[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"arXiv","department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"date_published":"2019-03-16T00:00:00Z","date_created":"2020-06-08T12:25:25Z","doi":"10.48550/arXiv.1903.06981","day":"16","type":"preprint","status":"public","date_updated":"2026-04-08T07:23:00Z","external_id":{"arxiv":["1903.06981"]},"arxiv":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.06981"}],"publication_status":"draft","year":"2019","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."}],"citation":{"short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.).","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>","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>.","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>.","ieee":"A. Biniaz <i>et al.</i>, “Token swapping on trees,” <i>arXiv</i>. .","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>","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."},"author":[{"full_name":"Biniaz, Ahmad","first_name":"Ahmad","last_name":"Biniaz"},{"last_name":"Jain","full_name":"Jain, Kshitij","first_name":"Kshitij"},{"first_name":"Anna","full_name":"Lubiw, Anna","last_name":"Lubiw"},{"last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","first_name":"Zuzana","full_name":"Masárová, Zuzana"},{"last_name":"Miltzow","full_name":"Miltzow, Tillmann","first_name":"Tillmann"},{"last_name":"Mondal","first_name":"Debajyoti","full_name":"Mondal, Debajyoti"},{"last_name":"Naredla","first_name":"Anurag Murty","full_name":"Naredla, Anurag Murty"},{"full_name":"Tkadlec, Josef","first_name":"Josef","last_name":"Tkadlec","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alexi","full_name":"Turcotte, Alexi","last_name":"Turcotte"}],"article_processing_charge":"No","oa":1,"_id":"7950","oa_version":"Preprint","article_number":"1903.06981","related_material":{"record":[{"id":"12833","status":"public","relation":"later_version"},{"id":"7944","status":"public","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"month":"03","title":"Token swapping on trees"},{"file":[{"date_updated":"2020-07-14T12:47:32Z","file_size":2170882,"access_level":"open_access","content_type":"application/pdf","file_id":"6516","checksum":"57b4df2f16a74eb499734ec8ee240178","creator":"mwintrae","date_created":"2019-06-03T09:30:01Z","file_name":"mainJournalFinal.pdf","relation":"main_file"}],"_id":"6515","author":[{"last_name":"Dyer","first_name":"Ramsay","full_name":"Dyer, Ramsay"},{"first_name":"Gert","full_name":"Vegter, Gert","last_name":"Vegter"},{"full_name":"Wintraecken, Mathijs","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken"}],"abstract":[{"lang":"eng","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."}],"publisher":"Carleton University","file_date_updated":"2020-07-14T12:47:32Z","year":"2019","page":"223–256","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"status":"public","ddc":["510"],"date_updated":"2021-01-12T08:07:50Z","date_published":"2019-07-01T00:00:00Z","day":"01","intvolume":"        10","publication":"Journal of Computational Geometry ","department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"ec_funded":1,"month":"07","title":"Simplices modelled on spaces of constant curvature","oa_version":"Published Version","issue":"1","oa":1,"has_accepted_license":"1","project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"citation":{"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>","short":"R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry  10 (2019) 223–256.","ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","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.","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>.","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>."},"quality_controlled":"1","publication_status":"published","type":"journal_article","volume":10,"scopus_import":1,"date_created":"2019-06-03T09:35:33Z","doi":"10.20382/jocg.v10i1a9","publication_identifier":{"issn":["1920-180X"]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"publication_status":"published","quality_controlled":"1","article_processing_charge":"No","isi":1,"citation":{"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.","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>","ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.","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>.","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>.","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>","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15."},"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","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"has_accepted_license":"1","related_material":{"record":[{"relation":"dissertation_contains","id":"7460","status":"public"}]},"oa":1,"oa_version":"Published Version","month":"08","title":"Holes and dependences in an ordered complex","ec_funded":1,"language":[{"iso":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1016/j.cagd.2019.06.003","date_created":"2019-07-07T21:59:20Z","scopus_import":"1","volume":73,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","type":"journal_article","year":"2019","page":"1-15","file_date_updated":"2020-07-14T12:47:34Z","publisher":"Elsevier","abstract":[{"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.","lang":"eng"}],"author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4672-8297","last_name":"Ölsböck","first_name":"Katharina","full_name":"Ölsböck, Katharina"}],"_id":"6608","file":[{"relation":"main_file","file_name":"Elsevier_2019_Edelsbrunner.pdf","date_created":"2019-07-08T15:24:26Z","creator":"kschuh","checksum":"7c99be505dc7533257d42eb1830cef04","file_id":"6624","content_type":"application/pdf","access_level":"open_access","file_size":2665013,"date_updated":"2020-07-14T12:47:34Z"}],"department":[{"_id":"HeEd"}],"publication":"Computer Aided Geometric Design","intvolume":"        73","day":"01","date_published":"2019-08-01T00:00:00Z","external_id":{"isi":["000485207800001"]},"date_updated":"2026-04-08T07:23:21Z","ddc":["000"],"tmp":{"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)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"status":"public"},{"has_accepted_license":"1","oa":1,"_id":"6628","oa_version":"Submitted Version","month":"08","ec_funded":1,"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","file":[{"file_name":"IntrinsicExtrinsicCCCG2019.pdf","relation":"main_file","access_level":"open_access","content_type":"application/pdf","date_updated":"2020-07-14T12:47:34Z","file_size":321176,"checksum":"ceabd152cfa55170d57763f9c6c60a53","date_created":"2019-07-12T08:32:46Z","creator":"mwintrae","file_id":"6629"}],"language":[{"iso":"eng"}],"page":"275-279","year":"2019","file_date_updated":"2020-07-14T12:47:34Z","publication_status":"published","quality_controlled":"1","citation":{"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.","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.","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.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279.","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."},"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."