[{"oa_version":"Preprint","page":"888-917","publication_status":"published","intvolume":"        63","project":[{"call_identifier":"FWF","grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1803.06710"}],"external_id":{"isi":["000538229000001"],"arxiv":["1803.06710"]},"arxiv":1,"author":[{"full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","last_name":"Pach"},{"first_name":"Bruce","full_name":"Reed, Bruce","last_name":"Reed"},{"full_name":"Yuditsky, Yelena","first_name":"Yelena","last_name":"Yuditsky"}],"issue":"4","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"06","year":"2020","quality_controlled":"1","isi":1,"article_type":"original","department":[{"_id":"HeEd"}],"article_processing_charge":"No","status":"public","oa":1,"date_created":"2020-06-14T22:00:51Z","_id":"7962","day":"05","publisher":"Springer Nature","date_updated":"2025-04-15T07:16:56Z","abstract":[{"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.","lang":"eng"}],"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"volume":63,"language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00213-z","citation":{"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.","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.","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>.","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>."},"title":"Almost all string graphs are intersection graphs of plane convex sets","publication":"Discrete and Computational Geometry","date_published":"2020-06-05T00:00:00Z","type":"journal_article","scopus_import":"1"},{"language":[{"iso":"eng"}],"volume":15,"file_date_updated":"2020-10-08T08:56:14Z","doi":"10.1007/978-3-030-43408-3_8","citation":{"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>","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.","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>.","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>","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.","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>.","short":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218."},"abstract":[{"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.","lang":"eng"}],"date_updated":"2026-04-07T12:35:47Z","publication_identifier":{"issn":["2193-2808"],"isbn":["9783030434076"],"eissn":["2197-8549"]},"date_created":"2020-07-19T22:00:59Z","oa":1,"publisher":"Springer Nature","day":"22","_id":"8135","status":"public","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).","article_processing_charge":"No","type":"conference","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19630"}]},"scopus_import":"1","publication":"Topological Data Analysis","ec_funded":1,"date_published":"2020-06-22T00:00:00Z","has_accepted_license":"1","title":"Radius functions on Poisson–Delaunay mosaics and related complexes experimentally","ddc":["510"],"external_id":{"isi":["001321861000008"]},"author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton","last_name":"Nikitenko","orcid":"0000-0002-0659-3201"},{"first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","full_name":"Ölsböck, Katharina","last_name":"Ölsböck","orcid":"0000-0002-4672-8297"},{"id":"331776E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","full_name":"Synak, Peter","last_name":"Synak"}],"intvolume":"        15","project":[{"call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"grant_number":"638176","call_identifier":"H2020","_id":"2533E772-B435-11E9-9278-68D0E5697425","name":"Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales"},{"call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"page":"181-218","publication_status":"published","file":[{"date_created":"2020-10-08T08:56:14Z","checksum":"7b5e0de10675d787a2ddb2091370b8d8","file_name":"2020-B-01-PoissonExperimentalSurvey.pdf","file_size":2207071,"relation":"main_file","success":1,"creator":"dernst","access_level":"open_access","file_id":"8628","content_type":"application/pdf","date_updated":"2020-10-08T08:56:14Z"}],"oa_version":"Submitted Version","department":[{"_id":"HeEd"}],"alternative_title":["Abel Symposia"],"isi":1,"year":"2020","quality_controlled":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"06"},{"date_created":"2020-07-24T07:09:18Z","oa":1,"corr_author":"1","_id":"8163","day":"24","publisher":"Akadémiai Kiadó","article_processing_charge":"No","status":"public","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.","volume":57,"language":[{"iso":"eng"}],"doi":"10.1556/012.2020.57.2.1454","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>.","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.","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>","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.","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>.","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>"},"file_date_updated":"2020-07-24T07:09:06Z","date_updated":"2025-04-15T07:16:57Z","abstract":[{"lang":"eng","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."