--- _id: '6515' abstract: - lang: eng text: We give non-degeneracy criteria for Riemannian simplices based on simplices in spaces of constant sectional curvature. It extends previous work on Riemannian simplices, where we developed Riemannian simplices with respect to Euclidean reference simplices. The criteria we give in this article are in terms of quality measures for spaces of constant curvature that we develop here. We see that simplices in spaces that have nearly constant curvature, are already non-degenerate under very weak quality demands. This is of importance because it allows for sampling of Riemannian manifolds based on anisotropy of the manifold and not (absolute) curvature. author: - first_name: Ramsay full_name: Dyer, Ramsay last_name: Dyer - first_name: Gert full_name: Vegter, Gert last_name: Vegter - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Dyer R, Vegter G, Wintraecken M. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 2019;10(1):223–256. doi:10.20382/jocg.v10i1a9 apa: Dyer, R., Vegter, G., & Wintraecken, M. (2019). Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . Carleton University. https://doi.org/10.20382/jocg.v10i1a9 chicago: Dyer, Ramsay, Gert Vegter, and Mathijs Wintraecken. “Simplices Modelled on Spaces of Constant Curvature.” Journal of Computational Geometry . Carleton University, 2019. https://doi.org/10.20382/jocg.v10i1a9. ieee: R. Dyer, G. Vegter, and M. Wintraecken, “Simplices modelled on spaces of constant curvature,” Journal of Computational Geometry , vol. 10, no. 1. Carleton University, pp. 223–256, 2019. ista: Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256. mla: Dyer, Ramsay, et al. “Simplices Modelled on Spaces of Constant Curvature.” Journal of Computational Geometry , vol. 10, no. 1, Carleton University, 2019, pp. 223–256, doi:10.20382/jocg.v10i1a9. short: R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10 (2019) 223–256. date_created: 2019-06-03T09:35:33Z date_published: 2019-07-01T00:00:00Z date_updated: 2021-01-12T08:07:50Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.20382/jocg.v10i1a9 ec_funded: 1 file: - access_level: open_access checksum: 57b4df2f16a74eb499734ec8ee240178 content_type: application/pdf creator: mwintrae date_created: 2019-06-03T09:30:01Z date_updated: 2020-07-14T12:47:32Z file_id: '6516' file_name: mainJournalFinal.pdf file_size: 2170882 relation: main_file file_date_updated: 2020-07-14T12:47:32Z has_accepted_license: '1' intvolume: ' 10' issue: '1' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '07' oa: 1 oa_version: Published Version page: 223–256 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 'Journal of Computational Geometry ' publication_identifier: issn: - 1920-180X publication_status: published publisher: Carleton University quality_controlled: '1' scopus_import: 1 status: public title: Simplices modelled on spaces of constant curvature 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: 10 year: '2019' ... --- _id: '6628' abstract: - lang: eng text: Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces in Euclidean space by piecewise flat triangular meshes with a given number of vertices on the hypersurface that are optimal with respect to Hausdorff distance. They proved that this Hausdorff distance decreases inversely proportional with m 2/(d−1), where m is the number of vertices and d is the dimension of Euclidean space. Moreover the pro-portionality constant can be expressed in terms of the Gaussian curvature, an intrinsic quantity. In this short note, we prove the extrinsic nature of this constant for manifolds of sufficiently high codimension. We do so by constructing an family of isometric embeddings of the flat torus in Euclidean space. author: - first_name: Gert full_name: Vegter, Gert last_name: Vegter - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: 'Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In: The 31st Canadian Conference in Computational Geometry. ; 2019:275-279.' apa: Vegter, G., & Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In The 31st Canadian Conference in Computational Geometry (pp. 275–279). Edmonton, Canada. chicago: Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” In The 31st Canadian Conference in Computational Geometry, 275–79, 2019. ieee: G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds,” in The 31st Canadian Conference in Computational Geometry, Edmonton, Canada, 2019, pp. 275–279. ista: 'Vegter G, Wintraecken M. 2019. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. The 31st Canadian Conference in Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 275–279.' mla: Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–79. short: G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279. conference: end_date: 2019-08-10 location: Edmonton, Canada name: 'CCCG: Canadian Conference in Computational Geometry' start_date: 2019-08-08 date_created: 2019-07-12T08:34:57Z date_published: 2019-08-01T00:00:00Z date_updated: 2021-01-12T08:08:16Z day: '01' ddc: - '004' department: - _id: HeEd ec_funded: 1 file: - access_level: open_access checksum: ceabd152cfa55170d57763f9c6c60a53 content_type: application/pdf creator: mwintrae date_created: 2019-07-12T08:32:46Z date_updated: 2020-07-14T12:47:34Z file_id: '6629' file_name: IntrinsicExtrinsicCCCG2019.pdf file_size: 321176 relation: main_file file_date_updated: 2020-07-14T12:47:34Z has_accepted_license: '1' language: - iso: eng month: '08' oa: 1 oa_version: Submitted Version page: 275-279 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: The 31st Canadian Conference in Computational Geometry publication_status: published quality_controlled: '1' scopus_import: 1 status: public title: The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2019' ... --- _id: '6648' abstract: - lang: eng text: "Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory\r\nneeded for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context." 