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This is of importance because it allows for sampling of Riemannian manifolds based on anisotropy of the manifold and not (absolute) curvature."}],"month":"07","intvolume":" 10","scopus_import":1,"file":[{"file_name":"mainJournalFinal.pdf","date_created":"2019-06-03T09:30:01Z","creator":"mwintrae","file_size":2170882,"date_updated":"2020-07-14T12:47:32Z","checksum":"57b4df2f16a74eb499734ec8ee240178","file_id":"6516","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1920-180X"]},"publication_status":"published","volume":10,"issue":"1","license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"short":"R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10 (2019) 223–256.","ieee":"R. Dyer, G. Vegter, and M. Wintraecken, “Simplices modelled on spaces of constant curvature,” Journal of Computational Geometry , vol. 10, no. 1. Carleton University, pp. 223–256, 2019.","ama":"Dyer R, Vegter G, Wintraecken M. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 2019;10(1):223–256. doi:10.20382/jocg.v10i1a9","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","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.","ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","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."},"title":"Simplices modelled on spaces of constant curvature","author":[{"last_name":"Dyer","full_name":"Dyer, Ramsay","first_name":"Ramsay"},{"last_name":"Vegter","full_name":"Vegter, Gert","first_name":"Gert"},{"last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","publisher":"Carleton University","oa":1,"day":"01","publication":"Journal of Computational Geometry ","has_accepted_license":"1","year":"2019","doi":"10.20382/jocg.v10i1a9","date_published":"2019-07-01T00:00:00Z","date_created":"2019-06-03T09:35:33Z","page":"223–256"},{"file_date_updated":"2020-07-14T12:47:34Z","title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","department":[{"_id":"HeEd"}],"author":[{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"ddc":["004"],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:08:16Z","citation":{"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.","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.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279.","ieee":"G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds,” in The 31st Canadian Conference in Computational Geometry, Edmonton, Canada, 2019, pp. 275–279.","apa":"Vegter, G., & Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In The 31st Canadian Conference in Computational Geometry (pp. 275–279). Edmonton, Canada.","ama":"Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In: The 31st Canadian Conference in Computational Geometry. ; 2019:275-279.","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."},"status":"public","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"conference":{"start_date":"2019-08-08","end_date":"2019-08-10","location":"Edmonton, Canada","name":"CCCG: Canadian Conference in Computational Geometry"},"type":"conference","_id":"6628","date_created":"2019-07-12T08:34:57Z","ec_funded":1,"date_published":"2019-08-01T00:00:00Z","page":"275-279","language":[{"iso":"eng"}],"publication":"The 31st Canadian Conference in Computational Geometry","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"ceabd152cfa55170d57763f9c6c60a53","file_id":"6629","creator":"mwintrae","date_updated":"2020-07-14T12:47:34Z","file_size":321176,"date_created":"2019-07-12T08:32:46Z","file_name":"IntrinsicExtrinsicCCCG2019.pdf"}],"day":"01","publication_status":"published","year":"2019","has_accepted_license":"1","month":"08","oa":1,"quality_controlled":"1","scopus_import":1,"oa_version":"Submitted Version","abstract":[{"text":"Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces in Euclidean space by piecewise flat triangular meshes with a given number of vertices on the hypersurface that are optimal with respect to Hausdorff distance. They proved that this Hausdorff distance decreases inversely proportional with m 2/(d−1), where m is the number of vertices and d is the dimension of Euclidean space. Moreover the pro-portionality constant can be expressed in terms of the Gaussian curvature, an intrinsic quantity. In this short note, we prove the extrinsic nature of this constant for manifolds of sufficiently high codimension. We do so by constructing an family of isometric embeddings of the flat torus in Euclidean space.","lang":"eng"}]},{"status":"public","type":"conference","conference":{"start_date":"2019-06-18","location":"Portland, OR, United States","end_date":"2019-06-21","name":"SoCG 2019: Symposium on Computational Geometry"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"6648","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:35Z","ddc":["510"],"date_updated":"2021-01-12T08:08:23Z","month":"06","intvolume":" 129","scopus_import":1,"alternative_title":["LIPIcs"],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory\r\nneeded for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context."