}],"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020"}],"author":[{"first_name":"Gert","full_name":"Vegter, Gert","last_name":"Vegter"},{"last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","full_name":"Wintraecken, Mathijs"}],"day":"01","date_published":"2019-08-01T00:00:00Z","date_created":"2019-07-12T08:34:57Z","date_updated":"2021-01-12T08:08:16Z","scopus_import":1,"ddc":["004"],"status":"public","type":"conference","conference":{"end_date":"2019-08-10","location":"Edmonton, Canada","start_date":"2019-08-08","name":"CCCG: Canadian Conference in Computational Geometry"},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"publication":"The 31st Canadian Conference in Computational Geometry"},{"publication_status":"published","isi":1,"citation":{"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>","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","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>","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.","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.","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>.","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>."},"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7"}],"article_processing_charge":"No","quality_controlled":"1","oa":1,"oa_version":"Preprint","issue":"2","language":[{"iso":"eng"}],"month":"06","ec_funded":1,"title":"Lower and upper bounds for the waists of different spaces","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2019-07-14T21:59:19Z","doi":"10.12775/TMNA.2019.008","type":"journal_article","scopus_import":"1","volume":53,"arxiv":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.06926"}],"year":"2019","page":"457-490","abstract":[{"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.","lang":"eng"}],"author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Hubard","full_name":"Hubard, Alfredo","first_name":"Alfredo"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"publisher":"Akademicka Platforma Czasopism","_id":"6634","department":[{"_id":"HeEd"}],"publication":"Topological Methods in Nonlinear Analysis","date_published":"2019-06-01T00:00:00Z","intvolume":"        53","day":"01","status":"public","external_id":{"isi":["000472541600004"],"arxiv":["1612.06926"]},"date_updated":"2025-04-15T06:50:28Z"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"isbn":["9783959771047"]},"doi":"10.4230/LIPICS.SOCG.2019.31","date_created":"2019-07-17T10:36:09Z","scopus_import":1,"volume":129,"arxiv":1,"type":"conference","publication_status":"published","quality_controlled":"1","citation":{"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>.","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>.","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.","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>","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.","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.","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>"},"project":[{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35"}],"has_accepted_license":"1","alternative_title":["LIPIcs"],"oa":1,"oa_version":"Published Version","month":"06","title":"Topological data analysis in information space","language":[{"iso":"eng"}],"conference":{"name":"SoCG 2019: Symposium on Computational Geometry","start_date":"2019-06-18","location":"Portland, OR, United States","end_date":"2019-06-21"},"publication":"35th International Symposium on Computational Geometry","department":[{"_id":"HeEd"}],"day":"01","intvolume":"       129","date_published":"2019-06-01T00:00:00Z","external_id":{"arxiv":["1903.08510"]},"date_updated":"2024-10-09T20:58:55Z","ddc":["510"],"status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"page":"31:1-31:14","year":"2019","file_date_updated":"2020-07-14T12:47:35Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","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."}],"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"last_name":"Virk","full_name":"Virk, Ziga","first_name":"Ziga"},{"full_name":"Wagner, Hubert","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"}],"_id":"6648","corr_author":"1","file":[{"relation":"main_file","file_name":"2019_LIPICS_Edelsbrunner.pdf","file_id":"6666","creator":"dernst","date_created":"2019-07-24T06:40:01Z","checksum":"8ec8720730d4c789bf7b06540f1c29f4","file_size":1355179,"date_updated":"2020-07-14T12:47:35Z","content_type":"application/pdf","access_level":"open_access"}]},{"date_published":"2019-06-01T00:00:00Z","intvolume":"         3","day":"01","ddc":["000"],"status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"date_updated":"2025-04-14T07:44:06Z","publication":"Journal of Applied and Computational Topology","department":[{"_id":"HeEd"}],"_id":"6671","file":[{"relation":"main_file","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf","file_id":"6741","date_created":"2019-07-31T08:09:56Z","creator":"dernst","checksum":"a5b244db9f751221409cf09c97ee0935","date_updated":"2020-07-14T12:47:36Z","file_size":2215157,"content_type":"application/pdf","access_level":"open_access"}],"corr_author":"1","file_date_updated":"2020-07-14T12:47:36Z","year":"2019","page":"29–58","abstract":[{"text":"In this paper we discuss three results. The first two concern general sets of positive reach: we first characterize the reach of a closed set by means of a bound on the metric distortion between the distance measured in the ambient Euclidean space and the shortest path distance measured in the set. Secondly, we prove that the intersection of a ball with radius less than the reach with the set is geodesically convex, meaning that the shortest path between any two points in the intersection lies itself in the intersection. For our third result we focus on manifolds with positive reach and give a bound on the angle between tangent spaces at two different points in terms of the reach and the distance between the two points.","lang":"eng"}],"author":[{"last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel"},{"full_name":"Lieutier, André","first_name":"André","last_name":"Lieutier"},{"last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","full_name":"Wintraecken, Mathijs"}],"publisher":"Springer Nature","date_created":"2019-07-24T08:37:29Z","doi":"10.1007/s41468-019-00029-8","type":"journal_article","article_type":"original","scopus_import":"1","volume":3,"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"oa_version":"Published Version","issue":"1-2","has_accepted_license":"1","language":[{"iso":"eng"}],"month":"06","ec_funded":1,"title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","publication_status":"published","citation":{"mla":"Boissonnat, Jean-Daniel, et al. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” <i>Journal of Applied and Computational Topology</i>, vol. 3, no. 1–2, Springer Nature, 2019, pp. 29–58, doi:<a href=\"https://doi.org/10.1007/s41468-019-00029-8\">10.1007/s41468-019-00029-8</a>.","chicago":"Boissonnat, Jean-Daniel, André Lieutier, and Mathijs Wintraecken. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s41468-019-00029-8\">https://doi.org/10.1007/s41468-019-00029-8</a>.","ista":"Boissonnat J-D, Lieutier A, Wintraecken M. 2019. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. 3(1–2), 29–58.","ieee":"J.