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: Ziga full_name: Virk, Ziga last_name: Virk - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: ama: 'Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:10.4230/LIPICS.SOCG.2019.31' apa: 'Edelsbrunner, H., Virk, Z., & Wagner, H. (2019). Topological data analysis in information space. In 35th International Symposium on Computational Geometry (Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.31' chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” In 35th International Symposium on Computational Geometry, 129:31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.SOCG.2019.31. ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” in 35th International Symposium on Computational Geometry, Portland, OR, United States, 2019, vol. 129, p. 31:1-31:14. ista: 'Edelsbrunner H, Virk Z, Wagner H. 2019. Topological data analysis in information space. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium on Computational Geometry, LIPIcs, vol. 129, 31:1-31:14.' mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14, doi:10.4230/LIPICS.SOCG.2019.31. short: H. Edelsbrunner, Z. Virk, H. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14. conference: end_date: 2019-06-21 location: Portland, OR, United States name: 'SoCG 2019: Symposium on Computational Geometry' start_date: 2019-06-18 date_created: 2019-07-17T10:36:09Z date_published: 2019-06-01T00:00:00Z date_updated: 2021-01-12T08:08:23Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPICS.SOCG.2019.31 external_id: arxiv: - '1903.08510' file: - access_level: open_access checksum: 8ec8720730d4c789bf7b06540f1c29f4 content_type: application/pdf creator: dernst date_created: 2019-07-24T06:40:01Z date_updated: 2020-07-14T12:47:35Z file_id: '6666' file_name: 2019_LIPICS_Edelsbrunner.pdf file_size: 1355179 relation: main_file file_date_updated: 2020-07-14T12:47:35Z has_accepted_license: '1' intvolume: ' 129' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 31:1-31:14 project: - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: 35th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771047' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Topological data analysis in information space 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: 129 year: '2019' ... --- _id: '6989' abstract: - lang: eng text: 'When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability. ' acknowledgement: This research was performed in part at the 33rd BellairsWinter Workshop on Computational Geometry. Wethank all other participants for a fruitful atmosphere. article_processing_charge: No author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Hugo A full_name: Akitaya, Hugo A last_name: Akitaya - first_name: Kenneth C full_name: Cheung, Kenneth C last_name: Cheung - first_name: Erik D full_name: Demaine, Erik D last_name: Demaine - first_name: Martin L full_name: Demaine, Martin L last_name: Demaine - first_name: Sandor P full_name: Fekete, Sandor P last_name: Fekete - first_name: Linda full_name: Kleist, Linda last_name: Kleist - first_name: Irina full_name: Kostitsyna, Irina last_name: Kostitsyna - first_name: Maarten full_name: Löffler, Maarten last_name: Löffler - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Klara full_name: Mundilova, Klara last_name: Mundilova - first_name: Christiane full_name: Schmidt, Christiane last_name: Schmidt citation: ama: 'Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. In: Proceedings of the 31st Canadian Conference on Computational Geometry. Canadian Conference on Computational Geometry; 2019:164-170.' apa: 'Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a cube. In Proceedings of the 31st Canadian Conference on Computational Geometry (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.' chicago: Aichholzer, Oswin, Hugo A Akitaya, Kenneth C Cheung, Erik D Demaine, Martin L Demaine, Sandor P Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” In Proceedings of the 31st Canadian Conference on Computational Geometry, 164–70. Canadian Conference on Computational Geometry, 2019. ieee: O. Aichholzer et al., “Folding polyominoes with holes into a cube,” in Proceedings of the 31st Canadian Conference on Computational Geometry, Edmonton, Canada, 2019, pp. 164–170. ista: 'Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference on Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 164–170.' mla: Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–70. short: O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, in:, Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–170. conference: end_date: 2019-08-10 location: Edmonton, Canada name: 'CCCG: Canadian Conference in Computational Geometry' start_date: 2019-08-08 date_created: 2019-11-04T16:46:11Z date_published: 2019-08-01T00:00:00Z date_updated: 2023-08-04T10:57:42Z day: '01' department: - _id: HeEd external_id: arxiv: - '1910.09917' language: - iso: eng main_file_link: - open_access: '1' url: https://cccg.ca/proceedings/2019/proceedings.pdf month: '08' oa: 1 oa_version: Published Version page: 164-170 publication: Proceedings of the 31st Canadian Conference on Computational Geometry publication_status: published publisher: Canadian Conference on Computational Geometry quality_controlled: '1' related_material: record: - id: '8317' relation: extended_version status: public scopus_import: '1' status: public title: Folding polyominoes with holes into a cube type: conference user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 year: '2019' ... --- _id: '6671' abstract: - lang: eng text: 'In this paper we discuss three results. The first two concern general sets of positive reach: we first characterize the reach of a closed set by means of a bound on the metric distortion between the distance measured in the ambient Euclidean space and the shortest path distance measured in the set. Secondly, we prove that the intersection of a ball with radius less than the reach with the set is geodesically convex, meaning that the shortest path between any two points in the intersection lies itself in the intersection. For our third result we focus on manifolds with positive reach and give a bound on the angle between tangent spaces at two different points in terms of the reach and the distance between the two points.' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Jean-Daniel full_name: Boissonnat, Jean-Daniel last_name: Boissonnat - first_name: André full_name: Lieutier, André last_name: Lieutier - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Boissonnat J-D, Lieutier A, Wintraecken M. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. 2019;3(1-2):29–58. doi:10.1007/s41468-019-00029-8 apa: Boissonnat, J.-D., Lieutier, A., & Wintraecken, M. (2019). The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-019-00029-8 chicago: Boissonnat, Jean-Daniel, André Lieutier, and Mathijs Wintraecken. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” Journal of Applied and Computational Topology. Springer Nature, 2019. https://doi.org/10.1007/s41468-019-00029-8. ieee: J.-D. Boissonnat, A. Lieutier, and M. Wintraecken, “The reach, metric distortion, geodesic convexity and the variation of tangent spaces,” Journal of Applied and Computational Topology, vol. 3, no. 1–2. Springer Nature, pp. 29–58, 2019. ista: Boissonnat J-D, Lieutier A, Wintraecken M. 2019. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. 3(1–2), 29–58. mla: Boissonnat, Jean-Daniel, et al. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” Journal of Applied and Computational Topology, vol. 3, no. 1–2, Springer Nature, 2019, pp. 29–58, doi:10.1007/s41468-019-00029-8. short: J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58. date_created: 2019-07-24T08:37:29Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-08-22T12:37:47Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s41468-019-00029-8 ec_funded: 1 file: - access_level: open_access checksum: a5b244db9f751221409cf09c97ee0935 content_type: application/pdf creator: dernst date_created: 2019-07-31T08:09:56Z date_updated: 2020-07-14T12:47:36Z file_id: '6741' file_name: 2019_JournAppliedComputTopol_Boissonnat.pdf file_size: 2215157 relation: main_file file_date_updated: 2020-07-14T12:47:36Z has_accepted_license: '1' intvolume: ' 3' issue: 1-2 language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 29–58 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Journal of Applied and Computational Topology publication_identifier: eissn: - 2367-1734 issn: - 2367-1726 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: The reach, metric distortion, geodesic convexity and the variation of tangent spaces 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 3 year: '2019' ... --- _id: '6050' abstract: - lang: eng text: 'We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely many families of pairs of circles for which such construction is possible. ' 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: Roman full_name: Fedorov, Roman last_name: Fedorov citation: ama: Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240 apa: Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240 chicago: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240. ieee: A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019. ista: Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102. mla: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society, vol. 147, AMS, 2019, pp. 91–102, doi:10.1090/proc/14240. short: A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102. date_created: 2019-02-24T22:59:19Z date_published: 2019-01-01T00:00:00Z date_updated: 2023-08-24T14:48:59Z day: '01' department: - _id: HeEd doi: 10.1090/proc/14240 external_id: arxiv: - '1709.02562' isi: - '000450363900008' intvolume: ' 147' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1709.02562 month: '01' oa: 1 oa_version: Preprint page: 91-102 publication: Proceedings of the American Mathematical Society publication_status: published publisher: AMS quality_controlled: '1' scopus_import: '1' status: public title: Two circles and only a straightedge type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 147 year: '2019' ... --- _id: '6634' abstract: - lang: eng text: In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure. 