[{"issue":"1","abstract":[{"lang":"eng","text":"We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric."}],"type":"journal_article","file":[{"content_type":"application/pdf","file_size":983307,"creator":"kschuh","file_name":"2021_DescreteCompGeopmetry_Boissonnat.pdf","access_level":"open_access","date_updated":"2021-08-06T09:52:29Z","date_created":"2021-08-06T09:52:29Z","checksum":"c848986091e56699dc12de85adb1e39c","success":1,"relation":"main_file","file_id":"9795"}],"oa_version":"Published Version","intvolume":" 66","status":"public","ddc":["516"],"title":"Triangulating submanifolds: An elementary and quantified version of Whitney’s method","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"8940","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","keyword":["Theoretical Computer Science","Computational Theory and Mathematics","Geometry and Topology","Discrete Mathematics and Combinatorics"],"date_published":"2021-07-01T00:00:00Z","page":"386-434","article_type":"original","citation":{"chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00250-8.","mla":"Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry, vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational Geometry 66 (2021) 386–434.","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 66(1), 386–434.","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds: An elementary and quantified version of Whitney’s method,” Discrete & Computational Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8"},"publication":"Discrete & Computational Geometry","ec_funded":1,"file_date_updated":"2021-08-06T09:52:29Z","volume":66,"date_created":"2020-12-12T11:07:02Z","date_updated":"2023-09-05T15:02:40Z","author":[{"full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel","last_name":"Boissonnat"},{"full_name":"Kachanovich, Siargey","first_name":"Siargey","last_name":"Kachanovich"},{"orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","first_name":"Mathijs","full_name":"Wintraecken, Mathijs"}],"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","year":"2021","acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding provided by the Institute of Science and Technology (IST Austria).","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"month":"07","language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00250-8","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"isi":1,"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000597770300001"]}},{"type":"journal_article","issue":"1","abstract":[{"lang":"eng","text":"We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space X equipped with a continuous function f:X→R. We first give a categorification of the mapper graph and the Reeb graph by interpreting them in terms of cosheaves and stratified covers of the real line R. We then introduce a variant of the classic mapper graph of Singh et al. (in: Eurographics symposium on point-based graphics, 2007), referred to as the enhanced mapper graph, and demonstrate that such a construction approximates the Reeb graph of (X,f) when it is applied to points randomly sampled from a probability density function concentrated on (X,f). Our techniques are based on the interleaving distance of constructible cosheaves and topological estimation via kernel density estimates. Following Munch and Wang (In: 32nd international symposium on computational geometry, volume 51 of Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, Germany, pp 53:1–53:16, 2016), we first show that the mapper graph of (X,f), a constructible R-space (with a fixed open cover), approximates the Reeb graph of the same space. We then construct an isomorphism between the mapper of (X,f) to the mapper of a super-level set of a probability density function concentrated on (X,f). Finally, building on the approach of Bobrowski et al. (Bernoulli 23(1):288–328, 2017b), we show that, with high probability, we can recover the mapper of the super-level set given a sufficiently large sample. Our work is the first to consider the mapper construction using the theory of cosheaves in a probabilistic setting. It is part of an ongoing effort to combine sheaf theory, probability, and statistics, to support topological data analysis with random data."}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"9111","intvolume":" 5","ddc":["510"],"status":"public","title":"Probabilistic convergence and stability of random mapper graphs","file":[{"content_type":"application/pdf","file_size":2090265,"creator":"dernst","access_level":"open_access","file_name":"2020_JourApplCompTopology_Brown.pdf","checksum":"3f02e9d47c428484733da0f588a3c069","success":1,"date_updated":"2021-02-11T14:43:59Z","date_created":"2021-02-11T14:43:59Z","relation":"main_file","file_id":"9112"}],"oa_version":"Published Version","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","citation":{"chicago":"Brown, Adam, Omer Bobrowski, Elizabeth Munch, and Bei Wang. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology. Springer Nature, 2021. https://doi.org/10.1007/s41468-020-00063-x.","short":"A. Brown, O. Bobrowski, E. Munch, B. Wang, Journal of Applied and Computational Topology 5 (2021) 99–140.","mla":"Brown, Adam, et al. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology, vol. 5, no. 1, Springer Nature, 2021, pp. 99–140, doi:10.1007/s41468-020-00063-x.","ieee":"A. Brown, O. Bobrowski, E. Munch, and B. Wang, “Probabilistic convergence and stability of random mapper graphs,” Journal of Applied and Computational Topology, vol. 5, no. 1. Springer Nature, pp. 99–140, 2021.","apa":"Brown, A., Bobrowski, O., Munch, E., & Wang, B. (2021). Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00063-x","ista":"Brown A, Bobrowski O, Munch E, Wang B. 2021. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 5(1), 99–140.","ama":"Brown A, Bobrowski O, Munch E, Wang B. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 2021;5(1):99-140. doi:10.1007/s41468-020-00063-x"},"publication":"Journal of Applied and Computational Topology","page":"99-140","article_type":"original","date_published":"2021-03-01T00:00:00Z","ec_funded":1,"file_date_updated":"2021-02-11T14:43:59Z","acknowledgement":"AB was supported in part by the European Union’s Horizon 2020 research and innovation\r\nprogramme under the Marie Sklodowska-Curie GrantAgreement No. 754411 and NSF IIS-1513616. OB was supported in part by the Israel Science Foundation, Grant 1965/19. BW was supported in part by NSF IIS-1513616 and DBI-1661375. EM was supported in part by NSF CMMI-1800466, DMS-1800446, and CCF-1907591.We would like to thank the Institute for Mathematics and its Applications for hosting a workshop titled Bridging Statistics and Sheaves in May 2018, where this work was conceived.\r\nOpen Access funding provided by Institute of Science and Technology (IST Austria).","year":"2021","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Brown, Adam","last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"full_name":"Bobrowski, Omer","last_name":"Bobrowski","first_name":"Omer"},{"full_name":"Munch, Elizabeth","last_name":"Munch","first_name":"Elizabeth"},{"first_name":"Bei","last_name":"Wang","full_name":"Wang, Bei"}],"volume":5,"date_created":"2021-02-11T14:41:02Z","date_updated":"2023-09-05T15:37:56Z","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"month":"03","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["1909.03488"]},"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"quality_controlled":"1","doi":"10.1007/s41468-020-00063-x","language":[{"iso":"eng"}]},{"alternative_title":["ISTA Thesis"],"type":"dissertation","abstract":[{"lang":"eng","text":"In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations. The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,\r\nand thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics. We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss the implications on persistence for periodic data sets."}],"ddc":["006","514","516"],"title":"Multi-cover persistence and Delaunay mosaics","status":"public","_id":"9056","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Published Version","file":[{"relation":"source_file","file_id":"9063","checksum":"bcf27986147cab0533b6abadd74e7629","date_created":"2021-02-02T14:09:25Z","date_updated":"2021-02-03T10:37:28Z","access_level":"closed","file_name":"thesis_source.zip","file_size":13446994,"content_type":"application/zip","creator":"patrickd"},{"file_id":"9064","relation":"main_file","date_updated":"2021-02-02T14:09:18Z","date_created":"2021-02-02T14:09:18Z","success":1,"checksum":"9cc8af266579a464385bbe2aff6af606","file_name":"thesis_pdfA2b.pdf","access_level":"open_access","creator":"patrickd","content_type":"application/pdf","file_size":5210329}],"day":"01","has_accepted_license":"1","article_processing_charge":"No","page":"134","citation":{"chicago":"Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9056.","mla":"Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9056.","short":"G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science and Technology Austria, 2021.","ista":"Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg: Institute of Science and Technology Austria.","apa":"Osang, G. F. (2021). Multi-cover persistence and Delaunay mosaics. Institute of Science and Technology Austria, Klosterneuburg. https://doi.org/10.15479/AT:ISTA:9056","ieee":"G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of Science and Technology Austria, Klosterneuburg, 2021.","ama":"Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056"},"date_published":"2021-02-01T00:00:00Z","place":"Klosterneuburg","file_date_updated":"2021-02-03T10:37:28Z","publication_status":"published","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"publisher":"Institute of Science and Technology Austria","year":"2021","date_updated":"2023-09-07T13:29:01Z","date_created":"2021-02-02T14:11:06Z","author":[{"full_name":"Osang, Georg F","last_name":"Osang","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"187"},{"status":"public","relation":"part_of_dissertation","id":"8703"}]},"month":"02","publication_identifier":{"issn":["2663-337X"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"degree_awarded":"PhD","supervisor":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"language":[{"iso":"eng"}],"doi":"10.15479/AT:ISTA:9056"},{"page":"9107-9115","article_type":"original","citation":{"chicago":"Osang, Georg F, Herbert Edelsbrunner, and Mohammad Saadatfar. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft Matter. Royal Society of Chemistry , 2021. https://doi.org/10.1039/d1sm00774b.","mla":"Osang, Georg F., et al. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft Matter, vol. 17, no. 40, Royal Society of Chemistry , 2021, pp. 9107–15, doi:10.1039/d1sm00774b.","short":"G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 9107–9115.","ista":"Osang GF, Edelsbrunner H, Saadatfar M. 2021. Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. 17(40), 9107–9115.","apa":"Osang, G. F., Edelsbrunner, H., & Saadatfar, M. (2021). Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. Royal Society of Chemistry . https://doi.org/10.1039/d1sm00774b","ieee":"G. F. Osang, H. Edelsbrunner, and M. Saadatfar, “Topological signatures and stability of hexagonal close packing and Barlow stackings,” Soft Matter, vol. 17, no. 40. Royal Society of Chemistry , pp. 9107–9115, 2021.","ama":"Osang GF, Edelsbrunner H, Saadatfar M. Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. 2021;17(40):9107-9115. doi:10.1039/d1sm00774b"},"publication":"Soft Matter","date_published":"2021-10-20T00:00:00Z","scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"20","intvolume":" 17","ddc":["540"],"status":"public","title":"Topological signatures and stability of hexagonal close packing and Barlow stackings","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"10204","file":[{"date_created":"2023-10-03T09:21:42Z","date_updated":"2023-10-03T09:21:42Z","checksum":"b4da0c420530295e61b153960f6cb350","success":1,"relation":"main_file","file_id":"14385","content_type":"application/pdf","file_size":4678788,"creator":"dernst","file_name":"2021_SoftMatter_acceptedversion_Osang.pdf","access_level":"open_access"}],"oa_version":"Submitted Version","type":"journal_article","issue":"40","abstract":[{"text":"Two common representations of close packings of identical spheres consisting of hexagonal layers, called Barlow stackings, appear abundantly in minerals and metals. These motifs, however, occupy an identical portion of space and bear identical first-order topological signatures as measured by persistent homology. Here we present a novel method based on k-fold covers that unambiguously distinguishes between these patterns. Moreover, our approach provides topological evidence that the FCC motif is the more stable of the two in the context of evolving experimental sphere packings during the transition from disordered to an ordered state. We conclude that our approach can be generalised to distinguish between various Barlow stackings manifested in minerals and metals.","lang":"eng"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF","name":"The Wittgenstein Prize"}],"isi":1,"quality_controlled":"1","external_id":{"isi":["000700090000001"],"pmid":["34569592"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1039/d1sm00774b","publication_identifier":{"issn":["1744-683X"],"eissn":["1744-6848"]},"month":"10","department":[{"_id":"HeEd"}],"publisher":"Royal Society of Chemistry ","publication_status":"published","pmid":1,"acknowledgement":"MS acknowledges the support by Australian Research Council funding through the ARC Training Centre for M3D Innovation (IC180100008). MS thanks M. Hanifpour and N. Francois for their input and valuable discussions. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant no. 788183 and from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","year":"2021","volume":17,"date_created":"2021-10-31T23:01:30Z","date_updated":"2023-10-03T09:24:27Z","author":[{"full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","first_name":"Georg F"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Saadatfar","first_name":"Mohammad","full_name":"Saadatfar, Mohammad"}],"ec_funded":1,"file_date_updated":"2023-10-03T09:21:42Z"},{"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2103.07823"]},"quality_controlled":"1","doi":"10.4230/LIPIcs.SoCG.2021.27","conference":{"name":"SoCG: International Symposium on Computational Geometry","end_date":"2021-06-11","start_date":"2021-06-07","location":"Online"},"language":[{"iso":"eng"}],"publication_identifier":{"issn":["18688969"],"isbn":["9783959771849"]},"month":"06","acknowledgement":"The authors want to thank the reviewers for many helpful comments and suggestions.","year":"2021","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"publication_status":"published","related_material":{"record":[{"id":"12709","relation":"later_version","status":"public"}],"link":[{"url":"https://arxiv.org/abs/2103.07823","relation":"extended_version"}]},"author":[{"full_name":"Corbet, René","first_name":"René","last_name":"Corbet"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"first_name":"Michael","last_name":"Lesnick","full_name":"Lesnick, Michael"},{"first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F"}],"volume":189,"date_created":"2021-06-27T22:01:49Z","date_updated":"2023-10-04T12:03:39Z","article_number":"27","file_date_updated":"2021-06-28T12:40:47Z","citation":{"chicago":"Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.27.","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” Leibniz International Proceedings in Informatics, vol. 189, 27, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.27.","apa":"Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2021). Computing the multicover bifiltration. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.27","ieee":"R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2021. Computing the multicover bifiltration. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 27.","ama":"Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.27"},"publication":"Leibniz International Proceedings in Informatics","date_published":"2021-06-02T00:00:00Z","scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"02","_id":"9605","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","intvolume":" 189","ddc":["516"],"status":"public","title":"Computing the multicover bifiltration","oa_version":"Published Version","file":[{"checksum":"0de217501e7ba8b267d58deed0d51761","success":1,"date_created":"2021-06-28T12:40:47Z","date_updated":"2021-06-28T12:40:47Z","relation":"main_file","file_id":"9610","file_size":"1367983","content_type":"application/pdf","creator":"cziletti","access_level":"open_access","file_name":"2021_LIPIcs_Corbet.pdf"}],"type":"conference","alternative_title":["LIPIcs"],"abstract":[{"lang":"eng","text":"Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness. "}]},{"place":"Dagstuhl, Germany","file_date_updated":"2021-06-02T10:22:33Z","ec_funded":1,"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"year":"2021","acknowledgement":"We thank Dominique Attali, Guilherme de Fonseca, Arijit Ghosh, Vincent Pilaud and Aurélien Alvarez for their comments and suggestions. We also acknowledge the reviewers.","date_created":"2021-06-02T10:10:55Z","date_updated":"2023-10-10T07:34:34Z","volume":189,"author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"first_name":"Siargey","last_name":"Kachanovich","full_name":"Kachanovich, Siargey"},{"first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"12960"}]},"month":"06","publication_identifier":{"isbn":["978-3-95977-184-9"],"issn":["1868-8969"]},"quality_controlled":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2021-06-11","start_date":"2021-06-07","location":"Virtual"},"doi":"10.4230/LIPIcs.SoCG.2021.17","alternative_title":["LIPIcs"],"type":"conference","abstract":[{"text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. submanifolds of ℝ^d defined as the zero set of some multivariate multivalued smooth function f: ℝ^d → ℝ^{d-n}, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M is to consider its Piecewise-Linear (PL) approximation M̂ based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ = 1/D (and unavoidably exponential in n). Since it is known that for δ = Ω (d^{2.5}), M̂ is O(D²)-close and isotopic to M, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M̂ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. ","lang":"eng"}],"status":"public","title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations","ddc":["005","516","514"],"intvolume":" 189","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","_id":"9441","file":[{"access_level":"open_access","file_name":"LIPIcs-SoCG-2021-17.pdf","creator":"mwintrae","content_type":"application/pdf","file_size":1972902,"file_id":"9442","relation":"main_file","success":1,"checksum":"c322aa48d5d35a35877896cc565705b6","date_created":"2021-06-02T10:22:33Z","date_updated":"2021-06-02T10:22:33Z"}],"oa_version":"Published Version","series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","day":"02","has_accepted_license":"1","article_processing_charge":"No","page":"17:1-17:16","publication":"37th International Symposium on Computational Geometry (SoCG 2021)","citation":{"ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 17:1-17:16.","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 17:1-17:16). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.17","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational GeometryLeibniz International Proceedings in Informatics (LIPIcs), LIPIcs, vol. 189, 17:1-17:16.","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:17:1-17:16. doi:10.4230/LIPIcs.SoCG.2021.17","chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn Triangulations.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:17:1-17:16. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.17.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2021, p. 17:1-17:16.","mla":"Boissonnat, Jean-Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn Triangulations.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 17:1-17:16, doi:10.4230/LIPIcs.SoCG.2021.17."},"date_published":"2021-06-02T00:00:00Z"},{"language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00240-w","isi":1,"quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1908.00856"}],"external_id":{"arxiv":["1908.00856"],"isi":["000564488500002"]},"month":"10","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"date_created":"2020-09-06T22:01:13Z","date_updated":"2024-03-07T14:51:11Z","volume":66,"author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alexander I.","last_name":"Bobenko","full_name":"Bobenko, Alexander I."},{"full_name":"Schief, Wolfgang K.","first_name":"Wolfgang K.","last_name":"Schief"},{"full_name":"Techter, Jan","first_name":"Jan","last_name":"Techter"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","acknowledgement":"This research was supported by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”. W.K.S. was also supported by the Australian Research Council (DP1401000851). A.V.A. was also supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha).","year":"2021","ec_funded":1,"date_published":"2021-10-01T00:00:00Z","article_type":"original","page":"938-976","publication":"Discrete and Computational Geometry","citation":{"ama":"Akopyan A, Bobenko AI, Schief WK, Techter J. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. 2021;66:938-976. doi:10.1007/s00454-020-00240-w","ista":"Akopyan A, Bobenko AI, Schief WK, Techter J. 2021. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. 66, 938–976.","ieee":"A. Akopyan, A. I. Bobenko, W. K. Schief, and J. Techter, “On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs,” Discrete and Computational Geometry, vol. 66. Springer Nature, pp. 938–976, 2021.","apa":"Akopyan, A., Bobenko, A. I., Schief, W. K., & Techter, J. (2021). On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00240-w","mla":"Akopyan, Arseniy, et al. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete and Computational Geometry, vol. 66, Springer Nature, 2021, pp. 938–76, doi:10.1007/s00454-020-00240-w.","short":"A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational Geometry 66 (2021) 938–976.","chicago":"Akopyan, Arseniy, Alexander I. Bobenko, Wolfgang K. Schief, and Jan Techter. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00240-w."},"day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","title":"On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs","status":"public","intvolume":" 66","_id":"8338","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics and systems of confocal quadrics. Intimate connections with classical deformations of quadrics that are isometric along asymptotic lines and circular cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces of Blaschke type generated by asymptotic and characteristic lines that are diagonally related to lines of curvature is proved theoretically and established constructively. Appropriate samplings (grids) of these webs lead to three-dimensional extensions of non-planar IC nets. Three-dimensional octahedral grids composed of planes and spatially extending (checkerboard) IC-nets are shown to arise in connection with systems of confocal quadrics in Minkowski space. In this context, the Laguerre geometric notion of conical octahedral grids of planes is introduced. The latter generalise the octahedral grids derived from systems of confocal quadrics in Minkowski space. An explicit construction of conical octahedral grids is presented. The results are accompanied by various illustrations which are based on the explicit formulae provided by the theory.","lang":"eng"}],"type":"journal_article"},{"oa_version":"Published Version","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"8248","intvolume":" 66","status":"public","ddc":["510"],"title":"Local conditions for triangulating submanifolds of Euclidean space","abstract":[{"text":"We consider the following setting: suppose that we are given a manifold M in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is, they are homeomorphic.","lang":"eng"}],"type":"journal_article","date_published":"2021-09-01T00:00:00Z","citation":{"short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, M. Wintraecken, Discrete and Computational Geometry 66 (2021) 666–686.","mla":"Boissonnat, Jean-Daniel, et al. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” Discrete and Computational Geometry, vol. 66, Springer Nature, 2021, pp. 666–86, doi:10.1007/s00454-020-00233-9.","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, Andre Lieutier, and Mathijs Wintraecken. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00233-9.","ama":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. 2021;66:666-686. doi:10.1007/s00454-020-00233-9","apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., Lieutier, A., & Wintraecken, M. (2021). Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00233-9","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, and M. Wintraecken, “Local conditions for triangulating submanifolds of Euclidean space,” Discrete and Computational Geometry, vol. 66. Springer Nature, pp. 666–686, 2021.","ista":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. 2021. Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. 66, 666–686."},"publication":"Discrete and Computational Geometry","page":"666-686","article_type":"original","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"last_name":"Dyer","first_name":"Ramsay","full_name":"Dyer, Ramsay"},{"first_name":"Arijit","last_name":"Ghosh","full_name":"Ghosh, Arijit"},{"full_name":"Lieutier, Andre","first_name":"Andre","last_name":"Lieutier"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs"}],"volume":66,"date_updated":"2024-03-07T14:54:59Z","date_created":"2020-08-11T07:11:51Z","year":"2021","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria). Arijit Ghosh is supported by the Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India.\r\nThis work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India. The fifth author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","ec_funded":1,"doi":"10.1007/s00454-020-00233-9","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000558119300001"]},"main_file_link":[{"url":"https://doi.org/10.1007/s00454-020-00233-9","open_access":"1"}],"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"month":"09"},{"file_date_updated":"2020-11-25T09:06:41Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). This work was partially supported by NSF IIS-1513616 and NSF ABI-1661375. The authors would like to thank the anonymous referees for their insightful comments.","year":"2021","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Brown, Adam","last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"last_name":"Wang","first_name":"Bei","full_name":"Wang, Bei"}],"volume":65,"date_created":"2020-05-30T10:26:04Z","date_updated":"2024-03-07T15:01:58Z","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"month":"06","external_id":{"isi":["000536324700001"],"arxiv":["1712.07734"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","isi":1,"doi":"10.1007/s00454-020-00206-y","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"text":"We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the given sheaf is constructible. In particular, when we choose to work with the local homology sheaf, our algorithm gives an alternative to the local homology transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2), 195–222, 2020). Additionally, we give examples of stratifications based on the geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018), illustrating how the sheaf-theoretic approach can be used to study stratifications from both topological and geometric perspectives. This approach also points toward future applications of sheaf theory in the study of topological data analysis by illustrating the utility of the language of sheaf theory in generalizing existing algorithms.","lang":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"7905","intvolume":" 65","title":"Sheaf-theoretic stratification learning from geometric and topological perspectives","ddc":["510"],"status":"public","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2020_DiscreteCompGeometry_Brown.pdf","creator":"dernst","content_type":"application/pdf","file_size":1013730,"file_id":"8803","relation":"main_file","success":1,"checksum":"487a84ea5841b75f04f66d7ebd71b67e","date_updated":"2020-11-25T09:06:41Z","date_created":"2020-11-25T09:06:41Z"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","citation":{"chicago":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00206-y.","mla":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” Discrete and Computational Geometry, vol. 65, Springer Nature, 2021, pp. 1166–98, doi:10.1007/s00454-020-00206-y.","short":"A. Brown, B. Wang, Discrete and Computational Geometry 65 (2021) 1166–1198.","ista":"Brown A, Wang B. 2021. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 65, 1166–1198.","ieee":"A. Brown and B. Wang, “Sheaf-theoretic stratification learning from geometric and topological perspectives,” Discrete and Computational Geometry, vol. 65. Springer Nature, pp. 1166–1198, 2021.","apa":"Brown, A., & Wang, B. (2021). Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00206-y","ama":"Brown A, Wang B. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 2021;65:1166-1198. doi:10.1007/s00454-020-00206-y"},"publication":"Discrete and Computational Geometry","page":"1166-1198","article_type":"original","date_published":"2021-06-01T00:00:00Z"},{"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"year":"2020","date_updated":"2021-01-12T08:14:13Z","date_created":"2020-03-05T13:30:18Z","volume":14,"author":[{"last_name":"Choudhary","first_name":"Aruni","full_name":"Choudhary, Aruni"},{"full_name":"Kachanovich, Siargey","last_name":"Kachanovich","first_name":"Siargey"},{"full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken"}],"file_date_updated":"2020-11-20T10:18:02Z","ec_funded":1,"quality_controlled":"1","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s11786-020-00461-5","month":"03","publication_identifier":{"eissn":["1661-8289"],"issn":["1661-8270"]},"status":"public","title":"Coxeter triangulations have good quality","ddc":["510"],"intvolume":" 14","_id":"7567","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"date_updated":"2020-11-20T10:18:02Z","date_created":"2020-11-20T10:18:02Z","checksum":"1d145f3ab50ccee735983cb89236e609","success":1,"relation":"main_file","file_id":"8783","content_type":"application/pdf","file_size":872275,"creator":"dernst","file_name":"2020_MathCompScie_Choudhary.pdf","access_level":"open_access"}],"type":"journal_article","abstract":[{"lang":"eng","text":"Coxeter triangulations are triangulations of Euclidean space based on a single simplex. By this we mean that given an individual simplex we can recover the entire triangulation of Euclidean space by inductively reflecting in the faces of the simplex. In this paper we establish that the quality of the simplices in all Coxeter triangulations is O(1/d−−√) of the quality of regular simplex. We further investigate the Delaunay property for these triangulations. Moreover, we consider an extension of the Delaunay property, namely protection, which is a measure of non-degeneracy of a Delaunay triangulation. In particular, one family of Coxeter triangulations achieves the protection O(1/d2). We conjecture that both bounds are optimal for triangulations in Euclidean space."}],"article_type":"original","page":"141-176","publication":"Mathematics in Computer Science","citation":{"ieee":"A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations have good quality,” Mathematics in Computer Science, vol. 14. Springer Nature, pp. 141–176, 2020.","apa":"Choudhary, A., Kachanovich, S., & Wintraecken, M. (2020). Coxeter triangulations have good quality. Mathematics in Computer Science. Springer Nature. https://doi.org/10.1007/s11786-020-00461-5","ista":"Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have good quality. Mathematics in Computer Science. 14, 141–176.","ama":"Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good quality. Mathematics in Computer Science. 2020;14:141-176. doi:10.1007/s11786-020-00461-5","chicago":"Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter Triangulations Have Good Quality.” Mathematics in Computer Science. Springer Nature, 2020. https://doi.org/10.1007/s11786-020-00461-5.","short":"A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science 14 (2020) 141–176.","mla":"Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” Mathematics in Computer Science, vol. 14, Springer Nature, 2020, pp. 141–76, doi:10.1007/s11786-020-00461-5."},"date_published":"2020-03-01T00:00:00Z","scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)"},{"page":"181-218","publication":"Topological Data Analysis","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.","ieee":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions on Poisson–Delaunay mosaics and related complexes experimentally,” in Topological Data Analysis, 2020, vol. 15, pp. 181–218.","apa":"Edelsbrunner, H., Nikitenko, A., Ölsböck, K., & Synak, P. (2020). Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In Topological Data Analysis (Vol. 15, pp. 181–218). Springer Nature. https://doi.org/10.1007/978-3-030-43408-3_8","ama":"Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In: Topological Data Analysis. Vol 15. Springer Nature; 2020:181-218. doi:10.1007/978-3-030-43408-3_8","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” In Topological Data Analysis, 15:181–218. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-43408-3_8.","mla":"Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” Topological Data Analysis, vol. 15, Springer Nature, 2020, pp. 181–218, doi:10.1007/978-3-030-43408-3_8.","short":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218."},"date_published":"2020-06-22T00:00:00Z","scopus_import":"1","day":"22","has_accepted_license":"1","article_processing_charge":"No","status":"public","ddc":["510"],"title":"Radius functions on Poisson–Delaunay mosaics and related complexes experimentally","intvolume":" 15","_id":"8135","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_name":"2020-B-01-PoissonExperimentalSurvey.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":2207071,"file_id":"8628","relation":"main_file","date_created":"2020-10-08T08:56:14Z","date_updated":"2020-10-08T08:56:14Z","success":1,"checksum":"7b5e0de10675d787a2ddb2091370b8d8"}],"oa_version":"Submitted Version","alternative_title":["Abel Symposia"],"type":"conference","abstract":[{"lang":"eng","text":"Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics."}],"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"call_identifier":"H2020","name":"Efficient Simulation of Natural Phenomena at Extremely Large Scales","grant_number":"638176","_id":"2533E772-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-43408-3_8","month":"06","publication_identifier":{"issn":["21932808"],"eissn":["21978549"],"isbn":["9783030434076"]},"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"year":"2020","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).","date_created":"2020-07-19T22:00:59Z","date_updated":"2021-01-12T08:17:06Z","volume":15,"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","first_name":"Anton"},{"full_name":"Ölsböck, Katharina","first_name":"Katharina","last_name":"Ölsböck","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Synak, Peter","last_name":"Synak","first_name":"Peter","id":"331776E2-F248-11E8-B48F-1D18A9856A87"}],"file_date_updated":"2020-10-08T08:56:14Z","ec_funded":1},{"file_date_updated":"2021-03-22T08:56:37Z","ec_funded":1,"acknowledgement":"This work has been partially supported by the European Research Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. ","year":"2020","publication_status":"published","publisher":"De Gruyter","department":[{"_id":"HeEd"}],"author":[{"full_name":"Biswas, Ranita","first_name":"Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890"},{"first_name":"Gaëlle","last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle"},{"last_name":"Zrour","first_name":"Rita","full_name":"Zrour, Rita"},{"last_name":"Andres","first_name":"Eric","full_name":"Andres, Eric"}],"date_created":"2021-03-16T08:55:19Z","date_updated":"2021-03-22T09:01:50Z","volume":4,"month":"11","publication_identifier":{"issn":["2353-3390"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"doi":"10.1515/mathm-2020-0106","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"lang":"eng","text":"Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system."}],"issue":"1","_id":"9249","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"status":"public","title":"Digital objects in rhombic dodecahedron grid","intvolume":" 4","file":[{"success":1,"checksum":"4a1043fa0548a725d464017fe2483ce0","date_updated":"2021-03-22T08:56:37Z","date_created":"2021-03-22T08:56:37Z","file_id":"9272","relation":"main_file","creator":"dernst","file_size":3668725,"content_type":"application/pdf","access_level":"open_access","file_name":"2020_MathMorpholTheoryAppl_Biswas.pdf"}],"oa_version":"Published Version","day":"17","has_accepted_license":"1","article_processing_charge":"No","publication":"Mathematical Morphology - Theory and Applications","citation":{"mla":"Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and Applications, vol. 4, no. 1, De Gruyter, 2020, pp. 143–58, doi:10.1515/mathm-2020-0106.","short":"R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.","chicago":"Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and Applications. De Gruyter, 2020. https://doi.org/10.1515/mathm-2020-0106.","ama":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 2020;4(1):143-158. doi:10.1515/mathm-2020-0106","ista":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 4(1), 143–158.","ieee":"R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects in rhombic dodecahedron grid,” Mathematical Morphology - Theory and Applications, vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.","apa":"Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2020). Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. De Gruyter. https://doi.org/10.1515/mathm-2020-0106"},"article_type":"original","page":"143-158","date_published":"2020-11-17T00:00:00Z"},{"publication_identifier":{"eissn":["1611-3349"],"isbn":["9783030687656"],"issn":["0302-9743"]},"month":"09","external_id":{"arxiv":["2006.14908"]},"main_file_link":[{"url":"https://arxiv.org/abs/2006.14908","open_access":"1"}],"oa":1,"project":[{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"quality_controlled":"1","doi":"10.1007/978-3-030-68766-3_28","conference":{"end_date":"2020-09-18","start_date":"2020-09-16","location":"Virtual, Online","name":"GD: Graph Drawing and Network Visualization"},"language":[{"iso":"eng"}],"year":"2020","acknowledgement":"Supported by the National Research, Development and Innovation Office, NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full version can be found at https://arxiv.org/abs/2006.14908.","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János"},{"first_name":"Gábor","last_name":"Tardos","full_name":"Tardos, Gábor"},{"last_name":"Tóth","first_name":"Géza","full_name":"Tóth, Géza"}],"volume":12590,"date_created":"2021-03-28T22:01:44Z","date_updated":"2021-04-06T11:32:32Z","scopus_import":"1","series_title":"LNCS","article_processing_charge":"No","day":"20","citation":{"ama":"Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: 28th International Symposium on Graph Drawing and Network Visualization. Vol 12590. LNCS. Springer Nature; 2020:359-371. doi:10.1007/978-3-030-68766-3_28","apa":"Pach, J., Tardos, G., & Tóth, G. (2020). Crossings between non-homotopic edges. In 28th International Symposium on Graph Drawing and Network Visualization (Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. https://doi.org/10.1007/978-3-030-68766-3_28","ieee":"J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,” in 28th International Symposium on Graph Drawing and Network Visualization, Virtual, Online, 2020, vol. 12590, pp. 359–371.","ista":"Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network VisualizationLNCS vol. 12590, 359–371.","short":"J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 359–371.","mla":"Pach, János, et al. “Crossings between Non-Homotopic Edges.” 28th International Symposium on Graph Drawing and Network Visualization, vol. 12590, Springer Nature, 2020, pp. 359–71, doi:10.1007/978-3-030-68766-3_28.","chicago":"Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic Edges.” In 28th International Symposium on Graph Drawing and Network Visualization, 12590:359–71. LNCS. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-68766-3_28."},"publication":"28th International Symposium on Graph Drawing and Network Visualization","page":"359-371","date_published":"2020-09-20T00:00:00Z","type":"conference","abstract":[{"text":"We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on n>1 vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and m>4n edges is larger than cm2n for some constant c>0 , and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and m⟶∞ .","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9299","intvolume":" 12590","title":"Crossings between non-homotopic edges","status":"public","oa_version":"Preprint"},{"publication_status":"published","publisher":"Carleton University","department":[{"_id":"HeEd"}],"year":"2020","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).","date_created":"2021-07-04T22:01:26Z","date_updated":"2021-08-11T12:26:34Z","volume":11,"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"license":"https://creativecommons.org/licenses/by/3.0/","file_date_updated":"2021-08-11T11:55:11Z","quality_controlled":"1","project":[{"name":"Discretization in Geometry and Dynamics","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","short":"CC BY (3.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.20382/jocg.v11i2a7","month":"12","publication_identifier":{"eissn":["1920180X"]},"title":"Topological data analysis in information space","ddc":["510","000"],"status":"public","intvolume":" 11","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","_id":"9630","oa_version":"Published Version","file":[{"file_size":1449234,"content_type":"application/pdf","creator":"asandaue","access_level":"open_access","file_name":"2020_JournalOfComputationalGeometry_Edelsbrunner.pdf","checksum":"f02d0b2b3838e7891a6c417fc34ffdcd","success":1,"date_created":"2021-08-11T11:55:11Z","date_updated":"2021-08-11T11:55:11Z","relation":"main_file","file_id":"9882"}],"type":"journal_article","abstract":[{"text":"Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context.","lang":"eng"}],"issue":"2","article_type":"original","page":"162-182","publication":"Journal of Computational Geometry","citation":{"chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” Journal of Computational Geometry. Carleton University, 2020. https://doi.org/10.20382/jocg.v11i2a7.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11 (2020) 162–182.","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” Journal of Computational Geometry, vol. 11, no. 2, Carleton University, 2020, pp. 162–82, doi:10.20382/jocg.v11i2a7.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis in information space. Journal of Computational Geometry. Carleton University. https://doi.org/10.20382/jocg.v11i2a7","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University, pp. 162–182, 2020.","ista":"Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. Journal of Computational Geometry. 11(2), 162–182.","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7"},"date_published":"2020-12-14T00:00:00Z","scopus_import":"1","day":"14","article_processing_charge":"Yes","has_accepted_license":"1"},{"doi":"10.1007/s40879-020-00426-9","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2001.02934"}],"external_id":{"arxiv":["2001.02934"]},"quality_controlled":"1","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"}],"month":"09","publication_identifier":{"eissn":["2199-6768"],"issn":["2199-675X"]},"author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"last_name":"Schwartz","first_name":"Richard","full_name":"Schwartz, Richard"},{"full_name":"Tabachnikov, Serge","last_name":"Tabachnikov","first_name":"Serge"}],"date_created":"2020-09-20T22:01:38Z","date_updated":"2021-12-02T15:10:17Z","acknowledgement":" This paper would not be written if not for Dan Reznik’s curiosity and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller for interesting discussions. It is a pleasure to thank the Mathematical Institute of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality. AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR 191.","year":"2020","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","ec_funded":1,"date_published":"2020-09-09T00:00:00Z","publication":"European Journal of Mathematics","citation":{"ama":"Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. European Journal of Mathematics. 