-D. Boissonnat, A. Lieutier, and M. Wintraecken, “The reach, metric distortion, geodesic convexity and the variation of tangent spaces,” <i>Journal of Applied and Computational Topology</i>, vol. 3, no. 1–2. Springer Nature, pp. 29–58, 2019.","apa":"Boissonnat, J.-D., Lieutier, A., &#38; Wintraecken, M. (2019). The reach, metric distortion, geodesic convexity and the variation of tangent spaces. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-019-00029-8\">https://doi.org/10.1007/s41468-019-00029-8</a>","short":"J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58.","ama":"Boissonnat J-D, Lieutier A, Wintraecken M. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. <i>Journal of Applied and Computational Topology</i>. 2019;3(1-2):29–58. doi:<a href=\"https://doi.org/10.1007/s41468-019-00029-8\">10.1007/s41468-019-00029-8</a>"},"project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"article_processing_charge":"Yes (via OA deal)","quality_controlled":"1"},{"publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","article_type":"original","arxiv":1,"volume":51,"type":"journal_article","doi":"10.1112/blms.12276","date_created":"2019-08-11T21:59:23Z","article_processing_charge":"No","quality_controlled":"1","isi":1,"citation":{"short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","ama":"Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli formula. <i>Bulletin of the London Mathematical Society</i>. 2019;51(5):765-775. doi:<a href=\"https://doi.org/10.1112/blms.12276\">10.1112/blms.12276</a>","chicago":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2019. <a href=\"https://doi.org/10.1112/blms.12276\">https://doi.org/10.1112/blms.12276</a>.","mla":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” <i>Bulletin of the London Mathematical Society</i>, vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:<a href=\"https://doi.org/10.1112/blms.12276\">10.1112/blms.12276</a>.","ista":"Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775.","apa":"Akopyan, A., &#38; Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/blms.12276\">https://doi.org/10.1112/blms.12276</a>","ieee":"A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” <i>Bulletin of the London Mathematical Society</i>, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019."},"project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"}],"publication_status":"published","ec_funded":1,"month":"10","title":"The Regge symmetry, confocal conics, and the Schläfli formula","language":[{"iso":"eng"}],"oa":1,"oa_version":"Preprint","issue":"5","department":[{"_id":"HeEd"}],"publication":"Bulletin of the London Mathematical Society","external_id":{"arxiv":["1903.04929"],"isi":["000478560200001"]},"date_updated":"2025-07-10T11:53:52Z","status":"public","intvolume":"        51","day":"01","date_published":"2019-10-01T00:00:00Z","publisher":"London Mathematical Society","abstract":[{"lang":"eng","text":"The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here, we give a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic geometry."}],"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","full_name":"Akopyan, Arseniy","first_name":"Arseniy"},{"last_name":"Izmestiev","first_name":"Ivan","full_name":"Izmestiev, Ivan"}],"year":"2019","page":"765-775","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.04929"}],"_id":"6793"},{"publication_identifier":{"issn":["0021-8693"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2019-08-22T07:54:13Z","doi":"10.1016/j.jalgebra.2019.07.027","type":"journal_article","article_type":"original","volume":538,"arxiv":1,"publication_status":"published","citation":{"chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” <i>Journal of Algebra</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">https://doi.org/10.1016/j.jalgebra.2019.07.027</a>.","mla":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” <i>Journal of Algebra</i>, vol. 538, Elsevier, 2019, pp. 261–89, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">10.1016/j.jalgebra.2019.07.027</a>.","ieee":"A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” <i>Journal of Algebra</i>, vol. 538. Elsevier, pp. 261–289, 2019.","apa":"Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. <i>Journal of Algebra</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">https://doi.org/10.1016/j.jalgebra.2019.07.027</a>","ista":"Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289.","short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","ama":"Brown A. Arakawa-Suzuki functors for Whittaker modules. <i>Journal of Algebra</i>. 2019;538:261-289. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">10.1016/j.jalgebra.2019.07.027</a>"},"isi":1,"article_processing_charge":"No","quality_controlled":"1","oa":1,"oa_version":"Preprint","language":[{"iso":"eng"}],"month":"11","title":"Arakawa-Suzuki functors for Whittaker modules","department":[{"_id":"HeEd"}],"publication":"Journal of Algebra","date_published":"2019-11-15T00:00:00Z","intvolume":"       538","day":"15","status":"public","date_updated":"2023-08-29T07:11:47Z","external_id":{"arxiv":["1805.04676"],"isi":["000487176300011"]},"main_file_link":[{"url":"https://arxiv.org/abs/1805.04676","open_access":"1"}],"year":"2019","page":"261-289","abstract":[{"lang":"eng","text":"In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type  to the category of finite-dimensional modules of the graded affine Hecke algebra of type . Using results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category  as a full subcategory, our results generalize results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between finite-dimensional representations of  and representations of the symmetric group ."}],"author":[{"full_name":"Brown, Adam","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown"}],"publisher":"Elsevier","_id":"6828"},{"conference":{"end_date":"2019-10-30","location":"Auckland, New Zealand","start_date":"2019-10-27","name":"ITSC: Intelligent Transportation Systems Conference"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"HeEd"}],"publication":"2019 IEEE Intelligent Transportation Systems Conference","publication_identifier":{"isbn":["9781538670248"]},"date_published":"2019-11-28T00:00:00Z","date_created":"2019-12-29T23:00:47Z","day":"28","doi":"10.1109/ITSC.2019.8917514","type":"conference","status":"public","scopus_import":"1","date_updated":"2023-09-06T14:50:28Z","external_id":{"isi":["000521238102050"]},"publication_status":"published","year":"2019","isi":1,"citation":{"ista":"Osang GF, Cook J, Fabrikant A, Gruteser M. 2019. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. 2019 IEEE Intelligent Transportation Systems Conference. ITSC: Intelligent Transportation Systems Conference, 8917514.","ieee":"G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale,” in <i>2019 IEEE Intelligent Transportation Systems Conference</i>, Auckland, New Zealand, 2019.","apa":"Osang, G. F., Cook, J., Fabrikant, A., &#38; Gruteser, M. (2019). LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In <i>2019 IEEE Intelligent Transportation Systems Conference</i>. Auckland, New Zealand: IEEE. <a href=\"https://doi.org/10.1109/ITSC.2019.8917514\">https://doi.org/10.1109/ITSC.2019.8917514</a>","chicago":"Osang, Georg F, James Cook, Alex Fabrikant, and Marco Gruteser. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” In <i>2019 IEEE Intelligent Transportation Systems Conference</i>. IEEE, 2019. <a href=\"https://doi.org/10.1109/ITSC.2019.8917514\">https://doi.org/10.1109/ITSC.2019.8917514</a>.","mla":"Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” <i>2019 IEEE Intelligent Transportation Systems Conference</i>, 8917514, IEEE, 2019, doi:<a href=\"https://doi.org/10.1109/ITSC.2019.8917514\">10.1109/ITSC.2019.8917514</a>.","ama":"Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In: <i>2019 IEEE Intelligent Transportation Systems Conference</i>. IEEE; 2019. doi:<a href=\"https://doi.org/10.1109/ITSC.2019.8917514\">10.1109/ITSC.2019.8917514</a>","short":"G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019."},"abstract":[{"text":"We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system to label a stream of noisy observations of transit vehicle trajectories with the transit routes they are serving (e.g., northbound bus #5). In order to scale efficiently to large transit networks, our system first retrieves a small set of candidate routes from a geometrically indexed data structure, then applies a fine-grained scoring step to choose the best match. Given that real-time data remains unavailable for the majority of the world’s transit agencies, these inferences can help feed a real-time map of a transit system’s trips, infer transit trip delays in real time, or measure and correct noisy transit tracking data. This system can run on vehicle observations from a variety of sources that don’t attach route information to vehicle observations, such as public imagery streams or user-contributed transit vehicle sightings.We abstract away the specifics of the sensing system and demonstrate the effectiveness of our system on a \"semisynthetic\" dataset of all New York City buses, where we simulate sensed trajectories by starting with fully labeled vehicle trajectories reported via the GTFS-Realtime protocol, removing the transit route IDs, and perturbing locations with synthetic noise. Using just the geometric shapes of the trajectories, we demonstrate that our system converges on the correct route ID within a few minutes, even after a vehicle switches from serving one trip to the next.","lang":"eng"}],"author":[{"full_name":"Osang, Georg F","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang"},{"last_name":"Cook","full_name":"Cook, James","first_name":"James"},{"full_name":"Fabrikant, Alex","first_name":"Alex","last_name":"Fabrikant"},{"first_name":"Marco","full_name":"Gruteser, Marco","last_name":"Gruteser"}],"article_processing_charge":"No","quality_controlled":"1","publisher":"IEEE","_id":"7216","oa_version":"None","article_number":"8917514","language":[{"iso":"eng"}],"title":"LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale","month":"11"},{"_id":"6050","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1709.02562"}],"page":"91-102","year":"2019","abstract":[{"text":"We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely many families of pairs of circles for which such construction is possible. ","lang":"eng"}],"author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan"},{"last_name":"Fedorov","full_name":"Fedorov, Roman","first_name":"Roman"}],"publisher":"American Mathematical Society","date_published":"2019-01-01T00:00:00Z","intvolume":"       147","day":"01","status":"public","external_id":{"isi":["000450363900008"],"arxiv":["1709.02562"]},"date_updated":"2026-07-06T12:23:38Z","department":[{"_id":"HeEd"}],"publication":"Proceedings of the American Mathematical Society","das_tickbox":"1","oa":1,"oa_version":"Preprint","language":[{"iso":"eng"}],"title":"Two circles and only a straightedge","month":"01","publication_status":"published","citation":{"ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” <i>Proceedings of the American Mathematical Society</i>, vol. 147. American Mathematical Society, pp. 91–102, 2019.","apa":"Akopyan, A., &#38; Fedorov, R. (2019). Two circles and only a straightedge. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/14240\">https://doi.org/10.1090/proc/14240</a>","ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","chicago":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2019. <a href=\"https://doi.org/10.1090/proc/14240\">https://doi.org/10.1090/proc/14240</a>.","mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” <i>Proceedings of the American Mathematical Society</i>, vol. 147, American Mathematical Society, 2019, pp. 91–102, doi:<a href=\"https://doi.org/10.1090/proc/14240\">10.1090/proc/14240</a>.","ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. <i>Proceedings of the American Mathematical Society</i>. 2019;147:91-102. doi:<a href=\"https://doi.org/10.1090/proc/14240\">10.1090/proc/14240</a>","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102."},"isi":1,"quality_controlled":"1","article_processing_charge":"No","date_created":"2019-02-24T22:59:19Z","doi":"10.1090/proc/14240","type":"journal_article","scopus_import":"1","volume":147,"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"article_number":"A163","_id":"6756","acknowledgement":"PP is grateful to Julian Borill from the Planck consortium for providing the data, and for the illuminating discussions and inputs. PP also thanks Hans Kristen Eriksen, Anne Ducout, and Francois R. Bouchet for significantly helpful discussions at various stages. The authors collectively thank the anonymous referee for the invaluable comments and suggestions that have added significant value to the contents of the manuscript. PP and RA acknowledge the support of ERC advanced grant Understanding Random Systems through Algebraic Topology (URSAT) (no: 320422, PI: RA). This work is also part of a project that has received funding for PP and TB from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement ERC advanced grant 740021– Advances in Research on THeories of the dark UniverSe (ARTHUS), PI: TB). HE and HW acknowledge the support by the Office of Naval Research, through grant N62909-18-1-2038, and by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics”, through grant I02979-N35 of the Austrian Science Fund (FWF). PP acknowledges the support and use of resources at the NERSC computing center.","file":[{"file_name":"2019_AstronomyAstrophysics_Pranav.pdf","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_size":14420451,"date_updated":"2020-07-14T12:47:39Z","checksum":"83b9209ed9eefbdcefd89019c5a97805","date_created":"2019-08-05T08:08:59Z","creator":"dernst","file_id":"6766"}],"OA_place":"publisher","year":"2019","OA_type":"hybrid","file_date_updated":"2020-07-14T12:47:39Z","publisher":"EDP Sciences","abstract":[{"lang":"eng","text":"We study the topology generated by the temperature fluctuations of the cosmic microwave background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over 𝕊2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of “masks” is of importance, we introduce the concept of relative homology. The parametric χ2-test shows differences between observations and simulations, yielding p-values at percent to less than permil levels roughly between 2 and 7°, with the difference in the number of components and holes peaking at more than 3σ sporadically at these scales. The highest observed deviation between the observations and simulations for b0 and b1 is approximately between 3σ and 4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66° in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and first Betti numbers, respectively. Further, since these topological descriptors show consistent anomalous behaviour over independent measurements of Planck and WMAP, instrumental and systematic errors may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations based on power-spectrum matching the characteristics of the observed dipped power spectrum are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB, whether cosmological in nature or arising due to late-time effects, is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate the study of primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology, including topological defect models."