}],"publication_identifier":{"issn":["0081-6906"],"eissn":["1588-2896"]},"has_accepted_license":"1","title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","ddc":["510"],"type":"journal_article","scopus_import":"1","ec_funded":1,"publication":"Studia Scientiarum Mathematicarum Hungarica","date_published":"2020-07-24T00:00:00Z","page":"193-199","publication_status":"published","file":[{"content_type":"application/pdf","date_updated":"2020-07-24T07:09:06Z","relation":"main_file","file_size":1476072,"file_id":"8164","access_level":"open_access","creator":"mwintrae","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","date_created":"2020-07-24T07:09:06Z"}],"oa_version":"Published Version","external_id":{"isi":["000570978400005"]},"author":[{"last_name":"Vegter","first_name":"Gert","full_name":"Vegter, Gert"},{"orcid":"0000-0002-7472-2220","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"intvolume":"        57","project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF"}],"year":"2020","quality_controlled":"1","issue":"2","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"07","department":[{"_id":"HeEd"}],"isi":1,"tmp":{"short":"CC BY-NC (4.0)","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","image":"/images/cc_by_nc.png","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"},"article_type":"original"},{"oa_version":"None","publication_status":"published","page":"571-574","intvolume":"        64","author":[{"last_name":"Pach","full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"}],"external_id":{"isi":["000561483500001"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-020-00237-5"}],"month":"10","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2020","article_type":"letter_note","isi":1,"department":[{"_id":"HeEd"}],"status":"public","article_processing_charge":"No","day":"01","publisher":"Springer Nature","_id":"8323","corr_author":"1","date_created":"2020-08-30T22:01:12Z","oa":1,"publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"date_updated":"2024-10-09T20:59:55Z","citation":{"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>.","ieee":"J. Pach, “A farewell to Ricky Pollack,” <i>Discrete and Computational Geometry</i>, vol. 64. Springer Nature, pp. 571–574, 2020.","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>.","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>","ista":"Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574."},"doi":"10.1007/s00454-020-00237-5","language":[{"iso":"eng"}],"volume":64,"title":"A farewell to Ricky Pollack","date_published":"2020-10-01T00:00:00Z","publication":"Discrete and Computational Geometry","scopus_import":"1","type":"journal_article"},{"oa_version":"None","article_processing_charge":"No","status":"public","_id":"8580","day":"01","publication_status":"published","publisher":"IEEE","date_created":"2020-09-28T08:59:27Z","publication_identifier":{"isbn":["9781728157511"]},"date_updated":"2023-08-22T09:33:34Z","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","citation":{"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.","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>.","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.","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.","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>","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>."},"author":[{"full_name":"Graff, Grzegorz","first_name":"Grzegorz","last_name":"Graff"},{"first_name":"Beata","full_name":"Graff, Beata","last_name":"Graff"},{"full_name":"Jablonski, Grzegorz","first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","last_name":"Jablonski"},{"first_name":"Krzysztof","full_name":"Narkiewicz, Krzysztof","last_name":"Narkiewicz"}],"language":[{"iso":"eng"}],"external_id":{"isi":["000621172600045"]},"month":"08","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","year":"2020","title":"The application of persistent homology in the analysis of heart rate variability","article_number":"9158054","date_published":"2020-08-01T00:00:00Z","isi":1,"conference":{"end_date":"2020-07-15","location":"Pisa, Italy","start_date":"2020-07-15","name":"ESGCO: European Study Group on Cardiovascular Oscillations"},"publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ","scopus_import":"1","department":[{"_id":"HeEd"}],"type":"conference"},{"citation":{"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>.","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.","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>","ista":"Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay triangulations. 28th Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms, LIPIcs, vol. 173, 75.","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>.","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>"},"file_date_updated":"2020-10-27T14:31:52Z","doi":"10.4230/LIPIcs.ESA.2020.75","volume":173,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959771627"]},"date_updated":"2026-04-08T07:01:29Z","abstract":[{"lang":"eng","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. "}],"_id":"8703","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","day":"26","oa":1,"license":"https://creativecommons.org/licenses/by/3.0/","date_created":"2020-10-25T23:01:18Z","corr_author":"1","article_processing_charge":"No","status":"public","scopus_import":"1","related_material":{"record":[{"relation":"dissertation_contains","id":"9056","status":"public"}]},"type":"conference","date_published":"2020-08-26T00:00:00Z","ec_funded":1,"publication":"28th Annual European Symposium on Algorithms","ddc":["000"],"has_accepted_license":"1","title":"Generalizing CGAL periodic Delaunay triangulations","author":[{"full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","last_name":"Osang","orcid":"0000-0002-8882-5116"},{"first_name":"Mael","full_name":"Rouxel-Labbé, Mael","last_name":"Rouxel-Labbé"},{"last_name":"Teillaud","first_name":"Monique","full_name":"Teillaud, Monique"}],"project":[{"call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"}],"intvolume":"       173","publication_status":"published","oa_version":"Published Version","file":[{"date_created":"2020-10-27T14:31:52Z","file_name":"2020_LIPIcs_Osang.pdf","checksum":"fe0f7c49a99ed870c671b911e10d5496","creator":"cziletti","access_level":"open_access","file_id":"8712","relation":"main_file","file_size":733291,"success":1,"date_updated":"2020-10-27T14:31:52Z","content_type":"application/pdf"}],"alternative_title":["LIPIcs"],"department":[{"_id":"HeEd"}],"article_number":"75","conference":{"location":"Virtual, Online; Pisa, Italy","start_date":"2020-09-07","name":"ESA: European Symposium on Algorithms","end_date":"2020-09-09"},"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","short":"CC