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Discrete and Computational Geometry. 2020;64:571-574. doi:10.1007/s00454-020-00237-5"},"article_type":"letter_note","page":"571-574","date_published":"2020-10-01T00:00:00Z","type":"journal_article","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"8323","status":"public","title":"A farewell to Ricky Pollack","intvolume":" 64","oa_version":"None","month":"10","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-020-00237-5"}],"external_id":{"isi":["000561483500001"]},"oa":1,"isi":1,"doi":"10.1007/s00454-020-00237-5","language":[{"iso":"eng"}],"year":"2020","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"author":[{"full_name":"Pach, János","last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"}],"date_updated":"2023-08-22T09:05:04Z","date_created":"2020-08-30T22:01:12Z","volume":64},{"author":[{"full_name":"Graff, Grzegorz","first_name":"Grzegorz","last_name":"Graff"},{"last_name":"Graff","first_name":"Beata","full_name":"Graff, Beata"},{"first_name":"Grzegorz","last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz"},{"full_name":"Narkiewicz, Krzysztof","last_name":"Narkiewicz","first_name":"Krzysztof"}],"date_created":"2020-09-28T08:59:27Z","date_updated":"2023-08-22T09:33:34Z","oa_version":"None","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"8580","year":"2020","title":"The application of persistent homology in the analysis of heart rate variability","status":"public","publication_status":"published","publisher":"IEEE","department":[{"_id":"HeEd"}],"abstract":[{"text":"We evaluate the usefulness of persistent homology in the analysis of heart rate variability. In our approach we extract several topological descriptors characterising datasets of RR-intervals, which are later used in classical machine learning algorithms. By this method we are able to differentiate the group of patients with the history of transient ischemic attack and the group of hypertensive patients.","lang":"eng"}],"article_number":"9158054","type":"conference","conference":{"location":"Pisa, Italy","start_date":"2020-07-15","end_date":"2020-07-15","name":"ESGCO: European Study Group on Cardiovascular Oscillations"},"doi":"10.1109/ESGCO49734.2020.9158054","date_published":"2020-08-01T00:00:00Z","language":[{"iso":"eng"}],"publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ","external_id":{"isi":["000621172600045"]},"citation":{"ama":"Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent homology in the analysis of heart rate variability. In: 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE; 2020. doi:10.1109/ESGCO49734.2020.9158054","ista":"Graff G, Graff B, Jablonski G, Narkiewicz K. 2020. The application of persistent homology in the analysis of heart rate variability. 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . ESGCO: European Study Group on Cardiovascular Oscillations, 9158054.","ieee":"G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of persistent homology in the analysis of heart rate variability,” in 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , Pisa, Italy, 2020.","apa":"Graff, G., Graff, B., Jablonski, G., & Narkiewicz, K. (2020). The application of persistent homology in the analysis of heart rate variability. In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . Pisa, Italy: IEEE. https://doi.org/10.1109/ESGCO49734.2020.9158054","mla":"Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , 9158054, IEEE, 2020, doi:10.1109/ESGCO49734.2020.9158054.","short":"G. Graff, B. Graff, G. Jablonski, K. Narkiewicz, in:, 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , IEEE, 2020.","chicago":"Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE, 2020. https://doi.org/10.1109/ESGCO49734.2020.9158054."},"quality_controlled":"1","isi":1,"day":"01","month":"08","publication_identifier":{"isbn":["9781728157511"]},"article_processing_charge":"No","scopus_import":"1"},{"intvolume":" 2020","status":"public","title":"Waist of balls in hyperbolic and spherical spaces","_id":"10867","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","type":"journal_article","issue":"3","abstract":[{"lang":"eng","text":"In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces."}],"page":"669-697","article_type":"original","citation":{"short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rny037.","ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” International Mathematics Research Notices, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020.","apa":"Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rny037","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697."