}],"author":[{"first_name":"Pratyush","full_name":"Pranav, Pratyush","last_name":"Pranav"},{"first_name":"Robert J.","full_name":"Adler, Robert J.","last_name":"Adler"},{"last_name":"Buchert","full_name":"Buchert, Thomas","first_name":"Thomas"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"full_name":"Jones, Bernard J.T.","first_name":"Bernard J.T.","last_name":"Jones"},{"last_name":"Schwartzman","first_name":"Armin","full_name":"Schwartzman, Armin"},{"last_name":"Wagner","orcid":"0009-0009-9111-8429","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert","first_name":"Hubert"},{"last_name":"Van De Weygaert","full_name":"Van De Weygaert, Rien","first_name":"Rien"}],"day":"17","intvolume":"       627","date_published":"2019-07-17T00:00:00Z","date_updated":"2026-07-08T06:46:14Z","external_id":{"arxiv":["1812.07678"],"isi":["000475839300003"]},"ddc":["520","530"],"status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"publication":"Astronomy & Astrophysics","department":[{"_id":"HeEd"}],"das_tickbox":"1","has_accepted_license":"1","oa":1,"oa_version":"Published Version","title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","month":"07","language":[{"iso":"eng"}],"publication_status":"published","article_processing_charge":"No","quality_controlled":"1","isi":1,"citation":{"ama":"Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature fluctuations in the cosmic microwave background. <i>Astronomy &#38; Astrophysics</i>. 2019;627. doi:<a href=\"https://doi.org/10.1051/0004-6361/201834916\">10.1051/0004-6361/201834916</a>","short":"P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy &#38; Astrophysics 627 (2019).","ista":"Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy &#38; Astrophysics. 627, A163.","apa":"Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman, A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations in the cosmic microwave background. <i>Astronomy &#38; Astrophysics</i>. EDP Sciences. <a href=\"https://doi.org/10.1051/0004-6361/201834916\">https://doi.org/10.1051/0004-6361/201834916</a>","ieee":"P. Pranav <i>et al.</i>, “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” <i>Astronomy &#38; Astrophysics</i>, vol. 627. EDP Sciences, 2019.","chicago":"Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner, Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” <i>Astronomy &#38; Astrophysics</i>. EDP Sciences, 2019. <a href=\"https://doi.org/10.1051/0004-6361/201834916\">https://doi.org/10.1051/0004-6361/201834916</a>.","mla":"Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” <i>Astronomy &#38; Astrophysics</i>, vol. 627, A163, EDP Sciences, 2019, doi:<a href=\"https://doi.org/10.1051/0004-6361/201834916\">10.1051/0004-6361/201834916</a>."},"project":[{"grant_number":"M62909-18-1-2038","_id":"265683E4-B435-11E9-9278-68D0E5697425","name":"Toward Computational Information Topology"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35"}],"doi":"10.1051/0004-6361/201834916","date_created":"2019-08-04T21:59:18Z","scopus_import":"1","article_type":"original","arxiv":1,"volume":627,"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0004-6361"],"eissn":["1432-0746"]}},{"date_created":"2019-11-04T16:46:11Z","type":"conference","arxiv":1,"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","oa":1,"related_material":{"record":[{"status":"public","id":"8317","relation":"extended_version"}]},"language":[{"iso":"eng"}],"month":"08","title":"Folding polyominoes with holes into a cube","publication_status":"published","citation":{"ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference on Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 164–170.","ieee":"O. Aichholzer <i>et al.</i>, “Folding polyominoes with holes into a cube,” in <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, Edmonton, Canada, 2019, pp. 164–170.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a cube. In <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i> (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, Canadian Conference on Computational Geometry, 2019, pp. 164–70.","chicago":"Aichholzer, Oswin, Hugo A Akitaya, Kenneth C Cheung, Erik D Demaine, Martin L Demaine, Sandor P Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” In <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, 164–70. Canadian Conference on Computational Geometry, 2019.","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. In: <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>. Canadian Conference on Computational Geometry; 2019:164-170.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, in:, Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–170."},"quality_controlled":"1","article_processing_charge":"No","date_published":"2019-08-01T00:00:00Z","day":"01","status":"public","ddc":["500"],"date_updated":"2026-07-28T13:08:49Z","external_id":{"arxiv":["1910.09917"]},"conference":{"start_date":"2019-08-08","name":"CCCG: Canadian Conference in Computational Geometry","location":"Edmonton, Canada","end_date":"2019-08-10"},"publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","department":[{"_id":"HeEd"}],"_id":"6989","OA_place":"publisher","acknowledgement":"This research was performed in part at the 33rd Bellairs Winter Workshop on Computational  Geometry. We thank all other participants for a fruitful atmosphere.","main_file_link":[{"url":"https://sites.ualberta.ca/~cccg2019/cccg2019_proceedings.pdf","open_access":"1"}],"page":"164-170","year":"2019","author":[{"first_name":"Oswin","full_name":"Aichholzer, Oswin","last_name":"Aichholzer"},{"first_name":"Hugo A","full_name":"Akitaya, Hugo A","last_name":"Akitaya"},{"last_name":"Cheung","first_name":"Kenneth C","full_name":"Cheung, Kenneth C"},{"last_name":"Demaine","first_name":"Erik D","full_name":"Demaine, Erik D"},{"last_name":"Demaine","full_name":"Demaine, Martin L","first_name":"Martin L"},{"last_name":"Fekete","first_name":"Sandor P","full_name":"Fekete, Sandor P"},{"full_name":"Kleist, Linda","first_name":"Linda","last_name":"Kleist"},{"first_name":"Irina","full_name":"Kostitsyna, Irina","last_name":"Kostitsyna"},{"last_name":"Löffler","full_name":"Löffler, Maarten","first_name":"Maarten"},{"full_name":"Masárová, Zuzana","first_name":"Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová"},{"last_name":"Mundilova","first_name":"Klara","full_name":"Mundilova, Klara"},{"last_name":"Schmidt","first_name":"Christiane","full_name":"Schmidt, Christiane"}],"abstract":[{"lang":"eng","text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability. "}],"publisher":"Canadian Conference on Computational Geometry"},{"publisher":"Springer","abstract":[{"lang":"eng","text":"The order-k Voronoi tessellation of a locally finite set 𝑋⊆ℝ𝑛 decomposes ℝ𝑛 into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold."}],"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","last_name":"Nikitenko","first_name":"Anton","full_name":"Nikitenko, Anton"}],"page":"865–878","year":"2019","OA_type":"hybrid","file_date_updated":"2020-07-14T12:47:10Z","corr_author":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant 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).\r\n\r\n","file":[{"file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","relation":"main_file","date_updated":"2020-07-14T12:47:10Z","file_size":599339,"content_type":"application/pdf","access_level":"open_access","file_id":"5932","date_created":"2019-02-06T10:10:46Z","creator":"dernst","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4"}],"OA_place":"publisher","_id":"5678","publication":"Discrete and Computational Geometry","department":[{"_id":"HeEd"}],"date_updated":"2026-07-28T13:38:08Z","external_id":{"arxiv":["1709.09380"],"isi":["000494042900008"]},"ddc":["516"],"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"status":"public","intvolume":"        62","day":"01","date_published":"2019-12-01T00:00:00Z","quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","citation":{"mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” <i>Discrete and Computational Geometry</i>, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:<a href=\"https://doi.org/10.1007/s00454-018-0049-2\">10.1007/s00454-018-0049-2</a>.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” <i>Discrete and Computational Geometry</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00454-018-0049-2\">https://doi.org/10.1007/s00454-018-0049-2</a>.","ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.","apa":"Edelsbrunner, H., &#38; Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. <i>Discrete and Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-018-0049-2\">https://doi.org/10.1007/s00454-018-0049-2</a>","ieee":"H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” <i>Discrete and Computational Geometry</i>, vol. 62, no. 4. Springer, pp. 865–878, 2019.","short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.","ama":"Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. <i>Discrete and Computational Geometry</i>. 2019;62(4):865–878. doi:<a href=\"https://doi.org/10.1007/s00454-018-0049-2\">10.1007/s00454-018-0049-2</a>"},"isi":1,"project":[{"call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35"}],"publication_status":"published","title":"Poisson–Delaunay Mosaics of Order k","ec_funded":1,"month":"12","language":[{"iso":"eng"}],"has_accepted_license":"1","related_material":{"record":[{"status":"public","id":"6287","relation":"dissertation_contains"}]},"oa":1,"oa_version":"Published Version","issue":"4","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","scopus_import":"1","volume":62,"arxiv":1,"type":"journal_article","doi":"10.1007/s00454-018-0049-2","date_created":"2018-12-16T22:59:20Z"},{"related_material":{"record":[{"relation":"later_version","id":"9317","status":"public"},{"id":"9056","status":"public","relation":"dissertation_contains"}]},"alternative_title":["LIPIcs"],"has_accepted_license":"1","oa_version":"Published Version","oa":1,"title":"The multi-cover persistence of Euclidean balls","month":"06","language":[{"iso":"eng"}],"publication_status":"published","quality_controlled":"1","project":[{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35"}],"citation":{"short":"H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.34\">10.4230/LIPIcs.SoCG.2018.34</a>","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.34\">https://doi.org/10.4230/LIPIcs.SoCG.2018.34</a>.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. <i>The Multi-Cover Persistence of Euclidean Balls</i>. Vol. 99, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.34\">10.4230/LIPIcs.SoCG.2018.34</a>.","ista":"Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.","apa":"Edelsbrunner, H., &#38; Osang, G. F. (2018). The multi-cover persistence of Euclidean balls (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.34\">https://doi.org/10.4230/LIPIcs.SoCG.2018.34</a>","ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99."},"doi":"10.4230/LIPIcs.SoCG.2018.34","date_created":"2018-12-11T11:45:05Z","volume":99,"scopus_import":1,"type":"conference","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"34","_id":"187","acknowledgement":"This work is 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).","file":[{"relation":"main_file","file_name":"2018_LIPIcs_Edelsbrunner_Osang.pdf","creator":"dernst","date_created":"2018-12-18T09:27:22Z","checksum":"d8c0533ad0018eb4ed1077475eb8fc18","file_id":"5738","content_type":"application/pdf","access_level":"open_access","date_updated":"2020-07-14T12:45:19Z","file_size":528018}],"year":"2018","file_date_updated":"2020-07-14T12:45:19Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Georg F","full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","last_name":"Osang"}],"abstract":[{"lang":"eng","text":"Given a locally finite X ⊆ ℝd and a radius r ≥ 0, the k-fold cover of X and r consists of all points in ℝd that have k or more points of X within distance r. We consider two filtrations - one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k - and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in ℝd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. "}],"day":"11","intvolume":"        99","publist_id":"7732","date_published":"2018-06-11T00:00:00Z","date_updated":"2026-04-08T07:01:29Z","status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"ddc":["516"],"conference":{"end_date":"2018-06-14","location":"Budapest, Hungary","start_date":"2018-06-11","name":"SoCG: Symposium on Computational Geometry"},"department":[{"_id":"HeEd"}]},{"publication_status":"published","quality_controlled":"1","project":[{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"citation":{"ista":"Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13.","apa":"Edelsbrunner, H., Virk, Z., &#38; Wagner, H. (2018). Smallest enclosing spheres and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.35\">https://doi.org/10.4230/LIPIcs.SoCG.2018.35</a>","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.","mla":"Edelsbrunner, Herbert, et al. <i>Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry</i>. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.35\">10.4230/LIPIcs.SoCG.2018.35</a>.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.35\">https://doi.org/10.4230/LIPIcs.SoCG.2018.35</a>.","ama":"Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:35:1-35:13. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.35\">10.4230/LIPIcs.SoCG.2018.35</a>","short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13."