[{"citation":{"short":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.","ieee":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, and M. Wintraecken, “The density fingerprint of a periodic point set,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 32:1-32:16.","apa":"Edelsbrunner, H., Heiss, T., Kurlin , V., Smith, P., & Wintraecken, M. (2021). The density fingerprint of a periodic point set. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 32:1-32:16). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.32","ama":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. The density fingerprint of a periodic point set. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16. doi:10.4230/LIPIcs.SoCG.2021.32","mla":"Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:10.4230/LIPIcs.SoCG.2021.32.","ista":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. 2021. The density fingerprint of a periodic point set. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol. 189, 32:1-32:16.","chicago":"Edelsbrunner, Herbert, Teresa Heiss, Vitaliy Kurlin , Philip Smith, and Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:32:1-32:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.32."},"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","article_processing_charge":"No","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"first_name":"Vitaliy","full_name":" Kurlin , Vitaliy","last_name":" Kurlin "},{"full_name":"Smith, Philip","last_name":"Smith","first_name":"Philip"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"title":"The density fingerprint of a periodic point set","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"I4887","name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"grant_number":"Z00312","name":"The Wittgenstein Prize","_id":"25C5A090-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"year":"2021","has_accepted_license":"1","publication":"37th International Symposium on Computational Geometry (SoCG 2021)","day":"02","page":"32:1-32:16","date_created":"2021-04-22T08:09:58Z","date_published":"2021-06-02T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2021.32","acknowledgement":"The authors thank Janos Pach for insightful discussions on the topic of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.","oa":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","date_updated":"2023-02-23T13:55:40Z","ddc":["004","516"],"department":[{"_id":"HeEd"}],"file_date_updated":"2021-04-22T08:08:14Z","_id":"9345","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"start_date":"2021-06-07","end_date":"2021-06-11","location":"Virtual","name":"SoCG: Symposium on Computational Geometry"},"type":"conference","status":"public","publication_status":"published","publication_identifier":{"issn":["1868-8969"]},"language":[{"iso":"eng"}],"file":[{"file_name":"df_socg_final_version.pdf","date_created":"2021-04-22T08:08:14Z","file_size":3117435,"date_updated":"2021-04-22T08:08:14Z","creator":"mwintrae","success":1,"file_id":"9346","checksum":"1787baef1523d6d93753b90d0c109a6d","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"volume":189,"abstract":[{"lang":"eng","text":"Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction."}],"oa_version":"Published Version","alternative_title":["LIPIcs"],"intvolume":" 189","month":"06"},{"department":[{"_id":"HeEd"}],"file_date_updated":"2021-06-28T13:11:39Z","ddc":["516"],"date_updated":"2023-02-23T14:02:28Z","status":"public","type":"conference","conference":{"name":"SoCG: International Symposium on Computational Geometry","end_date":"2021-06-11","location":"Online","start_date":"2021-06-07"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"9604","volume":189,"ec_funded":1,"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"9611","checksum":"22b11a719018b22ecba2471b51f2eb40","success":1,"creator":"asandaue","date_updated":"2021-06-28T13:11:39Z","file_size":727817,"date_created":"2021-06-28T13:11:39Z","file_name":"2021_LIPIcs_Biswas.pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["18688969"],"isbn":["9783959771849"]},"publication_status":"published","month":"06","intvolume":" 189","alternative_title":["LIPIcs"],"scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Generalizing Lee’s inductive argument for counting the cells of higher order Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse theoretic quantities for piecewise constant functions on planar arrangements. Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for 1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s first k-1 sublevel sets. We get similar expressions for the vertices, edges, and polygons of the order-k Voronoi tessellation."