[{"publication_identifier":{"eissn":["1617-9692"],"issn":["0075-8434"],"isbn":["9783030360191"],"eisbn":["9783030360207"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07350"}],"citation":{"ama":"Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Klartag B, Milman E, eds. <i>Geometric Aspects of Functional Analysis</i>. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>","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.","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.","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>","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","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>.","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>."},"type":"book_chapter","quality_controlled":"1","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"}],"day":"21","year":"2020","date_published":"2020-06-21T00:00:00Z","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"_id":"74","article_processing_charge":"No","publisher":"Springer Nature","volume":2256,"ec_funded":1,"status":"public","arxiv":1,"publication":"Geometric Aspects of Functional Analysis","page":"1-27","date_created":"2018-12-11T11:44:29Z","isi":1,"editor":[{"last_name":"Klartag","full_name":"Klartag, Bo'az","first_name":"Bo'az"},{"first_name":"Emanuel","full_name":"Milman, Emanuel","last_name":"Milman"}],"month":"06","intvolume":"      2256","oa":1,"oa_version":"Preprint","language":[{"iso":"eng"}],"series_title":"LNM","date_updated":"2025-07-10T11:54:33Z","publication_status":"published","scopus_import":"1","external_id":{"arxiv":["1808.07350"],"isi":["000557689300003"]},"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"}],"title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","doi":"10.1007/978-3-030-36020-7_1"},{"isi":1,"month":"02","page":"595-614","publication":"Theory of Probability and its Applications","date_created":"2020-03-01T23:00:39Z","oa":1,"intvolume":"        64","date_updated":"2025-07-10T11:54:44Z","publication_status":"published","scopus_import":"1","oa_version":"Preprint","language":[{"iso":"eng"}],"doi":"10.1137/S0040585X97T989726","external_id":{"isi":["000551393100007"],"arxiv":["1705.08735"]},"title":"Weighted Poisson–Delaunay mosaics","abstract":[{"text":"Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the smallest empty circumscribed sphere whose center lies in the $k$-plane gives a generalized discrete Morse function. Assuming the Voronoi tessellation is generated by a Poisson point process in ${R}^n$, we study the expected number of simplices in the $k$-dimensional weighted Delaunay mosaic as well as the expected number of intervals of the Morse function, both as functions of a radius threshold. As a by-product, we obtain a new proof for the expected number of connected components (clumps) in a line section of a circular Boolean model in ${R}^n$.","lang":"eng"}],"issue":"4","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.08735"}],"publication_identifier":{"eissn":["1095-7219"],"issn":["0040-585X"]},"type":"journal_article","project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"quality_controlled":"1","article_type":"original","citation":{"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>","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.","short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” <i>Theory of Probability and Its Applications</i>. SIAM, 2020. <a href=\"https://doi.org/10.1137/S0040585X97T989726\">https://doi.org/10.1137/S0040585X97T989726</a>.","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>","ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” <i>Theory of Probability and Its Applications</i>, vol. 64, no. 4, SIAM, 2020, pp. 595–614, doi:<a href=\"https://doi.org/10.1137/S0040585X97T989726\">10.1137/S0040585X97T989726</a>."},"author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","last_name":"Nikitenko","full_name":"Nikitenko, Anton"}],"_id":"7554","article_processing_charge":"No","publisher":"SIAM","day":"13","year":"2020","date_published":"2020-02-13T00:00:00Z","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"volume":64,"status":"public","ec_funded":1},{"publication_identifier":{"eissn":["1661-8289"],"issn":["1661-8270"]},"has_accepted_license":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","citation":{"mla":"Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” <i>Mathematics in Computer Science</i>, vol. 14, Springer Nature, 2020, pp. 141–76, doi:<a href=\"https://doi.org/10.1007/s11786-020-00461-5\">10.1007/s11786-020-00461-5</a>.","ama":"Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good quality. <i>Mathematics in Computer Science</i>. 2020;14:141-176. doi:<a href=\"https://doi.org/10.1007/s11786-020-00461-5\">10.1007/s11786-020-00461-5</a>","ista":"Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have good quality. Mathematics in Computer Science. 14, 141–176.","ieee":"A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations have good quality,” <i>Mathematics in Computer Science</i>, vol. 14. Springer Nature, pp. 141–176, 2020.","apa":"Choudhary, A., Kachanovich, S., &#38; Wintraecken, M. (2020). Coxeter triangulations have good quality. <i>Mathematics in Computer Science</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11786-020-00461-5\">https://doi.org/10.1007/s11786-020-00461-5</a>","chicago":"Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter Triangulations Have Good Quality.” <i>Mathematics in Computer Science</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11786-020-00461-5\">https://doi.org/10.1007/s11786-020-00461-5</a>.","short":"A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science 14 (2020) 141–176."