},"alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"has_accepted_license":"1","oa_version":"Published Version","oa":1,"title":"Smallest enclosing spheres and Chernoff points in Bregman geometry","month":"06","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.4230/LIPIcs.SoCG.2018.35","date_created":"2018-12-11T11:45:05Z","volume":99,"scopus_import":1,"type":"conference","year":"2018","page":"35:1 - 35:13","file_date_updated":"2020-07-14T12:45:20Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"last_name":"Virk","full_name":"Virk, Ziga","first_name":"Ziga"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","full_name":"Wagner, Hubert","first_name":"Hubert"}],"abstract":[{"lang":"eng","text":"Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex."}],"_id":"188","file":[{"file_id":"5724","checksum":"7509403803b3ac1aee94bbc2ad293d21","creator":"dernst","date_created":"2018-12-17T16:31:31Z","file_size":489080,"date_updated":"2020-07-14T12:45:20Z","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_name":"2018_LIPIcs_Edelsbrunner.pdf"}],"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","conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2018-06-11","end_date":"2018-06-14","location":"Budapest, Hungary"},"department":[{"_id":"HeEd"}],"intvolume":"        99","day":"11","publist_id":"7733","date_published":"2018-06-11T00:00:00Z","date_updated":"2021-01-12T06:53:48Z","status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"ddc":["000"]},{"publisher":"ACM","abstract":[{"lang":"eng","text":"We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki'16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block'16] for analyzing the hardware costs of an iMHF."}],"author":[{"id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87","last_name":"Alwen","full_name":"Alwen, Joel F","first_name":"Joel F"},{"last_name":"Gazi","first_name":"Peter","full_name":"Gazi, Peter"},{"first_name":"Chethan","full_name":"Kamath Hosdurg, Chethan","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","last_name":"Kamath Hosdurg"},{"full_name":"Klein, Karen","first_name":"Karen","last_name":"Klein","id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Osang, Georg F","first_name":"Georg F","last_name":"Osang","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pietrzak","orcid":"0000-0002-9139-1654","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","full_name":"Pietrzak, Krzysztof Z","first_name":"Krzysztof Z"},{"full_name":"Reyzin, Lenoid","first_name":"Lenoid","last_name":"Reyzin"},{"first_name":"Michal","full_name":"Rolinek, Michal","last_name":"Rolinek","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Michal","full_name":"Rybar, Michal","last_name":"Rybar","id":"2B3E3DE8-F248-11E8-B48F-1D18A9856A87"}],"page":"51 - 65","year":"2018","main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2016/783"}],"acknowledgement":"Leonid Reyzin was supported in part by IST Austria and by US NSF grants 1012910, 1012798, and 1422965; this research was performed while he was visiting IST Austria.","_id":"193","publication":"Proceedings of the 2018 on Asia Conference on Computer and Communication Security","department":[{"_id":"KrPi"},{"_id":"HeEd"},{"_id":"VlKo"}],"conference":{"name":"ASIACCS: Asia Conference on Computer and Communications Security ","start_date":"2018-06-04","location":"Incheon, Republic of Korea","end_date":"2018-06-08"},"date_updated":"2024-11-04T13:52:29Z","external_id":{"isi":["000516620100005"]},"status":"public","day":"01","date_published":"2018-06-01T00:00:00Z","publist_id":"7723","article_processing_charge":"No","quality_controlled":"1","citation":{"ieee":"J. F. Alwen <i>et al.</i>, “On the memory hardness of data independent password hashing functions,” in <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>, Incheon, Republic of Korea, 2018, pp. 51–65.","apa":"Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak, K. Z., … Rybar, M. (2018). On the memory hardness of data independent password hashing functions. In <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i> (pp. 51–65). Incheon, Republic of Korea: ACM. <a href=\"https://doi.org/10.1145/3196494.3196534\">https://doi.org/10.1145/3196494.3196534</a>","ista":"Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password hashing functions. Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ASIACCS: Asia Conference on Computer and Communications Security , 51–65.","chicago":"Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar. “On the Memory Hardness of Data Independent Password Hashing Functions.” In <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>, 51–65. ACM, 2018. <a href=\"https://doi.org/10.1145/3196494.3196534\">https://doi.org/10.1145/3196494.3196534</a>.","mla":"Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password Hashing Functions.” <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>, ACM, 2018, pp. 51–65, doi:<a href=\"https://doi.org/10.1145/3196494.3196534\">10.1145/3196494.3196534</a>.","ama":"Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data independent password hashing functions. In: <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>. ACM; 2018:51-65. doi:<a href=\"https://doi.org/10.1145/3196494.3196534\">10.1145/3196494.3196534</a>","short":"J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak, L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65."},"isi":1,"project":[{"call_identifier":"FP7","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425"},{"_id":"258AA5B2-B435-11E9-9278-68D0E5697425","name":"Teaching Old Crypto New Tricks","grant_number":"682815","call_identifier":"H2020"}],"publication_status":"published","ec_funded":1,"month":"06","title":"On the memory hardness of data independent password hashing functions","language":[{"iso":"eng"}],"oa":1,"oa_version":"Submitted Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","scopus_import":"1","type":"conference","doi":"10.1145/3196494.3196534","date_created":"2018-12-11T11:45:07Z"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:46:35Z","doi":"10.1090/tran/7292","type":"journal_article","volume":370,"arxiv":1,"scopus_import":"1","publication_status":"published","project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734"}],"citation":{"chicago":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2018. <a href=\"https://doi.org/10.1090/tran/7292\">https://doi.org/10.1090/tran/7292</a>.","mla":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” <i>Transactions of the American Mathematical Society</i>, vol. 370, no. 4, American Mathematical Society, 2018, pp. 2825–54, doi:<a href=\"https://doi.org/10.1090/tran/7292\">10.1090/tran/7292</a>.","ista":"Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 370(4), 2825–2854.","apa":"Akopyan, A., &#38; Bobenko, A. (2018). Incircular nets and confocal conics. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/7292\">https://doi.org/10.1090/tran/7292</a>","ieee":"A. Akopyan and A. Bobenko, “Incircular nets and confocal conics,” <i>Transactions of the American Mathematical Society</i>, vol. 370, no. 4. American Mathematical Society, pp. 2825–2854, 2018.","short":"A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society 370 (2018) 2825–2854.","ama":"Akopyan A, Bobenko A. Incircular nets and confocal conics. <i>Transactions of the American Mathematical Society</i>. 