BY (3.0)","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"quality_controlled":"1","year":"2020","month":"08","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"ddc":["510"],"title":"The weighted Gaussian curvature derivative of a space-filling diagram","has_accepted_license":"1","date_published":"2020-07-21T00:00:00Z","publication":"Computational and Mathematical Biophysics","ec_funded":1,"scopus_import":"1","type":"journal_article","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).","status":"public","article_processing_charge":"No","day":"21","publisher":"De Gruyter","_id":"9156","corr_author":"1","date_created":"2021-02-17T15:12:44Z","oa":1,"publication_identifier":{"issn":["2544-7297"]},"abstract":[{"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.","lang":"eng"}],"date_updated":"2025-04-14T07:48:34Z","doi":"10.1515/cmb-2020-0101","citation":{"short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 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>.","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.","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>","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>","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88."},"file_date_updated":"2021-02-19T13:33:19Z","language":[{"iso":"eng"}],"volume":8,"month":"07","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","quality_controlled":"1","year":"2020","article_type":"original","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"department":[{"_id":"HeEd"}],"oa_version":"Published Version","file":[{"date_updated":"2021-02-19T13:33:19Z","content_type":"application/pdf","date_created":"2021-02-19T13:33:19Z","checksum":"ca43a7440834eab6bbea29c59b56ef3a","file_name":"2020_CompMathBiophysics_Akopyan.pdf","creator":"dernst","access_level":"open_access","file_id":"9170","relation":"main_file","file_size":707452,"success":1}],"publication_status":"published","page":"74-88","project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"intvolume":"         8","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"arxiv":1,"external_id":{"arxiv":["1908.06777"]}},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","month":"06","year":"2020","quality_controlled":"1","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","department":[{"_id":"HeEd"}],"file":[{"content_type":"application/pdf","date_updated":"2021-02-19T13:56:24Z","date_created":"2021-02-19T13:56:24Z","file_name":"2020_CompMathBiophysics_Akopyan2.pdf","checksum":"cea41de9937d07a3b927d71ee8b4e432","file_size":562359,"relation":"main_file","success":1,"creator":"dernst","access_level":"open_access","file_id":"9171"}],"oa_version":"Published Version","page":"51-67","publication_status":"published","intvolume":"         8","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF"}],"author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"}],"title":"The weighted mean curvature derivative of a space-filling diagram","has_accepted_license":"1","ddc":["510"],"publication":"Computational and Mathematical Biophysics","ec_funded":1,"date_published":"2020-06-20T00:00:00Z","type":"journal_article","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).","status":"public","article_processing_charge":"No","corr_author":"1","date_created":"2021-02-17T15:13:01Z","oa":1,"publisher":"De Gruyter","day":"20","_id":"9157","abstract":[{"lang":"eng","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."}],"date_updated":"2025-04-14T07:48:35Z","publication_identifier":{"issn":["2544-7297"]},"language":[{"iso":"eng"}],"volume":8,"citation":{"short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 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>.","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.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","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>","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>."},"doi":"10.1515/cmb-2020-0100","file_date_updated":"2021-02-19T13:56:24Z"},{"ddc":["510"],"has_accepted_license":"1","title":"Digital objects in rhombic dodecahedron grid","type":"journal_article","date_published":"2020-11-17T00:00:00Z","publication":"Mathematical Morphology - Theory and Applications","ec_funded":1,"publisher":"De Gruyter","day":"17","_id":"9249","corr_author":"1","date_created":"2021-03-16T08:55:19Z","oa":1,"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. ","status":"public","article_processing_charge":"No","citation":{"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.","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>","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>","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>.","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.","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."},"doi":"10.1515/mathm-2020-0106","file_date_updated":"2021-03-22T08:56:37Z","language":[{"iso":"eng"}],"volume":4,"publication_identifier":{"issn":["2353-3390"]},"abstract":[{"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.","lang":"eng"}],"date_updated":"2025-04-14T07:48:35Z","quality_controlled":"1","year":"2020","month":"11","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","department":[{"_id":"HeEd"}],"article_type":"original","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publication_status":"published","page":"143-158","oa_version":"Published Version","file":[{"creator":"dernst","file_id":"9272","access_level":"open_access","relation":"main_file","file_size":3668725,"success":1,"date_created":"2021-03-22T08:56:37Z","file_name":"2020_MathMorpholTheoryAppl_Biswas.pdf","checksum":"4a1043fa0548a725d464017fe2483ce0","date_updated":"2021-03-22T08:56:37Z","content_type":"application/pdf"}],"author":[{"last_name":"Biswas","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"full_name":"Largeteau-Skapin, Gaëlle","first_name":"Gaëlle","last_name":"Largeteau-Skapin"},{"last_name":"Zrour","full_name":"Zrour, Rita","first_name":"Rita"},{"full_name":"Andres, Eric","first_name":"Eric","last_name":"Andres"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183"},{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"intvolume":"         