{"date_published":"2021-06-02T00:00:00Z","language":[{"iso":"eng"}],"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","date_created":"2021-04-22T08:09:58Z","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","title":"The density fingerprint of a periodic point set","intvolume":"       189","conference":{"start_date":"2021-06-07","end_date":"2021-06-11","location":"Virtual","name":"SoCG: Symposium on Computational Geometry"},"quality_controlled":"1","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"}],"date_updated":"2023-02-23T13:55:40Z","ec_funded":1,"month":"06","publication_identifier":{"issn":["1868-8969"]},"year":"2021","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_version":"Published Version","oa":1,"file":[{"file_id":"9346","success":1,"content_type":"application/pdf","checksum":"1787baef1523d6d93753b90d0c109a6d","date_created":"2021-04-22T08:08:14Z","file_size":3117435,"creator":"mwintrae","relation":"main_file","date_updated":"2021-04-22T08:08:14Z","file_name":"df_socg_final_version.pdf","access_level":"open_access"}],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","first_name":"Teresa"},{"last_name":" Kurlin ","full_name":" Kurlin , Vitaliy","first_name":"Vitaliy"},{"last_name":"Smith","first_name":"Philip","full_name":"Smith, Philip"},{"last_name":"Wintraecken","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","full_name":"Wintraecken, Mathijs"}],"day":"02","article_processing_charge":"No","doi":"10.4230/LIPIcs.SoCG.2021.32","_id":"9345","file_date_updated":"2021-04-22T08:08:14Z","type":"conference","department":[{"_id":"HeEd"}],"ddc":["004","516"],"status":"public","has_accepted_license":"1","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"},{"call_identifier":"FWF","_id":"25C5A090-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","grant_number":"Z00312"},{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"publication":"37th International Symposium on Computational Geometry (SoCG 2021)","volume":189,"alternative_title":["LIPIcs"],"citation":{"apa":"Edelsbrunner, H., Heiss, T.,  Kurlin , V., Smith, P., &#38; Wintraecken, M. (2021). The density fingerprint of a periodic point set. In <i>37th International Symposium on Computational Geometry (SoCG 2021)</i> (Vol. 189, p. 32:1-32:16). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">https://doi.org/10.4230/LIPIcs.SoCG.2021.32</a>","chicago":"Edelsbrunner, Herbert, Teresa Heiss, Vitaliy  Kurlin , Philip Smith, and Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>, 189:32:1-32:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">https://doi.org/10.4230/LIPIcs.SoCG.2021.32</a>.","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 <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>, Virtual, 2021, vol. 189, p. 32:1-32:16.","mla":"Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>, vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">10.4230/LIPIcs.SoCG.2021.32</a>.","ama":"Edelsbrunner H, Heiss T,  Kurlin  V, Smith P, Wintraecken M. The density fingerprint of a periodic point set. In: <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">10.4230/LIPIcs.SoCG.2021.32</a>","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."},"page":"32:1-32:16","tmp":{"short":"CC BY (4.0)","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)"}}