2018;370(4):2825-2854. doi:<a href=\"https://doi.org/10.1090/tran/7292\">10.1090/tran/7292</a>"},"isi":1,"article_processing_charge":"No","quality_controlled":"1","issue":"4","oa_version":"Preprint","oa":1,"language":[{"iso":"eng"}],"title":"Incircular nets and confocal conics","ec_funded":1,"month":"04","publication":"Transactions of the American Mathematical Society","department":[{"_id":"HeEd"}],"publist_id":"7363","date_published":"2018-04-01T00:00:00Z","intvolume":"       370","day":"01","status":"public","date_updated":"2025-06-04T08:06:10Z","external_id":{"arxiv":["1602.04637"],"isi":["000423197800019"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.04637"}],"year":"2018","page":"2825 - 2854","author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan"},{"last_name":"Bobenko","full_name":"Bobenko, Alexander","first_name":"Alexander"}],"abstract":[{"text":"We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics. Our main new results are on checkerboard IC-nets in the plane. These are congruences of straight lines in the plane with the combinatorics of the square grid, combinatorially colored as a checkerboard, such that all black coordinate quadrilaterals possess inscribed circles. We show how this larger class of IC-nets appears quite naturally in Laguerre geometry of oriented planes and spheres and leads to new remarkable incidence theorems. Most of our results are valid in hyperbolic and spherical geometries as well. We present also generalizations in spaces of higher dimension, called checkerboard IS-nets. The construction of these nets is based on a new 9 inspheres incidence theorem.","lang":"eng"}],"publisher":"American Mathematical Society","_id":"458","acknowledgement":"DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”; People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) REA grant agreement n◦[291734]","corr_author":"1"},{"page":"119 - 133","year":"2018","file_date_updated":"2020-07-14T12:46:38Z","publisher":"Elsevier","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Iglesias Ham, Mabel","first_name":"Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"text":"Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of Rn covered by at least k balls in a finite set. We implement two of the formulas in dimension n=3 and report on results obtained with our software.","lang":"eng"}],"_id":"530","corr_author":"1","file":[{"content_type":"application/pdf","access_level":"open_access","date_updated":"2020-07-14T12:46:38Z","file_size":708357,"creator":"dernst","date_created":"2019-02-12T06:47:52Z","checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","file_id":"5953","file_name":"2018_Edelsbrunner.pdf","relation":"main_file"}],"department":[{"_id":"HeEd"}],"publication":"Computational Geometry: Theory and Applications","day":"01","intvolume":"        68","publist_id":"7289","date_published":"2018-03-01T00:00:00Z","external_id":{"isi":["000415778300010"]},"date_updated":"2025-04-15T08:37:54Z","status":"public","ddc":["000"],"publication_status":"published","article_processing_charge":"No","quality_controlled":"1","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7"}],"isi":1,"citation":{"short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion. <i>Computational Geometry: Theory and Applications</i>. 2018;68:119-133. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">10.1016/j.comgeo.2017.06.014</a>","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2018. <a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">https://doi.org/10.1016/j.comgeo.2017.06.014</a>.","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” <i>Computational Geometry: Theory and Applications</i>, vol. 68, Elsevier, 2018, pp. 119–33, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">10.1016/j.comgeo.2017.06.014</a>.","apa":"Edelsbrunner, H., &#38; Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">https://doi.org/10.1016/j.comgeo.2017.06.014</a>","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” <i>Computational Geometry: Theory and Applications</i>, vol. 68. Elsevier, pp. 119–133, 2018.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133."},"has_accepted_license":"1","oa_version":"Preprint","oa":1,"title":"Multiple covers with balls I: Inclusion–exclusion","ec_funded":1,"month":"03","language":[{"iso":"eng"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","doi":"10.1016/j.comgeo.2017.06.014","date_created":"2018-12-11T11:46:59Z","volume":68,"scopus_import":"1","type":"journal_article"},{"department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"publication":"Forum of Mathematics, Sigma","day":"31","intvolume":"         6","date_published":"2018-05-31T00:00:00Z","external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"date_updated":"2026-04-08T07:25:54Z","status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"ddc":["510"],"year":"2018","file_date_updated":"2020-07-14T12:47:28Z","publisher":"Cambridge University Press","author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Avvakumov","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7840-5062","first_name":"Sergey","full_name":"Avvakumov, Sergey"}],"abstract":[{"lang":"eng","text":"We  prove  that  any  cyclic  quadrilateral  can  be  inscribed  in  any  closed  convex C1-curve.  The smoothness condition is not required if the quadrilateral is a rectangle."}],"article_number":"e7","_id":"6355","corr_author":"1","file":[{"access_level":"open_access","content_type":"application/pdf","file_size":249246,"date_updated":"2020-07-14T12:47:28Z","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","date_created":"2019-04-30T06:14:58Z","creator":"dernst","file_id":"6356","file_name":"2018_ForumMahtematics_Akopyan.pdf","relation":"main_file"}],"publication_identifier":{"issn":["2050-5094"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","doi":"10.1017/fms.2018.7","date_created":"2019-04-30T06:09:57Z","arxiv":1,"volume":6,"type":"journal_article","publication_status":"published","article_processing_charge":"No","quality_controlled":"1","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"}],"isi":1,"citation":{"ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. <i>Forum of Mathematics, Sigma</i>. 2018;6. doi:<a href=\"https://doi.org/10.1017/fms.2018.7\">10.1017/fms.2018.7</a>","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","apa":"Akopyan, A., &#38; Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2018.7\">https://doi.org/10.1017/fms.2018.7</a>","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” <i>Forum of Mathematics, Sigma</i>, vol. 6. Cambridge University Press, 2018.","chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2018. <a href=\"https://doi.org/10.1017/fms.2018.7\">https://doi.org/10.1017/fms.2018.7</a>.","mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” <i>Forum of Mathematics, Sigma</i>, vol. 6, e7, Cambridge University Press, 2018, doi:<a href=\"https://doi.org/10.1017/fms.2018.7\">10.1017/fms.2018.7</a>."},"related_material":{"record":[{"status":"public","id":"8156","relation":"dissertation_contains"}]},"has_accepted_license":"1","oa_version":"Published Version","oa":1,"ec_funded":1,"title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","month":"05","language":[{"iso":"eng"}]}]