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: Alfredo full_name: Hubard, Alfredo last_name: Hubard - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: ama: Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 2019;53(2):457-490. doi:10.12775/TMNA.2019.008 apa: Akopyan, A., Hubard, A., & Karasev, R. (2019). Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism. https://doi.org/10.12775/TMNA.2019.008 chicago: Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008. ieee: A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019. ista: Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490. mla: Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008. short: A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490. date_created: 2019-07-14T21:59:19Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-08-29T06:32:48Z day: '01' department: - _id: HeEd doi: 10.12775/TMNA.2019.008 ec_funded: 1 external_id: arxiv: - '1612.06926' isi: - '000472541600004' intvolume: ' 53' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1612.06926 month: '06' oa: 1 oa_version: Preprint page: 457-490 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Topological Methods in Nonlinear Analysis publication_status: published publisher: Akademicka Platforma Czasopism quality_controlled: '1' scopus_import: '1' status: public title: Lower and upper bounds for the waists of different spaces type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 53 year: '2019' ... --- _id: '6756' abstract: - lang: eng text: "We study the topology generated by the temperature fluctuations of the cosmic microwave background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over \U0001D54A2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of “masks” is of importance, we introduce the concept of relative homology. The parametric χ2-test shows differences between observations and simulations, yielding p-values at percent to less than permil levels roughly between 2 and 7°, with the difference in the number of components and holes peaking at more than 3σ sporadically at these scales. The highest observed deviation between the observations and simulations for b0 and b1 is approximately between 3σ and 4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66° in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and first Betti numbers, respectively. Further, since these topological descriptors show consistent anomalous behaviour over independent measurements of Planck and WMAP, instrumental and systematic errors may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations based on power-spectrum matching the characteristics of the observed dipped power spectrum are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB, whether cosmological in nature or arising due to late-time effects, is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate the study of primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology, including topological defect models." article_number: A163 article_processing_charge: No article_type: original author: - first_name: Pratyush full_name: Pranav, Pratyush last_name: Pranav - first_name: Robert J. full_name: Adler, Robert J. last_name: Adler - first_name: Thomas full_name: Buchert, Thomas last_name: Buchert - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Bernard J.T. full_name: Jones, Bernard J.T. last_name: Jones - first_name: Armin full_name: Schwartzman, Armin last_name: Schwartzman - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner - first_name: Rien full_name: Van De Weygaert, Rien last_name: Van De Weygaert citation: ama: Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 2019;627. doi:10.1051/0004-6361/201834916 apa: Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman, A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. EDP Sciences. https://doi.org/10.1051/0004-6361/201834916 chicago: Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner, Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics. EDP Sciences, 2019. https://doi.org/10.1051/0004-6361/201834916. ieee: P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 2019. ista: Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 627, A163. mla: Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627, A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916. short: P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019). date_created: 2019-08-04T21:59:18Z date_published: 2019-07-17T00:00:00Z date_updated: 2023-08-29T07:01:48Z day: '17' ddc: - '520' - '530' department: - _id: HeEd doi: 10.1051/0004-6361/201834916 external_id: arxiv: - '1812.07678' isi: - '000475839300003' file: - access_level: open_access checksum: 83b9209ed9eefbdcefd89019c5a97805 content_type: application/pdf creator: dernst date_created: 2019-08-05T08:08:59Z date_updated: 2020-07-14T12:47:39Z file_id: '6766' file_name: 