[{"status":"public","type":"conference","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)"},"conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2020-06-22","end_date":"2020-06-26","location":"Zürich, Switzerland"},"_id":"7952","file_date_updated":"2020-07-14T12:48:06Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2023-08-02T06:49:16Z","month":"06","intvolume":" 164","scopus_import":"1","alternative_title":["LIPIcs"],"oa_version":"Published Version","abstract":[{"text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine triangulation 𝒯. This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary. ","lang":"eng"}],"related_material":{"record":[{"relation":"later_version","id":"9649","status":"public"}]},"volume":164,"ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","file":[{"date_created":"2020-06-17T10:13:34Z","file_name":"2020_LIPIcsSoCG_Boissonnat.pdf","date_updated":"2020-07-14T12:48:06Z","file_size":1009739,"creator":"dernst","checksum":"38cbfa4f5d484d267a35d44d210df044","file_id":"7969","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-143-6"]},"publication_status":"published","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"article_number":"20:1-20:18","title":"The topological correctness of PL-approximations of isomanifolds","author":[{"last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” 36th International Symposium on Computational Geometry, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.20.","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations of isomanifolds. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.20","apa":"Boissonnat, J.-D., & Wintraecken, M. (2020). The topological correctness of PL-approximations of isomanifolds. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.20","short":"J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations of isomanifolds,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.","chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.20.","ista":"Boissonnat J-D, Wintraecken M. 2020. The topological correctness of PL-approximations of isomanifolds. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 20:1-20:18."},"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"doi":"10.4230/LIPIcs.SoCG.2020.20","date_published":"2020-06-01T00:00:00Z","date_created":"2020-06-09T07:24:11Z","day":"01","publication":"36th International Symposium on Computational Geometry","has_accepted_license":"1","year":"2020"},{"abstract":[{"lang":"eng","text":"We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about the waist of radially symmetric Gaussian measures. In particular, it turns our possible to extend Gromov’s original result to the case of not necessarily radially symmetric Gaussian measure. We also provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument to produce some estimates of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1808.07350","open_access":"1"}],"month":"06","intvolume":" 2256","publication_identifier":{"eisbn":["9783030360207"],"isbn":["9783030360191"],"eissn":["16179692"],"issn":["00758434"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":2256,"ec_funded":1,"_id":"74","series_title":"LNM","type":"book_chapter","status":"public","date_updated":"2023-08-17T13:48:31Z","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"publisher":"Springer Nature","quality_controlled":"1","oa":1,"isi":1,"year":"2020","day":"21","publication":"Geometric Aspects of Functional Analysis","page":"1-27","doi":"10.1007/978-3-030-36020-7_1","date_published":"2020-06-21T00:00:00Z","date_created":"2018-12-11T11:44:29Z","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"chicago":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1.","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.","mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.","ama":"Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1","apa":"Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.), Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer Nature. https://doi.org/10.1007/978-3-030-36020-7_1","ieee":"A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"article_processing_charge":"No","external_id":{"isi":["000557689300003"],"arxiv":["1808.07350"]},"editor":[{"full_name":"Klartag, Bo'az","last_name":"Klartag","first_name":"Bo'az"},{"last_name":"Milman","full_name":"Milman, Emanuel","first_name":"Emanuel"}],"title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures"},{"quality_controlled":"1","publisher":"SIAM","oa":1,"page":"595-614","doi":"10.1137/S0040585X97T989726","date_published":"2020-02-13T00:00:00Z","date_created":"2020-03-01T23:00:39Z","isi":1,"year":"2020","day":"13","publication":"Theory of Probability and its Applications","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","last_name":"Nikitenko","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton"}],"external_id":{"arxiv":["1705.08735"],"isi":["000551393100007"]},"article_processing_charge":"No","title":"Weighted Poisson–Delaunay mosaics","citation":{"mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications, vol. 64, no. 4, SIAM, 2020, pp. 595–614, doi:10.1137/S0040585X97T989726.","short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.","ieee":"H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” Theory of Probability and its Applications, vol. 64, no. 4. SIAM, pp. 595–614, 2020.","apa":"Edelsbrunner, H., & Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics. Theory of Probability and Its Applications. SIAM. https://doi.org/10.1137/S0040585X97T989726","ama":"Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 2020;64(4):595-614. doi:10.1137/S0040585X97T989726","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications. SIAM, 