}],"volume":129,"file":[{"checksum":"8ec8720730d4c789bf7b06540f1c29f4","file_id":"6666","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2019_LIPICS_Edelsbrunner.pdf","date_created":"2019-07-24T06:40:01Z","file_size":1355179,"date_updated":"2020-07-14T12:47:35Z","creator":"dernst"}],"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783959771047"]},"publication_status":"published","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"title":"Topological data analysis in information space","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Virk","full_name":"Virk, Ziga","first_name":"Ziga"},{"last_name":"Wagner","full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert"}],"external_id":{"arxiv":["1903.08510"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” in 35th International Symposium on Computational Geometry, Portland, OR, United States, 2019, vol. 129, p. 31:1-31:14.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2019). Topological data analysis in information space. In 35th International Symposium on Computational Geometry (Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.31","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:10.4230/LIPICS.SOCG.2019.31","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.","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."},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","oa":1,"doi":"10.4230/LIPICS.SOCG.2019.31","date_published":"2019-06-01T00:00:00Z","date_created":"2019-07-17T10:36:09Z","page":"31:1-31:14","day":"01","publication":"35th International Symposium on Computational Geometry","has_accepted_license":"1","year":"2019"},{"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"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.","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.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a cube. In Proceedings of the 31st Canadian Conference on Computational Geometry (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. In: Proceedings of the 31st Canadian Conference on Computational Geometry. Canadian Conference on Computational Geometry; 2019:164-170.","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.","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."},"date_updated":"2023-08-04T10:57:42Z","department":[{"_id":"HeEd"}],"title":"Folding polyominoes with holes into a cube","author":[{"first_name":"Oswin","full_name":"Aichholzer, Oswin","last_name":"Aichholzer"},{"first_name":"Hugo A","last_name":"Akitaya","full_name":"Akitaya, Hugo A"},{"first_name":"Kenneth C","last_name":"Cheung","full_name":"Cheung, Kenneth C"},{"last_name":"Demaine","full_name":"Demaine, Erik D","first_name":"Erik D"},{"last_name":"Demaine","full_name":"Demaine, Martin L","first_name":"Martin L"},{"full_name":"Fekete, Sandor P","last_name":"Fekete","first_name":"Sandor P"},{"full_name":"Kleist, Linda","last_name":"Kleist","first_name":"Linda"},{"last_name":"Kostitsyna","full_name":"Kostitsyna, Irina","first_name":"Irina"},{"last_name":"Löffler","full_name":"Löffler, Maarten","first_name":"Maarten"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","last_name":"Masárová"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"first_name":"Christiane","full_name":"Schmidt, Christiane","last_name":"Schmidt"}],"external_id":{"arxiv":["1910.09917"]},"article_processing_charge":"No","_id":"6989","status":"public","type":"conference","conference":{"end_date":"2019-08-10","location":"Edmonton, Canada","start_date":"2019-08-08","name":"CCCG: Canadian Conference in Computational Geometry"},"day":"01","publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","language":[{"iso":"eng"}],"publication_status":"published","year":"2019","date_published":"2019-08-01T00:00:00Z","related_material":{"record":[{"id":"8317","status":"public","relation":"extended_version"}]},"date_created":"2019-11-04T16:46:11Z","page":"164-170","oa_version":"Published Version","acknowledgement":"This research was performed in part at the 33rd BellairsWinter Workshop on Computational Geometry. Wethank all other participants for a fruitful atmosphere.","abstract":[{"text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability. ","lang":"eng"}],"month":"08","quality_controlled":"1","publisher":"Canadian Conference on Computational Geometry","scopus_import":"1","oa":1,"main_file_link":[{"url":"https://cccg.ca/proceedings/2019/proceedings.pdf","open_access":"1"}]},{"ec_funded":1,"volume":3,"issue":"1-2","language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"6741","checksum":"a5b244db9f751221409cf09c97ee0935","creator":"dernst","date_updated":"2020-07-14T12:47:36Z","file_size":2215157,"date_created":"2019-07-31T08:09:56Z","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf"}],"publication_status":"published","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"intvolume":" 3","month":"06","oa_version":"Published Version","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."