last_name":"Fillmore","first_name":"Christopher D","full_name":"Fillmore, Christopher D","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425"},{"id":"ee449b28-344d-11ef-a6d5-9ca430e9e9ff","full_name":"Ghosh, Ishika","last_name":"Ghosh","first_name":"Ishika"},{"first_name":"Andre","last_name":"Lieutier","full_name":"Lieutier, Andre"},{"first_name":"Elizabeth R","last_name":"Stephenson","orcid":"0000-0002-6862-208X","full_name":"Stephenson, Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs"}],"status":"public","alternative_title":["LIPIcs"],"publication":"40th International Symposium on Computational Geometry","article_number":"87","ddc":["000"],"acknowledgement":"This research has been supported by the European Research Council (ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant No. I02979-N35. Mathijs Wintraecken: Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant No. M-3073, and the welcome package from IDEX of the Université Côte d’Azur.\r\nWe thank Jean-Daniel Boissonnat, Herbert Edelsbrunner, and Mariette Yvinec for discussion.","volume":293,"ec_funded":1,"month":"06","file":[{"relation":"main_file","checksum":"9355c2e60b8ec285e1b22719c5b73f1a","date_updated":"2024-09-19T10:30:37Z","creator":"dernst","date_created":"2024-09-19T10:30:37Z","access_level":"open_access","file_size":3507177,"content_type":"application/pdf","file_name":"2024_LIPICs_Attali.pdf","success":1,"file_id":"18098"}],"language":[{"iso":"eng"}],"file_date_updated":"2024-09-19T10:30:37Z","doi":"10.4230/LIPIcs.SoCG.2024.87","oa_version":"Published Version","_id":"18097","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"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"},{"name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073"}],"quality_controlled":"1","date_created":"2024-09-19T10:29:48Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2024","publication_status":"published","department":[{"_id":"HeEd"}],"type":"conference","oa":1,"day":"06","title":"The ultimate frontier: An optimality construction for homotopy inference (media exposition)","article_processing_charge":"Yes","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"isbn":["9783959773164"]}},{"file":[{"access_level":"open_access","date_created":"2024-11-18T07:49:25Z","date_updated":"2024-11-18T07:49:25Z","creator":"dernst","checksum":"5f9b35e115c3d375e99be78da9054cb4","relation":"main_file","file_id":"18560","file_name":"2024_LIPIcs_CultreradiMontesano.pdf","success":1,"content_type":"application/pdf","file_size":908541}],"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, \"Discretization in Geometry and Dynamics\", Austrian Science Fund (FWF), grant no. I 02979-N35.","ec_funded":1,"volume":320,"article_number":"3","ddc":["510"],"month":"10","alternative_title":["LIPIcs"],"publication":"32nd International Symposium on Graph Drawing and Network Visualization","status":"public","author":[{"first_name":"Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano"},{"first_name":"Ondrej","orcid":"0000-0003-0464-3823","last_name":"Draganov","full_name":"Draganov, Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza"}],"date_updated":"2025-12-02T13:50:50Z","intvolume":"       320","has_accepted_license":"1","corr_author":"1","abstract":[{"lang":"eng","text":"Given a finite set, A ⊆ ℝ², and a subset, B ⊆ A, the MST-ratio is the combined length of the minimum spanning trees of B and A⧵B divided by the length of the minimum spanning tree of A. The question of the supremum, over all sets A, of the maximum, over all subsets B, is related to the Steiner ratio, and we prove this sup-max is between 2.154 and 2.427. Restricting ourselves to 2-dimensional lattices, we prove that the sup-max is 2, while the inf-max is 1.25. By some margin the most difficult of these results is the upper bound for the inf-max, which we prove by showing that the hexagonal lattice cannot have MST-ratio larger than 1.25."}],"citation":{"chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “The Euclidean MST-Ratio for Bi-Colored Lattices.” In <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, Vol. 320. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">https://doi.org/10.4230/LIPIcs.GD.2024.3</a>.","ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. The Euclidean MST-ratio for bi-colored lattices. In: <i>32nd International Symposium on Graph Drawing and Network Visualization</i>. Vol 320. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">10.4230/LIPIcs.GD.2024.3</a>","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (2024). The Euclidean MST-ratio for bi-colored lattices. In <i>32nd International Symposium on Graph Drawing and Network Visualization</i> (Vol. 320). Vienna, Austria: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">https://doi.org/10.4230/LIPIcs.GD.2024.3</a>","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","mla":"Cultrera di Montesano, Sebastiano, et al. “The Euclidean MST-Ratio for Bi-Colored Lattices.” <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, vol. 320, 3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">10.4230/LIPIcs.GD.2024.3</a>.","ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “The Euclidean MST-ratio for bi-colored lattices,” in <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, Vienna, Austria, 2024, vol. 320.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2024. The Euclidean MST-ratio for bi-colored lattices. 32nd International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LIPIcs, vol. 320, 3."},"conference":{"location":"Vienna, Austria","name":"GD: Graph Drawing and Network Visualization","end_date":"2024-09-20","start_date":"2024-09-18"},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2024-10-28T00:00:00Z","publication_identifier":{"issn":["1868-8969"],"isbn":["9783959773430"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"article_processing_charge":"Yes","title":"The Euclidean MST-ratio for bi-colored lattices","type":"conference","external_id":{"arxiv":["2403.10204"],"isi":["001540278400001"]},"day":"28","oa":1,"publication_status":"published","year":"2024","OA_type":"gold","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"date_created":"2024-11-17T23:01:47Z","isi":1,"project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"quality_controlled":"1","doi":"10.4230/LIPIcs.GD.2024.3","_id":"18556","scopus_import":"1","oa_version":"Published Version","file_date_updated":"2024-11-18T07:49:25Z","OA_place":"publisher","language":[{"iso":"eng"}]},{"page":"557-578","file":[{"success":1,"file_name":"2024_JourApplCompTopo_BiswasRa.pdf","file_id":"19612","file_size":522831,"content_type":"application/pdf","creator":"dernst","date_updated":"2025-04-23T08:01:36Z","date_created":"2025-04-23T08:01:36Z","access_level":"open_access","relation":"main_file","checksum":"0ee15c1493a6413cf356ab2f32c81a9e"}],"acknowledgement":"The authors thank Uli Wagner and Emo Welzl for comments on an earlier version of this paper, and for pointing out related work in the prior literature.