},"type":"journal_article","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"quality_controlled":"1","year":"2020","day":"01","date_published":"2020-03-01T00:00:00Z","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7567","article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Choudhary","full_name":"Choudhary, Aruni","first_name":"Aruni"},{"first_name":"Siargey","last_name":"Kachanovich","full_name":"Kachanovich, Siargey"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"publisher":"Springer Nature","volume":14,"file_date_updated":"2020-11-20T10:18:02Z","license":"https://creativecommons.org/licenses/by/4.0/","file":[{"file_size":872275,"date_created":"2020-11-20T10:18:02Z","date_updated":"2020-11-20T10:18:02Z","access_level":"open_access","relation":"main_file","file_id":"8783","success":1,"creator":"dernst","checksum":"1d145f3ab50ccee735983cb89236e609","content_type":"application/pdf","file_name":"2020_MathCompScie_Choudhary.pdf"}],"ec_funded":1,"status":"public","page":"141-176","publication":"Mathematics in Computer Science","date_created":"2020-03-05T13:30:18Z","corr_author":"1","ddc":["510"],"month":"03","intvolume":"        14","oa":1,"oa_version":"Published Version","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2025-04-14T07:44:03Z","scopus_import":"1","title":"Coxeter triangulations have good quality","abstract":[{"text":"Coxeter triangulations are triangulations of Euclidean space based on a single simplex. By this we mean that given an individual simplex we can recover the entire triangulation of Euclidean space by inductively reflecting in the faces of the simplex. In this paper we establish that the quality of the simplices in all Coxeter triangulations is O(1/d−−√) of the quality of regular simplex. We further investigate the Delaunay property for these triangulations. Moreover, we consider an extension of the Delaunay property, namely protection, which is a measure of non-degeneracy of a Delaunay triangulation. In particular, one family of Coxeter triangulations achieves the protection O(1/d2). We conjecture that both bounds are optimal for triangulations in Euclidean space.","lang":"eng"}],"doi":"10.1007/s11786-020-00461-5"},{"type":"journal_article","quality_controlled":"1","project":[{"name":"Persistent Homology, Algorithms and Stochastic Geometry","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"}],"article_type":"original","tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode"},"citation":{"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>.","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.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11 (2020) 162–182.","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>","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."},"issue":"2","publication_identifier":{"eissn":["1920-180X"]},"has_accepted_license":"1","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).","volume":11,"file_date_updated":"2021-08-11T11:55:11Z","license":"https://creativecommons.org/licenses/by/3.0/","file":[{"file_size":1449234,"date_created":"2021-08-11T11:55:11Z","date_updated":"2021-08-11T11:55:11Z","access_level":"open_access","relation":"main_file","file_id":"9882","success":1,"creator":"asandaue","content_type":"application/pdf","checksum":"f02d0b2b3838e7891a6c417fc34ffdcd","file_name":"2020_JournalOfComputationalGeometry_Edelsbrunner.pdf"}],"status":"public","_id":"9630","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","full_name":"Virk, Ziga","last_name":"Virk"},{"full_name":"Wagner, Hubert","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","orcid":"0009-0009-9111-8429"}],"article_processing_charge":"Yes","publisher":"Carleton University","day":"14","year":"2020","date_published":"2020-12-14T00:00:00Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"HeEd"}],"oa":1,"intvolume":"        11","corr_author":"1","ddc":["510","000"],"month":"12","publication":"Journal of Computational Geometry","page":"162-182","date_created":"2021-07-04T22:01:26Z","doi":"10.20382/jocg.v11i2a7","title":"Topological data analysis in information space","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 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."}],"publication_status":"published","date_updated":"2026-04-02T14:35:31Z","scopus_import":"1","oa_version":"Published Version","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"oa_version":"Submitted Version","publication_status":"published","date_updated":"2026-04-07T12:35:47Z","scopus_import":"1","external_id":{"isi":["001321861000008"]},"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"}],"title":"Radius functions on Poisson–Delaunay mosaics and related complexes experimentally","doi":"10.1007/978-3-030-43408-3_8","date_created":"2020-07-19T22:00:59Z","page":"181-218","publication":"Topological Data Analysis","month":"06","isi":1,"ddc":["510"],"intvolume":"        15","oa":1,"date_published":"2020-06-22T00:00:00Z","day":"22","year":"2020","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"HeEd"}],"_id":"8135","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton"},{"full_name":"Ölsböck, Katharina","last_name":"Ölsböck","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina","orcid":"0000-0002-4672-8297"},{"full_name":"Synak, Peter","last_name":"Synak","first_name":"Peter","id":"331776E2-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","alternative_title":["Abel