[{"article_type":"original","publisher":"Oxford University Press","quality_controlled":"1","page":"669-697","intvolume":"      2020","title":"Waist of balls in hyperbolic and spherical spaces","department":[{"_id":"HeEd"}],"date_created":"2022-03-18T11:39:30Z","article_processing_charge":"No","publication_status":"published","issue":"3","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"scopus_import":"1","_id":"10867","acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","volume":2020,"abstract":[{"text":"In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces.","lang":"eng"}],"day":"01","doi":"10.1093/imrn/rny037","arxiv":1,"external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]},"isi":1,"citation":{"chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2020. <a href=\"https://doi.org/10.1093/imrn/rny037\">https://doi.org/10.1093/imrn/rny037</a>.","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” <i>International Mathematics Research Notices</i>, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020.","apa":"Akopyan, A., &#38; Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rny037\">https://doi.org/10.1093/imrn/rny037</a>","ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. <i>International Mathematics Research Notices</i>. 2020;2020(3):669-697. doi:<a href=\"https://doi.org/10.1093/imrn/rny037\">10.1093/imrn/rny037</a>","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” <i>International Mathematics Research Notices</i>, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:<a href=\"https://doi.org/10.1093/imrn/rny037\">10.1093/imrn/rny037</a>."},"year":"2020","date_updated":"2023-08-24T14:19:55Z","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"month":"02","oa_version":"Preprint","publication":"International Mathematics Research Notices","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/1702.07513","open_access":"1"}],"oa":1,"publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"type":"journal_article","date_published":"2020-02-01T00:00:00Z"},{"file":[{"date_created":"2020-06-08T00:34:00Z","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","file_size":13661779,"date_updated":"2020-07-14T12:48:05Z","file_name":"THESIS_Zuzka_Masarova.pdf","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"7945","creator":"zmasarov"},{"date_created":"2020-06-08T00:35:30Z","file_size":32184006,"checksum":"45341a35b8f5529c74010b7af43ac188","date_updated":"2020-07-14T12:48:05Z","file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","content_type":"application/zip","access_level":"closed","relation":"source_file","file_id":"7946","creator":"zmasarov"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","related_material":{"record":[{"relation":"part_of_dissertation","id":"7950","status":"public"},{"status":"public","id":"5986","relation":"part_of_dissertation"}]},"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","short":"CC BY-SA (4.0)","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","image":"/images/cc_by_sa.png"},"type":"dissertation","date_published":"2020-06-09T00:00:00Z","publication_identifier":{"isbn":["978-3-99078-005-3"],"issn":["2663-337X"]},"oa":1,"supervisor":[{"first_name":"Uli","last_name":"Wagner","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"language":[{"iso":"eng"}],"has_accepted_license":"1","oa_version":"Published Version","month":"06","ddc":["516","514"],"year":"2020","citation":{"apa":"Masárová, Z. (2020). <i>Reconfiguration problems</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:7944\">https://doi.org/10.15479/AT:ISTA:7944</a>","ama":"Masárová Z. Reconfiguration problems. 2020. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7944\">10.15479/AT:ISTA:7944</a>","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. <a href=\"https://doi.org/10.15479/AT:ISTA:7944\">https://doi.org/10.15479/AT:ISTA:7944</a>.","ieee":"Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020.","mla":"Masárová, Zuzana. <i>Reconfiguration Problems</i>. Institute of Science and Technology Austria, 2020, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7944\">10.15479/AT:ISTA:7944</a>.","short":"Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020.","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria."},"date_updated":"2023-09-07T13:17:37Z","day":"09","doi":"10.15479/AT:ISTA:7944","degree_awarded":"PhD","abstract":[{"text":"This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars.","lang":"eng"}],"page":"160","file_date_updated":"2020-07-14T12:48:05Z","publisher":"Institute of Science and Technology Austria","_id":"7944","author":[{"first_name":"Zuzana","last_name":"Masárová","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"date_created":"2020-06-08T00:49:46Z","publication_status":"published","title":"Reconfiguration problems","alternative_title":["ISTA Thesis"]},{"language":[{"iso":"eng"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2020-06-22","location":"Zürich, Switzerland","end_date":"2020-06-26"},"has_accepted_license":"1","publication":"36th International Symposium on Computational Geometry","article_number":"20:1-20:18","month":"06","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"oa_version":"Published Version","related_material":{"record":[{"relation":"later_version","id":"9649","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"relation":"main_file","access_level":"open_access","creator":"dernst","file_id":"7969","checksum":"38cbfa4f5d484d267a35d44d210df044","file_size":1009739,"date_created":"2020-06-17T10:13:34Z","file_name":"2020_LIPIcsSoCG_Boissonnat.pdf","content_type":"application/pdf","date_updated":"2020-07-14T12:48:06Z"}],"type":"conference","date_published":"2020-06-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-143-6"]},"file_date_updated":"2020-07-14T12:48:06Z","ec_funded":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"7952","intvolume":"       164","alternative_title":["LIPIcs"],"title":"The topological correctness of PL-approximations of isomanifolds","department":[{"_id":"HeEd"}],"article_processing_charge":"No","date_created":"2020-06-09T07:24:11Z","publication_status":"published","ddc":["510"],"volume":164,"citation":{"chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” In <i>36th International Symposium on Computational Geometry</i>, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">https://doi.org/10.4230/LIPIcs.SoCG.2020.20</a>.","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations of isomanifolds,” in <i>36th International Symposium on Computational Geometry</i>, Zürich, Switzerland, 2020, vol. 164.","apa":"Boissonnat, J.-D., &#38; Wintraecken, M. (2020). The topological correctness of PL-approximations of isomanifolds. In <i>36th International Symposium on Computational Geometry</i> (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">https://doi.org/10.4230/LIPIcs.SoCG.2020.20</a>","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations of isomanifolds. In: <i>36th International Symposium on Computational Geometry</i>. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">10.4230/LIPIcs.SoCG.2020.20</a>","ista":"Boissonnat J-D, Wintraecken M. 2020. The topological correctness of PL-approximations of isomanifolds. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 20:1-20:18.","short":"J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” <i>36th International Symposium on Computational Geometry</i>, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">10.4230/LIPIcs.SoCG.2020.20</a>."},"year":"2020","date_updated":"2023-08-02T06:49:16Z","abstract":[{"text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine triangulation 𝒯. This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary. ","lang":"eng"}],"day":"01","doi":"10.4230/LIPIcs.SoCG.2020.20"},{"volume":63,"day":"05","arxiv":1,"doi":"10.1007/s00454-020-00213-z","abstract":[{"lang":"eng","text":"A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n→∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets."}],"year":"2020","citation":{"ama":"Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs of plane convex sets. <i>Discrete and Computational Geometry</i>. 2020;63(4):888-917. doi:<a href=\"https://doi.org/10.1007/s00454-020-00213-z\">10.1007/s00454-020-00213-z</a>","apa":"Pach, J., Reed, B., &#38; Yuditsky, Y. (2020). Almost all string graphs are intersection graphs of plane convex sets. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00213-z\">https://doi.org/10.1007/s00454-020-00213-z</a>","chicago":"Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00213-z\">https://doi.org/10.1007/s00454-020-00213-z</a>.","ieee":"J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection graphs of plane convex sets,” <i>Discrete and Computational Geometry</i>, vol. 63, no. 4. Springer Nature, pp. 888–917, 2020.","short":"J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917.","mla":"Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” <i>Discrete and Computational Geometry</i>, vol. 63, no. 4, Springer Nature, 2020, pp. 888–917, doi:<a href=\"https://doi.org/10.1007/s00454-020-00213-z\">10.1007/s00454-020-00213-z</a>.","ista":"Pach J, Reed B, Yuditsky Y. 2020. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 63(4), 888–917."},"date_updated":"2023-08-21T08:49:18Z","external_id":{"arxiv":["1803.06710"],"isi":["000538229000001"]},"isi":1,"publisher":"Springer Nature","article_type":"original","quality_controlled":"1","page":"888-917","date_created":"2020-06-14T22:00:51Z","article_processing_charge":"No","department":[{"_id":"HeEd"}],"publication_status":"published","intvolume":"        63","title":"Almost all string graphs are intersection graphs of plane convex sets","scopus_import":"1","_id":"7962","issue":"4","author":[{"last_name":"Pach","first_name":"János","full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"full_name":"Reed, Bruce","last_name":"Reed","first_name":"Bruce"},{"first_name":"Yelena","last_name":"Yuditsky","full_name":"Yuditsky, Yelena"}],"main_file_link":[{"url":"https://arxiv.org/abs/1803.06710","open_access":"1"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"oa":1,"type":"journal_article","date_published":"2020-06-05T00:00:00Z","language":[{"iso":"eng"}],"project":[{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","month":"06","publication":"Discrete and Computational Geometry"},{"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"first_name":"Anton","last_name":"Nikitenko","full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"},{"id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina","last_name":"Ölsböck","full_name":"Ölsböck, Katharina"},{"last_name":"Synak","first_name":"Peter","full_name":"Synak, Peter","id":"331776E2-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"8135","intvolume":"        15","alternative_title":["Abel Symposia"],"title":"Radius functions on Poisson–Delaunay mosaics and related complexes experimentally","department":[{"_id":"HeEd"}],"date_created":"2020-07-19T22:00:59Z","article_processing_charge":"No","publication_status":"published","file_date_updated":"2020-10-08T08:56:14Z","quality_controlled":"1","ec_funded":1,"page":"181-218","publisher":"Springer Nature","citation":{"apa":"Edelsbrunner, H., Nikitenko, A., Ölsböck, K., &#38; Synak, P. (2020). Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In <i>Topological Data Analysis</i> (Vol. 15, pp. 181–218). Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-43408-3_8\">https://doi.org/10.1007/978-3-030-43408-3_8</a>","ama":"Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In: <i>Topological Data Analysis</i>. Vol 15. Springer Nature; 2020:181-218. doi:<a href=\"https://doi.org/10.1007/978-3-030-43408-3_8\">10.1007/978-3-030-43408-3_8</a>","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” In <i>Topological Data Analysis</i>, 15:181–218. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-43408-3_8\">https://doi.org/10.1007/978-3-030-43408-3_8</a>.","ieee":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions on Poisson–Delaunay mosaics and related complexes experimentally,” in <i>Topological Data Analysis</i>, 2020, vol. 15, pp. 181–218.","short":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218.","mla":"Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” <i>Topological Data Analysis</i>, vol. 15, Springer Nature, 2020, pp. 181–218, doi:<a href=\"https://doi.org/10.1007/978-3-030-43408-3_8\">10.1007/978-3-030-43408-3_8</a>.","ista":"Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. 2020. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. Topological Data Analysis. , Abel Symposia, vol. 15, 181–218."},"year":"2020","date_updated":"2021-01-12T08:17:06Z","abstract":[{"lang":"eng","text":"Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics."}],"day":"22","doi":"10.1007/978-3-030-43408-3_8","ddc":["510"],"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 78818 Alpha and No 638176). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","volume":15,"has_accepted_license":"1","publication":"Topological Data Analysis","month":"06","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"H2020","_id":"2533E772-B435-11E9-9278-68D0E5697425","name":"Efficient Simulation of Natural Phenomena at Extremely Large Scales","grant_number":"638176"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"oa_version":"Submitted Version","language":[{"iso":"eng"}],"type":"conference","date_published":"2020-06-22T00:00:00Z","oa":1,"publication_identifier":{"issn":["21932808"],"eissn":["21978549"],"isbn":["9783030434076"]},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"access_level":"open_access","success":1,"relation":"main_file","creator":"dernst","file_id":"8628","checksum":"7b5e0de10675d787a2ddb2091370b8d8","file_size":2207071,"date_created":"2020-10-08T08:56:14Z","file_name":"2020-B-01-PoissonExperimentalSurvey.pdf","content_type":"application/pdf","date_updated":"2020-10-08T08:56:14Z"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"date_created":"2020-07-24T07:09:06Z","file_size":1476072,"date_updated":"2020-07-24T07:09:06Z","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"8164","creator":"mwintrae"}],"type":"journal_article","date_published":"2020-07-24T00:00:00Z","tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"},"oa":1,"publication_identifier":{"issn":["0081-6906"],"eissn":["1588-2896"]},"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Studia Scientiarum Mathematicarum Hungarica","month":"07","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","grant_number":"Z00342"}],"oa_version":"Published Version","ddc":["510"],"volume":57,"acknowledgement":"The authors are