}],"title":"Counting cells of order-k voronoi tessellations in ℝ3 with morse theory","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas"},{"orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza"}],"article_processing_charge":"No","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.16.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 16.","mla":"Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” Leibniz International Proceedings in Informatics, vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.16.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting cells of order-k voronoi tessellations in ℝ3 with morse theory,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2021). Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.16","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16"},"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","grant_number":"Z00342"},{"grant_number":"I4887","name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"}],"article_number":"16","date_published":"2021-06-02T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2021.16","date_created":"2021-06-27T22:01:48Z","day":"02","publication":"Leibniz International Proceedings in Informatics","has_accepted_license":"1","year":"2021","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","oa":1},{"department":[{"_id":"HeEd"}],"date_updated":"2022-05-31T06:58:21Z","status":"public","conference":{"end_date":"2021-05-27","location":"Uppsala, Sweden","start_date":"2021-05-24","name":"DGMM: International Conference on Discrete Geometry and Mathematical Morphology"},"type":"conference","_id":"9824","ec_funded":1,"volume":12708,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["16113349"],"isbn":["9783030766566"],"issn":["03029743"]},"intvolume":" 12708","month":"05","alternative_title":["LNCS"],"scopus_import":"1","oa_version":"None","abstract":[{"text":"We define a new compact coordinate system in which each integer triplet addresses a voxel in the BCC grid, and we investigate some of its properties. We propose a characterization of 3D discrete analytical planes with their topological features (in the Cartesian and in the new coordinate system) such as the interrelation between the thickness of the plane and the separability constraint we aim to obtain.","lang":"eng"}],"title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","article_processing_charge":"No","author":[{"full_name":"Čomić, Lidija","last_name":"Čomić","first_name":"Lidija"},{"first_name":"Rita","full_name":"Zrour, Rita","last_name":"Zrour"},{"first_name":"Gaëlle","full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin"},{"orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” Discrete Geometry and Mathematical Morphology, vol. 12708, Springer Nature, 2021, pp. 152–63, doi:10.1007/978-3-030-76657-3_10.","ama":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic grid - coordinate system and discrete analytical plane definition. In: Discrete Geometry and Mathematical Morphology. Vol 12708. Springer Nature; 2021:152-163. doi:10.1007/978-3-030-76657-3_10","apa":"Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., & Andres, E. (2021). Body centered cubic grid - coordinate system and discrete analytical plane definition. In Discrete Geometry and Mathematical Morphology (Vol. 12708, pp. 152–163). Uppsala, Sweden: Springer Nature. https://doi.org/10.1007/978-3-030-76657-3_10","short":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.","ieee":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered cubic grid - coordinate system and discrete analytical plane definition,” in Discrete Geometry and Mathematical Morphology, Uppsala, Sweden, 2021, vol. 12708, pp. 152–163.","chicago":"Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” In Discrete Geometry and Mathematical Morphology, 12708:152–63. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-76657-3_10.","ista":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered cubic grid - coordinate system and discrete analytical plane definition. Discrete Geometry and Mathematical Morphology. DGMM: International Conference on Discrete Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163."},"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"date_created":"2021-08-08T22:01:29Z","date_published":"2021-05-16T00:00:00Z","doi":"10.1007/978-3-030-76657-3_10","page":"152-163","publication":"Discrete Geometry and Mathematical Morphology","day":"16","year":"2021","quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"This work has been partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia through the project no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35 (RB)."