2019_AstronomyAstrophysics_Pranav.pdf file_size: 14420451 relation: main_file file_date_updated: 2020-07-14T12:47:39Z has_accepted_license: '1' intvolume: ' 627' isi: 1 language: - iso: eng month: '07' oa: 1 oa_version: Published Version project: - _id: 265683E4-B435-11E9-9278-68D0E5697425 grant_number: M62909-18-1-2038 name: Toward Computational Information Topology - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Astronomy and Astrophysics publication_identifier: eissn: - '14320746' issn: - '00046361' publication_status: published publisher: EDP Sciences quality_controlled: '1' scopus_import: '1' status: public title: Unexpected topology of the temperature fluctuations in the cosmic microwave background 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 627 year: '2019' ... --- _id: '6793' abstract: - lang: eng text: The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here, we give a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic geometry. 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 - first_name: Ivan full_name: Izmestiev, Ivan last_name: Izmestiev citation: ama: Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 2019;51(5):765-775. doi:10.1112/blms.12276 apa: Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12276 chicago: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society. London Mathematical Society, 2019. https://doi.org/10.1112/blms.12276. ieee: A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019. ista: Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775. mla: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society, vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:10.1112/blms.12276. short: A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775. date_created: 2019-08-11T21:59:23Z date_published: 2019-10-01T00:00:00Z date_updated: 2023-08-29T07:08:34Z day: '01' department: - _id: HeEd doi: 10.1112/blms.12276 ec_funded: 1 external_id: arxiv: - '1903.04929' isi: - '000478560200001' intvolume: ' 51' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1903.04929 month: '10' oa: 1 oa_version: Preprint page: 765-775 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended publication: Bulletin of the London Mathematical Society publication_identifier: eissn: - '14692120' issn: - '00246093' publication_status: published publisher: London Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: The Regge symmetry, confocal conics, and the Schläfli formula type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 51 year: '2019' ... --- _id: '6828' abstract: - lang: eng text: In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type to the category of finite-dimensional modules of the graded affine Hecke algebra of type . Using results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category as a full subcategory, our results generalize results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between finite-dimensional representations of and representations of the symmetric group . article_processing_charge: No article_type: original author: - first_name: Adam full_name: Brown, Adam id: 70B7FDF6-608D-11E9-9333-8535E6697425 last_name: Brown citation: ama: Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027 apa: Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2019.07.027 chicago: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027. ieee: A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra, vol. 538. Elsevier, pp. 261–289, 2019. ista: Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289. mla: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027. short: A. Brown, Journal of Algebra 538 (2019) 261–289. date_created: 2019-08-22T07:54:13Z date_published: 2019-11-15T00:00:00Z date_updated: 2023-08-29T07:11:47Z day: '15' department: - _id: HeEd doi: 10.1016/j.jalgebra.2019.07.027 external_id: arxiv: - '1805.04676' isi: - '000487176300011' intvolume: ' 538' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1805.04676 month: '11' oa: 1 oa_version: Preprint page: 261-289 publication: Journal of Algebra publication_identifier: issn: - 0021-8693 publication_status: published publisher: Elsevier quality_controlled: '1' status: public title: Arakawa-Suzuki functors for Whittaker modules type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 538 year: '2019' ... --- _id: '7216' abstract: - lang: eng text: 'We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system to label a stream of noisy observations of transit vehicle trajectories with the transit routes they are serving (e.g., northbound bus #5). In order to scale efficiently to large transit networks, our system first retrieves a small set of candidate routes from a geometrically indexed data structure, then applies a fine-grained scoring step to choose the best match. Given that real-time data remains unavailable for the majority of the world’s transit agencies, these inferences can help feed a real-time map of a transit system’s trips, infer transit trip delays in real time, or measure and correct noisy transit tracking data. This system can run on vehicle observations from a variety of sources that don’t attach route information to vehicle observations, such as public imagery streams or user-contributed transit vehicle sightings.We abstract away the specifics of the sensing