[{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Iglesias Ham, Mabel. “Multiple Covers with Balls.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1026.","ista":"Iglesias Ham M. 2018. Multiple covers with balls. Institute of Science and Technology Austria.","mla":"Iglesias Ham, Mabel. Multiple Covers with Balls. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1026.","short":"M. Iglesias Ham, Multiple Covers with Balls, Institute of Science and Technology Austria, 2018.","ieee":"M. Iglesias Ham, “Multiple covers with balls,” Institute of Science and Technology Austria, 2018.","ama":"Iglesias Ham M. Multiple covers with balls. 2018. doi:10.15479/AT:ISTA:th_1026","apa":"Iglesias Ham, M. (2018). Multiple covers with balls. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1026"},"title":"Multiple covers with balls","author":[{"full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7712","article_processing_charge":"No","day":"11","has_accepted_license":"1","year":"2018","date_published":"2018-06-11T00:00:00Z","doi":"10.15479/AT:ISTA:th_1026","date_created":"2018-12-11T11:45:10Z","page":"171","publisher":"Institute of Science and Technology Austria","oa":1,"ddc":["514","516"],"supervisor":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"date_updated":"2023-09-07T12:25:32Z","file_date_updated":"2020-07-14T12:45:24Z","department":[{"_id":"HeEd"}],"_id":"201","status":"public","pubrep_id":"1026","type":"dissertation","file":[{"access_level":"closed","relation":"source_file","content_type":"application/zip","checksum":"dd699303623e96d1478a6ae07210dd05","file_id":"5918","creator":"kschuh","date_updated":"2020-07-14T12:45:24Z","file_size":11827713,"date_created":"2019-02-05T07:43:31Z","file_name":"IST-2018-1025-v2+5_ist-thesis-iglesias-11June2018(1).zip"},{"date_created":"2019-02-05T07:43:45Z","file_name":"IST-2018-1025-v2+4_ThesisIglesiasFinal11June2018.pdf","creator":"kschuh","date_updated":"2020-07-14T12:45:24Z","file_size":4783846,"checksum":"ba163849a190d2b41d66fef0e4983294","file_id":"5919","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"month":"06","alternative_title":["ISTA Thesis"]},{"date_created":"2018-12-11T11:45:05Z","date_published":"2018-06-11T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2018.34","year":"2018","has_accepted_license":"1","day":"11","oa":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","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).","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Osang","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"}],"publist_id":"7732","title":"The multi-cover persistence of Euclidean balls","citation":{"ista":"Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 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.","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","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","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"article_number":"34","related_material":{"record":[{"relation":"later_version","id":"9317","status":"public"},{"status":"public","id":"9056","relation":"dissertation_contains"}]},"volume":99,"publication_status":"published","language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","checksum":"d8c0533ad0018eb4ed1077475eb8fc18","file_id":"5738","creator":"dernst","file_size":528018,"date_updated":"2020-07-14T12:45:19Z","file_name":"2018_LIPIcs_Edelsbrunner_Osang.pdf","date_created":"2018-12-18T09:27:22Z"}],"scopus_import":1,"alternative_title":["LIPIcs"],"intvolume":" 99","month":"06","abstract":[{"lang":"eng","text":"Given a locally finite X ⊆ ℝd and a radius r ≥ 0, the k-fold cover of X and r consists of all points in ℝd that have k or more points of X within distance r. We consider two filtrations - one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k - and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in ℝd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. "}],"oa_version":"Published Version","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:19Z","date_updated":"2023-09-07T13:29:00Z","ddc":["516"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"start_date":"2018-06-11","end_date":"2018-06-14","location":"Budapest, Hungary","name":"SoCG: Symposium on Computational Geometry"},"type":"conference","status":"public","_id":"187"},{"ddc":["510"],"date_updated":"2023-09-08T11:40:29Z","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:44Z","_id":"692","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"file_name":"2018_Springer_Akopyan.pdf","date_created":"2020-01-03T11:35:08Z","creator":"kschuh","file_size":1140860,"date_updated":"2020-07-14T12:47:44Z","file_id":"7222","checksum":"1febcfc1266486053a069e3425ea3713","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":194,"issue":"1","ec_funded":1,"oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"month":"06","intvolume":" 194","scopus_import":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","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.","ista":"Akopyan A. 2018. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 194(1), 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.","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","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.","short":"A. Akopyan, Geometriae Dedicata 194 (2018) 55–64."},"title":"3-Webs generated by confocal conics and circles","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"}],"publist_id":"7014","external_id":{"isi":["000431418800004"]},"article_processing_charge":"Yes (via OA deal)","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"day":"01","publication":"Geometriae Dedicata","isi":1,"has_accepted_license":"1","year":"2018","doi":"10.1007/s10711-017-0265-6","date_published":"2018-06-01T00:00:00Z","date_created":"2018-12-11T11:47:57Z","page":"55 - 64","publisher":"Springer","quality_controlled":"1","oa":1},{"date_updated":"2023-09-11T12:48:39Z","department":[{"_id":"HeEd"}],"_id":"58","type":"journal_article","status":"public","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"issue":"3","volume":32,"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."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.00960"}],"scopus_import":"1","intvolume":" 32","month":"09","citation":{"ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.","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.","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.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257.","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","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","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000450810500036"],"arxiv":["1604.00960"]},"article_processing_charge":"No","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"full_name":"Segal Halevi, Erel","last_name":"Segal Halevi","first_name":"Erel"}],"publist_id":"7996","title":"Counting blanks in polygonal arrangements","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"year":"2018","isi":1,"publication":"SIAM Journal on Discrete Mathematics","day":"06","page":"2242 - 2257","date_created":"2018-12-11T11:44:24Z","date_published":"2018-09-06T00:00:00Z","doi":"10.1137/16M110407X","oa":1,"quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics "},{"page":"2825 - 2854","date_created":"2018-12-11T11:46:35Z","date_published":"2018-04-01T00:00:00Z","doi":"10.1090/tran/7292","year":"2018","isi":1,"publication":"Transactions of the American Mathematical Society","day":"01","oa":1,"quality_controlled":"1","publisher":"American Mathematical Society","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]","external_id":{"isi":["000423197800019"]},"article_processing_charge":"No","publist_id":"7363","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Bobenko","full_name":"Bobenko, Alexander","first_name":"Alexander"}],"title":"Incircular nets and confocal conics","citation":{"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.","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","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","short":"A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society 370 (2018) 2825–2854.","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.","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.","ista":"Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 370(4), 2825–2854."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"ec_funded":1,"volume":370,"issue":"4","publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.04637"}],"scopus_import":"1","intvolume":" 370","month":"04","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."}],"oa_version":"Preprint","department":[{"_id":"HeEd"}],"date_updated":"2023-09-11T14:19:12Z","type":"journal_article","status":"public","_id":"458"},{"publication_status":"published","language":[{"iso":"eng"}],"issue":"3","volume":40,"abstract":[{"lang":"eng","text":"The goal of this article is to introduce the reader to the theory of intrinsic geometry of convex surfaces. We illustrate the power of the tools by proving a theorem on convex surfaces containing an arbitrarily long closed simple geodesic. Let us remind ourselves that a curve in a surface is called geodesic if every sufficiently short arc of the curve is length minimizing; if, in addition, it has no self-intersections, we call it simple geodesic. A tetrahedron with equal opposite edges is called isosceles. The axiomatic method of Alexandrov geometry allows us to work with the metrics of convex surfaces directly, without approximating it first by a smooth or polyhedral metric. Such approximations destroy the closed geodesics on the surface; therefore it is difficult (if at all possible) to apply approximations in the proof of our theorem. On the other hand, a proof in the smooth or polyhedral case usually admits a translation into Alexandrov’s language; such translation makes the result more general. In fact, our proof resembles a translation of the proof given by Protasov. Note that the main theorem implies in particular that a smooth convex surface does not have arbitrarily long simple closed geodesics. However we do not know a proof of this corollary that is essentially simpler than the one presented below."