},{"_id":"8317","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-08-04T10:57:42Z","department":[{"_id":"HeEd"}],"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 one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability."}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.09917v3"}],"month":"02","intvolume":" 93","publication_identifier":{"issn":["09257721"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":93,"related_material":{"record":[{"relation":"shorter_version","status":"public","id":"6989"}]},"article_number":"101700","project":[{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"citation":{"chicago":"Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications. Elsevier, 2021. https://doi.org/10.1016/j.comgeo.2020.101700.","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. 2021. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 93, 101700.","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications, vol. 93, 101700, Elsevier, 2021, doi:10.1016/j.comgeo.2020.101700.","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, Computational Geometry: Theory and Applications 93 (2021).","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2020.101700","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 2021;93. doi:10.1016/j.comgeo.2020.101700"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","full_name":"Cheung, Kenneth C.","last_name":"Cheung"},{"first_name":"Erik D.","last_name":"Demaine","full_name":"Demaine, Erik D."},{"first_name":"Martin L.","last_name":"Demaine","full_name":"Demaine, Martin L."},{"full_name":"Fekete, Sándor P.","last_name":"Fekete","first_name":"Sándor P."},{"first_name":"Linda","last_name":"Kleist","full_name":"Kleist, Linda"},{"first_name":"Irina","full_name":"Kostitsyna, Irina","last_name":"Kostitsyna"},{"full_name":"Löffler, Maarten","last_name":"Löffler","first_name":"Maarten"},{"orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"last_name":"Schmidt","full_name":"Schmidt, Christiane","first_name":"Christiane"}],"article_processing_charge":"No","external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"title":"Folding polyominoes with holes into a cube","acknowledgement":"This research was performed in part at the 33rd Bellairs Winter Workshop on Computational Geometry. We thank all other participants for a fruitful atmosphere. H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","quality_controlled":"1","publisher":"Elsevier","oa":1,"isi":1,"year":"2021","day":"01","publication":"Computational Geometry: Theory and Applications","date_published":"2021-02-01T00:00:00Z","doi":"10.1016/j.comgeo.2020.101700","date_created":"2020-08-30T22:01:09Z"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.08286"}],"month":"01","intvolume":" 149","abstract":[{"text":"Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.","lang":"eng"}],"oa_version":"Preprint","volume":149,"issue":"1","ec_funded":1,"publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]},"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","status":"public","keyword":["Applied Mathematics","General Mathematics"],"_id":"8773","department":[{"_id":"HeEd"}],"date_updated":"2023-08-04T11:11:47Z","quality_controlled":"1","publisher":"American Mathematical Society","oa":1,"acknowledgement":"We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059.","page":"37-52","doi":"10.1090/proc/15205","date_published":"2021-01-01T00:00:00Z","date_created":"2020-11-19T10:17:40Z","isi":1,"year":"2021","day":"01","publication":"Proceedings of the American Mathematical Society","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"author":[{"first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","full_name":"Brown, Adam"},{"full_name":"Romanov, Anna","last_name":"Romanov","first_name":"Anna"}],"article_processing_charge":"No","external_id":{"arxiv":["1910.08286"],"isi":["000600416300004"]},"title":"Contravariant forms on Whittaker modules","citation":{"chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/proc/15205.","ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52.","mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205.","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings of the American Mathematical