Symposia"],"publisher":"Springer Nature","file_date_updated":"2020-10-08T08:56:14Z","volume":15,"status":"public","ec_funded":1,"file":[{"creator":"dernst","success":1,"file_name":"2020-B-01-PoissonExperimentalSurvey.pdf","content_type":"application/pdf","checksum":"7b5e0de10675d787a2ddb2091370b8d8","relation":"main_file","file_id":"8628","date_updated":"2020-10-08T08:56:14Z","access_level":"open_access","file_size":2207071,"date_created":"2020-10-08T08:56:14Z"}],"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).","has_accepted_license":"1","publication_identifier":{"issn":["2193-2808"],"isbn":["9783030434076"],"eissn":["2197-8549"]},"related_material":{"record":[{"id":"19630","relation":"dissertation_contains","status":"public"}]},"citation":{"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.","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>","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.","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>.","short":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218.","mla":"Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” <i>Topological Data Analysis</i>, vol. 15, Springer Nature, 2020, pp. 181–218, doi:<a href=\"https://doi.org/10.1007/978-3-030-43408-3_8\">10.1007/978-3-030-43408-3_8</a>."},"project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"grant_number":"638176","_id":"2533E772-B435-11E9-9278-68D0E5697425","name":"Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales","call_identifier":"H2020"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35"}],"quality_controlled":"1","type":"conference"},{"conference":{"end_date":"2020-09-09","location":"Virtual, Online; Pisa, Italy","name":"ESA: European Symposium on Algorithms","start_date":"2020-09-07"},"file":[{"access_level":"open_access","date_updated":"2020-10-27T14:31:52Z","file_size":733291,"date_created":"2020-10-27T14:31:52Z","content_type":"application/pdf","checksum":"fe0f7c49a99ed870c671b911e10d5496","file_name":"2020_LIPIcs_Osang.pdf","success":1,"creator":"cziletti","file_id":"8712","relation":"main_file"}],"status":"public","ec_funded":1,"volume":173,"file_date_updated":"2020-10-27T14:31:52Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","alternative_title":["LIPIcs"],"article_processing_charge":"No","_id":"8703","author":[{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","last_name":"Osang"},{"last_name":"Rouxel-Labbé","full_name":"Rouxel-Labbé, Mael","first_name":"Mael"},{"full_name":"Teillaud, Monique","last_name":"Teillaud","first_name":"Monique"}],"department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"26","year":"2020","date_published":"2020-08-26T00:00:00Z","type":"conference","quality_controlled":"1","project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"}],"citation":{"mla":"Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.” <i>28th Annual European Symposium on Algorithms</i>, vol. 173, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2020.75\">10.4230/LIPIcs.ESA.2020.75</a>.","ista":"Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay triangulations. 28th Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms, LIPIcs, vol. 173, 75.","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>","short":"G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","chicago":"Osang, Georg F, Mael Rouxel-Labbé, and Monique Teillaud. “Generalizing CGAL Periodic Delaunay Triangulations.” In <i>28th Annual European Symposium on Algorithms</i>, Vol. 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2020.75\">https://doi.org/10.4230/LIPIcs.ESA.2020.75</a>.","ieee":"G. F. Osang, M. Rouxel-Labbé, and M. Teillaud, “Generalizing CGAL periodic Delaunay triangulations,” in <i>28th Annual European Symposium on Algorithms</i>, Virtual, Online; Pisa, Italy, 2020, vol. 173.","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>"},"tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode"},"article_number":"75","related_material":{"record":[{"id":"9056","status":"public","relation":"dissertation_contains"}]},"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959771627"]},"has_accepted_license":"1","doi":"10.4230/LIPIcs.ESA.2020.75","abstract":[{"text":"Even though Delaunay originally introduced his famous triangulations in the case of infinite point sets with translational periodicity, a software that computes such triangulations in the general case is not yet available, to the best of our knowledge. Combining and generalizing previous work, we present a practical algorithm for computing such triangulations. The algorithm has been implemented and experiments show that its performance is as good as the one of the CGAL package, which is restricted to cubic periodicity. ","lang":"eng"}],"title":"Generalizing CGAL periodic Delaunay triangulations","scopus_import":"1","publication_status":"published","date_updated":"2026-04-08T07:01:29Z","oa_version":"Published Version","language":[{"iso":"eng"}],"oa":1,"intvolume":"       173","ddc":["000"],"month":"08","corr_author":"1","publication":"28th Annual European Symposium on