greatly indebted to Dror Atariah, Günther Rote and John Sullivan for discussion and suggestions. The authors also thank Jean-Daniel Boissonnat, Ramsay Dyer, David de Laat and Rien van de Weijgaert for discussion. This work has been supported in part by the European Union’s Seventh Framework Programme for Research of the\r\nEuropean Commission, under FET-Open grant number 255827 (CGL Computational Geometry Learning) and ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions), the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement number 754411,and the Austrian Science Fund (FWF): Z00342 N31.","external_id":{"isi":["000570978400005"]},"isi":1,"citation":{"short":"G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199.","mla":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” <i>Studia Scientiarum Mathematicarum Hungarica</i>, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:<a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">10.1556/012.2020.57.2.1454</a>.","ista":"Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2), 193–199.","ama":"Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. <i>Studia Scientiarum Mathematicarum Hungarica</i>. 2020;57(2):193-199. doi:<a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">10.1556/012.2020.57.2.1454</a>","apa":"Vegter, G., &#38; Wintraecken, M. (2020). Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. <i>Studia Scientiarum Mathematicarum Hungarica</i>. Akadémiai Kiadó. <a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">https://doi.org/10.1556/012.2020.57.2.1454</a>","ieee":"G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes,” <i>Studia Scientiarum Mathematicarum Hungarica</i>, vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” <i>Studia Scientiarum Mathematicarum Hungarica</i>. Akadémiai Kiadó, 2020. <a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">https://doi.org/10.1556/012.2020.57.2.1454</a>."},"year":"2020","date_updated":"2023-10-10T13:05:27Z","abstract":[{"text":"Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces.","lang":"eng"}],"day":"24","doi":"10.1556/012.2020.57.2.1454","file_date_updated":"2020-07-24T07:09:06Z","ec_funded":1,"quality_controlled":"1","page":"193-199","article_type":"original","publisher":"Akadémiai Kiadó","issue":"2","author":[{"full_name":"Vegter, Gert","first_name":"Gert","last_name":"Vegter"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","first_name":"Mathijs","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220"}],"scopus_import":"1","_id":"8163","intvolume":"        57","title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","department":[{"_id":"HeEd"}],"article_processing_charge":"No","date_created":"2020-07-24T07:09:18Z","publication_status":"published"},{"date_created":"2020-08-30T22:01:12Z","department":[{"_id":"HeEd"}],"article_processing_charge":"No","publication_status":"published","intvolume":"        64","title":"A farewell to Ricky Pollack","scopus_import":"1","_id":"8323","author":[{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","last_name":"Pach","full_name":"Pach, János"}],"publisher":"Springer Nature","article_type":"letter_note","page":"571-574","day":"01","doi":"10.1007/s00454-020-00237-5","citation":{"apa":"Pach, J. (2020). A farewell to Ricky Pollack. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00237-5\">https://doi.org/10.1007/s00454-020-00237-5</a>","ama":"Pach J. A farewell to Ricky Pollack. <i>Discrete and Computational Geometry</i>. 2020;64:571-574. doi:<a href=\"https://doi.org/10.1007/s00454-020-00237-5\">10.1007/s00454-020-00237-5</a>","chicago":"Pach, János. “A Farewell to Ricky Pollack.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00237-5\">https://doi.org/10.1007/s00454-020-00237-5</a>.","ieee":"J. Pach, “A farewell to Ricky Pollack,” <i>Discrete and Computational Geometry</i>, vol. 64. Springer Nature, pp. 571–574, 2020.","short":"J. Pach, Discrete and Computational Geometry 64 (2020) 571–574.","mla":"Pach, János. “A Farewell to Ricky Pollack.” <i>Discrete and Computational Geometry</i>, vol. 64, Springer Nature, 2020, pp. 571–74, doi:<a href=\"https://doi.org/10.1007/s00454-020-00237-5\">10.1007/s00454-020-00237-5</a>.","ista":"Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574."},"year":"2020","date_updated":"2023-08-22T09:05:04Z","external_id":{"isi":["000561483500001"]},"isi":1,"volume":64,"oa_version":"None","month":"10","publication":"Discrete and Computational Geometry","language":[{"iso":"eng"}],"publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"oa":1,"type":"journal_article","date_published":"2020-10-01T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.1007/s00454-020-00237-5","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public"},{"external_id":{"arxiv":["2001.02934"]},"date_updated":"2021-12-02T15:10:17Z","year":"2020","citation":{"mla":"Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” <i>European Journal of Mathematics</i>, Springer Nature, 2020, doi:<a href=\"https://doi.org/10.1007/s40879-020-00426-9\">10.1007/s40879-020-00426-9</a>.","short":"A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics (2020).","ista":"Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited. European Journal of Mathematics.","apa":"Akopyan, A., Schwartz, R., &#38; Tabachnikov, S. (2020). Billiards in ellipses revisited. <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-020-00426-9\">https://doi.org/10.1007/s40879-020-00426-9</a>","ama":"Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. <i>European Journal of Mathematics</i>. 2020. doi:<a href=\"https://doi.org/10.1007/s40879-020-00426-9\">10.1007/s40879-020-00426-9</a>","ieee":"A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,” <i>European Journal of Mathematics</i>. Springer Nature, 2020.","chicago":"Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in Ellipses Revisited.” <i>European Journal of Mathematics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s40879-020-00426-9\">https://doi.org/10.1007/s40879-020-00426-9</a>."},"abstract":[{"text":"We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.","lang":"eng"}],"arxiv":1,"doi":"10.1007/s40879-020-00426-9","day":"09","acknowledgement":" This paper would not be written if not for Dan Reznik’s curiosity and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller for interesting discussions. It is a pleasure to thank the Mathematical Institute of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality. AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR 191.","author":[{"first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schwartz","first_name":"Richard","full_name":"Schwartz, Richard"},{"full_name":"Tabachnikov, Serge","last_name":"Tabachnikov","first_name":"Serge"}],"_id":"8538","scopus_import":"1","title":"Billiards in ellipses revisited","publication_status":"published","article_processing_charge":"No","date_created":"2020-09-20T22:01:38Z","department":[{"_id":"HeEd"}],"quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Springer Nature","date_published":"2020-09-09T00:00:00Z","type":"journal_article","oa":1,"publication_identifier":{"eissn":["2199-6768"],"issn":["2199-675X"]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2001.02934"}],"publication":"European Journal of