Society, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52.","ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205","apa":"Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15205"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"author":[{"first_name":"Georg","full_name":"Heiler, Georg","last_name":"Heiler"},{"first_name":"Tobias","full_name":"Reisch, Tobias","last_name":"Reisch"},{"first_name":"Jan","last_name":"Hurt","full_name":"Hurt, Jan"},{"first_name":"Mohammad","last_name":"Forghani","full_name":"Forghani, Mohammad"},{"full_name":"Omani, Aida","last_name":"Omani","first_name":"Aida"},{"first_name":"Allan","last_name":"Hanbury","full_name":"Hanbury, Allan"},{"id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","first_name":"Farid","full_name":"Karimipour, Farid","orcid":"0000-0001-6746-4174","last_name":"Karimipour"}],"article_processing_charge":"No","external_id":{"arxiv":["2008.10064"],"isi":["000662554703032"]},"title":"Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic","citation":{"ama":"Heiler G, Reisch T, Hurt J, et al. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In: 2020 IEEE International Conference on Big Data. IEEE; 2021:3123-3132. doi:10.1109/bigdata50022.2020.9378374","apa":"Heiler, G., Reisch, T., Hurt, J., Forghani, M., Omani, A., Hanbury, A., & Karimipour, F. (2021). Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In 2020 IEEE International Conference on Big Data (pp. 3123–3132). Atlanta, GA, United States: IEEE. https://doi.org/10.1109/bigdata50022.2020.9378374","ieee":"G. Heiler et al., “Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic,” in 2020 IEEE International Conference on Big Data, Atlanta, GA, United States, 2021, pp. 3123–3132.","short":"G. Heiler, T. Reisch, J. Hurt, M. Forghani, A. Omani, A. Hanbury, F. Karimipour, in:, 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–3132.","mla":"Heiler, Georg, et al. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–32, doi:10.1109/bigdata50022.2020.9378374.","ista":"Heiler G, Reisch T, Hurt J, Forghani M, Omani A, Hanbury A, Karimipour F. 2021. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. 2020 IEEE International Conference on Big Data. Big Data: International Conference on Big Data, 3123–3132.","chicago":"Heiler, Georg, Tobias Reisch, Jan Hurt, Mohammad Forghani, Aida Omani, Allan Hanbury, and Farid Karimipour. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” In 2020 IEEE International Conference on Big Data, 3123–32. IEEE, 2021. https://doi.org/10.1109/bigdata50022.2020.9378374."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","page":"3123-3132","doi":"10.1109/bigdata50022.2020.9378374","date_published":"2021-03-19T00:00:00Z","date_created":"2021-03-21T11:34:07Z","isi":1,"year":"2021","day":"19","publication":"2020 IEEE International Conference on Big Data","publisher":"IEEE","quality_controlled":"1","oa":1,"department":[{"_id":"HeEd"}],"date_updated":"2023-08-07T14:00:13Z","type":"conference","conference":{"name":"Big Data: International Conference on Big Data","start_date":"2020-12-10","end_date":"2020-12-13","location":"Atlanta, GA, United States"},"status":"public","_id":"9253","publication_identifier":{"isbn":["9781728162515"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2008.10064"}],"month":"03","abstract":[{"lang":"eng","text":"In March 2020, the Austrian government introduced a widespread lock-down in response to the COVID-19 pandemic. Based on subjective impressions and anecdotal evidence, Austrian public and private life came to a sudden halt. Here we assess the effect of the lock-down quantitatively for all regions in Austria and present an analysis of daily changes of human mobility throughout Austria using near-real-time anonymized mobile phone data. We describe an efficient data aggregation pipeline and analyze the mobility by quantifying mobile-phone traffic at specific point of interests (POIs), analyzing individual trajectories and investigating the cluster structure of the origin-destination graph. We found a reduction of commuters at Viennese metro stations of over 80% and the number of devices with a radius of gyration of less than 500 m almost doubled. The results of studying crowd-movement behavior highlight considerable changes in the structure of mobility networks, revealed by a higher modularity and an increase from 12 to 20 detected communities. We demonstrate the relevance of mobility data for epidemiological studies by showing a significant correlation of the outflow from the town of Ischgl (an early COVID-19 hotspot) and the reported COVID-19 cases with an 8-day time lag. This research indicates that mobile phone usage data permits the moment-by-moment quantification of mobility behavior for a whole country. We emphasize the need to improve the availability of such data in anonymized form to empower rapid response to combat COVID-19 and future pandemics."