Algorithms","date_created":"2020-10-25T23:01:18Z"},{"file_date_updated":"2020-07-14T12:48:05Z","status":"public","file":[{"date_updated":"2020-07-14T12:48:05Z","access_level":"open_access","file_size":13661779,"date_created":"2020-06-08T00:34:00Z","creator":"zmasarov","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","content_type":"application/pdf","file_name":"THESIS_Zuzka_Masarova.pdf","relation":"main_file","file_id":"7945"},{"file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","content_type":"application/zip","checksum":"45341a35b8f5529c74010b7af43ac188","creator":"zmasarov","file_id":"7946","relation":"source_file","access_level":"closed","date_updated":"2020-07-14T12:48:05Z","file_size":32184006,"date_created":"2020-06-08T00:35:30Z"}],"license":"https://creativecommons.org/licenses/by-sa/4.0/","_id":"7944","author":[{"last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana"}],"article_processing_charge":"No","alternative_title":["ISTA Thesis"],"publisher":"Institute of Science and Technology Austria","date_published":"2020-06-09T00:00:00Z","day":"09","year":"2020","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","type":"dissertation","tmp":{"short":"CC BY-SA (4.0)","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","image":"/images/cc_by_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode"},"citation":{"ieee":"Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020.","apa":"Masárová, Z. (2020). <i>Reconfiguration problems</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:7944\">https://doi.org/10.15479/AT:ISTA:7944</a>","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. <a href=\"https://doi.org/10.15479/AT:ISTA:7944\">https://doi.org/10.15479/AT:ISTA:7944</a>.","short":"Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020.","ama":"Masárová Z. Reconfiguration problems. 2020. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7944\">10.15479/AT:ISTA:7944</a>","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria.","mla":"Masárová, Zuzana. <i>Reconfiguration Problems</i>. Institute of Science and Technology Austria, 2020, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7944\">10.15479/AT:ISTA:7944</a>."},"related_material":{"record":[{"id":"7950","status":"public","relation":"part_of_dissertation"},{"id":"5986","status":"public","relation":"part_of_dissertation"}]},"has_accepted_license":"1","keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-005-3"]},"OA_place":"publisher","doi":"10.15479/AT:ISTA:7944","abstract":[{"text":"This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars.","lang":"eng"}],"title":"Reconfiguration problems","degree_awarded":"PhD","publication_status":"published","date_updated":"2026-04-08T07:23:01Z","language":[{"iso":"eng"}],"oa_version":"Published Version","oa":1,"supervisor":[{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","last_name":"Wagner","full_name":"Wagner, Uli"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"corr_author":"1","month":"06","ddc":["516","514"],"date_created":"2020-06-08T00:49:46Z","page":"160"},{"oa":1,"month":"02","ddc":["514"],"supervisor":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833"}],"corr_author":"1","date_created":"2020-02-06T14:56:53Z","page":"155","OA_place":"publisher","doi":"10.15479/AT:ISTA:7460","abstract":[{"text":"Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications.\r\n\r\nFor the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries.","lang":"eng"}],"title":"The hole system of triangulated shapes","degree_awarded":"PhD","date_updated":"2026-04-08T07:23:21Z","publication_status":"published","language":[{"iso":"eng"}],"oa_version":"Published Version","type":"dissertation","citation":{"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.","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.","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."},"tmp":{"short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode"},"related_material":{"record":[{"id":"6608","status":"public","relation":"part_of_dissertation"}]},"keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"],"has_accepted_license":"1","publication_identifier":{"issn":["2663-337X"]},"status":"public","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","file":[{"date_created":"2020-02-06T14:43:54Z","file_size":76195184,"access_level":"open_access","date_updated":"2020-07-14T12:47:58Z","file_id":"7461","relation":"main_file","checksum":"1df9f8c530b443c0e63a3f2e4fde412e","file_name":"thesis_ist-final_noack.pdf","content_type":"application/pdf","creator":"koelsboe"},{"date_updated":"2020-07-14T12:47:58Z","description":"latex source files, figures","access_level":"closed","file_size":122103715,"date_created":"2020-02-06T14:52:45Z","creator":"koelsboe","content_type":"application/x-zip-compressed","file_name":"latex-files.zip","checksum":"7a52383c812b0be64d3826546509e5a4","relation":"source_file","file_id":"7462"}],"file_date_updated":"2020-07-14T12:47:58Z","alternative_title":["ISTA Thesis"],"publisher":"Institute of Science and Technology Austria","article_processing_charge":"No","_id":"7460","author":[{"id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina","orcid":"0000-0002-4672-8297","full_name":"Ölsböck, Katharina","last_name":"Ölsböck"}],"department":[{"_id":"HeEd"},{"_id":"GradSch"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_published":"2020-02-10T00:00:00Z","year":"2020","day":"10"},{"quality_controlled":"1","type":"journal_article","citation":{"mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” <i>Proceedings of the American Mathematical Society</i>, vol. 147, AMS, 