--- _id: '201' 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.' alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Mabel full_name: Iglesias Ham, Mabel id: 41B58C0C-F248-11E8-B48F-1D18A9856A87 last_name: Iglesias Ham citation: 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 chicago: Iglesias Ham, Mabel. “Multiple Covers with Balls.” Institute of Science and Technology Austria, 2018. 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. 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. date_created: 2018-12-11T11:45:10Z date_published: 2018-06-11T00:00:00Z date_updated: 2023-09-07T12:25:32Z day: '11' ddc: - '514' - '516' degree_awarded: PhD department: - _id: HeEd doi: 10.15479/AT:ISTA:th_1026 file: - access_level: closed checksum: dd699303623e96d1478a6ae07210dd05 content_type: application/zip creator: kschuh date_created: 2019-02-05T07:43:31Z date_updated: 2020-07-14T12:45:24Z file_id: '5918' file_name: IST-2018-1025-v2+5_ist-thesis-iglesias-11June2018(1).zip file_size: 11827713 relation: source_file - access_level: open_access checksum: ba163849a190d2b41d66fef0e4983294 content_type: application/pdf creator: kschuh date_created: 2019-02-05T07:43:45Z date_updated: 2020-07-14T12:45:24Z file_id: '5919' file_name: IST-2018-1025-v2+4_ThesisIglesiasFinal11June2018.pdf file_size: 4783846 relation: main_file file_date_updated: 2020-07-14T12:45:24Z has_accepted_license: '1' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: '171' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria publist_id: '7712' pubrep_id: '1026' status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: Multiple covers with balls type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2018' ... --- _id: '187' 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. ' 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). alternative_title: - LIPIcs article_number: '34' author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang orcid: 0000-0002-8882-5116 citation: 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' 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. 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.' ista: 'Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.' 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. short: H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. conference: end_date: 2018-06-14 location: Budapest, Hungary name: 'SoCG: Symposium on Computational Geometry' start_date: 2018-06-11 date_created: 2018-12-11T11:45:05Z date_published: 2018-06-11T00:00:00Z date_updated: 2023-09-07T13:29:00Z day: '11' ddc: - '516' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2018.34 file: - access_level: open_access checksum: d8c0533ad0018eb4ed1077475eb8fc18 content_type: application/pdf creator: dernst date_created: 2018-12-18T09:27:22Z date_updated: 2020-07-14T12:45:19Z file_id: '5738' file_name: 2018_LIPIcs_Edelsbrunner_Osang.pdf file_size: 528018 relation: main_file file_date_updated: 2020-07-14T12:45:19Z has_accepted_license: '1' intvolume: ' 99' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '7732' quality_controlled: '1' related_material: record: - id: '9317' relation: later_version status: public - id: '9056' relation: dissertation_contains status: public scopus_import: 1 status: public title: The multi-cover persistence of Euclidean balls tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 99 year: '2018' ... --- _id: '692' 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. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X citation: 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 chicago: Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata. Springer, 2018. 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. 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. short: A. Akopyan, Geometriae Dedicata 194 (2018) 55–64. date_created: 2018-12-11T11:47:57Z date_published: 2018-06-01T00:00:00Z date_updated: 2023-09-08T11:40:29Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s10711-017-0265-6 ec_funded: 1 external_id: isi: - '000431418800004' file: - access_level: open_access checksum: 1febcfc1266486053a069e3425ea3713 content_type: application/pdf creator: kschuh date_created: 2020-01-03T11:35:08Z date_updated: 2020-07-14T12:47:44Z file_id: '7222' file_name: 2018_Springer_Akopyan.pdf file_size: 1140860 relation: main_file file_date_updated: 2020-07-14T12:47:44Z has_accepted_license: '1' intvolume: ' 194' isi: 1 issue: '1' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 55 - 64 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Geometriae Dedicata publication_status: published publisher: Springer publist_id: '7014' quality_controlled: '1' scopus_import: '1' status: public title: 3-Webs generated by confocal conics and circles tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 194 year: '2018' ... --- _id: '58' 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.' article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Erel full_name: Segal Halevi, Erel last_name: Segal Halevi 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 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. ista: Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 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. short: A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257. date_created: 2018-12-11T11:44:24Z date_published: 2018-09-06T00:00:00Z date_updated: 2023-09-11T12:48:39Z day: '06' department: - _id: HeEd doi: 10.1137/16M110407X ec_funded: 1 external_id: arxiv: - '1604.00960' isi: - '000450810500036' intvolume: ' 32' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1604.00960 month: '09' oa: 1 oa_version: Preprint page: 2242 - 2257 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: SIAM Journal on Discrete Mathematics publication_status: published publisher: 'Society for Industrial and Applied Mathematics ' publist_id: '7996' quality_controlled: '1' scopus_import: '1' status: public title: Counting blanks in polygonal arrangements type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 32 year: '2018' ... --- _id: '458' 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. 