},"publication":"International Mathematics Research Notices","date_published":"2020-02-01T00:00:00Z","keyword":["General Mathematics"],"scopus_import":"1","article_processing_charge":"No","day":"01","publisher":"Oxford University Press","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2020","acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","volume":2020,"date_created":"2022-03-18T11:39:30Z","date_updated":"2023-08-24T14:19:55Z","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"isi":1,"quality_controlled":"1","external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1702.07513","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1093/imrn/rny037","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"month":"02"},{"date_published":"2020-02-10T00:00:00Z","page":"155","citation":{"chicago":"Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460.","mla":"Ölsböck, Katharina. The Hole System of Triangulated Shapes. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7460.","short":"K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science and Technology Austria, 2020.","ista":"Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria.","ieee":"K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science and Technology Austria, 2020.","apa":"Ölsböck, K. (2020). The hole system of triangulated shapes. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7460","ama":"Ölsböck K. The hole system of triangulated shapes. 2020. doi:10.15479/AT:ISTA:7460"},"day":"10","article_processing_charge":"No","has_accepted_license":"1","keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"],"oa_version":"Published Version","file":[{"file_id":"7461","relation":"main_file","checksum":"1df9f8c530b443c0e63a3f2e4fde412e","date_updated":"2020-07-14T12:47:58Z","date_created":"2020-02-06T14:43:54Z","access_level":"open_access","file_name":"thesis_ist-final_noack.pdf","creator":"koelsboe","content_type":"application/pdf","file_size":76195184},{"relation":"source_file","file_id":"7462","checksum":"7a52383c812b0be64d3826546509e5a4","date_created":"2020-02-06T14:52:45Z","date_updated":"2020-07-14T12:47:58Z","access_level":"closed","description":"latex source files, figures","file_name":"latex-files.zip","file_size":122103715,"content_type":"application/x-zip-compressed","creator":"koelsboe"}],"status":"public","ddc":["514"],"title":"The hole system of triangulated shapes","_id":"7460","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","abstract":[{"text":"Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications.\r\n\r\nFor the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries.","lang":"eng"}],"alternative_title":["ISTA Thesis"],"type":"dissertation","degree_awarded":"PhD","supervisor":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"language":[{"iso":"eng"}],"doi":"10.15479/AT:ISTA:7460","oa":1,"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"month":"02","publication_identifier":{"issn":["2663-337X"]},"date_created":"2020-02-06T14:56:53Z","date_updated":"2023-09-07T13:15:30Z","author":[{"orcid":"0000-0002-4672-8297","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","last_name":"Ölsböck","first_name":"Katharina","full_name":"Ölsböck, Katharina"}],"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"6608"}]},"publication_status":"published","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"publisher":"Institute of Science and Technology Austria","year":"2020","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","file_date_updated":"2020-07-14T12:47:58Z"},{"date_published":"2020-06-09T00:00:00Z","page":"160","citation":{"ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944","ieee":"Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020.","apa":"Masárová, Z. (2020). Reconfiguration problems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7944","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria.","short":"Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020.","mla":"Masárová, Zuzana. Reconfiguration Problems. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7944.","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944."},"article_processing_charge":"No","has_accepted_license":"1","day":"09","keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"oa_version":"Published Version","file":[{"checksum":"df688bc5a82b50baee0b99d25fc7b7f0","date_updated":"2020-07-14T12:48:05Z","date_created":"2020-06-08T00:34:00Z","relation":"main_file","file_id":"7945","file_size":13661779,"content_type":"application/pdf","creator":"zmasarov","access_level":"open_access","file_name":"THESIS_Zuzka_Masarova.pdf"},{"creator":"zmasarov","content_type":"application/zip","file_size":32184006,"file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","access_level":"closed","date_updated":"2020-07-14T12:48:05Z","date_created":"2020-06-08T00:35:30Z","checksum":"45341a35b8f5529c74010b7af43ac188","file_id":"7946","relation":"source_file"}],"status":"public","title":"Reconfiguration problems","ddc":["516","514"],"_id":"7944","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","abstract":[{"lang":"eng","text":"This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars."}],"alternative_title":["ISTA Thesis"],"type":"dissertation","language":[{"iso":"eng"}],"supervisor":[{"full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"}],"degree_awarded":"PhD","doi":"10.15479/AT:ISTA:7944","oa":1,"tmp":{"short":"CC BY-SA (4.0)","image":"/images/cc_by_sa.png","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode"},"publication_identifier":{"isbn":["978-3-99078-005-3"],"issn":["2663-337X"]},"month":"06","date_created":"2020-06-08T00:49:46Z","date_updated":"2023-09-07T13:17:37Z","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"7950"},{"relation":"part_of_dissertation","status":"public","id":"5986"}]},"author":[{"full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana"}],"department":[{"_id":"HeEd"},{"_id":"UlWa"}],"publisher":"Institute of Science and Technology Austria","publication_status":"published","year":"2020","license":"https://creativecommons.org/licenses/by-sa/4.0/","file_date_updated":"2020-07-14T12:48:05Z"},{"month":"08","publication_identifier":{"issn":["18688969"],"isbn":["9783959771627"]},"language":[{"iso":"eng"}],"conference":{"name":"ESA: Annual European Symposium on Algorithms","location":"Virtual, Online; Pisa, Italy","start_date":"2020-09-07","end_date":"2020-09-09"},"doi":"10.4230/LIPIcs.ESA.2020.75","quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"}],"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","short":"CC BY (3.0)","image":"/images/cc_by.png"},"license":"https://creativecommons.org/licenses/by/3.0/","file_date_updated":"2020-10-27T14:31:52Z","ec_funded":1,"article_number":"75","date_created":"2020-10-25T23:01:18Z","date_updated":"2023-09-07T13:29:00Z","volume":173,"author":[{"full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","first_name":"Georg F","last_name":"Osang"},{"full_name":"Rouxel-Labbé, Mael","first_name":"Mael","last_name":"Rouxel-Labbé"},{"last_name":"Teillaud","first_name":"Monique","full_name":"Teillaud, Monique"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"9056"}]},"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2020","day":"26","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","date_published":"2020-08-26T00:00:00Z","publication":"28th Annual European Symposium on Algorithms","citation":{"ama":"Osang GF, Rouxel-Labbé M, Teillaud M. Generalizing CGAL periodic Delaunay triangulations. In: 28th Annual European Symposium on Algorithms. Vol 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.ESA.2020.75","apa":"Osang, G. F., Rouxel-Labbé, M., & Teillaud, M. (2020). Generalizing CGAL periodic Delaunay triangulations. In 28th Annual European Symposium on Algorithms (Vol. 173). Virtual, Online; Pisa, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2020.75","ieee":"G. F. Osang, M. Rouxel-Labbé, and M. Teillaud, “Generalizing CGAL periodic Delaunay triangulations,” in 28th Annual European Symposium on Algorithms, Virtual, Online; Pisa, Italy, 2020, vol. 173.","ista":"Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay triangulations. 28th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 173, 75.","short":"G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","mla":"Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.” 28th Annual European Symposium on Algorithms, vol. 173, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.ESA.2020.75.","chicago":"Osang, Georg F, Mael Rouxel-Labbé, and Monique Teillaud. “Generalizing CGAL Periodic Delaunay Triangulations.” In 28th Annual European Symposium on Algorithms, Vol. 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.ESA.2020.75."},"abstract":[{"text":"Even though Delaunay originally introduced his famous triangulations in the case of infinite point sets with translational periodicity, a software that computes such triangulations in the general case is not yet available, to the best of our knowledge. Combining and generalizing previous work, we present a practical algorithm for computing such triangulations. The algorithm has been implemented and experiments show that its performance is as good as the one of the CGAL package, which is restricted to cubic periodicity. ","lang":"eng"}],"alternative_title":["LIPIcs"],"type":"conference","file":[{"content_type":"application/pdf","file_size":733291,"creator":"cziletti","file_name":"2020_LIPIcs_Osang.pdf","access_level":"open_access","date_updated":"2020-10-27T14:31:52Z","date_created":"2020-10-27T14:31:52Z","checksum":"fe0f7c49a99ed870c671b911e10d5496","success":1,"relation":"main_file","file_id":"8712"}],"oa_version":"Published Version","ddc":["000"],"status":"public","title":"Generalizing CGAL periodic Delaunay triangulations","intvolume":" 