2019, pp. 91–102, doi:<a href=\"https://doi.org/10.1090/proc/14240\">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.","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>","apa":"Akopyan, A., &#38; Fedorov, R. (2019). Two circles and only a straightedge. <i>Proceedings of the American Mathematical Society</i>. AMS. <a href=\"https://doi.org/10.1090/proc/14240\">https://doi.org/10.1090/proc/14240</a>","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” <i>Proceedings of the American Mathematical Society</i>, vol. 147. AMS, pp. 91–102, 2019.","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102.","chicago":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” <i>Proceedings of the American Mathematical Society</i>. AMS, 2019. <a href=\"https://doi.org/10.1090/proc/14240\">https://doi.org/10.1090/proc/14240</a>."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1709.02562"}],"arxiv":1,"status":"public","volume":147,"publisher":"AMS","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"first_name":"Roman","last_name":"Fedorov","full_name":"Fedorov, Roman"}],"_id":"6050","article_processing_charge":"No","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2019-01-01T00:00:00Z","year":"2019","day":"01","oa":1,"intvolume":"       147","month":"01","isi":1,"date_created":"2019-02-24T22:59:19Z","page":"91-102","publication":"Proceedings of the American Mathematical Society","doi":"10.1090/proc/14240","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"}],"title":"Two circles and only a straightedge","external_id":{"isi":["000450363900008"],"arxiv":["1709.02562"]},"scopus_import":"1","publication_status":"published","date_updated":"2023-08-24T14:48:59Z","language":[{"iso":"eng"}],"oa_version":"Preprint"},{"type":"journal_article","quality_controlled":"1","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"citation":{"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.","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>","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>.","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.","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>","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>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"issue":"1","publication_identifier":{"issn":["1920-180X"]},"has_accepted_license":"1","file":[{"file_size":2170882,"date_created":"2019-06-03T09:30:01Z","date_updated":"2020-07-14T12:47:32Z","access_level":"open_access","relation":"main_file","file_id":"6516","creator":"mwintrae","checksum":"57b4df2f16a74eb499734ec8ee240178","file_name":"mainJournalFinal.pdf","content_type":"application/pdf"}],"status":"public","ec_funded":1,"file_date_updated":"2020-07-14T12:47:32Z","volume":10,"publisher":"Carleton University","_id":"6515","author":[{"full_name":"Dyer, Ramsay","last_name":"Dyer","first_name":"Ramsay"},{"last_name":"Vegter","full_name":"Vegter, Gert","first_name":"Gert"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"department":[{"_id":"HeEd"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2019","day":"01","date_published":"2019-07-01T00:00:00Z","oa":1,"intvolume":"        10","ddc":["510"],"month":"07","publication":"Journal of Computational Geometry ","page":"223–256","date_created":"2019-06-03T09:35:33Z","doi":"10.20382/jocg.v10i1a9","title":"Simplices modelled on spaces of constant curvature","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"}],"scopus_import":1,"publication_status":"published","date_updated":"2021-01-12T08:07:50Z","oa_version":"Published Version","language":[{"iso":"eng"}]},{"file":[{"file_id":"6629","relation":"main_file","content_type":"application/pdf","checksum":"ceabd152cfa55170d57763f9c6c60a53","file_name":"IntrinsicExtrinsicCCCG2019.pdf","creator":"mwintrae","file_size":321176,"date_created":"2019-07-12T08:32:46Z","access_level":"open_access","date_updated":"2020-07-14T12:47:34Z"}],"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","status":"public","ec_funded":1,"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."}],"file_date_updated":"2020-07-14T12:47:34Z","conference":{"end_date":"2019-08-10","location":"Edmonton, Canada","start_date":"2019-08-08","name":"CCCG: Canadian Conference in Computational Geometry"},"department":[{"_id":"HeEd"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","year":"2019","day":"01","date_published":"2019-08-01T00:00:00Z","language":[{"iso":"eng"}],"scopus_import":1,"author":[{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"_id":"6628","date_updated":"2021-01-12T08:08:16Z","publication_status":"published","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.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279.","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.","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.","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."},"type":"conference","oa":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"has_accepted_license":"1","page":"275-279","publication":"The 31st Canadian Conference in Computational Geometry","date_created":"2019-07-12T08:34:57Z","ddc":["004"],"month":"08"},{"intvolume":"        53","oa":1,"page":"457-490","publication":"Topological Methods in Nonlinear Analysis","date_created":"2019-07-14T21:59:19Z","isi":1,"month":"06","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."