system and demonstrate the effectiveness of our system on a "semisynthetic" dataset of all New York City buses, where we simulate sensed trajectories by starting with fully labeled vehicle trajectories reported via the GTFS-Realtime protocol, removing the transit route IDs, and perturbing locations with synthetic noise. Using just the geometric shapes of the trajectories, we demonstrate that our system converges on the correct route ID within a few minutes, even after a vehicle switches from serving one trip to the next.' article_number: '8917514' article_processing_charge: No author: - 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: James full_name: Cook, James last_name: Cook - first_name: Alex full_name: Fabrikant, Alex last_name: Fabrikant - first_name: Marco full_name: Gruteser, Marco last_name: Gruteser citation: ama: 'Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In: 2019 IEEE Intelligent Transportation Systems Conference. IEEE; 2019. doi:10.1109/ITSC.2019.8917514' apa: 'Osang, G. F., Cook, J., Fabrikant, A., & Gruteser, M. (2019). LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In 2019 IEEE Intelligent Transportation Systems Conference. Auckland, New Zealand: IEEE. https://doi.org/10.1109/ITSC.2019.8917514' chicago: 'Osang, Georg F, James Cook, Alex Fabrikant, and Marco Gruteser. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” In 2019 IEEE Intelligent Transportation Systems Conference. IEEE, 2019. https://doi.org/10.1109/ITSC.2019.8917514.' ieee: 'G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale,” in 2019 IEEE Intelligent Transportation Systems Conference, Auckland, New Zealand, 2019.' ista: 'Osang GF, Cook J, Fabrikant A, Gruteser M. 2019. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. 2019 IEEE Intelligent Transportation Systems Conference. ITSC: Intelligent Transportation Systems Conference, 8917514.' mla: 'Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” 2019 IEEE Intelligent Transportation Systems Conference, 8917514, IEEE, 2019, doi:10.1109/ITSC.2019.8917514.' short: G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019. conference: end_date: 2019-10-30 location: Auckland, New Zealand name: 'ITSC: Intelligent Transportation Systems Conference' start_date: 2019-10-27 date_created: 2019-12-29T23:00:47Z date_published: 2019-11-28T00:00:00Z date_updated: 2023-09-06T14:50:28Z day: '28' department: - _id: HeEd doi: 10.1109/ITSC.2019.8917514 external_id: isi: - '000521238102050' isi: 1 language: - iso: eng month: '11' oa_version: None publication: 2019 IEEE Intelligent Transportation Systems Conference publication_identifier: isbn: - '9781538670248' publication_status: published publisher: IEEE quality_controlled: '1' scopus_import: '1' status: public title: 'LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale' type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2019' ... --- _id: '5678' abstract: - lang: eng text: "The order-k Voronoi tessellation of a locally finite set \U0001D44B⊆ℝ\U0001D45B decomposes ℝ\U0001D45B into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold." article_processing_charge: Yes (via OA deal) 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. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2 apa: Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2 chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2. ieee: H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019. ista: Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878. mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2. short: H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878. date_created: 2018-12-16T22:59:20Z date_published: 2019-12-01T00:00:00Z date_updated: 2023-09-07T12:07:12Z day: '01' ddc: - '516' department: - _id: HeEd doi: 10.1007/s00454-018-0049-2 ec_funded: 1 external_id: arxiv: - '1709.09380' isi: - '000494042900008' file: - access_level: open_access checksum: f9d00e166efaccb5a76bbcbb4dcea3b4 content_type: application/pdf creator: dernst date_created: 2019-02-06T10:10:46Z date_updated: 2020-07-14T12:47:10Z file_id: '5932' file_name: 2018_DiscreteCompGeometry_Edelsbrunner.pdf file_size: 599339 relation: main_file file_date_updated: 2020-07-14T12:47:10Z has_accepted_license: '1' intvolume: ' 62' isi: 1 issue: '4' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 865–878 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Discrete and Computational Geometry publication_identifier: eissn: - '14320444' issn: - '01795376' publication_status: published publisher: Springer quality_controlled: '1' related_material: record: - id: '6287' relation: dissertation_contains status: public scopus_import: '1' status: public title: Poisson–Delaunay Mosaics of Order k 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 62 year: '2019' ... --- _id: '6608' abstract: - lang: eng text: We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram. 