2020. https://doi.org/10.1137/S0040585X97T989726.","ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.08735"}],"month":"02","intvolume":" 64","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"}],"oa_version":"Preprint","issue":"4","volume":64,"ec_funded":1,"publication_identifier":{"eissn":["10957219"],"issn":["0040585X"]},"publication_status":"published","language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","status":"public","_id":"7554","department":[{"_id":"HeEd"}],"date_updated":"2023-08-18T06:45:48Z"},{"_id":"7666","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","type":"journal_article","status":"public","date_updated":"2023-08-21T06:13:48Z","ddc":["510"],"file_date_updated":"2020-11-20T13:22:21Z","department":[{"_id":"HeEd"}],"abstract":[{"text":"Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 64","month":"03","publication_status":"published","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"language":[{"iso":"eng"}],"file":[{"success":1,"checksum":"f8cc96e497f00c38340b5dafe0cb91d7","file_id":"8786","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf","date_created":"2020-11-20T13:22:21Z","file_size":701673,"date_updated":"2020-11-20T13:22:21Z","creator":"dernst"}],"ec_funded":1,"volume":64,"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"citation":{"chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00188-x.","ista":"Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 759–75, doi:10.1007/s00454-020-00188-x.","apa":"Edelsbrunner, H., & Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00188-x","ama":"Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 2020;64:759-775. doi:10.1007/s00454-020-00188-x","short":"H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.","ieee":"H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 759–775, 2020."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000520918800001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"orcid":"0000-0002-4672-8297","full_name":"Ölsböck, Katharina","last_name":"Ölsböck","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina"}],"title":"Tri-partitions and bases of an ordered complex","acknowledgement":"This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF).","oa":1,"publisher":"Springer Nature","quality_controlled":"1","year":"2020","isi":1,"has_accepted_license":"1","publication":"Discrete and Computational Geometry","day":"20","page":"759-775","date_created":"2020-04-19T22:00:56Z","doi":"10.1007/s00454-020-00188-x","date_published":"2020-03-20T00:00:00Z"},{"project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342"}],"title":"Almost all string graphs are intersection graphs of plane convex sets","article_processing_charge":"No","external_id":{"isi":["000538229000001"],"arxiv":["1803.06710"]},"author":[{"full_name":"Pach, János","last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János"},{"full_name":"Reed, Bruce","last_name":"Reed","first_name":"Bruce"},{"first_name":"Yelena","last_name":"Yuditsky","full_name":"Yuditsky, Yelena"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Pach J, Reed B, Yuditsky Y. 2020. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 63(4), 888–917.","chicago":"Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00213-z.","apa":"Pach, J., Reed, B., & Yuditsky, Y. (2020). Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00213-z","ama":"Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 2020;63(4):888-917. doi:10.1007/s00454-020-00213-z","short":"J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917.","ieee":"J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection graphs of plane convex sets,” Discrete and Computational Geometry, vol. 63, no. 4. Springer Nature, pp. 888–917, 2020.","mla":"Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry, vol. 63, no. 4, Springer Nature, 2020, pp. 888–917, doi:10.1007/s00454-020-00213-z."},"oa":1,"quality_controlled":"1","publisher":"Springer Nature","date_created":"2020-06-14T22:00:51Z","date_published":"2020-06-05T00:00:00Z","doi":"10.1007/s00454-020-00213-z","page":"888-917","publication":"Discrete and Computational Geometry","day":"05","year":"2020","isi":1,"status":"public","type":"journal_article","article_type":"original","_id":"7962","department":[{"_id":"HeEd"}],"date_updated":"2023-08-21T08:49:18Z","intvolume":" 63","month":"06","main_file_link":[{"url":"https://arxiv.org/abs/1803.06710","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","text":"A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n→∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets."}],"issue":"4","volume":63,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]}},{"date_updated":"2023-08-22T09:05:04Z","department":[{"_id":"HeEd"}],"_id":"8323","status":"public","article_type":"letter_note","type":"journal_article","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"publication_status":"published","volume":64,"oa_version":"None","month":"10","intvolume":" 64","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-020-00237-5"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5.","ista":"Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574.","mla":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 571–74, doi:10.1007/s00454-020-00237-5.","short":"J. Pach, Discrete and Computational Geometry 64 (2020) 571–574.","ieee":"J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 571–574, 2020.","apa":"Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5","ama":"Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry. 2020;64:571-574. doi:10.1007/s00454-020-00237-5"},"title":"A farewell to