}],"oa_version":"Preprint"},{"page":"1296–1313","date_created":"2021-04-11T22:01:15Z","doi":"10.1007/s00454-021-00281-9","date_published":"2021-03-31T00:00:00Z","year":"2021","isi":1,"has_accepted_license":"1","publication":"Discrete and Computational Geometry","day":"31","oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha), and by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF)\r\nOpen Access funding provided by the Institute of Science and Technology (IST Austria).","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000635460400001"]},"author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F","last_name":"Osang"}],"title":"The multi-cover persistence of Euclidean balls","citation":{"apa":"Edelsbrunner, H., & Osang, G. F. (2021). The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00281-9","ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 2021;65:1296–1313. doi:10.1007/s00454-021-00281-9","short":"H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.","ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” Discrete and Computational Geometry, vol. 65. Springer Nature, pp. 1296–1313, 2021.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “The Multi-Cover Persistence of Euclidean Balls.” Discrete and Computational Geometry, vol. 65, Springer Nature, 2021, pp. 1296–1313, doi:10.1007/s00454-021-00281-9.","ista":"Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 65, 1296–1313.","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-021-00281-9."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"volume":65,"related_material":{"record":[{"status":"public","id":"187","relation":"earlier_version"}]},"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"59b4e1e827e494209bcb4aae22e1d347","file_id":"10394","creator":"cchlebak","file_size":677704,"date_updated":"2021-12-01T10:56:53Z","file_name":"2021_DisCompGeo_Edelsbrunner_Osang.pdf","date_created":"2021-12-01T10:56:53Z"}],"scopus_import":"1","intvolume":" 65","month":"03","abstract":[{"text":"Given a locally finite X⊆Rd and a radius r≥0, the k-fold cover of X and r consists of all points in Rd that have k or more points of X within distance r. We consider two filtrations—one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k—and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in Rd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.","lang":"eng"}],"oa_version":"Published Version","department":[{"_id":"HeEd"}],"file_date_updated":"2021-12-01T10:56:53Z","date_updated":"2023-08-07T14:35:44Z","ddc":["516"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","_id":"9317"},{"project":[{"name":"The Wittgenstein Prize","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"external_id":{"isi":["000702280800002"]},"article_processing_charge":"No","author":[{"last_name":"Pach","full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"first_name":"István","full_name":"Tomon, István","last_name":"Tomon"}],"title":"Erdős-Hajnal-type results for monotone paths","citation":{"ista":"Pach J, Tomon I. 2021. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. 151, 21–37.","chicago":"Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” Journal of Combinatorial Theory. Series B. Elsevier, 2021. https://doi.org/10.1016/j.jctb.2021.05.004.","apa":"Pach, J., & Tomon, I. (2021). Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. Elsevier. https://doi.org/10.1016/j.jctb.2021.05.004","ama":"Pach J, Tomon I. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory Series B. 2021;151:21-37. doi:10.1016/j.jctb.2021.05.004","ieee":"J. Pach and I. Tomon, “Erdős-Hajnal-type results for monotone paths,” Journal of Combinatorial Theory. Series B, vol. 151. Elsevier, pp. 21–37, 2021.","short":"J. Pach, I. Tomon, Journal of Combinatorial Theory. Series B 151 (2021) 21–37.","mla":"Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” Journal of Combinatorial Theory. Series B, vol. 151, Elsevier, 2021, pp. 21–37, doi:10.1016/j.jctb.2021.05.004."