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(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","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.","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.","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","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.","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.","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."},"publication":"37th International Symposium on Computational Geometry (SoCG 2021)","page":"32:1-32:16","date_published":"2021-06-02T00:00:00Z","article_processing_charge":"No","has_accepted_license":"1","day":"02","_id":"9345","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","intvolume":" 189","ddc":["004","516"],"title":"The density fingerprint of a periodic point set","status":"public","oa_version":"Published Version","file":[{"creator":"mwintrae","content_type":"application/pdf","file_size":3117435,"file_name":"df_socg_final_version.pdf","access_level":"open_access","date_created":"2021-04-22T08:08:14Z","date_updated":"2021-04-22T08:08:14Z","success":1,"checksum":"1787baef1523d6d93753b90d0c109a6d","file_id":"9346","relation":"main_file"}],"type":"conference","alternative_title":["LIPIcs"],"abstract":[{"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.","lang":"eng"}]},{"scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"02","citation":{"short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. 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Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16","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","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.","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."},"publication":"Leibniz International Proceedings in Informatics","date_published":"2021-06-02T00:00:00Z","type":"conference","alternative_title":["LIPIcs"],"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."}],"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","_id":"9604","intvolume":" 189","title":"Counting cells of order-k voronoi tessellations in ℝ3 with morse theory","status":"public","ddc":["516"],"oa_version":"Published Version","file":[{"file_id":"9611","relation":"main_file","date_updated":"2021-06-28T13:11:39Z","date_created":"2021-06-28T13:11:39Z","success":1,"checksum":"22b11a719018b22ecba2471b51f2eb40","file_name":"2021_LIPIcs_Biswas.pdf","access_level":"open_access","creator":"asandaue","content_type":"application/pdf","file_size":727817}],"publication_identifier":{"isbn":["9783959771849"],"issn":["18688969"]},"month":"06","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"}],"quality_controlled":"1","doi":"10.4230/LIPIcs.SoCG.2021.16","conference":{"name":"SoCG: International Symposium on Computational Geometry","start_date":"2021-06-07","location":"Online","end_date":"2021-06-11"},"language":[{"iso":"eng"}],"article_number":"16","ec_funded":1,"file_date_updated":"2021-06-28T13:11:39Z","year":"2021","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita"},{"full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","first_name":"Sebastiano"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"volume":189,"date_updated":"2023-02-23T14:02:28Z","date_created":"2021-06-27T22:01:48Z"},{"quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"conference":{"name":"DGMM: International Conference on Discrete Geometry and Mathematical Morphology","end_date":"2021-05-27","start_date":"2021-05-24","location":"Uppsala, Sweden"},"doi":"10.1007/978-3-030-76657-3_10","month":"05","publication_identifier":{"issn":["03029743"],"isbn":["9783030766566"],"eissn":["16113349"]},"publication_status":"published","department":[{"_id":"HeEd"}],"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).","year":"2021","date_created":"2021-08-08T22:01:29Z","date_updated":"2022-05-31T06:58:21Z","volume":12708,"author":[{"last_name":"Čomić","first_name":"Lidija","full_name":"Čomić, Lidija"},{"full_name":"Zrour, Rita","first_name":"Rita","last_name":"Zrour"},{"first_name":"Gaëlle","last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle"},{"first_name":"Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita"},{"full_name":"Andres, Eric","last_name":"Andres","first_name":"Eric"}],"ec_funded":1,"page":"152-163","publication":"Discrete Geometry and Mathematical Morphology","citation":{"short":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.","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.","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.","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","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.","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."},"date_published":"2021-05-16T00:00:00Z","scopus_import":"1","day":"16","article_processing_charge":"No","title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","status":"public","intvolume":" 12708","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9824","oa_version":"None","alternative_title":["LNCS"],"type":"conference","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"}]},{"project":[{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize"}],"quality_controlled":"1","isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/1910.09917v3","open_access":"1"}],"external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2020.101700","publication_identifier":{"issn":["09257721"]},"month":"02","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published","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.","year":"2021","volume":93,"date_updated":"2023-08-04T10:57:42Z","date_created":"2020-08-30T22:01:09Z","related_material":{"record":[{"status":"public","relation":"shorter_version","id":"6989"}]},"author":[{"full_name":"Aichholzer, Oswin","last_name":"Aichholzer","first_name":"Oswin"},{"last_name":"Akitaya","first_name":"Hugo A.","full_name":"Akitaya, Hugo A."},{"first_name":"Kenneth C.","last_name":"Cheung","full_name":"Cheung, Kenneth C."},{"first_name":"Erik D.","last_name":"Demaine","full_name":"Demaine, Erik D."},{"full_name":"Demaine, Martin L.","last_name":"Demaine","first_name":"Martin L."},{"full_name":"Fekete, Sándor P.","first_name":"Sándor P.","last_name":"Fekete"},{"first_name":"Linda","last_name":"Kleist","full_name":"Kleist, Linda"},{"last_name":"Kostitsyna","first_name":"Irina","full_name":"Kostitsyna, Irina"},{"first_name":"Maarten","last_name":"Löffler","full_name":"Löffler, Maarten"},{"full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana"},{"full_name":"Mundilova, Klara","last_name":"Mundilova","first_name":"Klara"},{"last_name":"Schmidt","first_name":"Christiane","full_name":"Schmidt, Christiane"}],"article_number":"101700","article_type":"original","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.","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).","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.","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","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.","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.","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"},"publication":"Computational Geometry: Theory and Applications","date_published":"2021-02-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","intvolume":" 93","status":"public","title":"Folding polyominoes with holes into a cube","_id":"8317","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","type":"journal_article","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."}]},{"_id":"8773","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 149","title":"Contravariant forms on Whittaker modules","status":"public","oa_version":"Preprint","type":"journal_article","issue":"1","abstract":[{"lang":"eng","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."}],"citation":{"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","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.","ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 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.","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."},"publication":"Proceedings of the American Mathematical Society","page":"37-52","article_type":"original","date_published":"2021-01-01T00:00:00Z","keyword":["Applied Mathematics","General Mathematics"],"article_processing_charge":"No","day":"01","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.","year":"2021","department":[{"_id":"HeEd"}],"publisher":"American Mathematical Society","publication_status":"published","author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","first_name":"Adam","full_name":"Brown, Adam"},{"full_name":"Romanov, Anna","first_name":"Anna","last_name":"Romanov"}],"volume":149,"date_created":"2020-11-19T10:17:40Z","date_updated":"2023-08-04T11:11:47Z","ec_funded":1,"main_file_link":[{"url":"https://arxiv.org/abs/1910.08286","open_access":"1"}],"external_id":{"arxiv":["1910.08286"],"isi":["000600416300004"]},"oa":1,"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"quality_controlled":"1","isi":1,"doi":"10.1090/proc/15205","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"month":"01"}]