Ricky Pollack","author":[{"last_name":"Pach","full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"}],"article_processing_charge":"No","external_id":{"isi":["000561483500001"]},"day":"01","publication":"Discrete and Computational Geometry","isi":1,"year":"2020","date_published":"2020-10-01T00:00:00Z","doi":"10.1007/s00454-020-00237-5","date_created":"2020-08-30T22:01:12Z","page":"571-574","publisher":"Springer Nature","oa":1},{"author":[{"last_name":"Graff","full_name":"Graff, Grzegorz","first_name":"Grzegorz"},{"last_name":"Graff","full_name":"Graff, Beata","first_name":"Beata"},{"first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","last_name":"Jablonski"},{"last_name":"Narkiewicz","full_name":"Narkiewicz, Krzysztof","first_name":"Krzysztof"}],"article_processing_charge":"No","external_id":{"isi":["000621172600045"]},"title":"The application of persistent homology in the analysis of heart rate variability","department":[{"_id":"HeEd"}],"date_updated":"2023-08-22T09:33:34Z","citation":{"mla":"Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , 9158054, IEEE, 2020, doi:10.1109/ESGCO49734.2020.9158054.","apa":"Graff, G., Graff, B., Jablonski, G., & Narkiewicz, K. (2020). The application of persistent homology in the analysis of heart rate variability. In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . Pisa, Italy: IEEE. https://doi.org/10.1109/ESGCO49734.2020.9158054","ama":"Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent homology in the analysis of heart rate variability. In: 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE; 2020. doi:10.1109/ESGCO49734.2020.9158054","short":"G. Graff, B. Graff, G. Jablonski, K. Narkiewicz, in:, 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , IEEE, 2020.","ieee":"G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of persistent homology in the analysis of heart rate variability,” in 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , Pisa, Italy, 2020.","chicago":"Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE, 2020. https://doi.org/10.1109/ESGCO49734.2020.9158054.","ista":"Graff G, Graff B, Jablonski G, Narkiewicz K. 2020. The application of persistent homology in the analysis of heart rate variability. 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . ESGCO: European Study Group on Cardiovascular Oscillations, 9158054."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","type":"conference","conference":{"end_date":"2020-07-15","location":"Pisa, Italy","start_date":"2020-07-15","name":"ESGCO: European Study Group on Cardiovascular Oscillations"},"status":"public","_id":"8580","article_number":"9158054","doi":"10.1109/ESGCO49734.2020.9158054","date_published":"2020-08-01T00:00:00Z","date_created":"2020-09-28T08:59:27Z","publication_identifier":{"isbn":["9781728157511"]},"isi":1,"year":"2020","publication_status":"published","day":"01","publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"IEEE","quality_controlled":"1","month":"08","abstract":[{"text":"We evaluate the usefulness of persistent homology in the analysis of heart rate variability. In our approach we extract several topological descriptors characterising datasets of RR-intervals, which are later used in classical machine learning algorithms. By this method we are able to differentiate the group of patients with the history of transient ischemic attack and the group of hypertensive patients.","lang":"eng"}],"oa_version":"None"},{"status":"public","keyword":["General Mathematics"],"article_type":"original","type":"journal_article","_id":"10867","department":[{"_id":"HeEd"}],"date_updated":"2023-08-24T14:19:55Z","month":"02","intvolume":" 2020","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1702.07513","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces."}],"issue":"3","volume":2020,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"publication_status":"published","title":"Waist of balls in hyperbolic and spherical spaces","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"article_processing_charge":"No","external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rny037.","ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037","apa":"Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rny037","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” International Mathematics Research Notices, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020.","short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037."},"quality_controlled":"1","publisher":"Oxford University Press","oa":1,"acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","date_published":"2020-02-01T00:00:00Z","doi":"10.1093/imrn/rny037","date_created":"2022-03-18T11:39:30Z","page":"669-697","day":"01","publication":"International Mathematics Research Notices","isi":1,"year":"2020"},{"oa":1,"publisher":"Institute of Science and Technology Austria","day":"10","year":"2020","has_accepted_license":"1","date_created":"2020-02-06T14:56:53Z","date_published":"2020-02-10T00:00:00Z","doi":"10.15479/AT:ISTA:7460","page":"155","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"short":"K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science and Technology Austria, 2020.","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:10.15479/AT:ISTA:7460","apa":"Ölsböck, K. (2020). The hole system of triangulated shapes. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7460","mla":"Ölsböck, Katharina. The Hole System of Triangulated Shapes. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7460.","ista":"Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria.","chicago":"Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460."