4"},{"title":"Crossings between non-homotopic edges","type":"conference","scopus_import":"1","publication":"28th International Symposium on Graph Drawing and Network Visualization","date_published":"2020-09-20T00:00:00Z","oa":1,"date_created":"2021-03-28T22:01:44Z","_id":"9299","day":"20","publisher":"Springer Nature","article_processing_charge":"No","status":"public","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.","language":[{"iso":"eng"}],"volume":12590,"doi":"10.1007/978-3-030-68766-3_28","citation":{"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>","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>.","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>","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.","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.","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>.","short":"J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 359–371."},"date_updated":"2025-04-15T07:16:52Z","abstract":[{"lang":"eng","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⟶∞ ."}],"publication_identifier":{"issn":["0302-9743"],"isbn":["9783030687656"],"eissn":["1611-3349"]},"year":"2020","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"09","department":[{"_id":"HeEd"}],"conference":{"end_date":"2020-09-18","start_date":"2020-09-16","location":"Virtual, Online","name":"GD: Graph Drawing and Network Visualization"},"page":"359-371","series_title":"LNCS","publication_status":"published","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/2006.14908","open_access":"1"}],"external_id":{"arxiv":["2006.14908"]},"arxiv":1,"author":[{"last_name":"Pach","full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János"},{"full_name":"Tardos, Gábor","first_name":"Gábor","last_name":"Tardos"},{"last_name":"Tóth","first_name":"Géza","full_name":"Tóth, Géza"}],"intvolume":"     12590","project":[{"call_identifier":"FWF","grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"}]},{"project":[{"name":"Persistent Homology, Algorithms and Stochastic Geometry","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"}],"intvolume":"        11","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Virk, Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","last_name":"Virk"},{"orcid":"0009-0009-9111-8429","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","full_name":"Wagner, Hubert"}],"oa_version":"Published Version","file":[{"access_level":"open_access","file_id":"9882","creator":"asandaue","success":1,"relation":"main_file","file_size":1449234,"checksum":"f02d0b2b3838e7891a6c417fc34ffdcd","file_name":"2020_JournalOfComputationalGeometry_Edelsbrunner.pdf","date_created":"2021-08-11T11:55:11Z","date_updated":"2021-08-11T11:55:11Z","content_type":"application/pdf"}],"publication_status":"published","page":"162-182","article_type":"original","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","short":"CC BY (3.0)","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"department":[{"_id":"HeEd"}],"month":"12","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","issue":"2","quality_controlled":"1","year":"2020","publication_identifier":{"eissn":["1920-180X"]},"abstract":[{"text":"Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms.  Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context.","lang":"eng"}],"date_updated":"2026-04-02T14:35:31Z","citation":{"chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” <i>Journal of Computational Geometry</i>. Carleton University, 2020. <a href=\"https://doi.org/10.20382/jocg.v11i2a7\">https://doi.org/10.20382/jocg.v11i2a7</a>.","apa":"Edelsbrunner, H., Virk, Z., &#38; Wagner, H. (2020). Topological data analysis in information space. <i>Journal of Computational Geometry</i>. Carleton University. <a href=\"https://doi.org/10.20382/jocg.v11i2a7\">https://doi.org/10.20382/jocg.v11i2a7</a>","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. <i>Journal of Computational Geometry</i>. 2020;11(2):162-182. doi:<a href=\"https://doi.org/10.20382/jocg.v11i2a7\">10.20382/jocg.v11i2a7</a>","ista":"Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. Journal of Computational Geometry. 11(2), 162–182.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” <i>Journal of Computational Geometry</i>, vol. 11, no. 2. Carleton University, pp. 162–182, 2020.","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” <i>Journal of Computational Geometry</i>, vol. 11, no. 2, Carleton University, 2020, pp. 162–82, doi:<a href=\"https://doi.org/10.20382/jocg.v11i2a7\">10.20382/jocg.v11i2a7</a>.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11 (2020) 162–182."},"doi":"10.20382/jocg.v11i2a7","file_date_updated":"2021-08-11T11:55:11Z","language":[{"iso":"eng"}],"volume":11,"acknowledgement":"This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","status":"public","article_processing_charge":"Yes","publisher":"Carleton University","day":"14","_id":"9630","corr_author":"1","oa":1,"date_created":"2021-07-04T22:01:26Z","date_published":"2020-12-14T00:00:00Z","publication":"Journal of Computational Geometry","scopus_import":"1","type":"journal_article","ddc":["510","000"],"has_accepted_license":"1","title":"Topological data analysis in information space"},{"title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","scopus_import":"1","type":"book_chapter","date_published":"2020-06-21T00:00:00Z","publication":"Geometric Aspects of Functional Analysis","ec_funded":1,"publisher":"Springer Nature","day":"21","_id":"74","oa":1,"date_created":"2018-12-11T11:44:29Z","status":"public","article_processing_charge":"No","doi":"10.1007/978-3-030-36020-7_1","citation":{"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>.","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","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.","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."