}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.05172"}],"month":"09","intvolume":" 40","date_updated":"2023-09-13T08:49:16Z","department":[{"_id":"HeEd"}],"_id":"106","type":"journal_article","status":"public","isi":1,"year":"2018","day":"01","publication":"Mathematical Intelligencer","page":"26 - 31","doi":"10.1007/s00283-018-9795-5","date_published":"2018-09-01T00:00:00Z","date_created":"2018-12-11T11:44:40Z","publisher":"Springer","quality_controlled":"1","oa":1,"citation":{"short":"A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31.","ieee":"A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” Mathematical Intelligencer, vol. 40, no. 3. Springer, pp. 26–31, 2018.","apa":"Akopyan, A., & Petrunin, A. (2018). Long geodesics on convex surfaces. Mathematical Intelligencer. Springer. https://doi.org/10.1007/s00283-018-9795-5","ama":"Akopyan A, Petrunin A. Long geodesics on convex surfaces. Mathematical Intelligencer. 2018;40(3):26-31. doi:10.1007/s00283-018-9795-5","mla":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer, vol. 40, no. 3, Springer, 2018, pp. 26–31, doi:10.1007/s00283-018-9795-5.","ista":"Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical Intelligencer. 40(3), 26–31.","chicago":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer. Springer, 2018. https://doi.org/10.1007/s00283-018-9795-5."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publist_id":"7948","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Anton","last_name":"Petrunin","full_name":"Petrunin, Anton"}],"article_processing_charge":"No","external_id":{"isi":["000444141200005"],"arxiv":["1702.05172"]},"title":"Long geodesics on convex surfaces"},{"project":[{"grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"citation":{"mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications, vol. 68, Elsevier, 2018, pp. 119–33, doi:10.1016/j.comgeo.2017.06.014.","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” Computational Geometry: Theory and Applications, vol. 68. Elsevier, pp. 119–133, 2018.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 2018;68:119-133. doi:10.1016/j.comgeo.2017.06.014","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.014","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications. Elsevier, 2018. https://doi.org/10.1016/j.comgeo.2017.06.014.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publist_id":"7289","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Iglesias Ham","full_name":"Iglesias Ham, Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel"}],"article_processing_charge":"No","external_id":{"isi":["000415778300010"]},"title":"Multiple covers with balls I: Inclusion–exclusion","quality_controlled":"1","publisher":"Elsevier","oa":1,"isi":1,"has_accepted_license":"1","year":"2018","day":"01","publication":"Computational Geometry: Theory and Applications","page":"119 - 133","doi":"10.1016/j.comgeo.2017.06.014","date_published":"2018-03-01T00:00:00Z","date_created":"2018-12-11T11:46:59Z","_id":"530","type":"journal_article","status":"public","date_updated":"2023-09-13T08:59:00Z","ddc":["000"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:46:38Z","abstract":[{"text":"Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of Rn covered by at least k balls in a finite set. We implement two of the formulas in dimension n=3 and report on results obtained with our software.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","month":"03","intvolume":" 68","publication_status":"published","file":[{"file_size":708357,"date_updated":"2020-07-14T12:46:38Z","creator":"dernst","file_name":"2018_Edelsbrunner.pdf","date_created":"2019-02-12T06:47:52Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","file_id":"5953"}],"language":[{"iso":"eng"}],"volume":68,"ec_funded":1},{"department":[{"_id":"KrPi"},{"_id":"HeEd"},{"_id":"VlKo"}],"date_updated":"2023-09-13T09:13:12Z","type":"conference","conference":{"name":"ASIACCS: Asia Conference on Computer and Communications Security ","location":"Incheon, Republic of Korea","end_date":"2018-06-08","start_date":"2018-06-04"},"status":"public","_id":"193","ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"url":"https://eprint.iacr.org/2016/783","open_access":"1"}],"month":"06","abstract":[{"text":"We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki'16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block'16] for analyzing the hardware costs of an iMHF.","lang":"eng"}],"oa_version":"Submitted Version","author":[{"last_name":"Alwen","full_name":"Alwen, Joel F","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87","first_name":"Joel F"},{"first_name":"Peter","last_name":"Gazi","full_name":"Gazi, Peter"},{"full_name":"Kamath Hosdurg, Chethan","last_name":"Kamath Hosdurg","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","first_name":"Chethan"},{"last_name":"Klein","full_name":"Klein, Karen","first_name":"Karen","id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","last_name":"Osang","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9139-1654","full_name":"Pietrzak, Krzysztof