}],"title":"Lower and upper bounds for the waists of different spaces","external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"doi":"10.12775/TMNA.2019.008","oa_version":"Preprint","language":[{"iso":"eng"}],"scopus_import":"1","date_updated":"2025-04-15T06:50:28Z","publication_status":"published","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>.","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","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.","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>","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>","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>."},"type":"journal_article","project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734"}],"quality_controlled":"1","issue":"2","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.06926"}],"ec_funded":1,"status":"public","volume":53,"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"day":"01","year":"2019","date_published":"2019-06-01T00:00:00Z","publisher":"Akademicka Platforma Czasopism","article_processing_charge":"No","_id":"6634","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X"},{"first_name":"Alfredo","last_name":"Hubard","full_name":"Hubard, Alfredo"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}]},{"has_accepted_license":"1","publication_identifier":{"isbn":["9783959771047"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"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.","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>","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.","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>","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.","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>."},"project":[{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35"}],"quality_controlled":"1","type":"conference","date_published":"2019-06-01T00:00:00Z","year":"2019","day":"01","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"first_name":"Ziga","full_name":"Virk, Ziga","last_name":"Virk"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"_id":"6648","alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","volume":129,"file_date_updated":"2020-07-14T12:47:35Z","status":"public","file":[{"date_updated":"2020-07-14T12:47:35Z","access_level":"open_access","file_size":1355179,"date_created":"2019-07-24T06:40:01Z","creator":"dernst","checksum":"8ec8720730d4c789bf7b06540f1c29f4","file_name":"2019_LIPICS_Edelsbrunner.pdf","content_type":"application/pdf","relation":"main_file","file_id":"6666"}],"arxiv":1,"conference":{"name":"SoCG 2019: Symposium on Computational Geometry","start_date":"2019-06-18","location":"Portland, OR, United States","end_date":"2019-06-21"},"date_created":"2019-07-17T10:36:09Z","publication":"35th International Symposium on Computational Geometry","page":"31:1-31:14","corr_author":"1","month":"06","ddc":["510"],"intvolume":"       129","oa":1,"language":[{"iso":"eng"}],"oa_version":"Published Version","publication_status":"published","date_updated":"2024-10-09T20:58:55Z","scopus_import":1,"external_id":{"arxiv":["1903.08510"]},"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\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.","lang":"eng"}],"title":"Topological data analysis in information space","doi":"10.4230/LIPICS.SOCG.2019.31"},{"date_updated":"2025-04-14T07:44:06Z","publication_status":"published","scopus_import":"1","oa_version":"Published Version","language":[{"iso":"eng"}],"doi":"10.1007/s41468-019-00029-8","title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","abstract":[{"lang":"eng","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."}],"corr_author":"1","ddc":["000"],"month":"06","page":"29–58","publication":"Journal of Applied and Computational Topology","date_created":"2019-07-24T08:37:29Z","oa":1,"intvolume":"         3","author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"_id":"6671","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","year":"2019","day":"01","date_published":"2019-06-01T00:00:00Z","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":3,"file_date_updated":"2020-07-14T12:47:36Z","file":[{"checksum":"a5b244db9f751221409cf09c97ee0935","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf","content_type":"application/pdf","creator":"dernst","file_id":"6741","relation":"main_file","access_level":"open_access","date_updated":"2020-07-14T12:47:36Z","file_size":2215157,"date_created":"2019-07-31T08:09:56Z"}],"ec_funded":1,"status":"public","issue":"1-2","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"has_accepted_license":"1","type":"journal_article","project":[{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","citation":{"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.","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>","short":"J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58.","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>.","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>","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>."}},{"publication_identifier":{"eissn":["1432-0746"],"issn":["0004-6361"]},"has_accepted_license":"1","article_number":"A163","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","OA_type":"hybrid","citation":{"mla":"Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” <i>Astronomy and 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>.","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 and Astrophysics. 