2020. doi:10.1007/s40879-020-00426-9","ista":"Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited. European Journal of Mathematics.","ieee":"A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,” European Journal of Mathematics. Springer Nature, 2020.","apa":"Akopyan, A., Schwartz, R., & Tabachnikov, S. (2020). Billiards in ellipses revisited. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00426-9","mla":"Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” European Journal of Mathematics, Springer Nature, 2020, doi:10.1007/s40879-020-00426-9.","short":"A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics (2020).","chicago":"Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in Ellipses Revisited.” European Journal of Mathematics. Springer Nature, 2020. https://doi.org/10.1007/s40879-020-00426-9."},"article_type":"original","day":"09","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"8538","status":"public","title":"Billiards in ellipses revisited","abstract":[{"text":"We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.","lang":"eng"}],"type":"journal_article"},{"oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2020_LIPIcsSoCG_Boissonnat.pdf","creator":"dernst","file_size":1009739,"content_type":"application/pdf","file_id":"7969","relation":"main_file","checksum":"38cbfa4f5d484d267a35d44d210df044","date_updated":"2020-07-14T12:48:06Z","date_created":"2020-06-17T10:13:34Z"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7952","intvolume":" 164","status":"public","title":"The topological correctness of PL-approximations of isomanifolds","ddc":["510"],"abstract":[{"lang":"eng","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. "}],"type":"conference","alternative_title":["LIPIcs"],"date_published":"2020-06-01T00:00:00Z","citation":{"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.","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.","short":"J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","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.","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.","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","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"},"publication":"36th International Symposium on Computational Geometry","article_processing_charge":"No","has_accepted_license":"1","day":"01","scopus_import":"1","related_material":{"record":[{"id":"9649","status":"public","relation":"later_version"}]},"author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"volume":164,"date_created":"2020-06-09T07:24:11Z","date_updated":"2023-08-02T06:49:16Z","year":"2020","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","ec_funded":1,"file_date_updated":"2020-07-14T12:48:06Z","article_number":"20:1-20:18","doi":"10.4230/LIPIcs.SoCG.2020.20","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2020-06-26","start_date":"2020-06-22","location":"Zürich, Switzerland"},"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"quality_controlled":"1","publication_identifier":{"isbn":["978-3-95977-143-6"],"issn":["1868-8969"]},"month":"06"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"74","intvolume":" 2256","title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","status":"public","oa_version":"Preprint","type":"book_chapter","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"}],"citation":{"short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” 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.","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.","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.","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."},"publication":"Geometric Aspects of Functional Analysis","page":"1-27","date_published":"2020-06-21T00:00:00Z","scopus_import":"1","series_title":"LNM","article_processing_charge":"No","day":"21","year":"2020","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"publisher":"Springer Nature","editor":[{"full_name":"Klartag, Bo'az","last_name":"Klartag","first_name":"Bo'az"},{"first_name":"Emanuel","last_name":"Milman","full_name":"Milman, Emanuel"}],"publication_status":"published","author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"volume":2256,"date_updated":"2023-08-17T13:48:31Z","date_created":"2018-12-11T11:44:29Z","ec_funded":1,"external_id":{"arxiv":["1808.07350"],"isi":["000557689300003"]},"main_file_link":[{"url":"https://arxiv.org/abs/1808.07350","open_access":"1"}],"oa":1,"project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"quality_controlled":"1","isi":1,"doi":"10.1007/978-3-030-36020-7_1","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["16179692"],"isbn":["9783030360191"],"issn":["00758434"],"eisbn":["9783030360207"]},"month":"06"},{"ec_funded":1,"publication_status":"published","publisher":"SIAM","department":[{"_id":"HeEd"}],"year":"2020","date_created":"2020-03-01T23:00:39Z","date_updated":"2023-08-18T06:45:48Z","volume":64,"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","first_name":"Anton","last_name":"Nikitenko"}],"month":"02","publication_identifier":{"issn":["0040585X"],"eissn":["10957219"]},"isi":1,"quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"external_id":{"isi":["000551393100007"],"arxiv":["1705.08735"]},"main_file_link":[{"url":"https://arxiv.org/abs/1705.08735","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1137/S0040585X97T989726","type":"journal_article","abstract":[{"lang":"eng","text":"Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the smallest empty circumscribed sphere whose center lies in the $k$-plane gives a generalized discrete Morse function. Assuming the Voronoi tessellation is generated by a Poisson point process in ${R}^n$, we study the expected number of simplices in the $k$-dimensional weighted Delaunay mosaic as well as the expected number of intervals of the Morse function, both as functions of a radius threshold. As a by-product, we obtain a new proof for the expected number of connected components (clumps) in a line section of a circular Boolean model in ${R}^n$."}],"issue":"4","status":"public","title":"Weighted Poisson–Delaunay mosaics","intvolume":" 64","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7554","oa_version":"Preprint","scopus_import":"1","day":"13","article_processing_charge":"No","article_type":"original","page":"595-614","publication":"Theory of Probability and its Applications","citation":{"ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 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.","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."},"date_published":"2020-02-13T00:00:00Z"},{"scopus_import":"1","day":"20","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","article_type":"original","page":"759-775","publication":"Discrete and Computational Geometry","citation":{"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","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","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.","ista":"Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775.","short":"H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 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.","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."},"date_published":"2020-03-20T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","text":"Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups."}],"ddc":["510"],"title":"Tri-partitions and bases of an ordered complex","status":"public","intvolume":" 64","_id":"7666","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"8786","date_created":"2020-11-20T13:22:21Z","date_updated":"2020-11-20T13:22:21Z","checksum":"f8cc96e497f00c38340b5dafe0cb91d7","success":1,"file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf","access_level":"open_access","file_size":701673,"content_type":"application/pdf","creator":"dernst"}],"month":"03","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"isi":1,"quality_controlled":"1","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000520918800001"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00188-x","file_date_updated":"2020-11-20T13:22:21Z","ec_funded":1,"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","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).","year":"2020","date_created":"2020-04-19T22:00:56Z","date_updated":"2023-08-21T06:13:48Z","volume":64,"author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Katharina","last_name":"Ölsböck","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4672-8297","full_name":"Ölsböck, Katharina"}]},{"month":"06","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"doi":"10.1007/s00454-020-00213-z","language":[{"iso":"eng"}],"external_id":{"arxiv":["1803.06710"],"isi":["000538229000001"]},"main_file_link":[{"url":"https://arxiv.org/abs/1803.06710","open_access":"1"}],"oa":1,"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FWF","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"}],"author":[{"first_name":"János","last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János"},{"full_name":"Reed, Bruce","first_name":"Bruce","last_name":"Reed"},{"last_name":"Yuditsky","first_name":"Yelena","full_name":"Yuditsky, Yelena"}],"date_created":"2020-06-14T22:00:51Z","date_updated":"2023-08-21T08:49:18Z","volume":63,"year":"2020","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"day":"05","article_processing_charge":"No","scopus_import":"1","date_published":"2020-06-05T00:00:00Z","publication":"Discrete and Computational Geometry","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.","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","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.","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","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.","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.","short":"J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917."},"article_type":"original","page":"888-917","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","type":"journal_article","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7962","status":"public","title":"Almost all string graphs are intersection graphs of plane convex sets","intvolume":" 63"},{"isi":1,"main_file_link":[{"url":"https://doi.org/10.1007/s00454-020-00237-5","open_access":"1"}],"external_id":{"isi":["000561483500001"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00237-5","month":"10","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","year":"2020","date_updated":"2023-08-22T09:05:04Z","date_created":"2020-08-30T22:01:12Z","volume":64,"author":[{"full_name":"Pach, János","first_name":"János","last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"}],"article_type":"letter_note","page":"571-574","publication":"Discrete and Computational Geometry","citation":{"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.","chicago":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry. Springer Nature, 2020. 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","ista":"Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574.","apa":"Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5","ieee":"J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 571–574, 2020."},"date_published":"2020-10-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","status":"public","title":"A farewell to Ricky Pollack","intvolume":" 64","_id":"8323","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"None","type":"journal_article"},{"_id":"8580","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2020","publication_status":"published","title":"The application of persistent homology in the analysis of heart rate variability","status":"public","publisher":"IEEE","department":[{"_id":"HeEd"}],"author":[{"full_name":"Graff, Grzegorz","first_name":"Grzegorz","last_name":"Graff"},{"full_name":"Graff, Beata","last_name":"Graff","first_name":"Beata"},{"orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","last_name":"Jablonski","first_name":"Grzegorz","full_name":"Jablonski, Grzegorz"},{"full_name":"Narkiewicz, Krzysztof","last_name":"Narkiewicz","first_name":"Krzysztof"}],"date_created":"2020-09-28T08:59:27Z","date_updated":"2023-08-22T09:33:34Z","oa_version":"None","article_number":"9158054","type":"conference","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"}],"publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ","external_id":{"isi":["000621172600045"]},"citation":{"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","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.","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","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.","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.","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.","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."},"quality_controlled":"1","isi":1,"conference":{"name":"ESGCO: European Study Group on Cardiovascular Oscillations","start_date":"2020-07-15","location":"Pisa, Italy","end_date":"2020-07-15"},"doi":"10.1109/ESGCO49734.2020.9158054","date_published":"2020-08-01T00:00:00Z","language":[{"iso":"eng"}],"scopus_import":"1","month":"08","day":"01","article_processing_charge":"No","publication_identifier":{"isbn":["9781728157511"]}},{"date_updated":"2023-08-24T14:19:55Z","date_created":"2022-03-18T11:39:30Z","volume":2020,"author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"publication_status":"published","publisher":"Oxford University Press","department":[{"_id":"HeEd"}],"acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","year":"2020","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rny037","quality_controlled":"1","isi":1,"external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.07513"}],"month":"02","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"oa_version":"Preprint","status":"public","title":"Waist of balls in hyperbolic and spherical spaces","intvolume":" 2020","_id":"10867","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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","type":"journal_article","date_published":"2020-02-01T00:00:00Z","article_type":"original","page":"669-697","publication":"International Mathematics Research Notices","citation":{"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.","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","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","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","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.","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."