Z","last_name":"Pietrzak"},{"first_name":"Lenoid","full_name":"Reyzin, Lenoid","last_name":"Reyzin"},{"first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","full_name":"Rolinek, Michal","last_name":"Rolinek"},{"full_name":"Rybar, Michal","last_name":"Rybar","id":"2B3E3DE8-F248-11E8-B48F-1D18A9856A87","first_name":"Michal"}],"publist_id":"7723","external_id":{"isi":["000516620100005"]},"article_processing_charge":"No","title":"On the memory hardness of data independent password hashing functions","citation":{"mla":"Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534.","apa":"Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak, K. Z., … Rybar, M. (2018). On the memory hardness of data independent password hashing functions. In Proceedings of the 2018 on Asia Conference on Computer and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534","ama":"Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data independent password hashing functions. In: Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534","short":"J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak, L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65.","ieee":"J. F. Alwen et al., “On the memory hardness of data independent password hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65.","chicago":"Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar. “On the Memory Hardness of Data Independent Password Hashing Functions.” In Proceedings of the 2018 on Asia Conference on Computer and Communication Security, 51–65. ACM, 2018. https://doi.org/10.1145/3196494.3196534.","ista":"Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password hashing functions. Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ASIACCS: Asia Conference on Computer and Communications Security , 51–65."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","name":"Teaching Old Crypto New Tricks","grant_number":"682815"}],"page":"51 - 65","date_published":"2018-06-01T00:00:00Z","doi":"10.1145/3196494.3196534","date_created":"2018-12-11T11:45:07Z","isi":1,"year":"2018","day":"01","publication":"Proceedings of the 2018 on Asia Conference on Computer and Communication Security","quality_controlled":"1","publisher":"ACM","oa":1,"acknowledgement":"Leonid Reyzin was supported in part by IST Austria and by US NSF grants 1012910, 1012798, and 1422965; this research was performed while he was visiting IST Austria."},{"article_processing_charge":"No","external_id":{"isi":["000428958900038"]},"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Iglesias Ham","full_name":"Iglesias Ham, Mabel","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7553","title":"On the optimality of the FCC lattice for soft sphere packing","citation":{"short":"H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “On the optimality of the FCC lattice for soft sphere packing,” SIAM J Discrete Math, vol. 32, no. 1. Society for Industrial and Applied Mathematics , pp. 750–782, 2018.","ama":"Edelsbrunner H, Iglesias Ham M. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 2018;32(1):750-782. doi:10.1137/16M1097201","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M1097201","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math, vol. 32, no. 1, Society for Industrial and Applied Mathematics , 2018, pp. 750–82, doi:10.1137/16M1097201.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 32(1), 750–782.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1097201."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"page":"750 - 782","date_created":"2018-12-11T11:45:46Z","doi":"10.1137/16M1097201","date_published":"2018-03-29T00:00:00Z","year":"2018","isi":1,"publication":"SIAM J Discrete Math","day":"29","oa":1,"quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics ","acknowledgement":"This work was partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics,” through grant I02979-N35 of the Austrian Science Fund (FWF).","department":[{"_id":"HeEd"}],"date_updated":"2023-09-13T09:34:38Z","article_type":"original","type":"journal_article","status":"public","_id":"312","issue":"1","volume":32,"publication_status":"published","publication_identifier":{"issn":["08954801"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf"}],"scopus_import":"1","intvolume":" 32","month":"03","abstract":[{"lang":"eng","text":"Motivated by biological questions, we study configurations of equal spheres that neither pack nor cover. Placing their centers on a lattice, we define the soft density of the configuration by penalizing multiple overlaps. Considering the 1-parameter family of diagonally distorted 3-dimensional integer lattices, we show that the soft density is maximized at the FCC lattice."}],"oa_version":"Submitted Version"},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:10.1016/j.crma.2018.03.005.","short":"A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.","ieee":"A. Akopyan, “On the number of non-hexagons in a planar tiling,” Comptes Rendus Mathematique, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.","apa":"Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. Elsevier. https://doi.org/10.1016/j.crma.2018.03.005","ama":"Akopyan A. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 2018;356(4):412-414. doi:10.1016/j.crma.2018.03.005","chicago":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique. Elsevier, 2018. https://doi.org/10.1016/j.crma.2018.03.005.","ista":"Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 356(4), 412–414."},"title":"On the number of non-hexagons in a planar tiling","author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"}],"publist_id":"7420","article_processing_charge":"No","external_id":{"arxiv":["1805.01652"],"isi":["000430402700009"]},"day":"01","publication":"Comptes Rendus Mathematique","isi":1,"year":"2018","date_published":"2018-04-01T00:00:00Z","doi":"10.1016/j.crma.2018.03.005","date_created":"2018-12-11T11:46:19Z","page":"412-414","quality_controlled":"1","publisher":"Elsevier","oa":1,"date_updated":"2023-09-13T09:34:12Z","department":[{"_id":"HeEd"}],"_id":"409","status":"public","type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1631073X"]},"publication_status":"published","volume":356,"issue":"4","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We give a simple proof of T. Stehling's result [4], whereby in any normal tiling of the plane with convex polygons with number of sides not less than six, all tiles except a finite number are hexagons."}],"month":"04","intvolume":" 356","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.01652"}]},{"issue":"5","related_material":{"record":[{"id":"6287","status":"public","relation":"dissertation_contains"}]},"volume":28,"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1705.02870","open_access":"1"}],"month":"10","intvolume":" 28","abstract":[{"lang":"eng","text":"Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. We find that the expectations are essentially the same as for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to the boundary complex of the convex hull in Rn+1, so we also get the expected number of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric to the standard n-simplex equipped with the Fisher information metric. It follows that the latter space has similar stochastic properties as the n-dimensional Euclidean space. Our results are therefore relevant in information geometry and in population genetics."}],"oa_version":"Preprint","department":[{"_id":"HeEd"}],"date_updated":"2023-09-15T12:10:35Z","type":"journal_article","article_type":"original","status":"public","_id":"87","page":"3215 - 3238","date_published":"2018-10-01T00:00:00Z","doi":"10.1214/18-AAP1389","date_created":"2018-12-11T11:44:33Z","isi":1,"year":"2018","day":"01","publication":"Annals of Applied Probability","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","last_name":"Nikitenko"}],"publist_id":"7967","article_processing_charge":"No","external_id":{"isi":["000442893500018"],"arxiv":["1705.02870"]},"title":"Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics","citation":{"mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability, vol. 28, no. 5, Institute of Mathematical Statistics, 2018, pp. 3215–38, doi:10.1214/18-AAP1389.","ieee":"H. Edelsbrunner and A. Nikitenko, “Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics,” Annals of Applied Probability, vol. 28, no. 5. Institute of Mathematical Statistics, pp. 3215–3238, 2018.","short":"H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238.","ama":"Edelsbrunner H, Nikitenko A. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 2018;28(5):3215-3238. doi:10.1214/18-AAP1389","apa":"Edelsbrunner, H., & Nikitenko, A. (2018). Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AAP1389","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability. Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/18-AAP1389.","ista":"Edelsbrunner H, Nikitenko A. 2018. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 28(5), 3215–3238."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}]},{"_id":"6355","status":"public","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2023-09-19T14:50:12Z","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:47:28Z","oa_version":"Published Version","abstract":[{"text":"We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle.","lang":"eng"}],"month":"05","intvolume":" 6","file":[{"checksum":"5a71b24ba712a3eb2e46165a38fbc30a","file_id":"6356","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2019-04-30T06:14:58Z","file_name":"2018_ForumMahtematics_Akopyan.pdf","creator":"dernst","date_updated":"2020-07-14T12:47:28Z","file_size":249246}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2050-5094"]},"publication_status":"published","volume":6,"related_material":{"record":[{"relation":"dissertation_contains","id":"8156","status":"public"}]},"ec_funded":1,"article_number":"e7","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge University Press, 2018.","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","apa":"Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2018.7","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7","mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6, e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma. Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7."},"title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Avvakumov, Sergey","last_name":"Avvakumov","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"article_processing_charge":"No","publisher":"Cambridge University Press","quality_controlled":"1","oa":1,"day":"31","publication":"Forum of Mathematics, Sigma","isi":1,"has_accepted_license":"1","year":"2018","doi":"10.1017/fms.2018.7","date_published":"2018-05-31T00:00:00Z","date_created":"2019-04-30T06:09:57Z"},{"volume":59,"issue":"4","ec_funded":1,"file":[{"file_id":"5844","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2019-01-18T09:27:36Z","file_name":"2018_DiscreteComp_Akopyan.pdf","date_updated":"2019-01-18T09:27:36Z","file_size":482518,"creator":"dernst"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"publication_status":"published","month":"06","intvolume":" 59","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets."}],"file_date_updated":"2019-01-18T09:27:36Z","department":[{"_id":"HeEd"}],"ddc":["516","000"],"date_updated":"2023-09-20T12:08:51Z","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"1064","date_published":"2018-06-01T00:00:00Z","doi":"10.1007/s00454-017-9883-x","date_created":"2018-12-11T11:49:57Z","page":"1001-1009","day":"01","publication":"Discrete & Computational Geometry","isi":1,"has_accepted_license":"1","year":"2018","quality_controlled":"1","publisher":"Springer","oa":1,"title":"On the circle covering theorem by A.W. Goodman and R.E. Goodman","publist_id":"6324","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"first_name":"Alexey","last_name":"Balitskiy","full_name":"Balitskiy, Alexey"},{"first_name":"Mikhail","last_name":"Grigorev","full_name":"Grigorev, Mikhail"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000432205500011"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"short":"A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry 59 (2018) 1001–1009.","ieee":"A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem by A.W. Goodman and R.E. Goodman,” Discrete & Computational Geometry, vol. 59, no. 4. Springer, pp. 1001–1009, 2018.","apa":"Akopyan, A., Balitskiy, A., & Grigorev, M. (2018). On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-017-9883-x","ama":"Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 2018;59(4):1001-1009. doi:10.1007/s00454-017-9883-x","mla":"Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry, vol. 59, no. 4, Springer, 2018, pp. 1001–09, doi:10.1007/s00454-017-9883-x.","ista":"Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 59(4), 1001–1009.","chicago":"Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry. Springer, 2018. https://doi.org/10.1007/s00454-017-9883-x."},"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}]},{"publisher":"arXiv","main_file_link":[{"url":"https://arxiv.org/abs/1804.03057","open_access":"1"}],"oa":1,"month":"09","abstract":[{"text":"We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥2; this result was previously known for prime powers m=pk. We also give a higher-dimensional generalization.","lang":"eng"}],"oa_version":"Preprint","related_material":{"record":[{"status":"public","id":"8156","relation":"dissertation_contains"}]},"doi":"10.48550/arXiv.1804.03057","date_published":"2018-09-13T00:00:00Z","ec_funded":1,"date_created":"2018-12-11T11:44:30Z","publication_status":"published","year":"2018","day":"13","language":[{"iso":"eng"}],"type":"preprint","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"status":"public","_id":"75","article_number":"1804.03057","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"last_name":"Avvakumov","full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey"},{"first_name":"Roman","last_name":"Karasev","full_name":"Karasev, Roman"}],"external_id":{"arxiv":["1804.03057"]},"article_processing_charge":"No","title":"Convex fair partitions into arbitrary number of pieces","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"citation":{"mla":"Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.","apa":"Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057","ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:10.48550/arXiv.1804.03057","ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018).","chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057.","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057."