},"title":"The hole system of triangulated shapes","article_processing_charge":"No","author":[{"first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","last_name":"Ölsböck","full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297"}],"oa_version":"Published Version","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"}],"month":"02","alternative_title":["ISTA Thesis"],"language":[{"iso":"eng"}],"file":[{"date_created":"2020-02-06T14:43:54Z","file_name":"thesis_ist-final_noack.pdf","date_updated":"2020-07-14T12:47:58Z","file_size":76195184,"creator":"koelsboe","checksum":"1df9f8c530b443c0e63a3f2e4fde412e","file_id":"7461","content_type":"application/pdf","access_level":"open_access","relation":"main_file"},{"file_name":"latex-files.zip","date_created":"2020-02-06T14:52:45Z","file_size":122103715,"date_updated":"2020-07-14T12:47:58Z","creator":"koelsboe","file_id":"7462","checksum":"7a52383c812b0be64d3826546509e5a4","description":"latex source files, figures","content_type":"application/x-zip-compressed","relation":"source_file","access_level":"closed"}],"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","related_material":{"record":[{"status":"public","id":"6608","relation":"part_of_dissertation"}]},"_id":"7460","keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"],"status":"public","tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)"},"type":"dissertation","ddc":["514"],"date_updated":"2023-09-07T13:15:30Z","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"department":[{"_id":"HeEd"},{"_id":"GradSch"}],"file_date_updated":"2020-07-14T12:47:58Z"},{"publisher":"Institute of Science and Technology Austria","oa":1,"date_published":"2020-06-09T00:00:00Z","doi":"10.15479/AT:ISTA:7944","date_created":"2020-06-08T00:49:46Z","page":"160","day":"09","has_accepted_license":"1","year":"2020","title":"Reconfiguration problems","author":[{"first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322"}],"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Masárová, Zuzana. Reconfiguration Problems. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7944.","short":"Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020.","ieee":"Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020.","ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944","apa":"Masárová, Z. (2020). Reconfiguration problems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7944","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944.","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria."},"month":"06","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"related_material":{"record":[{"relation":"part_of_dissertation","id":"7950","status":"public"},{"relation":"part_of_dissertation","id":"5986","status":"public"}]},"license":"https://creativecommons.org/licenses/by-sa/4.0/","file":[{"file_id":"7945","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"THESIS_Zuzka_Masarova.pdf","date_created":"2020-06-08T00:34:00Z","file_size":13661779,"date_updated":"2020-07-14T12:48:05Z","creator":"zmasarov"},{"date_created":"2020-06-08T00:35:30Z","file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","date_updated":"2020-07-14T12:48:05Z","file_size":32184006,"creator":"zmasarov","checksum":"45341a35b8f5529c74010b7af43ac188","file_id":"7946","content_type":"application/zip","access_level":"closed","relation":"source_file"}],"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-3-99078-005-3"],"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","status":"public","keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"type":"dissertation","tmp":{"short":"CC BY-SA (4.0)","image":"/images/cc_by_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)"},"_id":"7944","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"file_date_updated":"2020-07-14T12:48:05Z","ddc":["516","514"],"supervisor":[{"last_name":"Wagner","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"date_updated":"2023-09-07T13:17:37Z"},{"article_number":"75","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.” 28th Annual European Symposium on Algorithms, vol. 173, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.ESA.2020.75.","apa":"Osang, G. F., Rouxel-Labbé, M., & Teillaud, M. (2020). Generalizing CGAL periodic Delaunay triangulations. In 28th Annual European Symposium on Algorithms (Vol. 173). Virtual, Online; Pisa, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2020.75","ama":"Osang GF, Rouxel-Labbé M, Teillaud M. Generalizing CGAL periodic Delaunay triangulations. In: 28th Annual European Symposium on Algorithms. Vol 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.ESA.2020.75","short":"G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","ieee":"G. F. Osang, M. Rouxel-Labbé, and M. Teillaud, “Generalizing CGAL periodic Delaunay triangulations,” in 28th Annual European Symposium on Algorithms, Virtual, Online; Pisa, Italy, 2020, vol. 173.","chicago":"Osang, Georg F, Mael Rouxel-Labbé, and Monique Teillaud. “Generalizing CGAL Periodic Delaunay Triangulations.” In 28th Annual European Symposium on Algorithms, Vol. 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.ESA.2020.75.","ista":"Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay triangulations. 28th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 173, 75."