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.","ec_funded":1,"volume":8,"ddc":["510"],"month":"09","publication":"Journal of Applied and Computational Topology","status":"public","author":[{"orcid":"0000-0002-5372-7890","last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Sebastiano","orcid":"0000-0001-6249-0832","last_name":"Cultrera Di Montesano","full_name":"Cultrera Di Montesano, Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza"}],"date_updated":"2025-05-14T09:27:57Z","intvolume":"         8","corr_author":"1","has_accepted_license":"1","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. 2024;8:557-578. doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” <i>Journal of Applied and Computational Topology</i>, vol. 8. Springer Nature, pp. 557–578, 2024.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>, vol. 8, Springer Nature, 2024, pp. 557–78, doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Journal of Applied and Computational Topology. 8, 557–578."},"abstract":[{"text":"The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements.","lang":"eng"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"11658"}]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2024-09-01T00:00:00Z","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","type":"journal_article","external_id":{"pmid":["39308789"]},"pmid":1,"day":"01","oa":1,"OA_type":"hybrid","publication_status":"published","year":"2024","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"date_created":"2024-05-12T22:01:03Z","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"quality_controlled":"1","doi":"10.1007/s41468-024-00173-w","_id":"15380","oa_version":"Published Version","scopus_import":"1","article_type":"original","OA_place":"publisher","file_date_updated":"2025-04-23T08:01:36Z","language":[{"iso":"eng"}]},{"date_updated":"2025-04-15T07:16:58Z","intvolume":"       293","has_accepted_license":"1","abstract":[{"text":"We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let 𝒮 ⊆ ℝ^d be a fixed closed set that contains a bounding sphere. That is, the bounding sphere is part of the set 𝒮. Consider the space of C^{1,1} diffeomorphisms of ℝ^d to itself, which keep the bounding sphere invariant. The map from this space of diffeomorphisms (endowed with a Banach norm) to the space of closed subsets of ℝ^d (endowed with the Hausdorff distance), mapping a diffeomorphism F to the closure of the medial axis of F(𝒮), is Lipschitz. This extends a previous stability result of Chazal and Soufflet on the stability of the medial axis of C² manifolds under C² ambient diffeomorphisms.","lang":"eng"}],"citation":{"ista":"Kourimska H, Lieutier A, Wintraecken M. 2024. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 69.","chicago":"Kourimska, Hana, André Lieutier, and Mathijs Wintraecken. “The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">https://doi.org/10.4230/LIPIcs.SoCG.2024.69</a>.","ama":"Kourimska H, Lieutier A, Wintraecken M. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">10.4230/LIPIcs.SoCG.2024.69</a>","apa":"Kourimska, H., Lieutier, A., &#38; Wintraecken, M. (2024). The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">https://doi.org/10.4230/LIPIcs.SoCG.2024.69</a>","short":"H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ieee":"H. Kourimska, A. Lieutier, and M. Wintraecken, “The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms,” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","mla":"Kourimska, Hana, et al. “The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 69, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">10.4230/LIPIcs.SoCG.2024.69</a>."},"conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Athens, Greece","end_date":"2024-06-14"},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2024-06-01T00:00:00Z","file":[{"file_id":"17150","success":1,"file_name":"2024_LIPICS_Kourimska.pdf","content_type":"application/pdf","file_size":1612558,"date_created":"2024-06-17T08:33:40Z","access_level":"open_access","creator":"dernst","date_updated":"2024-06-17T08:33:40Z","checksum":"b40ff456c19294adb5d9613fcfd751c6","relation":"main_file"}],"acknowledgement":"This research has been supported by the European Research Council (ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant No. I 02979-N35.\r\nSupported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant No. M-3073, and the welcome package from IDEX of the Université Cô d'Azur.\r\nWe are greatly indebted to Fred Chazal for sharing his insights. We further thank Erin Chambers, Christopher Fillmore, and Elizabeth Stephenson for early discussions and all members of the Edelsbrunner group (Institute of Science and Technology Austria) and the Datashape team (Inria) for the atmosphere in which this research was conducted.","ec_funded":1,"volume":293,"article_number":"69","ddc":["510"],"month":"06","alternative_title":["LIPIcs"],"publication":"40th International Symposium on Computational Geometry","status":"public","author":[{"id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","full_name":"Kourimska, Hana","orcid":"0000-0001-7841-0091","last_name":"Kourimska","first_name":"Hana"},{"last_name":"Lieutier","first_name":"André","full_name":"Lieutier, André"},{"full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","first_name":"Mathijs"}],"date_created":"2024-06-16T22:01:06Z","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342"},{"grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073"}],"quality_controlled":"1","doi":"10.4230/LIPIcs.SoCG.2024.69","_id":"17144","scopus_import":"1","oa_version":"Published Version","file_date_updated":"2024-06-17T08:33:40Z","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959773164"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"article_processing_charge":"No","title":"The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms","type":"conference","external_id":{"arxiv":["2212.01118"]},"day":"01","oa":1,"year":"2024","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}]}]