}],"file_date_updated":"2020-07-14T12:47:36Z","department":[{"_id":"HeEd"}],"ddc":["000"],"date_updated":"2023-08-22T12:37:47Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"6671","date_created":"2019-07-24T08:37:29Z","doi":"10.1007/s41468-019-00029-8","date_published":"2019-06-01T00:00:00Z","page":"29–58","publication":"Journal of Applied and Computational Topology","day":"01","year":"2019","has_accepted_license":"1","oa":1,"publisher":"Springer Nature","quality_controlled":"1","title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Jean-Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58.","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.","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","ama":"Boissonnat J-D, Lieutier A, Wintraecken M. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. 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Springer Nature, 2019. https://doi.org/10.1007/s41468-019-00029-8."},"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}]},{"oa":1,"publisher":"AMS","quality_controlled":"1","date_created":"2019-02-24T22:59:19Z","date_published":"2019-01-01T00:00:00Z","doi":"10.1090/proc/14240","page":"91-102","publication":"Proceedings of the American Mathematical Society","day":"01","year":"2019","isi":1,"title":"Two circles and only a straightedge","article_processing_charge":"No","external_id":{"isi":["000450363900008"],"arxiv":["1709.02562"]},"author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"full_name":"Fedorov, Roman","last_name":"Fedorov","first_name":"Roman"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","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.","apa":"Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240","ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102.","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.","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."},"intvolume":" 147","month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1709.02562"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"text":"We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely many families of pairs of circles for which such construction is possible. ","lang":"eng"}],"volume":147,"language":[{"iso":"eng"}],"publication_status":"published","status":"public","type":"journal_article","_id":"6050","department":[{"_id":"HeEd"}],"date_updated":"2023-08-24T14:48:59Z"},{"year":"2019","isi":1,"publication":"Topological Methods in Nonlinear Analysis","day":"01","page":"457-490","date_created":"2019-07-14T21:59:19Z","doi":"10.12775/TMNA.2019.008","date_published":"2019-06-01T00:00:00Z","oa":1,"publisher":"Akademicka Platforma Czasopism","quality_controlled":"1","citation":{"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.","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.","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","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","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.","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","mla":"Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000472541600004"],"arxiv":["1612.06926"]},"author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"first_name":"Alfredo","last_name":"Hubard","full_name":"Hubard, Alfredo"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"title":"Lower and upper bounds for the waists of different spaces","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"volume":53,"issue":"2","abstract":[{"text":"In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1612.06926","open_access":"1"}],"scopus_import":"1","intvolume":" 53","month":"06","date_updated":"2023-08-29T06:32:48Z","department":[{"_id":"HeEd"}],"_id":"6634","type":"journal_article","status":"public"},{"citation":{"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","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","ieee":"P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 2019.","short":"P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).","mla":"Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627, A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["1812.07678"],"isi":["000475839300003"]},"article_processing_charge":"No","author":[{"first_name":"Pratyush","last_name":"Pranav","full_name":"Pranav, Pratyush"},{"last_name":"Adler","full_name":"Adler, Robert J.","first_name":"Robert J."