627, A163.","ama":"Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature fluctuations in the cosmic microwave background. <i>Astronomy and 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 and Astrophysics 627 (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 and Astrophysics</i>. EDP Sciences, 2019. <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 and Astrophysics</i>, vol. 627. EDP Sciences, 2019.","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 and Astrophysics</i>. EDP Sciences. <a href=\"https://doi.org/10.1051/0004-6361/201834916\">https://doi.org/10.1051/0004-6361/201834916</a>"},"type":"journal_article","project":[{"_id":"265683E4-B435-11E9-9278-68D0E5697425","name":"Toward Computational Information Topology","grant_number":"M62909-18-1-2038"},{"grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","year":"2019","day":"17","date_published":"2019-07-17T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"author":[{"last_name":"Pranav","full_name":"Pranav, Pratyush","first_name":"Pratyush"},{"last_name":"Adler","full_name":"Adler, Robert J.","first_name":"Robert J."},{"last_name":"Buchert","full_name":"Buchert, Thomas","first_name":"Thomas"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"first_name":"Bernard J.T.","last_name":"Jones","full_name":"Jones, Bernard J.T."},{"first_name":"Armin","full_name":"Schwartzman, Armin","last_name":"Schwartzman"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert"},{"last_name":"Van De Weygaert","full_name":"Van De Weygaert, Rien","first_name":"Rien"}],"_id":"6756","article_processing_charge":"No","publisher":"EDP Sciences","file_date_updated":"2020-07-14T12:47:39Z","volume":627,"file":[{"access_level":"open_access","date_updated":"2020-07-14T12:47:39Z","file_size":14420451,"date_created":"2019-08-05T08:08:59Z","file_name":"2019_AstronomyAstrophysics_Pranav.pdf","checksum":"83b9209ed9eefbdcefd89019c5a97805","content_type":"application/pdf","creator":"dernst","file_id":"6766","relation":"main_file"}],"status":"public","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.","arxiv":1,"publication":"Astronomy and Astrophysics","date_created":"2019-08-04T21:59:18Z","isi":1,"ddc":["520","530"],"month":"07","intvolume":"       627","oa":1,"oa_version":"Published Version","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2025-05-20T08:01:55Z","scopus_import":"1","external_id":{"arxiv":["1812.07678"],"isi":["000475839300003"]},"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."}],"title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","doi":"10.1051/0004-6361/201834916","OA_place":"publisher"},{"article_processing_charge":"No","_id":"6793","author":[{"orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"first_name":"Ivan","last_name":"Izmestiev","full_name":"Izmestiev, Ivan"}],"publisher":"London Mathematical Society","year":"2019","day":"01","date_published":"2019-10-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"arxiv":1,"volume":51,"status":"public","ec_funded":1,"issue":"5","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.04929"}],"publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"type":"journal_article","project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"}],"quality_controlled":"1","article_type":"original","citation":{"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>","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.","short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","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>.","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.","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>."},"date_updated":"2025-07-10T11:53:52Z","publication_status":"published","scopus_import":"1","oa_version":"Preprint","language":[{"iso":"eng"}],"doi":"10.1112/blms.12276","external_id":{"isi":["000478560200001"],"arxiv":["1903.04929"]},"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."}],"title":"The Regge symmetry, confocal conics, and the Schläfli formula","isi":1,"month":"10","publication":"Bulletin of the London Mathematical Society","page":"765-775","date_created":"2019-08-11T21:59:23Z","oa":1,"intvolume":"        51"},{"isi":1,"month":"11","publication":"Journal of Algebra","page":"261-289","date_created":"2019-08-22T07:54:13Z","oa":1,"intvolume":"       538","date_updated":"2023-08-29T07:11:47Z","publication_status":"published","oa_version":"Preprint","language":[{"iso":"eng"}],"doi":"10.1016/j.jalgebra.2019.07.027","abstract":[{"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 .","lang":"eng"}],"title":"Arakawa-Suzuki functors for Whittaker modules","external_id":{"isi":["000487176300011"],"arxiv":["1805.04676"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.04676"}],"publication_identifier":{"issn":["0021-8693"]},"type":"journal_article","quality_controlled":"1","citation":{"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>.","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>.","short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","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.","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>"},"article_type":"original","publisher":"Elsevier","_id":"6828","author":[{"full_name":"Brown, Adam","last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam"}],"article_processing_charge":"No","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2019","day":"15","date_published":"2019-11-15T00:00:00Z","arxiv":1,"status":"public","volume":538},{"citation":{"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>","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.","short":"G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019.","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>.","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>","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.","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>."