},"title":"Generalizing CGAL periodic Delaunay triangulations","author":[{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F"},{"full_name":"Rouxel-Labbé, Mael","last_name":"Rouxel-Labbé","first_name":"Mael"},{"first_name":"Monique","last_name":"Teillaud","full_name":"Teillaud, Monique"}],"article_processing_charge":"No","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","oa":1,"day":"26","publication":"28th Annual European Symposium on Algorithms","has_accepted_license":"1","year":"2020","date_published":"2020-08-26T00:00:00Z","doi":"10.4230/LIPIcs.ESA.2020.75","date_created":"2020-10-25T23:01:18Z","_id":"8703","status":"public","type":"conference","conference":{"name":"ESA: Annual European Symposium on Algorithms","end_date":"2020-09-09","location":"Virtual, Online; Pisa, Italy","start_date":"2020-09-07"},"tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"ddc":["000"],"date_updated":"2023-09-07T13:29:00Z","department":[{"_id":"HeEd"}],"file_date_updated":"2020-10-27T14:31:52Z","oa_version":"Published Version","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"}],"month":"08","intvolume":" 173","scopus_import":"1","alternative_title":["LIPIcs"],"file":[{"success":1,"checksum":"fe0f7c49a99ed870c671b911e10d5496","file_id":"8712","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2020_LIPIcs_Osang.pdf","date_created":"2020-10-27T14:31:52Z","creator":"cziletti","file_size":733291,"date_updated":"2020-10-27T14:31:52Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783959771627"],"issn":["18688969"]},"publication_status":"published","volume":173,"related_material":{"record":[{"relation":"dissertation_contains","id":"9056","status":"public"}]},"ec_funded":1,"license":"https://creativecommons.org/licenses/by/3.0/"},{"date_created":"2020-07-24T07:09:18Z","doi":"10.1556/012.2020.57.2.1454","date_published":"2020-07-24T00:00:00Z","page":"193-199","publication":"Studia Scientiarum Mathematicarum Hungarica","day":"24","year":"2020","isi":1,"has_accepted_license":"1","oa":1,"publisher":"Akadémiai Kiadó","quality_controlled":"1","acknowledgement":"The authors are greatly indebted to Dror Atariah, Günther Rote and John Sullivan for discussion and suggestions. The authors also thank Jean-Daniel Boissonnat, Ramsay Dyer, David de Laat and Rien van de Weijgaert for discussion. This work has been supported in part by the European Union’s Seventh Framework Programme for Research of the\r\nEuropean Commission, under FET-Open grant number 255827 (CGL Computational Geometry Learning) and ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions), the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement number 754411,and the Austrian Science Fund (FWF): Z00342 N31.","title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","article_processing_charge":"No","external_id":{"isi":["000570978400005"]},"author":[{"first_name":"Gert","last_name":"Vegter","full_name":"Vegter, Gert"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó, 2020. https://doi.org/10.1556/012.2020.57.2.1454.","ista":"Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2), 193–199.","mla":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:10.1556/012.2020.57.2.1454.","short":"G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199.","ieee":"G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes,” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020.","ama":"Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 2020;57(2):193-199. doi:10.1556/012.2020.57.2.1454","apa":"Vegter, G., & Wintraecken, M. (2020). Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó. https://doi.org/10.1556/012.2020.57.2.1454"},"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"name":"The Wittgenstein Prize","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc/4.0/","volume":57,"issue":"2","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"8164","file_size":1476072,"date_updated":"2020-07-24T07:09:06Z","creator":"mwintrae","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","date_created":"2020-07-24T07:09:06Z"}],"publication_status":"published","publication_identifier":{"eissn":["1588-2896"],"issn":["0081-6906"]},"intvolume":" 57","month":"07","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces.","lang":"eng"}],"file_date_updated":"2020-07-24T07:09:06Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2023-10-10T13:05:27Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)"},"article_type":"original","type":"journal_article","_id":"8163"},{"citation":{"chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0100.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:10.1515/cmb-2020-0100.","apa":"Akopyan, A., & Edelsbrunner, H. (2020). The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0100","ama":"Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):51-67. doi:10.1515/cmb-2020-0100","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 51–67, 2020.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"title":"The weighted mean curvature derivative of a space-filling diagram","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"year":"2020","has_accepted_license":"1","publication":"Computational and Mathematical Biophysics","day":"20","page":"51-67","date_created":"2021-02-17T15:13:01Z","doi":"10.1515/cmb-2020-0100","date_published":"2020-06-20T00:00:00Z","acknowledgement":"The authors of this paper thank Roland Roth for suggesting the analysis of the weighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations and for his continued encouragement. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","oa":1,"quality_controlled":"1","publisher":"De Gruyter","date_updated":"2023-10-17T12:34:51Z","ddc":["510"],"department":[{"_id":"HeEd"}],"file_date_updated":"2021-02-19T13:56:24Z","_id":"9157","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","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"issn":["2544-7297"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"9171","checksum":"cea41de9937d07a3b927d71ee8b4e432","file_size":562359,"date_updated":"2021-02-19T13:56:24Z","creator":"dernst","file_name":"2020_CompMathBiophysics_Akopyan2.pdf","date_created":"2021-02-19T13:56:24Z"}],"ec_funded":1,"volume":8,"issue":"1","abstract":[{"text":"Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy.","lang":"eng"}],"oa_version":"Published Version","intvolume":" 8","month":"06"},{"date_published":"2020-07-21T00:00:00Z","doi":"10.1515/cmb-2020-0101","date_created":"2021-02-17T15:12:44Z","page":"74-88","day":"21","publication":"Computational and Mathematical Biophysics","has_accepted_license":"1","year":"2020","publisher":"De Gruyter","quality_controlled":"1","oa":1,"acknowledgement":"The authors of this paper thank Roland Roth for suggesting the analysis of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","title":"The weighted Gaussian curvature derivative of a space-filling diagram","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"arxiv":["1908.06777"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.","apa":"Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0101","ama":"Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88. doi:10.1515/cmb-2020-0101","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88."},"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"issue":"1","volume":8,"ec_funded":1,"file":[{"success":1,"file_id":"9170","checksum":"ca43a7440834eab6bbea29c59b56ef3a","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2020_CompMathBiophysics_Akopyan.pdf","date_created":"2021-02-19T13:33:19Z","file_size":707452,"date_updated":"2021-02-19T13:33:19Z","creator":"dernst"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2544-7297"]},"publication_status":"published","month":"07","intvolume":" 8","oa_version":"Published Version","abstract":[{"lang":"eng","text":"The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy."}],"file_date_updated":"2021-02-19T13:33:19Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2023-10-17T12:35:10Z","status":"public","article_type":"original","type":"journal_article","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)"},"_id":"9156"},{"author":[{"last_name":"Bauer","full_name":"Bauer, U.","first_name":"U."},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","last_name":"Jablonski","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz"},{"full_name":"Mrozek, M.","last_name":"Mrozek","first_name":"M."}],"article_processing_charge":"Yes (via OA deal)","title":"Čech-Delaunay gradient flow and homology inference for self-maps","citation":{"ista":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 4(4), 455–480.","chicago":"Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology. Springer Nature, 2020. https://doi.org/10.1007/s41468-020-00058-8.","ieee":"U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient flow and homology inference for self-maps,” Journal of Applied and Computational Topology, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.","short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480.","apa":"Bauer, U., Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2020). Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00058-8","ama":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 2020;4(4):455-480. doi:10.1007/s41468-020-00058-8","mla":"Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:10.1007/s41468-020-00058-8."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"455-480","date_published":"2020-12-01T00:00:00Z","doi":"10.1007/s41468-020-00058-8","date_created":"2024-03-04T10:47:49Z","has_accepted_license":"1","year":"2020","day":"01","publication":"Journal of Applied and Computational Topology","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"This research has been supported by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding provided by Projekt DEAL.","file_date_updated":"2024-03-04T10:52:42Z","department":[{"_id":"HeEd"}],"date_updated":"2024-03-04T10:54:04Z","ddc":["500"],"type":"journal_article","article_type":"original","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)"},"status":"public","_id":"15064","issue":"4","volume":4,"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"publication_status":"published","file":[{"file_size":851190,"date_updated":"2024-03-04T10:52:42Z","creator":"dernst","file_name":"2020_JourApplCompTopology_Bauer.pdf","date_created":"2024-03-04T10:52:42Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"15065","checksum":"eed1168b6e66cd55272c19bb7fca8a1c"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"12","intvolume":" 4","abstract":[{"text":"We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.","lang":"eng"}],"oa_version":"Published Version"},{"has_accepted_license":"1","year":"2019","day":"01","publication":"Journal of Computational Geometry ","page":"223–256","date_published":"2019-07-01T00:00:00Z","doi":"10.20382/jocg.v10i1a9","date_created":"2019-06-03T09:35:33Z","publisher":"Carleton University","quality_controlled":"1","oa":1,"citation":{"chicago":"Dyer, Ramsay, Gert Vegter, and Mathijs Wintraecken. “Simplices Modelled on Spaces of Constant Curvature.” Journal of Computational Geometry . Carleton University, 2019. https://doi.org/10.20382/jocg.v10i1a9.","ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","mla":"Dyer, Ramsay, et al. “Simplices Modelled on Spaces of Constant Curvature.” Journal of Computational Geometry , vol. 10, no. 1, Carleton University, 2019, pp. 223–256, doi:10.20382/jocg.v10i1a9.","apa":"Dyer, R., Vegter, G., & Wintraecken, M. (2019). Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . Carleton University. https://doi.org/10.20382/jocg.v10i1a9","ama":"Dyer R, Vegter G, Wintraecken M. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 2019;10(1):223–256. doi:10.20382/jocg.v10i1a9","ieee":"R. Dyer, G. Vegter, and M. Wintraecken, “Simplices modelled on spaces of constant curvature,” Journal of Computational Geometry , vol. 10, no. 1. Carleton University, pp. 223–256, 2019.","short":"R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10 (2019) 223–256."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Ramsay","last_name":"Dyer","full_name":"Dyer, Ramsay"},{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"title":"Simplices modelled on spaces of constant curvature","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"publication_identifier":{"issn":["1920-180X"]},"publication_status":"published","file":[{"file_id":"6516","checksum":"57b4df2f16a74eb499734ec8ee240178","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2019-06-03T09:30:01Z","file_name":"mainJournalFinal.pdf","creator":"mwintrae","date_updated":"2020-07-14T12:47:32Z","file_size":2170882}],"language":[{"iso":"eng"}],"issue":"1","volume":10,"ec_funded":1,"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."}],"oa_version":"Published Version","scopus_import":1,"month":"07","intvolume":" 10","date_updated":"2021-01-12T08:07:50Z","ddc":["510"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:32Z","_id":"6515","type":"journal_article","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)"},"status":"public"},{"page":"275-279","date_published":"2019-08-01T00:00:00Z","date_created":"2019-07-12T08:34:57Z","ec_funded":1,"has_accepted_license":"1","year":"2019","publication_status":"published","day":"01","file":[{"file_id":"6629","checksum":"ceabd152cfa55170d57763f9c6c60a53","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"IntrinsicExtrinsicCCCG2019.pdf","date_created":"2019-07-12T08:32:46Z","creator":"mwintrae","file_size":321176,"date_updated":"2020-07-14T12:47:34Z"}],"language":[{"iso":"eng"}],"publication":"The 31st Canadian Conference in Computational Geometry","scopus_import":1,"quality_controlled":"1","oa":1,"month":"08","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."}],"oa_version":"Submitted Version","author":[{"first_name":"Gert","full_name":"Vegter, Gert","last_name":"Vegter"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"department":[{"_id":"HeEd"}],"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","file_date_updated":"2020-07-14T12:47:34Z","citation":{"mla":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–79.","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 The 31st Canadian Conference in Computational Geometry, Edmonton, Canada, 2019, pp. 275–279.","apa":"Vegter, G., & Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In The 31st Canadian Conference in Computational Geometry (pp. 275–279). Edmonton, Canada.","ama":"Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In: The 31st Canadian Conference in Computational Geometry. ; 2019:275-279.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” In The 31st Canadian Conference in Computational Geometry, 275–79, 2019.","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."},"date_updated":"2021-01-12T08:08:16Z","ddc":["004"],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","type":"conference","conference":{"start_date":"2019-08-08","end_date":"2019-08-10","location":"Edmonton, Canada","name":"CCCG: Canadian Conference in Computational Geometry"},"status":"public","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"_id":"6628"},{"oa_version":"Published Version","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."}],"month":"06","intvolume":" 129","scopus_import":1,"alternative_title":["LIPIcs"],"file":[{"date_created":"2019-07-24T06:40:01Z","file_name":"2019_LIPICS_Edelsbrunner.pdf","date_updated":"2020-07-14T12:47:35Z","file_size":1355179,"creator":"dernst","file_id":"6666","checksum":"8ec8720730d4c789bf7b06540f1c29f4","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783959771047"]},"publication_status":"published","volume":129,"_id":"6648","status":"public","type":"conference","conference":{"name":"SoCG 2019: Symposium on Computational Geometry","start_date":"2019-06-18","end_date":"2019-06-21","location":"Portland, OR, United States"},"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)"},"ddc":["510"],"date_updated":"2021-01-12T08:08:23Z","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:35Z","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"day":"01","publication":"35th International Symposium on Computational Geometry","has_accepted_license":"1","year":"2019","date_published":"2019-06-01T00:00:00Z","doi":"10.4230/LIPICS.SOCG.2019.31","date_created":"2019-07-17T10:36:09Z","page":"31:1-31:14","project":[{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” In 35th International Symposium on Computational Geometry, 129:31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.SOCG.2019.31.","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.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” in 35th International Symposium on Computational Geometry, Portland, OR, United States, 2019, vol. 129, p. 31:1-31:14.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2019). Topological data analysis in information space. In 35th International Symposium on Computational Geometry (Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.31","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:10.4230/LIPICS.SOCG.2019.31","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14, doi:10.4230/LIPICS.SOCG.2019.31."