},"day":"01","article_processing_charge":"No","keyword":["General Mathematics"],"scopus_import":"1"},{"day":"10","article_processing_charge":"No","has_accepted_license":"1","keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"],"date_published":"2020-02-10T00:00:00Z","citation":{"chicago":"Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460.","short":"K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science and Technology Austria, 2020.","mla":"Ölsböck, Katharina. The Hole System of Triangulated Shapes. Institute of Science and Technology Austria, 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","ieee":"K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science and Technology Austria, 2020.","ista":"Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria.","ama":"Ölsböck K. The hole system of triangulated shapes. 2020. doi:10.15479/AT:ISTA:7460"},"page":"155","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"}],"type":"dissertation","alternative_title":["ISTA Thesis"],"file":[{"checksum":"1df9f8c530b443c0e63a3f2e4fde412e","date_created":"2020-02-06T14:43:54Z","date_updated":"2020-07-14T12:47:58Z","file_id":"7461","relation":"main_file","creator":"koelsboe","file_size":76195184,"content_type":"application/pdf","access_level":"open_access","file_name":"thesis_ist-final_noack.pdf"},{"date_updated":"2020-07-14T12:47:58Z","date_created":"2020-02-06T14:52:45Z","checksum":"7a52383c812b0be64d3826546509e5a4","file_id":"7462","relation":"source_file","creator":"koelsboe","file_size":122103715,"content_type":"application/x-zip-compressed","file_name":"latex-files.zip","description":"latex source files, figures","access_level":"closed"}],"oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"7460","status":"public","title":"The hole system of triangulated shapes","ddc":["514"],"month":"02","publication_identifier":{"issn":["2663-337X"]},"doi":"10.15479/AT:ISTA:7460","supervisor":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"}],"degree_awarded":"PhD","language":[{"iso":"eng"}],"tmp":{"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","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"oa":1,"file_date_updated":"2020-07-14T12:47:58Z","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","author":[{"full_name":"Ölsböck, Katharina","last_name":"Ölsböck","first_name":"Katharina","orcid":"0000-0002-4672-8297","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"id":"6608","relation":"part_of_dissertation","status":"public"}]},"date_created":"2020-02-06T14:56:53Z","date_updated":"2023-09-07T13:15:30Z","year":"2020","publication_status":"published","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"publisher":"Institute of Science and Technology Austria"},{"publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-005-3"]},"month":"06","language":[{"iso":"eng"}],"supervisor":[{"first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"degree_awarded":"PhD","doi":"10.15479/AT:ISTA:7944","oa":1,"tmp":{"short":"CC BY-SA (4.0)","image":"/images/cc_by_sa.png","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode"},"license":"https://creativecommons.org/licenses/by-sa/4.0/","file_date_updated":"2020-07-14T12:48:05Z","date_updated":"2023-09-07T13:17:37Z","date_created":"2020-06-08T00:49:46Z","related_material":{"record":[{"id":"7950","relation":"part_of_dissertation","status":"public"},{"id":"5986","status":"public","relation":"part_of_dissertation"}]},"author":[{"full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"}],"publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"publication_status":"published","year":"2020","has_accepted_license":"1","article_processing_charge":"No","day":"09","keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"date_published":"2020-06-09T00:00:00Z","page":"160","citation":{"chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944.","short":"Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020.","mla":"Masárová, Zuzana. Reconfiguration Problems. Institute of Science and Technology Austria, 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","ieee":"Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020.","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria.","ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944"},"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."}],"alternative_title":["ISTA Thesis"],"type":"dissertation","oa_version":"Published Version","file":[{"date_updated":"2020-07-14T12:48:05Z","date_created":"2020-06-08T00:34:00Z","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","relation":"main_file","file_id":"7945","content_type":"application/pdf","file_size":13661779,"creator":"zmasarov","file_name":"THESIS_Zuzka_Masarova.pdf","access_level":"open_access"},{"file_id":"7946","relation":"source_file","date_updated":"2020-07-14T12:48:05Z","date_created":"2020-06-08T00:35:30Z","checksum":"45341a35b8f5529c74010b7af43ac188","file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","access_level":"closed","creator":"zmasarov","content_type":"application/zip","file_size":32184006}],"title":"Reconfiguration problems","ddc":["516","514"],"status":"public","_id":"7944","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"_id":"8703","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Generalizing CGAL periodic Delaunay triangulations","ddc":["000"],"intvolume":" 173","oa_version":"Published Version","file":[{"file_name":"2020_LIPIcs_Osang.pdf","access_level":"open_access","creator":"cziletti","file_size":733291,"content_type":"application/pdf","file_id":"8712","relation":"main_file","date_created":"2020-10-27T14:31:52Z","date_updated":"2020-10-27T14:31:52Z","success":1,"checksum":"fe0f7c49a99ed870c671b911e10d5496"}],"type":"conference","alternative_title":["LIPIcs"],"abstract":[{"lang":"eng","text":"Even though Delaunay originally introduced his famous triangulations in the case of infinite point sets with translational periodicity, a software that computes such triangulations in the general case is not yet available, to the best of our knowledge. Combining and generalizing previous work, we present a practical algorithm for computing such triangulations. The algorithm has been implemented and experiments show that its performance is as good as the one of the CGAL package, which is restricted to cubic periodicity. "}],"publication":"28th Annual European Symposium on Algorithms","citation":{"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","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.","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","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.","short":"G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","mla":"Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.” 28th Annual European Symposium on Algorithms, vol. 173, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.ESA.2020.75.","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."},"date_published":"2020-08-26T00:00:00Z","scopus_import":"1","day":"26","has_accepted_license":"1","article_processing_charge":"No","year":"2020","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","author":[{"last_name":"Osang","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F"},{"full_name":"Rouxel-Labbé, Mael","first_name":"Mael","last_name":"Rouxel-Labbé"},{"full_name":"Teillaud, Monique","last_name":"Teillaud","first_name":"Monique"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"9056"}]},"date_created":"2020-10-25T23:01:18Z","date_updated":"2023-09-07T13:29:00Z","volume":173,"article_number":"75","file_date_updated":"2020-10-27T14:31:52Z","ec_funded":1,"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","short":"CC BY (3.0)","image":"/images/cc_by.png"},"quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"}],"conference":{"name":"ESA: Annual European Symposium on Algorithms","start_date":"2020-09-07","location":"Virtual, Online; Pisa, Italy","end_date":"2020-09-09"},"doi":"10.4230/LIPIcs.ESA.2020.75","language":[{"iso":"eng"}],"month":"08","publication_identifier":{"issn":["18688969"],"isbn":["9783959771627"]}},{"ec_funded":1,"file_date_updated":"2020-07-24T07:09:06Z","license":"https://creativecommons.org/licenses/by-nc/4.0/","author":[{"full_name":"Vegter, Gert","first_name":"Gert","last_name":"Vegter"},{"first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"volume":57,"date_updated":"2023-10-10T13:05:27Z","date_created":"2020-07-24T07:09:18Z","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.","year":"2020","department":[{"_id":"HeEd"}],"publisher":"Akadémiai Kiadó","publication_status":"published","publication_identifier":{"eissn":["1588-2896"],"issn":["0081-6906"]},"month":"07","doi":"10.1556/012.2020.57.2.1454","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)"},"external_id":{"isi":["000570978400005"]},"oa":1,"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"isi":1,"quality_controlled":"1","issue":"2","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"}],"type":"journal_article","file":[{"access_level":"open_access","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","content_type":"application/pdf","file_size":1476072,"creator":"mwintrae","relation":"main_file","file_id":"8164","date_created":"2020-07-24T07:09:06Z","date_updated":"2020-07-24T07:09:06Z"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8163","intvolume":" 57","title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","status":"public","ddc":["510"],"article_processing_charge":"No","has_accepted_license":"1","day":"24","scopus_import":"1","date_published":"2020-07-24T00:00:00Z","citation":{"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","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.","ista":"Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2), 193–199.","ama":"Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 2020;57(2):193-199. doi:10.1556/012.2020.57.2.1454","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.","short":"G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199.","mla":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:10.1556/012.2020.57.2.1454."},"publication":"Studia Scientiarum Mathematicarum Hungarica","page":"193-199","article_type":"original"},{"article_type":"original","page":"51-67","publication":"Computational and Mathematical Biophysics","citation":{"ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","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","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.","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","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.","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.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67."},"date_published":"2020-06-20T00:00:00Z","day":"20","article_processing_charge":"No","has_accepted_license":"1","title":"The weighted mean curvature derivative of a space-filling diagram","ddc":["510"],"status":"public","intvolume":" 8","_id":"9157","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"success":1,"checksum":"cea41de9937d07a3b927d71ee8b4e432","date_created":"2021-02-19T13:56:24Z","date_updated":"2021-02-19T13:56:24Z","file_id":"9171","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":562359,"access_level":"open_access","file_name":"2020_CompMathBiophysics_Akopyan2.pdf"}],"type":"journal_article","abstract":[{"lang":"eng","text":"Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy."}],"issue":"1","quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1515/cmb-2020-0100","month":"06","publication_identifier":{"issn":["2544-7297"]},"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"De Gruyter","year":"2020","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).","date_updated":"2023-10-17T12:34:51Z","date_created":"2021-02-17T15:13:01Z","volume":8,"author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"file_date_updated":"2021-02-19T13:56:24Z","ec_funded":1},{"file":[{"creator":"dernst","file_size":707452,"content_type":"application/pdf","file_name":"2020_CompMathBiophysics_Akopyan.pdf","access_level":"open_access","date_created":"2021-02-19T13:33:19Z","date_updated":"2021-02-19T13:33:19Z","success":1,"checksum":"ca43a7440834eab6bbea29c59b56ef3a","file_id":"9170","relation":"main_file"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9156","ddc":["510"],"status":"public","title":"The weighted Gaussian curvature derivative of a space-filling diagram","intvolume":" 8","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."}],"issue":"1","type":"journal_article","date_published":"2020-07-21T00:00:00Z","publication":"Computational and Mathematical Biophysics","citation":{"short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 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.","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","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","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.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88."},"article_type":"original","page":"74-88","day":"21","has_accepted_license":"1","article_processing_charge":"No","author":[{"last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}],"date_created":"2021-02-17T15:12:44Z","date_updated":"2023-10-17T12:35:10Z","volume":8,"year":"2020","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).","publication_status":"published","publisher":"De Gruyter","department":[{"_id":"HeEd"}],"file_date_updated":"2021-02-19T13:33:19Z","ec_funded":1,"doi":"10.1515/cmb-2020-0101","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1908.06777"]},"oa":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"month":"07","publication_identifier":{"issn":["2544-7297"]}},{"type":"journal_article","issue":"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"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"15064","intvolume":" 4","ddc":["500"],"title":"Čech-Delaunay gradient flow and homology inference for self-maps","status":"public","file":[{"access_level":"open_access","file_name":"2020_JourApplCompTopology_Bauer.pdf","content_type":"application/pdf","file_size":851190,"creator":"dernst","relation":"main_file","file_id":"15065","checksum":"eed1168b6e66cd55272c19bb7fca8a1c","success":1,"date_updated":"2024-03-04T10:52:42Z","date_created":"2024-03-04T10:52:42Z"}],"oa_version":"Published Version","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","citation":{"short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480.","mla":"Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:10.1007/s41468-020-00058-8.","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.","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","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.","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","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."},"publication":"Journal of Applied and Computational Topology","page":"455-480","article_type":"original","date_published":"2020-12-01T00:00:00Z","file_date_updated":"2024-03-04T10:52:42Z","year":"2020","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.","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"first_name":"U.","last_name":"Bauer","full_name":"Bauer, U."