Mathematics","month":"09","oa_version":"Preprint","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"language":[{"iso":"eng"}]},{"author":[{"full_name":"Graff, Grzegorz","first_name":"Grzegorz","last_name":"Graff"},{"last_name":"Graff","first_name":"Beata","full_name":"Graff, Beata"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","last_name":"Jablonski","first_name":"Grzegorz","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866"},{"last_name":"Narkiewicz","first_name":"Krzysztof","full_name":"Narkiewicz, Krzysztof"}],"publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ","_id":"8580","scopus_import":"1","title":"The application of persistent homology in the analysis of heart rate variability","month":"08","article_number":"9158054","publication_status":"published","oa_version":"None","date_created":"2020-09-28T08:59:27Z","department":[{"_id":"HeEd"}],"article_processing_charge":"No","language":[{"iso":"eng"}],"quality_controlled":"1","conference":{"name":"ESGCO: European Study Group on Cardiovascular Oscillations","start_date":"2020-07-15","location":"Pisa, Italy","end_date":"2020-07-15"},"publisher":"IEEE","date_published":"2020-08-01T00:00:00Z","isi":1,"type":"conference","external_id":{"isi":["000621172600045"]},"date_updated":"2023-08-22T09:33:34Z","year":"2020","citation":{"ama":"Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent homology in the analysis of heart rate variability. In: <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>. IEEE; 2020. doi:<a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">10.1109/ESGCO49734.2020.9158054</a>","apa":"Graff, G., Graff, B., Jablonski, G., &#38; Narkiewicz, K. (2020). The application of persistent homology in the analysis of heart rate variability. In <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>. Pisa, Italy: IEEE. <a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">https://doi.org/10.1109/ESGCO49734.2020.9158054</a>","ieee":"G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of persistent homology in the analysis of heart rate variability,” in <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>, Pisa, Italy, 2020.","chicago":"Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” In <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>. IEEE, 2020. <a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">https://doi.org/10.1109/ESGCO49734.2020.9158054</a>.","mla":"Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>, 9158054, IEEE, 2020, doi:<a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">10.1109/ESGCO49734.2020.9158054</a>.","short":"G. Graff, B. Graff, G. Jablonski, K. Narkiewicz, in:, 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , IEEE, 2020.","ista":"Graff G, Graff B, Jablonski G, Narkiewicz K. 2020. The application of persistent homology in the analysis of heart rate variability. 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . ESGCO: European Study Group on Cardiovascular Oscillations, 9158054."},"abstract":[{"lang":"eng","text":"We evaluate the usefulness of persistent homology in the analysis of heart rate variability. In our approach we extract several topological descriptors characterising datasets of RR-intervals, which are later used in classical machine learning algorithms. By this method we are able to differentiate the group of patients with the history of transient ischemic attack and the group of hypertensive patients."}],"doi":"10.1109/ESGCO49734.2020.9158054","publication_identifier":{"isbn":["9781728157511"]},"day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public"},{"_id":"8703","scopus_import":"1","author":[{"first_name":"Georg F","last_name":"Osang","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Rouxel-Labbé, Mael","last_name":"Rouxel-Labbé","first_name":"Mael"},{"full_name":"Teillaud, Monique","first_name":"Monique","last_name":"Teillaud"}],"publication_status":"published","date_created":"2020-10-25T23:01:18Z","department":[{"_id":"HeEd"}],"article_processing_charge":"No","alternative_title":["LIPIcs"],"title":"Generalizing CGAL periodic Delaunay triangulations","intvolume":"       173","ec_funded":1,"quality_controlled":"1","file_date_updated":"2020-10-27T14:31:52Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","date_updated":"2023-09-07T13:29:00Z","citation":{"apa":"Osang, G. F., Rouxel-Labbé, M., &#38; Teillaud, M. (2020). Generalizing CGAL periodic Delaunay triangulations. In <i>28th Annual European Symposium on Algorithms</i> (Vol. 173). Virtual, Online; Pisa, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2020.75\">https://doi.org/10.4230/LIPIcs.ESA.2020.75</a>","ama":"Osang GF, Rouxel-Labbé M, Teillaud M. Generalizing CGAL periodic Delaunay triangulations. In: <i>28th Annual European Symposium on Algorithms</i>. Vol 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2020.75\">10.4230/LIPIcs.ESA.2020.75</a>","chicago":"Osang, Georg F, Mael Rouxel-Labbé, and Monique Teillaud. “Generalizing CGAL Periodic Delaunay Triangulations.” In <i>28th Annual European Symposium on Algorithms</i>, Vol. 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2020.75\">https://doi.org/10.4230/LIPIcs.ESA.2020.75</a>.","ieee":"G. F. Osang, M. Rouxel-Labbé, and M. Teillaud, “Generalizing CGAL periodic Delaunay triangulations,” in <i>28th Annual European Symposium on Algorithms</i>, Virtual, Online; Pisa, Italy, 2020, vol. 173.","short":"G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","mla":"Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.” <i>28th Annual European Symposium on Algorithms</i>, vol. 173, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2020.75\">10.4230/LIPIcs.ESA.2020.75</a>.","ista":"Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay triangulations. 28th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 173, 75."},"year":"2020","doi":"10.4230/LIPIcs.ESA.2020.75","day":"26","abstract":[{"text":"Even though Delaunay originally introduced his famous triangulations in the case of infinite point sets with translational periodicity, a software that computes such triangulations in the general case is not yet available, to the best of our knowledge. Combining and generalizing previous work, we present a practical algorithm for computing such triangulations. The algorithm has been implemented and experiments show that its performance is as good as the one of the CGAL package, which is restricted to cubic periodicity. ","lang":"eng"}],"volume":173,"ddc":["000"],"publication":"28th Annual European Symposium on Algorithms","has_accepted_license":"1","oa_version":"Published Version","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"month":"08","article_number":"75","language":[{"iso":"eng"}],"conference":{"end_date":"2020-09-09","location":"Virtual, Online; Pisa, Italy","start_date":"2020-09-07","name":"ESA: Annual European Symposium on Algorithms"},"tmp":{"name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","image":"/images/cc_by.png","short":"CC BY (3.0)","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode"},"date_published":"2020-08-26T00:00:00Z","type":"conference","publication_identifier":{"isbn":["9783959771627"],"issn":["18688969"]},"oa":1,"file":[{"file_id":"8712","creator":"cziletti","access_level":"open_access","relation":"main_file","success":1,"date_updated":"2020-10-27T14:31:52Z","content_type":"application/pdf","file_name":"2020_LIPIcs_Osang.pdf","date_created":"2020-10-27T14:31:52Z","file_size":733291,"checksum":"fe0f7c49a99ed870c671b911e10d5496"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"9056","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07350"}],"oa":1,"publication_identifier":{"isbn":["9783030360191"],"issn":["00758434"],"eissn":["16179692"],"eisbn":["9783030360207"]},"date_published":"2020-06-21T00:00:00Z","type":"book_chapter","language":[{"iso":"eng"}],"month":"06","oa_version":"Preprint","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"publication":"Geometric Aspects of Functional Analysis","volume":2256,"abstract":[{"lang":"eng","text":"We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean  space,  motivated  by  the  famous  theorem  of  Gromov  about  the  waist  of  radially symmetric Gaussian measures.  