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] article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alexander full_name: Bobenko, Alexander last_name: Bobenko citation: 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 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. 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. ista: Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 370(4), 2825–2854. 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. date_created: 2018-12-11T11:46:35Z date_published: 2018-04-01T00:00:00Z date_updated: 2023-09-11T14:19:12Z day: '01' department: - _id: HeEd doi: 10.1090/tran/7292 ec_funded: 1 external_id: isi: - '000423197800019' intvolume: ' 370' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1602.04637 month: '04' oa: 1 oa_version: Preprint page: 2825 - 2854 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Transactions of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '7363' quality_controlled: '1' scopus_import: '1' status: public title: Incircular nets and confocal conics type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 370 year: '2018' ... --- _id: '106' 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. article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Anton full_name: Petrunin, Anton last_name: Petrunin citation: ama: Akopyan A, Petrunin A. Long geodesics on convex surfaces. Mathematical Intelligencer. 2018;40(3):26-31. doi:10.1007/s00283-018-9795-5 apa: Akopyan, A., & Petrunin, A. (2018). Long geodesics on convex surfaces. Mathematical Intelligencer. Springer. https://doi.org/10.1007/s00283-018-9795-5 chicago: Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer. Springer, 2018. https://doi.org/10.1007/s00283-018-9795-5. ieee: A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” Mathematical Intelligencer, vol. 40, no. 3. Springer, pp. 26–31, 2018. ista: Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical Intelligencer. 40(3), 26–31. 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. short: A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31. date_created: 2018-12-11T11:44:40Z date_published: 2018-09-01T00:00:00Z date_updated: 2023-09-13T08:49:16Z day: '01' department: - _id: HeEd doi: 10.1007/s00283-018-9795-5 external_id: arxiv: - '1702.05172' isi: - '000444141200005' intvolume: ' 40' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1702.05172 month: '09' oa: 1 oa_version: Preprint page: 26 - 31 publication: Mathematical Intelligencer publication_status: published publisher: Springer publist_id: '7948' quality_controlled: '1' scopus_import: '1' status: public title: Long geodesics on convex surfaces type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 40 year: '2018' ... --- _id: '530' abstract: - lang: eng 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. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Mabel full_name: Iglesias Ham, Mabel id: 41B58C0C-F248-11E8-B48F-1D18A9856A87 last_name: Iglesias Ham citation: 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.' 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.' ista: 'Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133.' 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.' date_created: 2018-12-11T11:46:59Z date_published: 2018-03-01T00:00:00Z date_updated: 2023-09-13T08:59:00Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2017.06.014 ec_funded: 1 external_id: isi: - '000415778300010' file: - access_level: open_access checksum: 1c8d58cd489a66cd3e2064c1141c8c5e content_type: application/pdf creator: dernst date_created: 2019-02-12T06:47:52Z date_updated: 2020-07-14T12:46:38Z file_id: '5953' file_name: 2018_Edelsbrunner.pdf file_size: 708357 relation: main_file file_date_updated: 2020-07-14T12:46:38Z has_accepted_license: '1' intvolume: ' 68' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Preprint page: 119 - 133 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '7289' quality_controlled: '1' scopus_import: '1' status: public title: 'Multiple covers with balls I: Inclusion–exclusion' type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 68 year: '2018' ... --- _id: '193' abstract: - lang: eng text: 'We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki''16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block''16] for analyzing the hardware costs of an iMHF.' 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 author: - first_name: Joel F full_name: Alwen, Joel F id: 2A8DFA8C-F248-11E8-B48F-1D18A9856A87 last_name: Alwen - first_name: Peter full_name: Gazi, Peter last_name: Gazi - first_name: Chethan full_name: Kamath Hosdurg, Chethan id: 4BD3F30E-F248-11E8-B48F-1D18A9856A87 last_name: Kamath Hosdurg - first_name: Karen full_name: Klein, Karen id: 3E83A2F8-F248-11E8-B48F-1D18A9856A87 last_name: Klein - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang orcid: 0000-0002-8882-5116 - first_name: Krzysztof Z full_name: Pietrzak, Krzysztof Z id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87 last_name: Pietrzak orcid: 0000-0002-9139-1654 - first_name: Lenoid full_name: Reyzin, Lenoid last_name: Reyzin - first_name: Michal full_name: Rolinek, Michal id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87 last_name: Rolinek - first_name: Michal full_name: Rybar, Michal id: 2B3E3DE8-F248-11E8-B48F-1D18A9856A87 last_name: Rybar citation: 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' 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' 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. 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. 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.' 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. 