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"publisher":"Elsevier","quality_controlled":"1","acknowledgement":"We would like to thank the anonymous referees for their useful comments and suggestions. János Pach is partially supported by Austrian Science Fund (FWF) grant Z 342-N31 and by ERC Advanced grant “GeoScape.” István Tomon is partially supported by Swiss National Science Foundation grant no. 200021_196965, and thanks the support of MIPT Moscow. Both authors are partially supported by The Russian Government in the framework of MegaGrant no. 075-15-2019-1926.","page":"21-37","date_created":"2021-06-27T22:01:47Z","date_published":"2021-06-09T00:00:00Z","doi":"10.1016/j.jctb.2021.05.004","year":"2021","has_accepted_license":"1","isi":1,"publication":"Journal of Combinatorial Theory. Series B","day":"09","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","_id":"9602","department":[{"_id":"HeEd"}],"file_date_updated":"2021-06-28T13:33:23Z","date_updated":"2023-08-10T13:38:00Z","ddc":["510"],"scopus_import":"1","intvolume":" 151","month":"06","abstract":[{"text":"An ordered graph is a graph with a linear ordering on its vertex set. We prove that for every positive integer k, there exists a constant ck > 0 such that any ordered graph G on n vertices with the property that neither G nor its complement contains an induced monotone path of size k, has either a clique or an independent set of size at least n^ck . This strengthens a result of Bousquet, Lagoutte, and Thomassé, who proved the analogous result for unordered graphs.\r\nA key idea of the above paper was to show that any unordered graph on n vertices that does not contain an induced path of size k, and whose maximum degree is at most c(k)n for some small c(k) > 0, contains two disjoint linear size subsets with no edge between them. This approach fails for ordered graphs, because the analogous statement is false for k ≥ 3, by a construction of Fox. We provide some further examples showing that this statement also fails for ordered graphs avoiding other ordered trees.","lang":"eng"}],"oa_version":"Published Version","volume":151,"publication_status":"published","publication_identifier":{"issn":["0095-8956"]},"language":[{"iso":"eng"}],"file":[{"creator":"asandaue","file_size":418168,"date_updated":"2021-06-28T13:33:23Z","file_name":"2021_JournalOfCombinatorialTheory_Pach.pdf","date_created":"2021-06-28T13:33:23Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"9612","checksum":"15fbc9064cd9d1c777ac0043b78c8f12"}]},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","_id":"9821","file_date_updated":"2021-08-09T09:25:41Z","department":[{"_id":"HeEd"}],"date_updated":"2023-08-10T14:21:42Z","ddc":["006"],"scopus_import":"1","intvolume":" 16","month":"07","abstract":[{"lang":"eng","text":"Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent homology is a novel data analysis tool developed in the recent decades that is rooted at algebraic topology. The Topological Data Analysis (TDA) approach focuses on examining the shape of the data in terms of connectedness and holes, and has recently proved to be very effective in various fields of research. In this paper we propose the use of persistent homology to the hrv analysis. We recall selected topological descriptors used in the literature and we introduce some new topological descriptors that reflect the specificity of hrv, and we discuss their relation to the standard hrv measures. In particular, we show that this novel approach provides a collection of indices that might be at least as useful as the classical parameters in differentiating between series of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering from a stroke episode."}],"pmid":1,"oa_version":"Published Version","issue":"7","volume":16,"publication_status":"published","publication_identifier":{"eissn":["19326203"]},"language":[{"iso":"eng"}],"file":[{"date_updated":"2021-08-09T09:25:41Z","file_size":2706919,"creator":"asandaue","date_created":"2021-08-09T09:25:41Z","file_name":"2021_PLoSONE_Graff.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"9832","checksum":"0277aa155d5db1febd2cb384768bba5f","success":1}],"article_number":"e0253851","external_id":{"pmid":["34292957"],"isi":["000678124900050"]},"article_processing_charge":"Yes","author":[{"first_name":"Grzegorz","full_name":"Graff, Grzegorz","last_name":"Graff"},{"first_name":"Beata","last_name":"Graff","full_name":"Graff, Beata"},{"id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel","last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel"},{"last_name":"Jablonski","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz"},{"last_name":"Gąsecki","full_name":"Gąsecki, Dariusz","first_name":"Dariusz"},{"last_name":"Narkiewicz","full_name":"Narkiewicz, Krzysztof","first_name":"Krzysztof"}],"title":"Persistent homology as a new method of the assessment of heart rate variability","citation":{"mla":"Graff, Grzegorz, et al. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” PLoS ONE, vol. 16, no. 7, e0253851, Public Library of Science, 2021, doi:10.1371/journal.pone.0253851.","ieee":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, and K. Narkiewicz, “Persistent homology as a new method of the assessment of heart rate variability,” PLoS ONE, vol. 16, no. 7. Public Library of Science, 2021.","short":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, K. Narkiewicz, PLoS ONE 16 (2021).","ama":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 2021;16(7). doi:10.1371/journal.pone.0253851","apa":"Graff, G., Graff, B., Pilarczyk, P., Jablonski, G., Gąsecki, D., & Narkiewicz, K. (2021). Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. Public Library of Science. https://doi.org/10.1371/journal.pone.0253851","chicago":"Graff, Grzegorz, Beata Graff, Pawel Pilarczyk, Grzegorz Jablonski, Dariusz Gąsecki, and Krzysztof Narkiewicz. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” PLoS ONE. Public Library of Science, 2021. https://doi.org/10.1371/journal.pone.0253851.","ista":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. 2021. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 16(7), e0253851."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"Public Library of Science","acknowledgement":"We express our gratitude to the anonymous referees who provided constructive comments that helped us improve the quality of the paper.","date_created":"2021-08-08T22:01:28Z","doi":"10.1371/journal.pone.0253851","date_published":"2021-07-01T00:00:00Z","year":"2021","has_accepted_license":"1","isi":1,"publication":"PLoS ONE","day":"01"},{"file":[{"file_name":"2023_ExperimentalMath_Akopyan.pdf","date_created":"2023-08-14T11:55:10Z","creator":"dernst","file_size":1966019,"date_updated":"2023-08-14T11:55:10Z","success":1,"checksum":"3514382e3a1eb87fa6c61ad622874415","file_id":"14053","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1058-6458"],"eissn":["1944-950X"]},"publication_status":"published","ec_funded":1,"oa_version":"Published Version","abstract":[{"text":"Consider a random set of points on the unit sphere in ℝd, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the case d = 3, for which there are elementary proofs and fascinating formulas for metric properties. In particular, we study the fraction of acute facets, the expected intrinsic volumes, the total edge length, and the distance to a fixed point. Finally we generalize the results to the ellipsoid with homeoid density.","lang":"eng"}],"month":"10","scopus_import":"1","ddc":["510"],"date_updated":"2023-08-14T11:57:07Z","department":[{"_id":"HeEd"}],"file_date_updated":"2023-08-14T11:55:10Z","_id":"10222","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"25","publication":"Experimental Mathematics","has_accepted_license":"1","isi":1,"year":"2021","doi":"10.1080/10586458.2021.1980459","date_published":"2021-10-25T00:00:00Z","date_created":"2021-11-07T23:01:25Z","page":"1-15","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.\r\nWe are grateful to Dmitry Zaporozhets and Christoph Thäle for valuable comments and for directing us to relevant references. We also thank to Anton Mellit for a useful discussion on Bessel functions.","quality_controlled":"1","publisher":"Taylor and Francis","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Akopyan, Arseniy, Herbert Edelsbrunner, and Anton Nikitenko. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics. Taylor and Francis, 2021. https://doi.org/10.1080/10586458.2021.1980459.","ista":"Akopyan A, Edelsbrunner H, Nikitenko A. 2021. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics., 1–15.","mla":"Akopyan, Arseniy, et al. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics, Taylor and Francis, 2021, pp. 1–15, doi:10.1080/10586458.2021.1980459.","ama":"Akopyan A, Edelsbrunner H, Nikitenko A. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. 2021:1-15. doi:10.1080/10586458.2021.1980459","apa":"Akopyan, A., Edelsbrunner, H., & Nikitenko, A. (2021). The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. Taylor and Francis. https://doi.org/10.1080/10586458.2021.1980459","short":"A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15.","ieee":"A. Akopyan, H. Edelsbrunner, and A. Nikitenko, “The beauty of random polytopes inscribed in the 2-sphere,” Experimental Mathematics. Taylor and Francis, pp. 1–15, 2021."},"title":"The beauty of random polytopes inscribed in the 2-sphere","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","last_name":"Nikitenko","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000710893500001"],"arxiv":["2007.07783"]},"article_processing_charge":"Yes (via OA deal)","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Discretization in Geometry and Dynamics"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}]}]