},"volume":2256,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1617-9692"],"eisbn":["9783030360207"],"isbn":["9783030360191"],"issn":["0075-8434"]},"abstract":[{"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.","lang":"eng"}],"date_updated":"2025-07-10T11:54:33Z","quality_controlled":"1","year":"2020","month":"06","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"isi":1,"publication_status":"published","series_title":"LNM","page":"1-27","oa_version":"Preprint","editor":[{"last_name":"Klartag","full_name":"Klartag, Bo'az","first_name":"Bo'az"},{"full_name":"Milman, Emanuel","first_name":"Emanuel","last_name":"Milman"}],"author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"arxiv":1,"external_id":{"isi":["000557689300003"],"arxiv":["1808.07350"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07350"}],"project":[{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"}],"intvolume":"      2256"},{"language":[{"iso":"eng"}],"doi":"10.15479/AT:ISTA:7460","citation":{"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>","ista":"Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria.","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>.","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>","ieee":"K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science and Technology Austria, 2020.","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."},"file_date_updated":"2020-07-14T12:47:58Z","abstract":[{"lang":"eng","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."}],"date_updated":"2026-04-08T07:23:21Z","publication_identifier":{"issn":["2663-337X"]},"corr_author":"1","oa":1,"date_created":"2020-02-06T14:56:53Z","publisher":"Institute of Science and Technology Austria","day":"10","_id":"7460","status":"public","article_processing_charge":"No","type":"dissertation","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"6608"}]},"date_published":"2020-02-10T00:00:00Z","title":"The hole system of triangulated shapes","has_accepted_license":"1","ddc":["514"],"OA_place":"publisher","author":[{"orcid":"0000-0002-4672-8297","last_name":"Ölsböck","full_name":"Ölsböck, Katharina","first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87"}],"page":"155","publication_status":"published","degree_awarded":"PhD","file":[{"file_size":76195184,"relation":"main_file","access_level":"open_access","file_id":"7461","creator":"koelsboe","file_name":"thesis_ist-final_noack.pdf","checksum":"1df9f8c530b443c0e63a3f2e4fde412e","date_created":"2020-02-06T14:43:54Z","content_type":"application/pdf","date_updated":"2020-07-14T12:47:58Z"},{"relation":"source_file","file_size":122103715,"access_level":"closed","file_id":"7462","creator":"koelsboe","checksum":"7a52383c812b0be64d3826546509e5a4","file_name":"latex-files.zip","date_created":"2020-02-06T14:52:45Z","content_type":"application/x-zip-compressed","description":"latex source files, figures","date_updated":"2020-07-14T12:47:58Z"}],"oa_version":"Published Version","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"alternative_title":["ISTA Thesis"],"tmp":{"image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)"},"supervisor":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"year":"2020","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","month":"02","keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"]},{"date_created":"2020-03-01T23:00:39Z","oa":1,"day":"13","publisher":"SIAM","_id":"7554","status":"public","article_processing_charge":"No","language":[{"iso":"eng"}],"volume":64,"doi":"10.1137/S0040585X97T989726","citation":{"short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 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>.","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.","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>.","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>","ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614.","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>"},"abstract":[{"lang":"eng","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 ${R}^n$."}],"date_updated":"2025-07-10T11:54:44Z","publication_identifier":{"eissn":["1095-7219"],"issn":["0040-585X"]},"title":"Weighted Poisson–Delaunay mosaics","type":"journal_article","scopus_import":"1","publication":"Theory of Probability and its Applications","ec_funded":1,"date_published":"2020-02-13T00:00:00Z","page":"595-614","publication_status":"published","oa_version":"Preprint","external_id":{"isi":["000551393100007"],"arxiv":["1705.08735"]},"main_file_link":[{"url":"https://arxiv.org/abs/1705.08735","open_access":"1"}],"author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","last_name":"Nikitenko"}],"arxiv":1,"intvolume":"        64","project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"year":"2020","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"4","month":"02","department":[{"_id":"HeEd"}],"isi":1,"article_type":"original"},{"title":"Token swapping on