},"date_updated":"2023-12-18T10:51:02Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"acknowledgement":"Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.","quality_controlled":"1","publisher":"World Scientific Publishing","oa":1,"has_accepted_license":"1","year":"2017","day":"13","publication":"International Journal of Computational Geometry and Applications","page":"211 - 229","date_published":"2017-04-13T00:00:00Z","doi":"10.1142/S0218195916600050","date_created":"2018-12-11T11:46:43Z","citation":{"mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050.","short":"T. Biedl, S. Huber, P. Palfrader, International Journal of Computational Geometry and Applications 26 (2017) 211–229.","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017.","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229. doi:10.1142/S0218195916600050","apa":"Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195916600050","chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050.","ista":"Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 26(3–4), 211–229."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publist_id":"7338","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"last_name":"Huber","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"title":"Planar matchings for weighted straight skeletons","abstract":[{"text":"We introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist. Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings.","lang":"eng"}],"oa_version":"Published Version","scopus_import":1,"month":"04","intvolume":" 26","publication_status":"published","file":[{"date_updated":"2020-07-14T12:46:35Z","file_size":769296,"creator":"system","date_created":"2018-12-12T10:09:34Z","file_name":"IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"f79e8558bfe4b368dfefeb8eec2e3a5e","file_id":"4758"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"id":"10892","status":"public","relation":"earlier_version"}]},"volume":26,"issue":"3-4","_id":"481","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"949","date_updated":"2023-02-21T16:06:22Z","ddc":["004","514","516"],"file_date_updated":"2020-07-14T12:46:35Z","department":[{"_id":"HeEd"}]},{"day":"01","publication":"Topology and its Applications","language":[{"iso":"eng"}],"publication_identifier":{"issn":["01668641"]},"year":"2017","publication_status":"published","volume":215,"date_published":"2017-01-01T00:00:00Z","doi":"10.1016/j.topol.2016.10.005","date_created":"2018-12-11T11:46:56Z","page":"45 - 57","oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension."}],"month":"01","intvolume":" 215","quality_controlled":"1","publisher":"Elsevier","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.03954v1"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:01:21Z","citation":{"ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57.","chicago":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.","short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.","ama":"Austin K, Virk Z. Higson compactification and dimension raising. Topology and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005","apa":"Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005","mla":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005."},"title":"Higson compactification and dimension raising","department":[{"_id":"HeEd"}],"publist_id":"7299","author":[{"full_name":"Austin, Kyle","last_name":"Austin","first_name":"Kyle"},{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga"}],"_id":"521","status":"public","type":"journal_article"},{"type":"journal_article","status":"public","_id":"568","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_updated":"2021-01-12T08:03:12Z","main_file_link":[{"url":"https://arxiv.org/abs/1507.04310","open_access":"1"}],"scopus_import":1,"intvolume":" 19","month":"01","abstract":[{"lang":"eng","text":"We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C)."}],"oa_version":"Submitted Version","ec_funded":1,"volume":19,"issue":"2","publication_status":"published","publication_identifier":{"issn":["15320073"]},"language":[{"iso":"eng"}],"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)","grant_number":"701309","call_identifier":"H2020","_id":"2590DB08-B435-11E9-9278-68D0E5697425"}],"publist_id":"7246","author":[{"last_name":"Franek","full_name":"Franek, Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","full_name":"Krcál, Marek","last_name":"Krcál"}],"title":"Persistence of zero sets","citation":{"apa":"Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16","ama":"Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications. 2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.","short":"P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.","mla":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.","ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","oa":1,"quality_controlled":"1","publisher":"International Press","page":"313 - 342","date_created":"2018-12-11T11:47:14Z","doi":"10.4310/HHA.2017.v19.n2.a16","date_published":"2017-01-01T00:00:00Z","year":"2017","publication":"Homology, Homotopy and Applications","day":"01"},{"department":[{"_id":"HeEd"}],"date_updated":"2022-01-28T07:48:24Z","extern":"1","type":"book_chapter","conference":{"start_date":"2017-06-19","end_date":"2017-06-21","location":"Plovdiv, Bulgaria","name":"IWCIA: International Workshop on Combinatorial Image Analysis"},"status":"public","_id":"5803","volume":10256,"publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["978-3-319-59107-0","978-3-319-59108-7"]},"publication_status":"published","language":[{"iso":"eng"}],"alternative_title":["LNCS"],"month":"05","place":"Cham","intvolume":" 10256","abstract":[{"text":"Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept.","lang":"eng"}],"oa_version":"None","author":[{"first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita"},{"last_name":"Bhowmick","full_name":"Bhowmick, Partha","first_name":"Partha"}],"article_processing_charge":"No","title":"Construction of persistent Voronoi diagram on 3D digital plane","citation":{"chicago":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104. Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.","ista":"Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.","mla":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.","apa":"Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256, pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8","ama":"Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature; 2017:93-104. doi:10.1007/978-3-319-59108-7_8","ieee":"R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104.","short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","page":"93-104","date_published":"2017-05-17T00:00:00Z","doi":"10.1007/978-3-319-59108-7_8","date_created":"2019-01-08T20:42:56Z","year":"2017","day":"17","publication":"Combinatorial image analysis","quality_controlled":"1","publisher":"Springer Nature"},{"day":"01","year":"2017","has_accepted_license":"1","date_created":"2018-12-11T11:47:56Z","date_published":"2017-06-01T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2017.39","page":"391-3916","oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"short":"H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916.","ieee":"H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,” presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia, 2017, vol. 77, pp. 391–3916.","ama":"Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916. doi:10.4230/LIPIcs.SoCG.2017.39","apa":"Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2017.39","mla":"Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.","ista":"Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.","chicago":"Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39."},"title":"Topological data analysis with Bregman divergences","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","full_name":"Wagner, Hubert","last_name":"Wagner"}],"publist_id":"7021","language":[{"iso":"eng"}],"file":[{"file_id":"4856","checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2018-12-12T10:11:03Z","file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf","creator":"system","date_updated":"2020-07-14T12:47:42Z","file_size":990546}],"publication_status":"published","publication_identifier":{"issn":["18688969"]},"volume":77,"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. "}],"intvolume":" 77","month":"06","alternative_title":["LIPIcs"],"scopus_import":1,"ddc":["514","516"],"date_updated":"2021-01-12T08:09:26Z","file_date_updated":"2020-07-14T12:47:42Z","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"_id":"688","pubrep_id":"895","status":"public","conference":{"name":"Symposium on Computational Geometry, SoCG","start_date":"2017-07-04","location":"Brisbane, Australia","end_date":"2017-07-07"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"conference"},{"author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"publist_id":"6982","title":"A tight estimate for the waist of the ball ","citation":{"chicago":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society. Wiley-Blackwell, 2017. https://doi.org/10.1112/blms.12062.","ista":"Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 49(4), 690–693.","mla":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society, vol. 49, no. 4, Wiley-Blackwell, 2017, pp. 690–93, doi:10.1112/blms.12062.","short":"A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693.","ieee":"A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,” Bulletin of the London Mathematical Society, vol. 49, no. 4. Wiley-Blackwell, pp. 690–693, 2017.","apa":"Akopyan, A., & Karasev, R. (2017). A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. Wiley-Blackwell. https://doi.org/10.1112/blms.12062","ama":"Akopyan A, Karasev R. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 2017;49(4):690-693. doi:10.1112/blms.12062"},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"page":"690 - 693","date_created":"2018-12-11T11:48:02Z","doi":"10.1112/blms.12062","date_published":"2017-08-01T00:00:00Z","year":"2017","publication":"Bulletin of the London Mathematical Society","day":"01","oa":1,"publisher":"Wiley-Blackwell","quality_controlled":"1","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T08:11:41Z","type":"journal_article","status":"public","_id":"707","ec_funded":1,"issue":"4","volume":49,"publication_status":"published","publication_identifier":{"issn":["00246093"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.06279"}],"scopus_import":1,"intvolume":" 49","month":"08","abstract":[{"text":"We answer a question of M. Gromov on the waist of the unit ball.","lang":"eng"}],"oa_version":"Preprint"}]