In particular, it turns our possible to extend Gromov’s original result  to  the  case  of  not  necessarily  radially  symmetric  Gaussian  measure.   We  also  provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe  use  a  simpler  form  of  Gromov’s  pancake  argument  to  produce  some  estimates  of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."}],"arxiv":1,"doi":"10.1007/978-3-030-36020-7_1","day":"21","isi":1,"external_id":{"arxiv":["1808.07350"],"isi":["000557689300003"]},"date_updated":"2023-08-17T13:48:31Z","citation":{"ama":"Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Klartag B, Milman E, eds. <i>Geometric Aspects of Functional Analysis</i>. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>","apa":"Akopyan, A., &#38; Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag &#38; E. Milman (Eds.), <i>Geometric Aspects of Functional Analysis</i> (Vol. 2256, pp. 1–27). Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">https://doi.org/10.1007/978-3-030-36020-7_1</a>","chicago":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In <i>Geometric Aspects of Functional Analysis</i>, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">https://doi.org/10.1007/978-3-030-36020-7_1</a>.","ieee":"A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in <i>Geometric Aspects of Functional Analysis</i>, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” <i>Geometric Aspects of Functional Analysis</i>, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>.","ista":"Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis. vol. 2256, 1–27."},"year":"2020","publisher":"Springer Nature","editor":[{"full_name":"Klartag, Bo'az","first_name":"Bo'az","last_name":"Klartag"},{"full_name":"Milman, Emanuel","last_name":"Milman","first_name":"Emanuel"}],"page":"1-27","series_title":"LNM","ec_funded":1,"quality_controlled":"1","title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","intvolume":"      2256","publication_status":"published","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"date_created":"2018-12-11T11:44:29Z","article_processing_charge":"No","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"_id":"74","scopus_import":"1"},{"supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"}],"oa":1,"publication_identifier":{"issn":["2663-337X"]},"date_published":"2020-02-10T00:00:00Z","type":"dissertation","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","related_material":{"record":[{"relation":"part_of_dissertation","id":"6608","status":"public"}]},"file":[{"date_created":"2020-02-06T14:43:54Z","checksum":"1df9f8c530b443c0e63a3f2e4fde412e","file_size":76195184,"date_updated":"2020-07-14T12:47:58Z","file_name":"thesis_ist-final_noack.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"7461","creator":"koelsboe"},{"description":"latex source files, figures","relation":"source_file","access_level":"closed","creator":"koelsboe","file_id":"7462","checksum":"7a52383c812b0be64d3826546509e5a4","file_size":122103715,"date_created":"2020-02-06T14:52:45Z","file_name":"latex-files.zip","content_type":"application/x-zip-compressed","date_updated":"2020-07-14T12:47:58Z"}],"month":"02","oa_version":"Published Version","has_accepted_license":"1","language":[{"iso":"eng"}],"keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"],"abstract":[{"text":"Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications.\r\n\r\nFor the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries.","lang":"eng"}],"degree_awarded":"PhD","doi":"10.15479/AT:ISTA:7460","day":"10","date_updated":"2023-09-07T13:15:30Z","year":"2020","citation":{"ieee":"K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science and Technology Austria, 2020.","chicago":"Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute of Science and Technology Austria, 2020. <a href=\"https://doi.org/10.15479/AT:ISTA:7460\">https://doi.org/10.15479/AT:ISTA:7460</a>.","ama":"Ölsböck K. The hole system of triangulated shapes. 2020. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7460\">10.15479/AT:ISTA:7460</a>","apa":"Ölsböck, K. (2020). <i>The hole system of triangulated shapes</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:7460\">https://doi.org/10.15479/AT:ISTA:7460</a>","ista":"Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria.","mla":"Ölsböck, Katharina. <i>The Hole System of Triangulated Shapes</i>. Institute of Science and Technology Austria, 2020, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7460\">10.15479/AT:ISTA:7460</a>.","short":"K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science and Technology Austria, 2020."},"ddc":["514"],"alternative_title":["ISTA Thesis"],"title":"The hole system of triangulated shapes","publication_status":"published","date_created":"2020-02-06T14:56:53Z","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"article_processing_charge":"No","author":[{"full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297","last_name":"Ölsböck","first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87"}],"_id":"7460","publisher":"Institute of Science and Technology Austria","file_date_updated":"2020-07-14T12:47:58Z","page":"155"},{"intvolume":"        64","title":"Weighted Poisson–Delaunay mosaics","date_created":"2020-03-01T23:00:39Z","article_processing_charge":"No","department":[{"_id":"HeEd"}],"publication_status":"published","issue":"4","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","last_name":"Nikitenko","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton"}],"scopus_import":"1","_id":"7554","article_type":"original","publisher":"SIAM","ec_funded":1,"quality_controlled":"1","page":"595-614","abstract":[{"text":"Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the smallest empty circumscribed sphere whose center lies in the $k$-plane gives a generalized discrete Morse function. Assuming the Voronoi tessellation is generated by a Poisson point process in ${R}^n$, we study the expected number of simplices in the $k$-dimensional weighted Delaunay mosaic as well as the expected number of intervals of the Morse function, both as functions of a radius threshold. As a by-product, we obtain a new proof for the expected number of connected components (clumps) in a line section of a circular Boolean model in ${R}^n$.","lang":"eng"}],"day":"13","arxiv":1,"doi":"10.1137/S0040585X97T989726","external_id":{"isi":["000551393100007"],"arxiv":["1705.08735"]},"isi":1,"citation":{"ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” <i>Theory of Probability and Its Applications</i>, vol. 64, no. 4, SIAM, 2020, pp. 595–614, doi:<a href=\"https://doi.org/10.1137/S0040585X97T989726\">10.1137/S0040585X97T989726</a>.","short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” <i>Theory of Probability and Its Applications</i>. SIAM, 2020. <a href=\"https://doi.org/10.1137/S0040585X97T989726\">https://doi.org/10.1137/S0040585X97T989726</a>.","ieee":"H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” <i>Theory of Probability and its Applications</i>, vol. 64, no. 4. SIAM, pp. 595–614, 2020.","apa":"Edelsbrunner, H., &#38; Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics. <i>Theory of Probability and Its Applications</i>. SIAM. <a href=\"https://doi.org/10.1137/S0040585X97T989726\">https://doi.org/10.1137/S0040585X97T989726</a>","ama":"Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. <i>Theory of Probability and its Applications</i>. 