},"quality_controlled":"1","type":"conference","date_created":"2019-12-29T23:00:47Z","publication":"2019 IEEE Intelligent Transportation Systems Conference","publication_identifier":{"isbn":["9781538670248"]},"month":"11","article_number":"8917514","isi":1,"external_id":{"isi":["000521238102050"]},"abstract":[{"lang":"eng","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."}],"status":"public","title":"LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale","conference":{"end_date":"2019-10-30","location":"Auckland, New Zealand","name":"ITSC: Intelligent Transportation Systems Conference","start_date":"2019-10-27"},"doi":"10.1109/ITSC.2019.8917514","date_published":"2019-11-28T00:00:00Z","language":[{"iso":"eng"}],"oa_version":"None","day":"28","year":"2019","department":[{"_id":"HeEd"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_status":"published","_id":"7216","article_processing_charge":"No","author":[{"full_name":"Osang, Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","orcid":"0000-0002-8882-5116"},{"first_name":"James","last_name":"Cook","full_name":"Cook, James"},{"full_name":"Fabrikant, Alex","last_name":"Fabrikant","first_name":"Alex"},{"full_name":"Gruteser, Marco","last_name":"Gruteser","first_name":"Marco"}],"date_updated":"2023-09-06T14:50:28Z","scopus_import":"1","publisher":"IEEE"},{"doi":"10.48550/arXiv.1903.06981","arxiv":1,"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."}],"title":"Token swapping on trees","status":"public","external_id":{"arxiv":["1903.06981"]},"_id":"7950","article_processing_charge":"No","publication_status":"draft","author":[{"first_name":"Ahmad","full_name":"Biniaz, Ahmad","last_name":"Biniaz"},{"full_name":"Jain, Kshitij","last_name":"Jain","first_name":"Kshitij"},{"first_name":"Anna","last_name":"Lubiw","full_name":"Lubiw, Anna"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová"},{"first_name":"Tillmann","full_name":"Miltzow, Tillmann","last_name":"Miltzow"},{"last_name":"Mondal","full_name":"Mondal, Debajyoti","first_name":"Debajyoti"},{"first_name":"Anurag Murty","full_name":"Naredla, Anurag Murty","last_name":"Naredla"},{"last_name":"Tkadlec","full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef"},{"first_name":"Alexi","full_name":"Turcotte, Alexi","last_name":"Turcotte"}],"date_updated":"2026-04-08T07:23:00Z","department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"16","year":"2019","oa_version":"Preprint","date_published":"2019-03-16T00:00:00Z","language":[{"iso":"eng"}],"type":"preprint","oa":1,"citation":{"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>.","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.).","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>","ieee":"A. Biniaz <i>et al.</i>, “Token swapping on trees,” <i>arXiv</i>. .","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>","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.","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>."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.06981"}],"article_number":"1903.06981","month":"03","related_material":{"record":[{"status":"public","relation":"later_version","id":"12833"},{"relation":"dissertation_contains","status":"public","id":"7944"}]},"publication":"arXiv","date_created":"2020-06-08T12:25:25Z"},{"doi":"10.1016/j.cagd.2019.06.003","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"}],"title":"Holes and dependences in an ordered complex","external_id":{"isi":["000485207800001"]},"scopus_import":"1","publication_status":"published","date_updated":"2026-04-08T07:23:21Z","language":[{"iso":"eng"}],"oa_version":"Published Version","oa":1,"intvolume":"        73","month":"08","isi":1,"ddc":["000"],"date_created":"2019-07-07T21:59:20Z","publication":"Computer Aided Geometric Design","page":"1-15","status":"public","ec_funded":1,"file":[{"relation":"main_file","file_id":"6624","creator":"kschuh","content_type":"application/pdf","checksum":"7c99be505dc7533257d42eb1830cef04","file_name":"Elsevier_2019_Edelsbrunner.pdf","file_size":2665013,"date_created":"2019-07-08T15:24:26Z","date_updated":"2020-07-14T12:47:34Z","access_level":"open_access"}],"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","file_date_updated":"2020-07-14T12:47:34Z","volume":73,"publisher":"Elsevier","_id":"6608","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4672-8297","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina","last_name":"Ölsböck","full_name":"Ölsböck, Katharina"}],"article_processing_charge":"No","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2019-08-01T00:00:00Z","day":"01","year":"2019","quality_controlled":"1","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"}],"type":"journal_article","citation":{"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>","ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.","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.","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>."},"tmp":{"short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"7460"}]},"has_accepted_license":"1"}]