trees","year":"2019","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"03","type":"preprint","department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"related_material":{"record":[{"status":"public","id":"12833","relation":"later_version"},{"id":"7944","relation":"dissertation_contains","status":"public"}]},"publication":"arXiv","article_number":"1903.06981","date_published":"2019-03-16T00:00:00Z","date_created":"2020-06-08T12:25:25Z","oa":1,"publication_status":"draft","day":"16","_id":"7950","status":"public","article_processing_charge":"No","oa_version":"Preprint","external_id":{"arxiv":["1903.06981"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1903.06981","open_access":"1"}],"author":[{"last_name":"Biniaz","first_name":"Ahmad","full_name":"Biniaz, Ahmad"},{"last_name":"Jain","full_name":"Jain, Kshitij","first_name":"Kshitij"},{"last_name":"Lubiw","first_name":"Anna","full_name":"Lubiw, Anna"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","last_name":"Masárová"},{"full_name":"Miltzow, Tillmann","first_name":"Tillmann","last_name":"Miltzow"},{"full_name":"Mondal, Debajyoti","first_name":"Debajyoti","last_name":"Mondal"},{"first_name":"Anurag Murty","full_name":"Naredla, Anurag Murty","last_name":"Naredla"},{"orcid":"0000-0002-1097-9684","last_name":"Tkadlec","full_name":"Tkadlec, Josef","first_name":"Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Turcotte","first_name":"Alexi","full_name":"Turcotte, Alexi"}],"arxiv":1,"doi":"10.48550/arXiv.1903.06981","citation":{"mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” <i>ArXiv</i>, 1903.06981, doi:<a href=\"https://doi.org/10.48550/arXiv.1903.06981\">10.48550/arXiv.1903.06981</a>.","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.).","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981.","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.1903.06981\">10.48550/arXiv.1903.06981</a>","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.1903.06981\">https://doi.org/10.48550/arXiv.1903.06981</a>","chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.1903.06981\">https://doi.org/10.48550/arXiv.1903.06981</a>.","ieee":"A. Biniaz <i>et al.</i>, “Token swapping on trees,” <i>arXiv</i>. ."},"abstract":[{"lang":"eng","text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex.  The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete.  We present some partial results:\r\n1.  An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2.  Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3.  Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.\r\n3.  A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars.  In this version, tokens and  vertices  have  colours,  and  colours  have  weights.   The  goal  is  to  get  every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved."}],"date_updated":"2026-04-08T07:23:00Z"},{"ec_funded":1,"publication":"Journal of Computational Geometry ","date_published":"2019-07-01T00:00:00Z","type":"journal_article","scopus_import":1,"title":"Simplices modelled on spaces of constant curvature","has_accepted_license":"1","ddc":["510"],"date_updated":"2021-01-12T08:07:50Z","abstract":[{"text":"We give non-degeneracy criteria for Riemannian simplices based on simplices in spaces of constant sectional curvature. It extends previous work on Riemannian simplices, where we developed Riemannian simplices with respect to Euclidean reference simplices. The criteria we give in this article are in terms of quality measures for spaces of constant curvature that we develop here. We see that simplices in spaces that have nearly constant curvature, are already non-degenerate under very weak quality demands. This is of importance because it allows for sampling of Riemannian manifolds based on anisotropy of the manifold and not (absolute) curvature.","lang":"eng"}],"publication_identifier":{"issn":["1920-180X"]},"language":[{"iso":"eng"}],"volume":10,"citation":{"mla":"Dyer, Ramsay, et al. “Simplices Modelled on Spaces of Constant Curvature.” <i>Journal of Computational Geometry </i>, vol. 10, no. 1, Carleton University, 2019, pp. 223–256, doi:<a href=\"https://doi.org/10.20382/jocg.v10i1a9\">10.20382/jocg.v10i1a9</a>.","short":"R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry  10 (2019) 223–256.","ama":"Dyer R, Vegter G, Wintraecken M. Simplices modelled on spaces of constant curvature. <i>Journal of Computational Geometry </i>. 2019;10(1):223–256. doi:<a href=\"https://doi.org/10.20382/jocg.v10i1a9\">10.20382/jocg.v10i1a9</a>","ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","chicago":"Dyer, Ramsay, Gert Vegter, and Mathijs Wintraecken. “Simplices Modelled on Spaces of Constant Curvature.” <i>Journal of Computational Geometry </i>. Carleton University, 2019. <a href=\"https://doi.org/10.20382/jocg.v10i1a9\">https://doi.org/10.20382/jocg.v10i1a9</a>.","apa":"Dyer, R., Vegter, G., &#38; Wintraecken, M. (2019). Simplices modelled on spaces of constant curvature. <i>Journal of Computational Geometry </i>. Carleton University. <a href=\"https://doi.org/10.20382/jocg.v10i1a9\">https://doi.org/10.20382/jocg.v10i1a9</a>","ieee":"R. Dyer, G. Vegter, and M. Wintraecken, “Simplices modelled on spaces of constant curvature,” <i>Journal of Computational Geometry </i>, vol. 10, no. 1. Carleton University, pp. 223–256, 2019."},"doi":"10.20382/jocg.v10i1a9","file_date_updated":"2020-07-14T12:47:32Z","status":"public","oa":1,"date_created":"2019-06-03T09:35:33Z","_id":"6515","publisher":"Carleton University","day":"01","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"department":[{"_id":"HeEd"}],"issue":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"07","year":"2019","quality_controlled":"1","intvolume":"        10","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"author":[{"last_name":"Dyer","first_name":"Ramsay","full_name":"Dyer, Ramsay"},{"first_name":"Gert","full_name":"Vegter, Gert","last_name":"Vegter"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"file":[{"date_created":"2019-06-03T09:30:01Z","file_name":"mainJournalFinal.pdf","checksum":"57b4df2f16a74eb499734ec8ee240178","file_size":2170882,"relation":"main_file","creator":"mwintrae","access_level":"open_access","file_id":"6516","content_type":"application/pdf","date_updated":"2020-07-14T12:47:32Z"}],"oa_version":"Published Version","page":"223–256","publication_status":"published"},{"oa":1,"date_created":"2019-07-07T21:59:20Z","publisher":"Elsevier","day":"01","_id":"6608","status":"public","article_processing_charge":"No","language":[{"iso":"eng"}],"volume":73,"doi":"10.1016/j.cagd.2019.06.003","file_date_updated":"2020-07-14T12:47:34Z","citation":{"mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” <i>Computer Aided Geometric Design</i>, vol. 73, Elsevier, 2019, pp. 1–15, doi:<a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">10.1016/j.cagd.2019.06.003</a>.","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.","ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.","ama":"Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. <i>Computer Aided Geometric Design</i>. 