},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"last_name":"Jablonski","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","full_name":"Jablonski, Grzegorz"},{"first_name":"M.","last_name":"Mrozek","full_name":"Mrozek, M."}],"volume":4,"date_created":"2024-03-04T10:47:49Z","date_updated":"2024-03-04T10:54:04Z","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"month":"12","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","doi":"10.1007/s41468-020-00058-8","language":[{"iso":"eng"}]},{"scopus_import":1,"has_accepted_license":"1","day":"01","citation":{"ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","apa":"Dyer, R., Vegter, G., & Wintraecken, M. (2019). Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . Carleton University. https://doi.org/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.","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","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.","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.","short":"R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10 (2019) 223–256."},"publication":"Journal of Computational Geometry ","page":"223–256","date_published":"2019-07-01T00:00:00Z","type":"journal_article","issue":"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."}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"6515","intvolume":" 10","ddc":["510"],"status":"public","title":"Simplices modelled on spaces of constant curvature","file":[{"creator":"mwintrae","content_type":"application/pdf","file_size":2170882,"access_level":"open_access","file_name":"mainJournalFinal.pdf","checksum":"57b4df2f16a74eb499734ec8ee240178","date_created":"2019-06-03T09:30:01Z","date_updated":"2020-07-14T12:47:32Z","file_id":"6516","relation":"main_file"}],"oa_version":"Published Version","publication_identifier":{"issn":["1920-180X"]},"month":"07","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","doi":"10.20382/jocg.v10i1a9","language":[{"iso":"eng"}],"ec_funded":1,"file_date_updated":"2020-07-14T12:47:32Z","year":"2019","department":[{"_id":"HeEd"}],"publisher":"Carleton University","publication_status":"published","author":[{"last_name":"Dyer","first_name":"Ramsay","full_name":"Dyer, Ramsay"},{"full_name":"Vegter, Gert","first_name":"Gert","last_name":"Vegter"},{"first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"volume":10,"date_created":"2019-06-03T09:35:33Z","date_updated":"2021-01-12T08:07:50Z"},{"scopus_import":1,"has_accepted_license":"1","day":"01","month":"08","citation":{"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.","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.","ista":"Vegter G, Wintraecken M. 2019. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. The 31st Canadian Conference in Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 275–279.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279.","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.","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."},"oa":1,"publication":"The 31st Canadian Conference in Computational Geometry","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"page":"275-279","quality_controlled":"1","date_published":"2019-08-01T00:00:00Z","conference":{"start_date":"2019-08-08","location":"Edmonton, Canada","end_date":"2019-08-10","name":"CCCG: Canadian Conference in Computational Geometry"},"language":[{"iso":"eng"}],"type":"conference","ec_funded":1,"file_date_updated":"2020-07-14T12:47:34Z","abstract":[{"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.","lang":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"6628","year":"2019","department":[{"_id":"HeEd"}],"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","publication_status":"published","status":"public","ddc":["004"],"author":[{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs"}],"oa_version":"Submitted Version","file":[{"checksum":"ceabd152cfa55170d57763f9c6c60a53","date_created":"2019-07-12T08:32:46Z","date_updated":"2020-07-14T12:47:34Z","file_id":"6629","relation":"main_file","creator":"mwintrae","content_type":"application/pdf","file_size":321176,"access_level":"open_access","file_name":"IntrinsicExtrinsicCCCG2019.pdf"}],"date_created":"2019-07-12T08:34:57Z","date_updated":"2021-01-12T08:08:16Z"},{"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."}],"type":"conference","alternative_title":["LIPIcs"],"file":[{"content_type":"application/pdf","file_size":1355179,"creator":"dernst","file_name":"2019_LIPICS_Edelsbrunner.pdf","access_level":"open_access","date_created":"2019-07-24T06:40:01Z","date_updated":"2020-07-14T12:47:35Z","checksum":"8ec8720730d4c789bf7b06540f1c29f4","relation":"main_file","file_id":"6666"}],"oa_version":"Published Version","_id":"6648","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"status":"public","title":"Topological data analysis in information space","intvolume":" 129","day":"01","has_accepted_license":"1","scopus_import":1,"date_published":"2019-06-01T00:00:00Z","publication":"35th International Symposium on Computational Geometry","citation":{"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","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.","ista":"Edelsbrunner H, Virk Z, Wagner H. 2019. Topological data analysis in information space. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium on Computational Geometry, LIPIcs, vol. 129, 31:1-31:14.","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. In: 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","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.","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."},"page":"31:1-31:14","file_date_updated":"2020-07-14T12:47:35Z","author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Virk, Ziga","first_name":"Ziga","last_name":"Virk"},{"last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert"}],"date_created":"2019-07-17T10:36:09Z","date_updated":"2021-01-12T08:08:23Z","volume":129,"year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","month":"06","publication_identifier":{"isbn":["9783959771047"]},"conference":{"name":"SoCG 2019: Symposium on Computational Geometry","end_date":"2019-06-21","location":"Portland, OR, United States","start_date":"2019-06-18"},"doi":"10.4230/LIPICS.SOCG.2019.31","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1903.08510"]},"oa":1,"quality_controlled":"1","project":[{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}]},{"publisher":"Canadian Conference on Computational Geometry","department":[{"_id":"HeEd"}],"title":"Folding polyominoes with holes into a cube","status":"public","publication_status":"published","_id":"6989","acknowledgement":"This research was performed in part at the 33rd BellairsWinter Workshop on Computational Geometry. Wethank all other participants for a fruitful atmosphere.","year":"2019","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","oa_version":"Published Version","date_created":"2019-11-04T16:46:11Z","date_updated":"2023-08-04T10:57:42Z","related_material":{"record":[{"status":"public","relation":"extended_version","id":"8317"}]},"author":[{"full_name":"Aichholzer, Oswin","last_name":"Aichholzer","first_name":"Oswin"},{"last_name":"Akitaya","first_name":"Hugo A","full_name":"Akitaya, Hugo A"},{"full_name":"Cheung, Kenneth C","first_name":"Kenneth C","last_name":"Cheung"},{"first_name":"Erik D","last_name":"Demaine","full_name":"Demaine, Erik D"},{"full_name":"Demaine, Martin L","last_name":"Demaine","first_name":"Martin L"},{"full_name":"Fekete, Sandor P","first_name":"Sandor P","last_name":"Fekete"},{"last_name":"Kleist","first_name":"Linda","full_name":"Kleist, Linda"},{"first_name":"Irina","last_name":"Kostitsyna","full_name":"Kostitsyna, Irina"},{"full_name":"Löffler, Maarten","first_name":"Maarten","last_name":"Löffler"},{"last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"last_name":"Schmidt","first_name":"Christiane","full_name":"Schmidt, Christiane"}],"type":"conference","abstract":[{"lang":"eng","text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability. "}],"page":"164-170","quality_controlled":"1","external_id":{"arxiv":["1910.09917"]},"main_file_link":[{"open_access":"1","url":"https://cccg.ca/proceedings/2019/proceedings.pdf"}],"oa":1,"citation":{"ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference on Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 164–170.","ieee":"O. Aichholzer 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.","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.","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.","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.","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.","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."},"publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","language":[{"iso":"eng"}],"date_published":"2019-08-01T00:00:00Z","conference":{"end_date":"2019-08-10","location":"Edmonton, Canada","start_date":"2019-08-08","name":"CCCG: Canadian Conference in Computational Geometry"},"scopus_import":"1","article_processing_charge":"No","month":"08","day":"01"},{"author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"full_name":"Lieutier, André","first_name":"André","last_name":"Lieutier"},{"first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"volume":3,"date_updated":"2023-08-22T12:37:47Z","date_created":"2019-07-24T08:37:29Z","year":"2019","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","ec_funded":1,"file_date_updated":"2020-07-14T12:47:36Z","doi":"10.1007/s41468-019-00029-8","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"month":"06","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"6741","checksum":"a5b244db9f751221409cf09c97ee0935","date_created":"2019-07-31T08:09:56Z","date_updated":"2020-07-14T12:47:36Z","access_level":"open_access","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf","file_size":2215157,"content_type":"application/pdf","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"6671","intvolume":" 3","title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","status":"public","ddc":["000"],"issue":"1-2","abstract":[{"text":"In this paper we discuss three results. The first two concern general sets of positive reach: we first characterize the reach of a closed set by means of a bound on the metric distortion between the distance measured in the ambient Euclidean space and the shortest path distance measured in the set. Secondly, we prove that the intersection of a ball with radius less than the reach with the set is geodesically convex, meaning that the shortest path between any two points in the intersection lies itself in the intersection. For our third result we focus on manifolds with positive reach and give a bound on the angle between tangent spaces at two different points in terms of the reach and the distance between the two points.","lang":"eng"}],"type":"journal_article","date_published":"2019-06-01T00:00:00Z","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","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.","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.","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.","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.” Journal of Applied and Computational Topology. Springer Nature, 2019. https://doi.org/10.1007/s41468-019-00029-8."},"publication":"Journal of Applied and Computational Topology","page":"29–58","article_type":"original","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01"},{"year":"2019","publisher":"AMS","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"},{"last_name":"Fedorov","first_name":"Roman","full_name":"Fedorov, Roman"}],"volume":147,"date_created":"2019-02-24T22:59:19Z","date_updated":"2023-08-24T14:48:59Z","oa":1,"external_id":{"isi":["000450363900008"],"arxiv":["1709.02562"]},"main_file_link":[{"url":"https://arxiv.org/abs/1709.02562","open_access":"1"}],"quality_controlled":"1","isi":1,"doi":"10.1090/proc/14240","language":[{"iso":"eng"}],"month":"01","_id":"6050","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 147","status":"public","title":"Two circles and only a straightedge","oa_version":"Preprint","type":"journal_article","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"}],"citation":{"ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.","apa":"Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240","ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240","chicago":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240.","mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society, vol. 147, AMS, 2019, pp. 91–102, doi:10.1090/proc/14240.","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102."},"publication":"Proceedings of the American Mathematical Society","page":"91-102","date_published":"2019-01-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01"},{"type":"journal_article","abstract":[{"text":"In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure.","lang":"eng"}],"issue":"2","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6634","status":"public","title":"Lower and upper bounds for the waists of different spaces","intvolume":" 53","oa_version":"Preprint","scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Topological Methods in Nonlinear Analysis","citation":{"chicago":"Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008.","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","mla":"Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008.","apa":"Akopyan, A., Hubard, A., & Karasev, R. (2019). Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism. https://doi.org/10.12775/TMNA.2019.008","ieee":"A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.","ista":"Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.","ama":"Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 2019;53(2):457-490. doi:10.12775/TMNA.2019.008"},"page":"457-490","date_published":"2019-06-01T00:00:00Z","ec_funded":1,"year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Akademicka Platforma Czasopism","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"full_name":"Hubard, Alfredo","last_name":"Hubard","first_name":"Alfredo"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"date_updated":"2023-08-29T06:32:48Z","date_created":"2019-07-14T21:59:19Z","volume":53,"month":"06","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1612.06926","open_access":"1"}],"external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"isi":1,"quality_controlled":"1","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"doi":"10.12775/TMNA.2019.008","language":[{"iso":"eng"}]},{"type":"journal_article","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."