},{"last_name":"Buchert","full_name":"Buchert, Thomas","first_name":"Thomas"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"first_name":"Bernard J.T.","full_name":"Jones, Bernard J.T.","last_name":"Jones"},{"first_name":"Armin","last_name":"Schwartzman","full_name":"Schwartzman, Armin"},{"last_name":"Wagner","full_name":"Wagner, Hubert","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Rien","last_name":"Van De Weygaert","full_name":"Van De Weygaert, Rien"}],"title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","article_number":"A163","project":[{"_id":"265683E4-B435-11E9-9278-68D0E5697425","name":"Toward Computational Information Topology","grant_number":"M62909-18-1-2038"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"year":"2019","isi":1,"has_accepted_license":"1","publication":"Astronomy and Astrophysics","day":"17","date_created":"2019-08-04T21:59:18Z","date_published":"2019-07-17T00:00:00Z","doi":"10.1051/0004-6361/201834916","oa":1,"publisher":"EDP Sciences","quality_controlled":"1","date_updated":"2023-08-29T07:01:48Z","ddc":["520","530"],"file_date_updated":"2020-07-14T12:47:39Z","department":[{"_id":"HeEd"}],"_id":"6756","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"eissn":["14320746"],"issn":["00046361"]},"language":[{"iso":"eng"}],"file":[{"checksum":"83b9209ed9eefbdcefd89019c5a97805","file_id":"6766","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2019_AstronomyAstrophysics_Pranav.pdf","date_created":"2019-08-05T08:08:59Z","creator":"dernst","file_size":14420451,"date_updated":"2020-07-14T12:47:39Z"}],"volume":627,"abstract":[{"text":"We study the topology generated by the temperature fluctuations of the cosmic microwave background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over 𝕊2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of “masks” is of importance, we introduce the concept of relative homology. The parametric χ2-test shows differences between observations and simulations, yielding p-values at percent to less than permil levels roughly between 2 and 7°, with the difference in the number of components and holes peaking at more than 3σ sporadically at these scales. The highest observed deviation between the observations and simulations for b0 and b1 is approximately between 3σ and 4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66° in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and first Betti numbers, respectively. Further, since these topological descriptors show consistent anomalous behaviour over independent measurements of Planck and WMAP, instrumental and systematic errors may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations based on power-spectrum matching the characteristics of the observed dipped power spectrum are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB, whether cosmological in nature or arising due to late-time effects, is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate the study of primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology, including topological defect models.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 627","month":"07"},{"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."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.04929"}],"scopus_import":"1","intvolume":" 51","month":"10","publication_status":"published","publication_identifier":{"issn":["00246093"],"eissn":["14692120"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":51,"issue":"5","_id":"6793","type":"journal_article","article_type":"original","status":"public","date_updated":"2023-08-29T07:08:34Z","department":[{"_id":"HeEd"}],"oa":1,"publisher":"London Mathematical Society","quality_controlled":"1","year":"2019","isi":1,"publication":"Bulletin of the London Mathematical Society","day":"01","page":"765-775","date_created":"2019-08-11T21:59:23Z","doi":"10.1112/blms.12276","date_published":"2019-10-01T00:00:00Z","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"}],"citation":{"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.","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.","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.","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"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000478560200001"],"arxiv":["1903.04929"]},"article_processing_charge":"No","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"first_name":"Ivan","last_name":"Izmestiev","full_name":"Izmestiev, Ivan"}],"title":"The Regge symmetry, confocal conics, and the Schläfli formula"},{"oa":1,"publisher":"Elsevier","quality_controlled":"1","date_created":"2019-08-22T07:54:13Z","date_published":"2019-11-15T00:00:00Z","doi":"10.1016/j.jalgebra.2019.07.027","page":"261-289","publication":"Journal of Algebra","day":"15","year":"2019","isi":1,"title":"Arakawa-Suzuki functors for Whittaker modules","article_processing_charge":"No","external_id":{"isi":["000487176300011"],"arxiv":["1805.04676"]},"author":[{"full_name":"Brown, Adam","last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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","ieee":"A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra, vol. 538. Elsevier, pp. 261–289, 2019.","short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027.","ista":"Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289."},"intvolume":" 538","month":"11","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.04676"}],"oa_version":"Preprint","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 ."}],"volume":538,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0021-8693"]},"status":"public","article_type":"original","type":"journal_article","_id":"6828","department":[{"_id":"HeEd"}],"date_updated":"2023-08-29T07:11:47Z"}]