},"title":"Topological data analysis in information space","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["1903.08510"]}},{"date_updated":"2023-08-04T10:57:42Z","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.","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 Proceedings of the 31st Canadian Conference on Computational Geometry, 164–70. Canadian Conference on Computational Geometry, 2019.","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.","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” in Proceedings of the 31st Canadian Conference on Computational Geometry, Edmonton, Canada, 2019, pp. 164–170.","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. In: Proceedings of the 31st Canadian Conference on Computational Geometry. Canadian Conference on Computational Geometry; 2019:164-170.","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 Proceedings of the 31st Canadian Conference on Computational Geometry (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–70."},"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","article_processing_charge":"No","external_id":{"arxiv":["1910.09917"]},"author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"last_name":"Akitaya","full_name":"Akitaya, Hugo A","first_name":"Hugo A"},{"last_name":"Cheung","full_name":"Cheung, Kenneth C","first_name":"Kenneth C"},{"first_name":"Erik D","last_name":"Demaine","full_name":"Demaine, Erik D"},{"full_name":"Demaine, Martin L","last_name":"Demaine","first_name":"Martin L"},{"first_name":"Sandor P","full_name":"Fekete, Sandor P","last_name":"Fekete"},{"last_name":"Kleist","full_name":"Kleist, Linda","first_name":"Linda"},{"first_name":"Irina","full_name":"Kostitsyna, Irina","last_name":"Kostitsyna"},{"last_name":"Löffler","full_name":"Löffler, Maarten","first_name":"Maarten"},{"last_name":"Masárová","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mundilova","full_name":"Mundilova, Klara","first_name":"Klara"},{"first_name":"Christiane","full_name":"Schmidt, Christiane","last_name":"Schmidt"}],"title":"Folding polyominoes with holes into a cube","department":[{"_id":"HeEd"}],"_id":"6989","conference":{"name":"CCCG: Canadian Conference in Computational Geometry","start_date":"2019-08-08","end_date":"2019-08-10","location":"Edmonton, Canada"},"type":"conference","status":"public","publication_status":"published","year":"2019","publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","language":[{"iso":"eng"}],"day":"01","page":"164-170","date_created":"2019-11-04T16:46:11Z","related_material":{"record":[{"relation":"extended_version","status":"public","id":"8317"}]},"date_published":"2019-08-01T00:00:00Z","abstract":[{"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. ","lang":"eng"}],"acknowledgement":"This research was performed in part at the 33rd BellairsWinter Workshop on Computational Geometry. Wethank all other participants for a fruitful atmosphere.","oa_version":"Published Version","main_file_link":[{"url":"https://cccg.ca/proceedings/2019/proceedings.pdf","open_access":"1"}],"oa":1,"quality_controlled":"1","publisher":"Canadian Conference on Computational Geometry","scopus_import":"1","month":"08"},{"_id":"6671","article_type":"original","type":"journal_article","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)"},"status":"public","date_updated":"2023-08-22T12:37:47Z","ddc":["000"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:36Z","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."}],"oa_version":"Published Version","month":"06","intvolume":" 3","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"publication_status":"published","file":[{"checksum":"a5b244db9f751221409cf09c97ee0935","file_id":"6741","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2019-07-31T08:09:56Z","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf","creator":"dernst","date_updated":"2020-07-14T12:47:36Z","file_size":2215157}],"language":[{"iso":"eng"}],"volume":3,"issue":"1-2","ec_funded":1,"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"citation":{"ama":"Boissonnat J-D, Lieutier A, Wintraecken M. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. 2019;3(1-2):29–58. doi:10.1007/s41468-019-00029-8","apa":"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. Springer Nature. https://doi.org/10.1007/s41468-019-00029-8","ieee":"J.-D. Boissonnat, A. Lieutier, and M. Wintraecken, “The reach, metric distortion, geodesic convexity and the variation of tangent spaces,” Journal of Applied and Computational Topology, vol. 3, no. 1–2. Springer Nature, pp. 29–58, 2019.","short":"J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58.","mla":"Boissonnat, Jean-Daniel, et al. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” Journal of Applied and Computational Topology, vol. 3, no. 1–2, Springer Nature, 2019, pp. 29–58, doi:10.1007/s41468-019-00029-8.","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.","chicago":"Boissonnat, Jean-Daniel, André Lieutier, and Mathijs Wintraecken. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” Journal of Applied and Computational Topology. Springer Nature, 2019. https://doi.org/10.1007/s41468-019-00029-8."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Jean-Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel"},{"last_name":"Lieutier","full_name":"Lieutier, André","first_name":"André"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"article_processing_charge":"Yes (via OA deal)","title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","publisher":"Springer Nature","quality_controlled":"1","oa":1,"has_accepted_license":"1","year":"2019","day":"01","publication":"Journal of Applied and Computational Topology","page":"29–58","date_published":"2019-06-01T00:00:00Z","doi":"10.1007/s41468-019-00029-8","date_created":"2019-07-24T08:37:29Z"}]