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. conference: end_date: 2018-06-08 location: Incheon, Republic of Korea name: 'ASIACCS: Asia Conference on Computer and Communications Security ' start_date: 2018-06-04 date_created: 2018-12-11T11:45:07Z date_published: 2018-06-01T00:00:00Z date_updated: 2023-09-13T09:13:12Z day: '01' department: - _id: KrPi - _id: HeEd - _id: VlKo doi: 10.1145/3196494.3196534 ec_funded: 1 external_id: isi: - '000516620100005' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://eprint.iacr.org/2016/783 month: '06' oa: 1 oa_version: Submitted Version page: 51 - 65 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' - _id: 258AA5B2-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '682815' name: Teaching Old Crypto New Tricks publication: Proceedings of the 2018 on Asia Conference on Computer and Communication Security publication_status: published publisher: ACM publist_id: '7723' quality_controlled: '1' scopus_import: '1' status: public title: On the memory hardness of data independent password hashing functions type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2018' ... --- _id: '312' 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. 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). article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Mabel full_name: Iglesias Ham, Mabel id: 41B58C0C-F248-11E8-B48F-1D18A9856A87 last_name: Iglesias Ham citation: 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 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. 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. 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. 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. short: H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782. date_created: 2018-12-11T11:45:46Z date_published: 2018-03-29T00:00:00Z date_updated: 2023-09-13T09:34:38Z day: '29' department: - _id: HeEd doi: 10.1137/16M1097201 external_id: isi: - '000428958900038' intvolume: ' 32' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf month: '03' oa: 1 oa_version: Submitted Version page: 750 - 782 project: - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: SIAM J Discrete Math publication_identifier: issn: - '08954801' publication_status: published publisher: 'Society for Industrial and Applied Mathematics ' publist_id: '7553' quality_controlled: '1' scopus_import: '1' status: public title: On the optimality of the FCC lattice for soft sphere packing type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 32 year: '2018' ... --- _id: '409' 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. article_processing_charge: No article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X citation: 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 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 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. 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. ista: Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 356(4), 412–414. 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. date_created: 2018-12-11T11:46:19Z date_published: 2018-04-01T00:00:00Z date_updated: 2023-09-13T09:34:12Z day: '01' department: - _id: HeEd doi: 10.1016/j.crma.2018.03.005 external_id: arxiv: - '1805.01652' isi: - '000430402700009' intvolume: ' 356' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1805.01652 month: '04' oa: 1 oa_version: Preprint page: 412-414 publication: Comptes Rendus Mathematique publication_identifier: issn: - 1631073X publication_status: published publisher: Elsevier publist_id: '7420' quality_controlled: '1' scopus_import: '1' status: public title: On the number of non-hexagons in a planar tiling type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 356 year: '2018' ... --- _id: '87' 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. article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko orcid: 0000-0002-0659-3201 citation: 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. 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. 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. 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. short: H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238. date_created: 2018-12-11T11:44:33Z date_published: 2018-10-01T00:00:00Z date_updated: 2023-09-15T12:10:35Z day: '01' department: - _id: HeEd doi: 10.1214/18-AAP1389 external_id: arxiv: - '1705.02870' isi: - '000442893500018' intvolume: ' 28' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1705.02870 month: '10' oa: 1 oa_version: Preprint page: 3215 - 3238 project: - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Annals of Applied Probability publication_status: published publisher: Institute of Mathematical Statistics publist_id: '7967' quality_controlled: '1' related_material: record: - id: '6287' relation: dissertation_contains status: public scopus_import: '1' status: public title: Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 28 year: '2018' ... --- _id: '6355' abstract: - lang: eng text: We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle. article_number: e7 article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov citation: 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 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 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. 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. ista: Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7. 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. short: A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018). date_created: 2019-04-30T06:09:57Z date_published: 2018-05-31T00:00:00Z date_updated: 2023-09-19T14:50:12Z day: '31' ddc: - '510' department: - _id: UlWa - _id: HeEd - _id: JaMa doi: 10.1017/fms.2018.7 ec_funded: 1 external_id: arxiv: - '1712.10205' isi: - '000433915500001' file: - access_level: open_access checksum: 5a71b24ba712a3eb2e46165a38fbc30a content_type: application/pdf creator: dernst date_created: 2019-04-30T06:14:58Z date_updated: 2020-07-14T12:47:28Z file_id: '6356' file_name: 2018_ForumMahtematics_Akopyan.pdf file_size: 249246 relation: main_file file_date_updated: 2020-07-14T12:47:28Z has_accepted_license: '1' intvolume: ' 6' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Forum of Mathematics, Sigma publication_identifier: issn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '8156' relation: dissertation_contains status: public status: public title: Any cyclic quadrilateral can be inscribed in any closed convex smooth curve tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 6 year: '2018' ... --- _id: '1064' 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.' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alexey full_name: Balitskiy, Alexey last_name: Balitskiy - first_name: Mikhail full_name: Grigorev, Mikhail last_name: Grigorev citation: 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 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 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. 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. 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. 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. short: A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry 59 (2018) 1001–1009. date_created: 2018-12-11T11:49:57Z date_published: 2018-06-01T00:00:00Z date_updated: 2023-09-20T12:08:51Z day: '01' ddc: - '516' - '000' department: - _id: HeEd doi: 10.1007/s00454-017-9883-x ec_funded: 1 external_id: isi: - '000432205500011' file: - access_level: open_access content_type: application/pdf creator: dernst date_created: 2019-01-18T09:27:36Z date_updated: 2019-01-18T09:27:36Z file_id: '5844' file_name: 2018_DiscreteComp_Akopyan.pdf file_size: 482518 relation: main_file success: 1 file_date_updated: 2019-01-18T09:27:36Z has_accepted_license: '1' intvolume: ' 59' isi: 1 issue: '4' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 1001-1009 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Discrete & Computational Geometry publication_identifier: eissn: - '14320444' issn: - '01795376' publication_status: published publisher: Springer publist_id: '6324' quality_controlled: '1' scopus_import: '1' status: public title: On the circle covering theorem by A.W. Goodman and R.E. Goodman tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 59 year: '2018' ... --- _id: '75' abstract: - lang: eng 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. article_number: '1804.03057' article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: ama: Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 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 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. ieee: A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018. ista: Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057. mla: Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057. short: A. Akopyan, S. Avvakumov, R. Karasev, (2018). date_created: 2018-12-11T11:44:30Z date_published: 2018-09-13T00:00:00Z date_updated: 2023-12-18T10:51:02Z day: '13' department: - _id: HeEd - _id: JaMa doi: 10.48550/arXiv.1804.03057 ec_funded: 1 external_id: arxiv: - '1804.03057' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1804.03057 month: '09' oa: 1 oa_version: Preprint project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication_status: published publisher: arXiv related_material: record: - id: '8156' relation: dissertation_contains status: public status: public title: Convex fair partitions into arbitrary number of pieces type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2018' ... --- _id: '481' abstract: - lang: eng 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. acknowledgement: 'Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.' author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: 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. 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. 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. 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. date_created: 2018-12-11T11:46:43Z date_published: 2017-04-13T00:00:00Z date_updated: 2023-02-21T16:06:22Z day: '13' ddc: - '004' - '514' - '516' department: - _id: HeEd doi: 10.1142/S0218195916600050 file: - access_level: open_access checksum: f79e8558bfe4b368dfefeb8eec2e3a5e content_type: application/pdf creator: system date_created: 2018-12-12T10:09:34Z date_updated: 2020-07-14T12:46:35Z file_id: '4758' file_name: IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf file_size: 769296 relation: main_file file_date_updated: 2020-07-14T12:46:35Z has_accepted_license: '1' intvolume: ' 26' issue: 3-4 language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 211 - 229 publication: International Journal of Computational Geometry and Applications publication_status: published publisher: World Scientific Publishing publist_id: '7338' pubrep_id: '949' quality_controlled: '1' related_material: record: - id: '10892' relation: earlier_version status: public scopus_import: 1 status: public title: Planar matchings for weighted straight skeletons tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2017' ... --- _id: '521' 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. author: - first_name: Kyle full_name: Austin, Kyle last_name: Austin - first_name: Ziga full_name: Virk, Ziga id: 2E36B656-F248-11E8-B48F-1D18A9856A87 last_name: Virk citation: 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 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. ieee: K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017. ista: Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57. 