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: Katharina full_name: Ölsböck, Katharina id: 4D4AA390-F248-11E8-B48F-1D18A9856A87 last_name: Ölsböck orcid: 0000-0002-4672-8297 citation: ama: Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003 apa: Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered complex. Computer Aided Geometric Design. Elsevier. https://doi.org/10.1016/j.cagd.2019.06.003 chicago: Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design. Elsevier, 2019. https://doi.org/10.1016/j.cagd.2019.06.003. ieee: H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” Computer Aided Geometric Design, vol. 73. Elsevier, pp. 1–15, 2019. ista: Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15. mla: Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019, pp. 1–15, doi:10.1016/j.cagd.2019.06.003. short: H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15. date_created: 2019-07-07T21:59:20Z date_published: 2019-08-01T00:00:00Z date_updated: 2023-09-07T13:15:29Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.cagd.2019.06.003 ec_funded: 1 external_id: isi: - '000485207800001' file: - access_level: open_access checksum: 7c99be505dc7533257d42eb1830cef04 content_type: application/pdf creator: kschuh date_created: 2019-07-08T15:24:26Z date_updated: 2020-07-14T12:47:34Z file_id: '6624' file_name: Elsevier_2019_Edelsbrunner.pdf file_size: 2665013 relation: main_file file_date_updated: 2020-07-14T12:47:34Z has_accepted_license: '1' intvolume: ' 73' isi: 1 language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '08' oa: 1 oa_version: Published Version page: 1-15 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Computer Aided Geometric Design publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '7460' relation: dissertation_contains status: public scopus_import: '1' status: public title: Holes and dependences in an ordered complex tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 73 year: '2019' ... --- _id: '7950' abstract: - lang: eng text: "The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:\r\n1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices \ have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved." article_number: '1903.06981' article_processing_charge: No author: - first_name: Ahmad full_name: Biniaz, Ahmad last_name: Biniaz - first_name: Kshitij full_name: Jain, Kshitij last_name: Jain - first_name: Anna full_name: Lubiw, Anna last_name: Lubiw - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Tillmann full_name: Miltzow, Tillmann last_name: Miltzow - first_name: Debajyoti full_name: Mondal, Debajyoti last_name: Mondal - first_name: Anurag Murty full_name: Naredla, Anurag Murty last_name: Naredla - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Alexi full_name: Turcotte, Alexi last_name: Turcotte citation: ama: Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv. apa: Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. arXiv. chicago: Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” ArXiv, n.d. ieee: A. Biniaz et al., “Token swapping on trees,” arXiv. . ista: Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981. mla: Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981. short: A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.). date_created: 2020-06-08T12:25:25Z date_published: 2019-03-16T00:00:00Z date_updated: 2024-01-04T12:42:08Z day: '16' department: - _id: HeEd - _id: UlWa - _id: KrCh external_id: arxiv: - '1903.06981' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1903.06981 month: '03' oa: 1 oa_version: Preprint publication: arXiv publication_status: submitted related_material: record: - id: '7944' relation: dissertation_contains status: public - id: '12833' relation: later_version status: public status: public title: Token swapping on trees type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2019' ... --- _id: '188' abstract: - lang: eng text: Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex. acknowledgement: This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund alternative_title: - Leibniz International Proceedings in Information, 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: Ziga full_name: Virk, Ziga last_name: Virk - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: ama: 'Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:35:1-35:13. doi:10.4230/LIPIcs.SoCG.2018.35' apa: 'Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35' chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.35. ieee: 'H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.' ista: 'Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13.' mla: Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35. short: H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13. 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: 2021-01-12T06:53:48Z day: '11' ddc: - '000' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2018.35 file: - access_level: open_access checksum: 7509403803b3ac1aee94bbc2ad293d21 content_type: application/pdf creator: dernst date_created: 2018-12-17T16:31:31Z date_updated: 2020-07-14T12:45:20Z file_id: '5724' file_name: 2018_LIPIcs_Edelsbrunner.pdf file_size: 489080 relation: main_file file_date_updated: 2020-07-14T12:45:20Z has_accepted_license: '1' intvolume: ' 99' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 35:1 - 35:13 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: '7733' quality_controlled: '1' scopus_import: 1 status: public title: Smallest enclosing spheres and Chernoff points in Bregman geometry 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: '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' ...