2019;73:1-15. doi:<a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">10.1016/j.cagd.2019.06.003</a>","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” <i>Computer Aided Geometric Design</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">https://doi.org/10.1016/j.cagd.2019.06.003</a>.","apa":"Edelsbrunner, H., &#38; Ölsböck, K. (2019). Holes and dependences in an ordered complex. <i>Computer Aided Geometric Design</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">https://doi.org/10.1016/j.cagd.2019.06.003</a>","ieee":"H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” <i>Computer Aided Geometric Design</i>, vol. 73. Elsevier, pp. 1–15, 2019."},"abstract":[{"lang":"eng","text":"We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram."}],"date_updated":"2026-04-08T07:23:21Z","title":"Holes and dependences in an ordered complex","has_accepted_license":"1","ddc":["000"],"type":"journal_article","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"7460"}]},"scopus_import":"1","publication":"Computer Aided Geometric Design","ec_funded":1,"date_published":"2019-08-01T00:00:00Z","page":"1-15","publication_status":"published","file":[{"content_type":"application/pdf","date_updated":"2020-07-14T12:47:34Z","relation":"main_file","file_size":2665013,"access_level":"open_access","file_id":"6624","creator":"kschuh","file_name":"Elsevier_2019_Edelsbrunner.pdf","checksum":"7c99be505dc7533257d42eb1830cef04","date_created":"2019-07-08T15:24:26Z"}],"oa_version":"Published Version","external_id":{"isi":["000485207800001"]},"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina","full_name":"Ölsböck, Katharina","last_name":"Ölsböck","orcid":"0000-0002-4672-8297"}],"intvolume":"        73","project":[{"call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"year":"2019","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"08","department":[{"_id":"HeEd"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"isi":1},{"language":[{"iso":"eng"}],"author":[{"last_name":"Vegter","first_name":"Gert","full_name":"Vegter, Gert"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","orcid":"0000-0002-7472-2220"}],"citation":{"ama":"Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In: <i>The 31st Canadian Conference in Computational Geometry</i>. ; 2019:275-279.","ista":"Vegter G, Wintraecken M. 2019. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. The 31st Canadian Conference in Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 275–279.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” In <i>The 31st Canadian Conference in Computational Geometry</i>, 275–79, 2019.","apa":"Vegter, G., &#38; Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In <i>The 31st Canadian Conference in Computational Geometry</i> (pp. 275–279). Edmonton, Canada.","ieee":"G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds,” in <i>The 31st Canadian Conference in Computational Geometry</i>, Edmonton, Canada, 2019, pp. 275–279.","mla":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” <i>The 31st Canadian Conference in Computational Geometry</i>, 2019, pp. 275–79.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279."},"file_date_updated":"2020-07-14T12:47:34Z","abstract":[{"lang":"eng","text":"Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces in Euclidean space by piecewise  flat  triangular  meshes  with  a  given  number of  vertices  on  the  hypersurface  that  are  optimal  with respect  to  Hausdorff  distance.   They  proved  that  this Hausdorff distance decreases inversely proportional with m 2/(d−1),  where m is  the  number  of  vertices  and d is the  dimension  of  Euclidean  space.   Moreover  the  pro-portionality constant can be expressed in terms of the Gaussian curvature, an intrinsic quantity.  In this short note, we prove the extrinsic nature of this constant for manifolds of sufficiently high codimension.  We do so by constructing an family of isometric embeddings of the flat torus in Euclidean space."}],"date_updated":"2021-01-12T08:08:16Z","project":[{"call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"page":"275-279","oa":1,"date_created":"2019-07-12T08:34:57Z","publication_status":"published","day":"01","_id":"6628","status":"public","file":[{"checksum":"ceabd152cfa55170d57763f9c6c60a53","file_name":"IntrinsicExtrinsicCCCG2019.pdf","date_created":"2019-07-12T08:32:46Z","relation":"main_file","file_size":321176,"file_id":"6629","access_level":"open_access","creator":"mwintrae","content_type":"application/pdf","date_updated":"2020-07-14T12:47:34Z"}],"oa_version":"Submitted Version","type":"conference","department":[{"_id":"HeEd"}],"scopus_import":1,"conference":{"end_date":"2019-08-10","start_date":"2019-08-08","location":"Edmonton, Canada","name":"CCCG: Canadian Conference in Computational Geometry"},"publication":"The 31st Canadian Conference in Computational Geometry","ec_funded":1,"date_published":"2019-08-01T00:00:00Z","title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","has_accepted_license":"1","year":"2019","ddc":["004"],"quality_controlled":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"08"},{"oa_version":"Preprint","page":"457-490","publication_status":"published","intvolume":"        53","project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"external_id":{"isi":["000472541600004"],"arxiv":["1612.06926"]},"main_file_link":[{"url":"https://arxiv.org/abs/1612.06926","open_access":"1"}],"author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"last_name":"Hubard","full_name":"Hubard, Alfredo","first_name":"Alfredo"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"2","month":"06","year":"2019","quality_controlled":"1","isi":1,"department":[{"_id":"HeEd"}],"status":"public","article_processing_charge":"No","date_created":"2019-07-14T21:59:19Z","oa":1,"publisher":"Akademicka Platforma Czasopism","day":"01","_id":"6634","abstract":[{"lang":"eng","text":"In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure."}],"date_updated":"2025-04-15T06:50:28Z","language":[{"iso":"eng"}],"volume":53,"citation":{"chicago":"Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” <i>Topological Methods in Nonlinear Analysis</i>. Akademicka Platforma Czasopism, 2019. <a href=\"https://doi.org/10.12775/TMNA.2019.008\">https://doi.org/10.12775/TMNA.2019.008</a>.","apa":"Akopyan, A., Hubard, A., &#38; Karasev, R. (2019). Lower and upper bounds for the waists of different spaces. <i>Topological Methods in Nonlinear Analysis</i>. Akademicka Platforma Czasopism. <a href=\"https://doi.org/10.12775/TMNA.2019.008\">https://doi.org/10.12775/TMNA.2019.008</a>","ista":"Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.","ama":"Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different spaces. <i>Topological Methods in Nonlinear Analysis</i>. 2019;53(2):457-490. doi:<a href=\"https://doi.org/10.12775/TMNA.2019.008\">10.12775/TMNA.2019.008</a>","ieee":"A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” <i>Topological Methods in Nonlinear Analysis</i>, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.","mla":"Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” <i>Topological Methods in Nonlinear Analysis</i>, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:<a href=\"https://doi.org/10.12775/TMNA.2019.008\">10.12775/TMNA.2019.008</a>.","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490."},"doi":"10.12775/TMNA.2019.008","title":"Lower and upper bounds for the waists of different spaces","publication":"Topological Methods in Nonlinear Analysis","ec_funded":1,"date_published":"2019-06-01T00:00:00Z","type":"journal_article","scopus_import":"1"},{"external_id":{"arxiv":["1903.08510"]},"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Virk","full_name":"Virk, Ziga","first_name":"Ziga"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner"}],"arxiv":1,"intvolume":"       129","project":[{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35"}],"page":"31:1-31:14","publication_status":"published","file":[{"date_updated":"2020-07-14T12:47:35Z","content_type":"application/pdf","creator":"dernst","file_id":"6666","access_level":"open_access","file_size":1355179,"relation":"main_file","date_created":"2019-07-24T06:40:01Z","file_name":"2019_LIPICS_Edelsbrunner.pdf","checksum":"8ec8720730d4c789bf7b06540f1c29f4"}],"oa_version":"Published Version","department":[{"_id":"HeEd"}],"alternative_title":["LIPIcs"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"conference":{"start_date":"2019-06-18","location":"Portland, OR, United States","name":"SoCG 2019: Symposium on Computational Geometry","end_date":"2019-06-21"},"year":"2019","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"06","volume":129,"language":[{"iso":"eng"}],"citation":{"short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14.","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” <i>35th International Symposium on Computational Geometry</i>, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14, doi:<a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.31\">10.4230/LIPICS.SOCG.2019.31</a>.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” in <i>35th International Symposium on Computational Geometry</i>, Portland, OR, United States, 2019, vol. 129, p. 31:1-31:14.","ista":"Edelsbrunner H, Virk Z, Wagner H. 2019. Topological data analysis in information space. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium on Computational Geometry, LIPIcs, vol. 129, 31:1-31:14.","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. In: <i>35th International Symposium on Computational Geometry</i>. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:<a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.31\">10.4230/LIPICS.SOCG.2019.31</a>","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” In <i>35th International Symposium on Computational Geometry</i>, 129:31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. <a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.31\">https://doi.org/10.4230/LIPICS.SOCG.2019.31</a>.","apa":"Edelsbrunner, H., Virk, Z., &#38; Wagner, H. (2019). Topological data analysis in information space. In <i>35th International Symposium on Computational Geometry</i> (Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.31\">https://doi.org/10.4230/LIPICS.SOCG.2019.31</a>"},"doi":"10.4230/LIPICS.SOCG.2019.31","file_date_updated":"2020-07-14T12:47:35Z","abstract":[{"lang":"eng","text":"Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory\r\nneeded for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context."}],"date_updated":"2024-10-09T20:58:55Z","publication_identifier":{"isbn":["9783959771047"]},"corr_author":"1","date_created":"2019-07-17T10:36:09Z","oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","day":"01","_id":"6648","status":"public","type":"conference","scopus_import":1,"publication":"35th International Symposium on Computational Geometry","date_published":"2019-06-01T00:00:00Z","has_accepted_license":"1","title":"Topological data analysis in information space","ddc":["510"]}]