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. short: K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57. date_created: 2018-12-11T11:46:56Z date_published: 2017-01-01T00:00:00Z date_updated: 2021-01-12T08:01:21Z day: '01' department: - _id: HeEd doi: 10.1016/j.topol.2016.10.005 intvolume: ' 215' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1608.03954v1 month: '01' oa: 1 oa_version: Submitted Version page: 45 - 57 publication: Topology and its Applications publication_identifier: issn: - '01668641' publication_status: published publisher: Elsevier publist_id: '7299' quality_controlled: '1' status: public title: Higson compactification and dimension raising type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 215 year: '2017' ... --- _id: '568' 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).' author: - first_name: Peter full_name: Franek, Peter id: 473294AE-F248-11E8-B48F-1D18A9856A87 last_name: Franek - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál citation: 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 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 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. ieee: P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017. ista: Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 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. short: P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342. date_created: 2018-12-11T11:47:14Z date_published: 2017-01-01T00:00:00Z date_updated: 2021-01-12T08:03:12Z day: '01' department: - _id: UlWa - _id: HeEd doi: 10.4310/HHA.2017.v19.n2.a16 ec_funded: 1 intvolume: ' 19' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1507.04310 month: '01' oa: 1 oa_version: Submitted Version page: 313 - 342 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: 2590DB08-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '701309' name: Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020) publication: Homology, Homotopy and Applications publication_identifier: issn: - '15320073' publication_status: published publisher: International Press publist_id: '7246' quality_controlled: '1' scopus_import: 1 status: public title: Persistence of zero sets type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 19 year: '2017' ... --- _id: '5803' abstract: - lang: eng 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. alternative_title: - LNCS article_processing_charge: No author: - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Partha full_name: Bhowmick, Partha last_name: Bhowmick citation: 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' 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' 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.' 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.' 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. short: R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104. conference: end_date: 2017-06-21 location: Plovdiv, Bulgaria name: 'IWCIA: International Workshop on Combinatorial Image Analysis' start_date: 2017-06-19 date_created: 2019-01-08T20:42:56Z date_published: 2017-05-17T00:00:00Z date_updated: 2022-01-28T07:48:24Z day: '17' department: - _id: HeEd doi: 10.1007/978-3-319-59108-7_8 extern: '1' intvolume: ' 10256' language: - iso: eng month: '05' oa_version: None page: 93-104 place: Cham publication: Combinatorial image analysis publication_identifier: isbn: - 978-3-319-59107-0 - 978-3-319-59108-7 issn: - 0302-9743 - 1611-3349 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Construction of persistent Voronoi diagram on 3D digital plane type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 10256 year: '2017' ... --- _id: '688' 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. ' alternative_title: - LIPIcs author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: 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' 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. 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. ista: Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916. 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. short: H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916. conference: end_date: 2017-07-07 location: Brisbane, Australia name: Symposium on Computational Geometry, SoCG start_date: 2017-07-04 date_created: 2018-12-11T11:47:56Z date_published: 2017-06-01T00:00:00Z date_updated: 2021-01-12T08:09:26Z day: '01' ddc: - '514' - '516' department: - _id: HeEd - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2017.39 file: - access_level: open_access checksum: 067ab0cb3f962bae6c3af6bf0094e0f3 content_type: application/pdf creator: system date_created: 2018-12-12T10:11:03Z date_updated: 2020-07-14T12:47:42Z file_id: '4856' file_name: IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf file_size: 990546 relation: main_file file_date_updated: 2020-07-14T12:47:42Z has_accepted_license: '1' intvolume: ' 77' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 391-3916 publication_identifier: issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '7021' pubrep_id: '895' quality_controlled: '1' scopus_import: 1 status: public title: Topological data analysis with Bregman divergences tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 77 year: '2017' ... --- _id: '707' abstract: - lang: eng text: We answer a question of M. Gromov on the waist of the unit ball. author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: 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 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 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. 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. 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. date_created: 2018-12-11T11:48:02Z date_published: 2017-08-01T00:00:00Z date_updated: 2021-01-12T08:11:41Z day: '01' department: - _id: HeEd doi: 10.1112/blms.12062 ec_funded: 1 intvolume: ' 49' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1608.06279 month: '08' oa: 1 oa_version: Preprint page: 690 - 693 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Bulletin of the London Mathematical Society publication_identifier: issn: - '00246093' publication_status: published publisher: Wiley-Blackwell publist_id: '6982' quality_controlled: '1' scopus_import: 1 status: public title: 'A tight estimate for the waist of the ball ' type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 49 year: '2017' ...