}],"_id":"6756","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 627","status":"public","ddc":["520","530"],"title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","oa_version":"Published Version","file":[{"file_size":14420451,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2019_AstronomyAstrophysics_Pranav.pdf","checksum":"83b9209ed9eefbdcefd89019c5a97805","date_updated":"2020-07-14T12:47:39Z","date_created":"2019-08-05T08:08:59Z","relation":"main_file","file_id":"6766"}],"scopus_import":"1","has_accepted_license":"1","article_processing_charge":"No","day":"17","citation":{"ama":"Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 2019;627. doi:10.1051/0004-6361/201834916","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. Astronomy and Astrophysics. EDP Sciences. https://doi.org/10.1051/0004-6361/201834916","ieee":"P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 2019.","ista":"Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 627, A163.","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).","mla":"Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627, A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916.","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.” Astronomy and Astrophysics. EDP Sciences, 2019. https://doi.org/10.1051/0004-6361/201834916."},"publication":"Astronomy and Astrophysics","article_type":"original","date_published":"2019-07-17T00:00:00Z","article_number":"A163","file_date_updated":"2020-07-14T12:47:39Z","year":"2019","department":[{"_id":"HeEd"}],"publisher":"EDP Sciences","publication_status":"published","author":[{"first_name":"Pratyush","last_name":"Pranav","full_name":"Pranav, Pratyush"},{"first_name":"Robert J.","last_name":"Adler","full_name":"Adler, Robert J."},{"first_name":"Thomas","last_name":"Buchert","full_name":"Buchert, Thomas"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Jones, Bernard J.T.","last_name":"Jones","first_name":"Bernard J.T."},{"first_name":"Armin","last_name":"Schwartzman","full_name":"Schwartzman, Armin"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Van De Weygaert, Rien","first_name":"Rien","last_name":"Van De Weygaert"}],"volume":627,"date_updated":"2023-08-29T07:01:48Z","date_created":"2019-08-04T21:59:18Z","publication_identifier":{"eissn":["14320746"],"issn":["00046361"]},"month":"07","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000475839300003"],"arxiv":["1812.07678"]},"project":[{"name":"Toward Computational Information Topology","_id":"265683E4-B435-11E9-9278-68D0E5697425","grant_number":"M62909-18-1-2038"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"isi":1,"quality_controlled":"1","doi":"10.1051/0004-6361/201834916","language":[{"iso":"eng"}]},{"year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"London Mathematical Society","author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"full_name":"Izmestiev, Ivan","first_name":"Ivan","last_name":"Izmestiev"}],"date_created":"2019-08-11T21:59:23Z","date_updated":"2023-08-29T07:08:34Z","volume":51,"ec_funded":1,"external_id":{"isi":["000478560200001"],"arxiv":["1903.04929"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1903.04929","open_access":"1"}],"quality_controlled":"1","isi":1,"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"}],"doi":"10.1112/blms.12276","language":[{"iso":"eng"}],"month":"10","publication_identifier":{"eissn":["14692120"],"issn":["00246093"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6793","status":"public","title":"The Regge symmetry, confocal conics, and the Schläfli formula","intvolume":" 51","oa_version":"Preprint","type":"journal_article","abstract":[{"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.","lang":"eng"}],"issue":"5","publication":"Bulletin of the London Mathematical Society","citation":{"apa":"Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12276","ieee":"A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019.","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.","ama":"Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 2019;51(5):765-775. doi:10.1112/blms.12276","chicago":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society. London Mathematical Society, 2019. https://doi.org/10.1112/blms.12276.","short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","mla":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society, vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:10.1112/blms.12276."},"article_type":"original","page":"765-775","date_published":"2019-10-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.04676"}],"oa":1,"external_id":{"arxiv":["1805.04676"],"isi":["000487176300011"]},"quality_controlled":"1","isi":1,"doi":"10.1016/j.jalgebra.2019.07.027","language":[{"iso":"eng"}],"month":"11","publication_identifier":{"issn":["0021-8693"]},"year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier","author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","first_name":"Adam","full_name":"Brown, Adam"}],"date_updated":"2023-08-29T07:11:47Z","date_created":"2019-08-22T07:54:13Z","volume":538,"publication":"Journal of Algebra","citation":{"chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027.","short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","mla":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027.","apa":"Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2019.07.027","ieee":"A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra, vol. 538. Elsevier, pp. 261–289, 2019.","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. Journal of Algebra. 2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027"},"article_type":"original","page":"261-289","date_published":"2019-11-15T00:00:00Z","day":"15","article_processing_charge":"No","_id":"6828","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"Arakawa-Suzuki functors for Whittaker modules","intvolume":" 538","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type to the category of finite-dimensional modules of the graded affine Hecke algebra of type . Using results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category as a full subcategory, our results generalize results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between finite-dimensional representations of and representations of the symmetric group ."}]},{"scopus_import":"1","day":"28","month":"11","article_processing_charge":"No","publication_identifier":{"isbn":["9781538670248"]},"quality_controlled":"1","isi":1,"publication":"2019 IEEE Intelligent Transportation Systems Conference","external_id":{"isi":["000521238102050"]},"citation":{"short":"G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019.","mla":"Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” 2019 IEEE Intelligent Transportation Systems Conference, 8917514, IEEE, 2019, doi:10.1109/ITSC.2019.8917514.","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 2019 IEEE Intelligent Transportation Systems Conference. IEEE, 2019. https://doi.org/10.1109/ITSC.2019.8917514.","ama":"Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In: 2019 IEEE Intelligent Transportation Systems Conference. IEEE; 2019. doi:10.1109/ITSC.2019.8917514","ieee":"G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale,” in 2019 IEEE Intelligent Transportation Systems Conference, Auckland, New Zealand, 2019.","apa":"Osang, G. F., Cook, J., Fabrikant, A., & Gruteser, M. (2019). LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In 2019 IEEE Intelligent Transportation Systems Conference. Auckland, New Zealand: IEEE. https://doi.org/10.1109/ITSC.2019.8917514","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."},"language":[{"iso":"eng"}],"conference":{"start_date":"2019-10-27","location":"Auckland, New Zealand","end_date":"2019-10-30","name":"ITSC: Intelligent Transportation Systems Conference"},"doi":"10.1109/ITSC.2019.8917514","date_published":"2019-11-28T00:00:00Z","article_number":"8917514","type":"conference","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","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"IEEE","_id":"7216","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","year":"2019","date_created":"2019-12-29T23:00:47Z","date_updated":"2023-09-06T14:50:28Z","oa_version":"None","author":[{"full_name":"Osang, Georg F","last_name":"Osang","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Cook, James","last_name":"Cook","first_name":"James"},{"first_name":"Alex","last_name":"Fabrikant","full_name":"Fabrikant, Alex"},{"last_name":"Gruteser","first_name":"Marco","full_name":"Gruteser, Marco"}]},{"type":"journal_article","abstract":[{"lang":"eng","text":"The order-k Voronoi tessellation of a locally finite set 𝑋⊆ℝ𝑛 decomposes ℝ𝑛 into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold."}],"issue":"4","title":"Poisson–Delaunay Mosaics of Order k","ddc":["516"],"status":"public","intvolume":" 62","_id":"5678","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","file":[{"file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":599339,"file_id":"5932","relation":"main_file","date_updated":"2020-07-14T12:47:10Z","date_created":"2019-02-06T10:10:46Z","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4"}],"scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","article_type":"original","page":"865–878","publication":"Discrete and Computational Geometry","citation":{"chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2.","short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.","ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.","ieee":"H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019.","apa":"Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2","ama":"Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2"},"date_published":"2019-12-01T00:00:00Z","file_date_updated":"2020-07-14T12:47:10Z","ec_funded":1,"publication_status":"published","publisher":"Springer","department":[{"_id":"HeEd"}],"year":"2019","date_created":"2018-12-16T22:59:20Z","date_updated":"2023-09-07T12:07:12Z","volume":62,"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Nikitenko, Anton","first_name":"Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201"}],"related_material":{"record":[{"id":"6287","relation":"dissertation_contains","status":"public"}]},"month":"12","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"isi":1,"quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000494042900008"],"arxiv":["1709.09380"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00454-018-0049-2"},{"month":"08","doi":"10.1016/j.cagd.2019.06.003","language":[{"iso":"eng"}],"tmp":{"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","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"external_id":{"isi":["000485207800001"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"file_date_updated":"2020-07-14T12:47:34Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"first_name":"Katharina","last_name":"Ölsböck","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4672-8297","full_name":"Ölsböck, Katharina"}],"related_material":{"record":[{"id":"7460","relation":"dissertation_contains","status":"public"}]},"date_created":"2019-07-07T21:59:20Z","date_updated":"2023-09-07T13:15:29Z","volume":73,"year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier","day":"01","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","date_published":"2019-08-01T00:00:00Z","publication":"Computer Aided Geometric Design","citation":{"ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.","apa":"Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered complex. Computer Aided Geometric Design. Elsevier. https://doi.org/10.1016/j.cagd.2019.06.003","ieee":"H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” Computer Aided Geometric Design, vol. 73. Elsevier, pp. 1–15, 2019.","ama":"Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design. Elsevier, 2019. https://doi.org/10.1016/j.cagd.2019.06.003.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019, pp. 1–15, doi:10.1016/j.cagd.2019.06.003.","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15."},"page":"1-15","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"}],"type":"journal_article","file":[{"date_created":"2019-07-08T15:24:26Z","date_updated":"2020-07-14T12:47:34Z","checksum":"7c99be505dc7533257d42eb1830cef04","file_id":"6624","relation":"main_file","creator":"kschuh","content_type":"application/pdf","file_size":2665013,"file_name":"Elsevier_2019_Edelsbrunner.pdf","access_level":"open_access"}],"oa_version":"Published Version","_id":"6608","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","ddc":["000"],"title":"Holes and dependences in an ordered complex","intvolume":" 73"},{"publication":"arXiv","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.” ArXiv, n.d.","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981.","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.).","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981.","ieee":"A. Biniaz et al., “Token swapping on trees,” arXiv. .","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. arXiv.","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv."},"external_id":{"arxiv":["1903.06981"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.06981"}],"oa":1,"language":[{"iso":"eng"}],"date_published":"2019-03-16T00:00:00Z","day":"16","month":"03","article_processing_charge":"No","publication_status":"submitted","status":"public","title":"Token swapping on trees","department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"year":"2019","_id":"7950","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2020-06-08T12:25:25Z","date_updated":"2024-01-04T12:42:08Z","oa_version":"Preprint","author":[{"first_name":"Ahmad","last_name":"Biniaz","full_name":"Biniaz, Ahmad"},{"full_name":"Jain, Kshitij","last_name":"Jain","first_name":"Kshitij"},{"first_name":"Anna","last_name":"Lubiw","full_name":"Lubiw, Anna"},{"full_name":"Masárová, Zuzana","first_name":"Zuzana","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322"},{"full_name":"Miltzow, Tillmann","first_name":"Tillmann","last_name":"Miltzow"},{"last_name":"Mondal","first_name":"Debajyoti","full_name":"Mondal, Debajyoti"},{"last_name":"Naredla","first_name":"Anurag Murty","full_name":"Naredla, Anurag Murty"},{"last_name":"Tkadlec","first_name":"Josef","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","full_name":"Tkadlec, Josef"},{"full_name":"Turcotte, Alexi","last_name":"Turcotte","first_name":"Alexi"}],"related_material":{"record":[{"id":"7944","status":"public","relation":"dissertation_contains"},{"id":"12833","status":"public","relation":"later_version"}]},"article_number":"1903.06981","type":"preprint","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."}]},{"file":[{"relation":"main_file","file_id":"5724","date_updated":"2020-07-14T12:45:20Z","date_created":"2018-12-17T16:31:31Z","checksum":"7509403803b3ac1aee94bbc2ad293d21","file_name":"2018_LIPIcs_Edelsbrunner.pdf","access_level":"open_access","content_type":"application/pdf","file_size":489080,"creator":"dernst"}],"oa_version":"Published Version","intvolume":" 99","status":"public","ddc":["000"],"title":"Smallest enclosing spheres and Chernoff points in Bregman geometry","_id":"188","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex."}],"alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"type":"conference","date_published":"2018-06-11T00:00:00Z","page":"35:1 - 35:13","citation":{"chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.35.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13.","mla":"Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.","ista":"Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13.","ama":"Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:35:1-35:13. doi:10.4230/LIPIcs.SoCG.2018.35"},"has_accepted_license":"1","day":"11","scopus_import":1,"volume":99,"date_created":"2018-12-11T11:45:05Z","date_updated":"2021-01-12T06:53:48Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Virk, Ziga","first_name":"Ziga","last_name":"Virk"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Hubert","full_name":"Wagner, Hubert"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"publication_status":"published","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","year":"2018","publist_id":"7733","file_date_updated":"2020-07-14T12:45:20Z","language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.SoCG.2018.35","conference":{"start_date":"2018-06-11","location":"Budapest, Hungary","end_date":"2018-06-14","name":"SoCG: Symposium on Computational Geometry"},"project":[{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"month":"06"},{"type":"dissertation","alternative_title":["ISTA Thesis"],"abstract":[{"text":"We describe arrangements of three-dimensional spheres from a geometrical and topological point of view. Real data (fitting this setup) often consist of soft spheres which show certain degree of deformation while strongly packing against each other. In this context, we answer the following questions: If we model a soft packing of spheres by hard spheres that are allowed to overlap, can we measure the volume in the overlapped areas? Can we be more specific about the overlap volume, i.e. quantify how much volume is there covered exactly twice, three times, or k times? What would be a good optimization criteria that rule the arrangement of soft spheres while making a good use of the available space? Fixing a particular criterion, what would be the optimal sphere configuration? The first result of this thesis are short formulas for the computation of volumes covered by at least k of the balls. The formulas exploit information contained in the order-k Voronoi diagrams and its closely related Level-k complex. The used complexes lead to a natural generalization into poset diagrams, a theoretical formalism that contains the order-k and degree-k diagrams as special cases. In parallel, we define different criteria to determine what could be considered an optimal arrangement from a geometrical point of view. Fixing a criterion, we find optimal soft packing configurations in 2D and 3D where the ball centers lie on a lattice. As a last step, we use tools from computational topology on real physical data, to show the potentials of higher-order diagrams in the description of melting crystals. The results of the experiments leaves us with an open window to apply the theories developed in this thesis in real applications.","lang":"eng"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"201","ddc":["514","516"],"title":"Multiple covers with balls","status":"public","pubrep_id":"1026","oa_version":"Published Version","file":[{"access_level":"closed","file_name":"IST-2018-1025-v2+5_ist-thesis-iglesias-11June2018(1).zip","file_size":11827713,"content_type":"application/zip","creator":"kschuh","relation":"source_file","file_id":"5918","checksum":"dd699303623e96d1478a6ae07210dd05","date_updated":"2020-07-14T12:45:24Z","date_created":"2019-02-05T07:43:31Z"},{"file_name":"IST-2018-1025-v2+4_ThesisIglesiasFinal11June2018.pdf","access_level":"open_access","file_size":4783846,"content_type":"application/pdf","creator":"kschuh","relation":"main_file","file_id":"5919","date_created":"2019-02-05T07:43:45Z","date_updated":"2020-07-14T12:45:24Z","checksum":"ba163849a190d2b41d66fef0e4983294"}],"article_processing_charge":"No","has_accepted_license":"1","day":"11","citation":{"apa":"Iglesias Ham, M. (2018). Multiple covers with balls. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1026","ieee":"M. Iglesias Ham, “Multiple covers with balls,” Institute of Science and Technology Austria, 2018.","ista":"Iglesias Ham M. 2018. Multiple covers with balls. Institute of Science and Technology Austria.","ama":"Iglesias Ham M. Multiple covers with balls. 2018. doi:10.15479/AT:ISTA:th_1026","chicago":"Iglesias Ham, Mabel. “Multiple Covers with Balls.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1026.","short":"M. Iglesias Ham, Multiple Covers with Balls, Institute of Science and Technology Austria, 2018.","mla":"Iglesias Ham, Mabel. Multiple Covers with Balls. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1026."},"page":"171","date_published":"2018-06-11T00:00:00Z","publist_id":"7712","file_date_updated":"2020-07-14T12:45:24Z","year":"2018","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Iglesias Ham, Mabel","first_name":"Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2023-09-07T12:25:32Z","date_created":"2018-12-11T11:45:10Z","publication_identifier":{"issn":["2663-337X"]},"month":"06","oa":1,"doi":"10.15479/AT:ISTA:th_1026","language":[{"iso":"eng"}],"degree_awarded":"PhD","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}]},{"month":"06","quality_controlled":"1","project":[{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2018-06-14","location":"Budapest, Hungary","start_date":"2018-06-11"},"doi":"10.4230/LIPIcs.SoCG.2018.34","article_number":"34","file_date_updated":"2020-07-14T12:45:19Z","publist_id":"7732","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"acknowledgement":"This work is partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","year":"2018","date_updated":"2023-09-07T13:29:00Z","date_created":"2018-12-11T11:45:05Z","volume":99,"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","first_name":"Georg F","last_name":"Osang","full_name":"Osang, Georg F"}],"related_material":{"record":[{"id":"9317","relation":"later_version","status":"public"},{"status":"public","relation":"dissertation_contains","id":"9056"}]},"scopus_import":1,"day":"11","has_accepted_license":"1","citation":{"ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.","apa":"Edelsbrunner, H., & Osang, G. F. (2018). The multi-cover persistence of Euclidean balls (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.34","ista":"Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.","ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.34","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.34.","short":"H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. The Multi-Cover Persistence of Euclidean Balls. Vol. 99, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.34."},"date_published":"2018-06-11T00:00:00Z","alternative_title":["LIPIcs"],"type":"conference","abstract":[{"text":"Given a locally finite X ⊆ ℝd and a radius r ≥ 0, the k-fold cover of X and r consists of all points in ℝd that have k or more points of X within distance r. We consider two filtrations - one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k - and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in ℝd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. ","lang":"eng"}],"title":"The multi-cover persistence of Euclidean balls","status":"public","ddc":["516"],"intvolume":" 99","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"187","oa_version":"Published Version","file":[{"checksum":"d8c0533ad0018eb4ed1077475eb8fc18","date_created":"2018-12-18T09:27:22Z","date_updated":"2020-07-14T12:45:19Z","relation":"main_file","file_id":"5738","file_size":528018,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2018_LIPIcs_Edelsbrunner_Osang.pdf"}]},{"type":"journal_article","issue":"1","abstract":[{"text":"We consider families of confocal conics and two pencils of Apollonian circles having the same foci. We will show that these families of curves generate trivial 3-webs and find the exact formulas describing them.","lang":"eng"}],"intvolume":" 194","ddc":["510"],"title":"3-Webs generated by confocal conics and circles","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"692","oa_version":"Published Version","file":[{"file_name":"2018_Springer_Akopyan.pdf","access_level":"open_access","creator":"kschuh","file_size":1140860,"content_type":"application/pdf","file_id":"7222","relation":"main_file","date_created":"2020-01-03T11:35:08Z","date_updated":"2020-07-14T12:47:44Z","checksum":"1febcfc1266486053a069e3425ea3713"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","page":"55 - 64","article_type":"original","citation":{"chicago":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0265-6.","short":"A. Akopyan, Geometriae Dedicata 194 (2018) 55–64.","mla":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata, vol. 194, no. 1, Springer, 2018, pp. 55–64, doi:10.1007/s10711-017-0265-6.","apa":"Akopyan, A. (2018). 3-Webs generated by confocal conics and circles. Geometriae Dedicata. Springer. https://doi.org/10.1007/s10711-017-0265-6","ieee":"A. Akopyan, “3-Webs generated by confocal conics and circles,” Geometriae Dedicata, vol. 194, no. 1. Springer, pp. 55–64, 2018.","ista":"Akopyan A. 2018. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 194(1), 55–64.","ama":"Akopyan A. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 2018;194(1):55-64. doi:10.1007/s10711-017-0265-6"},"publication":"Geometriae Dedicata","date_published":"2018-06-01T00:00:00Z","publist_id":"7014","ec_funded":1,"file_date_updated":"2020-07-14T12:47:44Z","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2018","volume":194,"date_updated":"2023-09-08T11:40:29Z","date_created":"2018-12-11T11:47:57Z","author":[{"last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"}],"month":"06","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"quality_controlled":"1","isi":1,"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000431418800004"]},"language":[{"iso":"eng"}],"doi":"10.1007/s10711-017-0265-6"},{"oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"58","intvolume":" 32","status":"public","title":"Counting blanks in polygonal arrangements","issue":"3","abstract":[{"lang":"eng","text":"Inside a two-dimensional region (``cake""), there are m nonoverlapping tiles of a certain kind (``toppings""). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,"" such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks."}],"type":"journal_article","date_published":"2018-09-06T00:00:00Z","citation":{"ama":"Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 2018;32(3):2242-2257. doi:10.1137/16M110407X","apa":"Akopyan, A., & Segal Halevi, E. (2018). Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M110407X","ieee":"A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,” SIAM Journal on Discrete Mathematics, vol. 32, no. 3. Society for Industrial and Applied Mathematics , pp. 2242–2257, 2018.","ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257.","mla":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics, vol. 32, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 2242–57, doi:10.1137/16M110407X.","chicago":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M110407X."},"publication":"SIAM Journal on Discrete Mathematics","page":"2242 - 2257","article_processing_charge":"No","day":"06","scopus_import":"1","author":[{"last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"full_name":"Segal Halevi, Erel","last_name":"Segal Halevi","first_name":"Erel"}],"volume":32,"date_updated":"2023-09-11T12:48:39Z","date_created":"2018-12-11T11:44:24Z","year":"2018","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"HeEd"}],"publication_status":"published","ec_funded":1,"publist_id":"7996","doi":"10.1137/16M110407X","language":[{"iso":"eng"}],"external_id":{"arxiv":["1604.00960"],"isi":["000450810500036"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1604.00960","open_access":"1"}],"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"quality_controlled":"1","isi":1,"month":"09"},{"author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alexander","last_name":"Bobenko","full_name":"Bobenko, Alexander"}],"date_created":"2018-12-11T11:46:35Z","date_updated":"2023-09-11T14:19:12Z","volume":370,"acknowledgement":"DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”; People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) REA grant agreement n◦[291734]","year":"2018","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"American Mathematical Society","ec_funded":1,"publist_id":"7363","doi":"10.1090/tran/7292","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.04637"}],"external_id":{"isi":["000423197800019"]},"isi":1,"quality_controlled":"1","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"month":"04","oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"458","title":"Incircular nets and confocal conics","status":"public","intvolume":" 370","abstract":[{"lang":"eng","text":"We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics. Our main new results are on checkerboard IC-nets in the plane. These are congruences of straight lines in the plane with the combinatorics of the square grid, combinatorially colored as a checkerboard, such that all black coordinate quadrilaterals possess inscribed circles. We show how this larger class of IC-nets appears quite naturally in Laguerre geometry of oriented planes and spheres and leads to new remarkable incidence theorems. Most of our results are valid in hyperbolic and spherical geometries as well. We present also generalizations in spaces of higher dimension, called checkerboard IS-nets. The construction of these nets is based on a new 9 inspheres incidence theorem."}],"issue":"4","type":"journal_article","date_published":"2018-04-01T00:00:00Z","publication":"Transactions of the American Mathematical Society","citation":{"ista":"Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 370(4), 2825–2854.","apa":"Akopyan, A., & Bobenko, A. (2018). Incircular nets and confocal conics. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/7292","ieee":"A. Akopyan and A. Bobenko, “Incircular nets and confocal conics,” Transactions of the American Mathematical Society, vol. 370, no. 4. American Mathematical Society, pp. 2825–2854, 2018.","ama":"Akopyan A, Bobenko A. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 2018;370(4):2825-2854. doi:10.1090/tran/7292","chicago":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” Transactions of the American Mathematical Society. American Mathematical Society, 2018. https://doi.org/10.1090/tran/7292.","mla":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” Transactions of the American Mathematical Society, vol. 370, no. 4, American Mathematical Society, 2018, pp. 2825–54, doi:10.1090/tran/7292.","short":"A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society 370 (2018) 2825–2854."},"page":"2825 - 2854","day":"01","article_processing_charge":"No","scopus_import":"1"}]