2020;64(4):595-614. doi:<a href=\"https://doi.org/10.1137/S0040585X97T989726\">10.1137/S0040585X97T989726</a>"},"year":"2020","date_updated":"2023-08-18T06:45:48Z","volume":64,"month":"02","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","publication":"Theory of Probability and its Applications","language":[{"iso":"eng"}],"oa":1,"publication_identifier":{"issn":["0040585X"],"eissn":["10957219"]},"type":"journal_article","date_published":"2020-02-13T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.08735"}]},{"publication_status":"published","article_processing_charge":"Yes (via OA deal)","date_created":"2020-03-05T13:30:18Z","department":[{"_id":"HeEd"}],"title":"Coxeter triangulations have good quality","intvolume":"        14","_id":"7567","scopus_import":"1","author":[{"full_name":"Choudhary, Aruni","first_name":"Aruni","last_name":"Choudhary"},{"full_name":"Kachanovich, Siargey","first_name":"Siargey","last_name":"Kachanovich"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"publisher":"Springer Nature","article_type":"original","page":"141-176","ec_funded":1,"quality_controlled":"1","file_date_updated":"2020-11-20T10:18:02Z","doi":"10.1007/s11786-020-00461-5","day":"01","abstract":[{"lang":"eng","text":"Coxeter triangulations are triangulations of Euclidean space based on a single simplex. By this we mean that given an individual simplex we can recover the entire triangulation of Euclidean space by inductively reflecting in the faces of the simplex. In this paper we establish that the quality of the simplices in all Coxeter triangulations is O(1/d−−√) of the quality of regular simplex. We further investigate the Delaunay property for these triangulations. Moreover, we consider an extension of the Delaunay property, namely protection, which is a measure of non-degeneracy of a Delaunay triangulation. In particular, one family of Coxeter triangulations achieves the protection O(1/d2). We conjecture that both bounds are optimal for triangulations in Euclidean space."}],"date_updated":"2021-01-12T08:14:13Z","year":"2020","citation":{"short":"A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science 14 (2020) 141–176.","mla":"Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” <i>Mathematics in Computer Science</i>, vol. 14, Springer Nature, 2020, pp. 141–76, doi:<a href=\"https://doi.org/10.1007/s11786-020-00461-5\">10.1007/s11786-020-00461-5</a>.","ista":"Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have good quality. Mathematics in Computer Science. 14, 141–176.","apa":"Choudhary, A., Kachanovich, S., &#38; Wintraecken, M. (2020). Coxeter triangulations have good quality. <i>Mathematics in Computer Science</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11786-020-00461-5\">https://doi.org/10.1007/s11786-020-00461-5</a>","ama":"Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good quality. <i>Mathematics in Computer Science</i>. 2020;14:141-176. doi:<a href=\"https://doi.org/10.1007/s11786-020-00461-5\">10.1007/s11786-020-00461-5</a>","chicago":"Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter Triangulations Have Good Quality.” <i>Mathematics in Computer Science</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11786-020-00461-5\">https://doi.org/10.1007/s11786-020-00461-5</a>.","ieee":"A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations have good quality,” <i>Mathematics in Computer Science</i>, vol. 14. Springer Nature, pp. 141–176, 2020."},"volume":14,"ddc":["510"],"oa_version":"Published Version","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"month":"03","publication":"Mathematics in Computer Science","has_accepted_license":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1661-8270"],"eissn":["1661-8289"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2020-03-01T00:00:00Z","type":"journal_article","file":[{"date_created":"2020-11-20T10:18:02Z","checksum":"1d145f3ab50ccee735983cb89236e609","file_size":872275,"date_updated":"2020-11-20T10:18:02Z","file_name":"2020_MathCompScie_Choudhary.pdf","content_type":"application/pdf","success":1,"relation":"main_file","access_level":"open_access","file_id":"8783","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public"},{"date_published":"2020-03-20T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"file_id":"8786","creator":"dernst","success":1,"relation":"main_file","access_level":"open_access","date_updated":"2020-11-20T13:22:21Z","file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf","content_type":"application/pdf","date_created":"2020-11-20T13:22:21Z","checksum":"f8cc96e497f00c38340b5dafe0cb91d7","file_size":701673}],"publication":"Discrete and Computational Geometry","has_accepted_license":"1","month":"03","oa_version":"Published Version","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"language":[{"iso":"eng"}],"isi":1,"external_id":{"isi":["000520918800001"]},"date_updated":"2023-08-21T06:13:48Z","citation":{"ista":"Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” <i>Discrete and Computational Geometry</i>, vol. 64, Springer Nature, 2020, pp. 759–75, doi:<a href=\"https://doi.org/10.1007/s00454-020-00188-x\">10.1007/s00454-020-00188-x</a>.","short":"H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00188-x\">https://doi.org/10.1007/s00454-020-00188-x</a>.","ieee":"H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” <i>Discrete and Computational Geometry</i>, vol. 64. Springer Nature, pp. 759–775, 2020.","ama":"Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. <i>Discrete and Computational Geometry</i>. 2020;64:759-775. doi:<a href=\"https://doi.org/10.1007/s00454-020-00188-x\">10.1007/s00454-020-00188-x</a>","apa":"Edelsbrunner, H., &#38; Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00188-x\">https://doi.org/10.1007/s00454-020-00188-x</a>"},"year":"2020","abstract":[{"lang":"eng","text":"Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups."}],"doi":"10.1007/s00454-020-00188-x","day":"20","ddc":["510"],"acknowledgement":"This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF).","volume":64,"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297","last_name":"Ölsböck","first_name":"Katharina"}],"_id":"7666","scopus_import":"1","title":"Tri-partitions and bases of an ordered complex","intvolume":"        64","publication_status":"published","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"HeEd"}],"date_created":"2020-04-19T22:00:56Z","file_date_updated":"2020-11-20T13:22:21Z","page":"759-775","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Springer Nature"},{"publication_status":"published","department":[{"_id":"HeEd"}],"date_created":"2024-03-04T10:47:49Z","article_processing_charge":"Yes (via OA deal)","title":"Čech-Delaunay gradient flow and homology inference for self-maps","intvolume":"         4","_id":"15064","scopus_import":"1","author":[{"full_name":"Bauer, U.","last_name":"Bauer","first_name":"U."},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","last_name":"Jablonski","first_name":"Grzegorz","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866"},{"full_name":"Mrozek, M.","first_name":"M.","last_name":"Mrozek"}],"issue":"4","publisher":"Springer Nature","article_type":"original","page":"455-480","quality_controlled":"1","file_date_updated":"2024-03-04T10:52:42Z","doi":"10.1007/s41468-020-00058-8","day":"01","abstract":[{"lang":"eng","text":"We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems."}],"date_updated":"2024-03-04T10:54:04Z","citation":{"short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480.","mla":"Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” <i>Journal of Applied and Computational Topology</i>, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:<a href=\"https://doi.org/10.1007/s41468-020-00058-8\">10.1007/s41468-020-00058-8</a>.","ista":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 4(4), 455–480.","ama":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. <i>Journal of Applied and Computational Topology</i>. 2020;4(4):455-480. doi:<a href=\"https://doi.org/10.1007/s41468-020-00058-8\">10.1007/s41468-020-00058-8</a>","apa":"Bauer, U., Edelsbrunner, H., Jablonski, G., &#38; Mrozek, M. (2020). Čech-Delaunay gradient flow and homology inference for self-maps. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-020-00058-8\">https://doi.org/10.1007/s41468-020-00058-8</a>","ieee":"U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient flow and homology inference for self-maps,” <i>Journal of Applied and Computational Topology</i>, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.","chicago":"Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s41468-020-00058-8\">https://doi.org/10.1007/s41468-020-00058-8</a>."},"year":"2020","volume":4,"acknowledgement":"This research has been supported by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding provided by Projekt DEAL.","ddc":["500"],"oa_version":"Published Version","month":"12","publication":"Journal of Applied and Computational Topology","has_accepted_license":"1","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2020-12-01T00:00:00Z","type":"journal_article","file":[{"file_size":851190,"checksum":"eed1168b6e66cd55272c19bb7fca8a1c","date_created":"2024-03-04T10:52:42Z","file_name":"2020_JourApplCompTopology_Bauer.pdf","content_type":"application/pdf","date_updated":"2024-03-04T10:52:42Z","access_level":"open_access","relation":"main_file","success":1,"creator":"dernst","file_id":"15065"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"ddc":["510"],"volume":8,"acknowledgement":"The authors of this paper thank Roland Roth for suggesting the analysis of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","abstract":[{"lang":"eng","text":"The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy."}],"doi":"10.1515/cmb-2020-0101","arxiv":1,"day":"21","external_id":{"arxiv":["1908.06777"]},"date_updated":"2023-10-17T12:35:10Z","citation":{"ieee":"A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative of a space-filling diagram,” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/cmb-2020-0101\">https://doi.org/10.1515/cmb-2020-0101</a>.","ama":"Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. 2020;8(1):74-88. doi:<a href=\"https://doi.org/10.1515/cmb-2020-0101\">10.1515/cmb-2020-0101</a>","apa":"Akopyan, A., &#38; Edelsbrunner, H. (2020). The weighted Gaussian curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. De Gruyter. <a href=\"https://doi.org/10.1515/cmb-2020-0101\">https://doi.org/10.1515/cmb-2020-0101</a>","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:<a href=\"https://doi.org/10.1515/cmb-2020-0101\">10.1515/cmb-2020-0101</a>.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88."},"year":"2020","article_type":"original","publisher":"De Gruyter","file_date_updated":"2021-02-19T13:33:19Z","page":"74-88","quality_controlled":"1","ec_funded":1,"title":"The weighted Gaussian curvature derivative of a space-filling diagram","intvolume":"         8","publication_status":"published","article_processing_charge":"No","date_created":"2021-02-17T15:12:44Z","department":[{"_id":"HeEd"}],"author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"issue":"1","_id":"9156","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"file_name":"2020_CompMathBiophysics_Akopyan.pdf","content_type":"application/pdf","date_updated":"2021-02-19T13:33:19Z","file_size":707452,"checksum":"ca43a7440834eab6bbea29c59b56ef3a","date_created":"2021-02-19T13:33:19Z","creator":"dernst","file_id":"9170","access_level":"open_access","success":1,"relation":"main_file"}],"oa":1,"publication_identifier":{"issn":["2544-7297"]},"date_published":"2020-07-21T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"language":[{"iso":"eng"}],"month":"07","oa_version":"Published Version","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","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"}],"publication":"Computational and Mathematical Biophysics","has_accepted_license":"1"},{"publication_identifier":{"issn":["2544-7297"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2020-06-20T00:00:00Z","file":[{"creator":"dernst","file_id":"9171","relation":"main_file","success":1,"access_level":"open_access","file_name":"2020_CompMathBiophysics_Akopyan2.pdf","content_type":"application/pdf","date_updated":"2021-02-19T13:56:24Z","checksum":"cea41de9937d07a3b927d71ee8b4e432","file_size":562359,"date_created":"2021-02-19T13:56:24Z"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"oa_version":"Published Version","month":"06","has_accepted_license":"1","publication":"Computational and Mathematical Biophysics","language":[{"iso":"eng"}],"day":"20","doi":"10.1515/cmb-2020-0100","abstract":[{"text":"Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy.","lang":"eng"}],"citation":{"chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/cmb-2020-0100\">https://doi.org/10.1515/cmb-2020-0100</a>.","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of a space-filling diagram,” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1. De Gruyter, pp. 51–67, 2020.","ama":"Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. 2020;8(1):51-67. doi:<a href=\"https://doi.org/10.1515/cmb-2020-0100\">10.1515/cmb-2020-0100</a>","apa":"Akopyan, A., &#38; Edelsbrunner, H. (2020). The weighted mean curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. De Gruyter. <a href=\"https://doi.org/10.1515/cmb-2020-0100\">https://doi.org/10.1515/cmb-2020-0100</a>","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:<a href=\"https://doi.org/10.1515/cmb-2020-0100\">10.1515/cmb-2020-0100</a>.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67."},"year":"2020","date_updated":"2023-10-17T12:34:51Z","acknowledgement":"The authors of this paper thank Roland Roth for suggesting the analysis of the weighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations and for his continued encouragement. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","volume":8,"ddc":["510"],"department":[{"_id":"HeEd"}],"article_processing_charge":"No","date_created":"2021-02-17T15:13:01Z","publication_status":"published","intvolume":"         8","title":"The weighted mean curvature derivative of a space-filling diagram","_id":"9157","issue":"1","author":[{"last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"publisher":"De Gruyter","article_type":"original","ec_funded":1,"quality_controlled":"1","page":"51-67","file_date_updated":"2021-02-19T13:56:24Z"},{"title":"Digital objects in rhombic dodecahedron grid","intvolume":"         4","publication_status":"published","date_created":"2021-03-16T08:55:19Z","department":[{"_id":"HeEd"}],"article_processing_charge":"No","author":[{"first_name":"Ranita","last_name":"Biswas","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Largeteau-Skapin, Gaëlle","first_name":"Gaëlle","last_name":"Largeteau-Skapin"},{"first_name":"Rita","last_name":"Zrour","full_name":"Zrour, Rita"},{"first_name":"Eric","last_name":"Andres","full_name":"Andres, Eric"}],"issue":"1","_id":"9249","article_type":"original","publisher":"De Gruyter","file_date_updated":"2021-03-22T08:56:37Z","page":"143-158","ec_funded":1,"quality_controlled":"1","abstract":[{"lang":"eng","text":"Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system."}],"doi":"10.1515/mathm-2020-0106","day":"17","date_updated":"2021-03-22T09:01:50Z","citation":{"mla":"Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” <i>Mathematical Morphology - Theory and Applications</i>, vol. 4, no. 1, De Gruyter, 2020, pp. 143–58, doi:<a href=\"https://doi.org/10.1515/mathm-2020-0106\">10.1515/mathm-2020-0106</a>.","short":"R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.","ista":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 4(1), 143–158.","apa":"Biswas, R., Largeteau-Skapin, G., Zrour, R., &#38; Andres, E. (2020). Digital objects in rhombic dodecahedron grid. <i>Mathematical Morphology - Theory and Applications</i>. De Gruyter. <a href=\"https://doi.org/10.1515/mathm-2020-0106\">https://doi.org/10.1515/mathm-2020-0106</a>","ama":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic dodecahedron grid. <i>Mathematical Morphology - Theory and Applications</i>. 2020;4(1):143-158. doi:<a href=\"https://doi.org/10.1515/mathm-2020-0106\">10.1515/mathm-2020-0106</a>","ieee":"R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects in rhombic dodecahedron grid,” <i>Mathematical Morphology - Theory and Applications</i>, vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.","chicago":"Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital Objects in Rhombic Dodecahedron Grid.” <i>Mathematical Morphology - Theory and Applications</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/mathm-2020-0106\">https://doi.org/10.1515/mathm-2020-0106</a>."},"year":"2020","ddc":["510"],"acknowledgement":"This work has been partially supported by the European Research Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. ","volume":4,"month":"11","oa_version":"Published Version","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"publication":"Mathematical Morphology - Theory and Applications","has_accepted_license":"1","language":[{"iso":"eng"}],"oa":1,"publication_identifier":{"issn":["2353-3390"]},"date_published":"2020-11-17T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"creator":"dernst","file_id":"9272","access_level":"open_access","success":1,"relation":"main_file","file_name":"2020_MathMorpholTheoryAppl_Biswas.pdf","content_type":"application/pdf","date_updated":"2021-03-22T08:56:37Z","checksum":"4a1043fa0548a725d464017fe2483ce0","file_size":3668725,"date_created":"2021-03-22T08:56:37Z"}]},{"main_file_link":[{"url":"https://arxiv.org/abs/2006.14908","open_access":"1"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"conference","date_published":"2020-09-20T00:00:00Z","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783030687656"]},"oa":1,"language":[{"iso":"eng"}],"conference":{"location":"Virtual, Online","end_date":"2020-09-18","start_date":"2020-09-16","name":"GD: Graph Drawing and Network Visualization"},"publication":"28th International Symposium on Graph Drawing and Network Visualization","project":[{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize"}],"oa_version":"Preprint","month":"09","volume":12590,"acknowledgement":"Supported by the National Research, Development and Innovation Office, NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full version can be found at https://arxiv.org/abs/2006.14908.","citation":{"ama":"Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: <i>28th International Symposium on Graph Drawing and Network Visualization</i>. Vol 12590. LNCS. Springer Nature; 2020:359-371. doi:<a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">10.1007/978-3-030-68766-3_28</a>","apa":"Pach, J., Tardos, G., &#38; Tóth, G. (2020). Crossings between non-homotopic edges. In <i>28th International Symposium on Graph Drawing and Network Visualization</i> (Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">https://doi.org/10.1007/978-3-030-68766-3_28</a>","ieee":"J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,” in <i>28th International Symposium on Graph Drawing and Network Visualization</i>, Virtual, Online, 2020, vol. 12590, pp. 359–371.","chicago":"Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic Edges.” In <i>28th International Symposium on Graph Drawing and Network Visualization</i>, 12590:359–71. LNCS. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">https://doi.org/10.1007/978-3-030-68766-3_28</a>.","short":"J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 359–371.","mla":"Pach, János, et al. “Crossings between Non-Homotopic Edges.” <i>28th International Symposium on Graph Drawing and Network Visualization</i>, vol. 12590, Springer Nature, 2020, pp. 359–71, doi:<a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">10.1007/978-3-030-68766-3_28</a>.","ista":"Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network VisualizationLNCS vol. 12590, 359–371."},"year":"2020","date_updated":"2021-04-06T11:32:32Z","external_id":{"arxiv":["2006.14908"]},"day":"20","doi":"10.1007/978-3-030-68766-3_28","arxiv":1,"abstract":[{"text":"We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on   n>1  vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and   m>4n  edges is larger than   cm2n  for some constant   c>0 , and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and   m⟶∞ .","lang":"eng"}],"series_title":"LNCS","quality_controlled":"1","page":"359-371","publisher":"Springer Nature","scopus_import":"1","_id":"9299","author":[{"full_name":"Pach, János","last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"last_name":"Tardos","first_name":"Gábor","full_name":"Tardos, Gábor"},{"first_name":"Géza","last_name":"Tóth","full_name":"Tóth, Géza"}],"department":[{"_id":"HeEd"}],"date_created":"2021-03-28T22:01:44Z","article_processing_charge":"No","publication_status":"published","intvolume":"     12590","title":"Crossings between non-homotopic edges"}]