173","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8703"},{"month":"07","publication_identifier":{"eissn":["1588-2896"],"issn":["0081-6906"]},"doi":"10.1556/012.2020.57.2.1454","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)"},"external_id":{"isi":["000570978400005"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize"}],"file_date_updated":"2020-07-24T07:09:06Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc/4.0/","author":[{"last_name":"Vegter","first_name":"Gert","full_name":"Vegter, Gert"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2020-07-24T07:09:18Z","date_updated":"2023-10-10T13:05:27Z","volume":57,"year":"2020","acknowledgement":"The authors are greatly indebted to Dror Atariah, Günther Rote and John Sullivan for discussion and suggestions. The authors also thank Jean-Daniel Boissonnat, Ramsay Dyer, David de Laat and Rien van de Weijgaert for discussion. This work has been supported in part by the European Union’s Seventh Framework Programme for Research of the\r\nEuropean Commission, under FET-Open grant number 255827 (CGL Computational Geometry Learning) and ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions), the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement number 754411,and the Austrian Science Fund (FWF): Z00342 N31.","publication_status":"published","publisher":"Akadémiai Kiadó","department":[{"_id":"HeEd"}],"day":"24","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","date_published":"2020-07-24T00:00:00Z","publication":"Studia Scientiarum Mathematicarum Hungarica","citation":{"ieee":"G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes,” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020.","apa":"Vegter, G., & Wintraecken, M. (2020). Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó. https://doi.org/10.1556/012.2020.57.2.1454","ista":"Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2), 193–199.","ama":"Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 2020;57(2):193-199. doi:10.1556/012.2020.57.2.1454","chicago":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó, 2020. https://doi.org/10.1556/012.2020.57.2.1454.","short":"G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199.","mla":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:10.1556/012.2020.57.2.1454."},"article_type":"original","page":"193-199","abstract":[{"lang":"eng","text":"Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces."}],"issue":"2","type":"journal_article","oa_version":"Published Version","file":[{"date_created":"2020-07-24T07:09:06Z","date_updated":"2020-07-24T07:09:06Z","relation":"main_file","file_id":"8164","file_size":1476072,"content_type":"application/pdf","creator":"mwintrae","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","access_level":"open_access"}],"_id":"8163","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","status":"public","ddc":["510"],"intvolume":" 57"},{"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"De Gruyter","year":"2020","acknowledgement":"The authors of this paper thank Roland Roth for suggesting the analysis of the weighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations and for his continued encouragement. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis 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). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","date_updated":"2023-10-17T12:34:51Z","date_created":"2021-02-17T15:13:01Z","volume":8,"author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"}],"file_date_updated":"2021-02-19T13:56:24Z","ec_funded":1,"quality_controlled":"1","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"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"},"language":[{"iso":"eng"}],"doi":"10.1515/cmb-2020-0100","month":"06","publication_identifier":{"issn":["2544-7297"]},"title":"The weighted mean curvature derivative of a space-filling diagram","status":"public","ddc":["510"],"intvolume":" 8","_id":"9157","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"file_name":"2020_CompMathBiophysics_Akopyan2.pdf","access_level":"open_access","file_size":562359,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"9171","date_updated":"2021-02-19T13:56:24Z","date_created":"2021-02-19T13:56:24Z","checksum":"cea41de9937d07a3b927d71ee8b4e432","success":1}],"type":"journal_article","abstract":[{"lang":"eng","text":"Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy."}],"issue":"1","article_type":"original","page":"51-67","publication":"Computational and Mathematical Biophysics","citation":{"short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:10.1515/cmb-2020-0100.","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0100.","ama":"Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):51-67. doi:10.1515/cmb-2020-0100","apa":"Akopyan, A., & Edelsbrunner, H. (2020). The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0100","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 51–67, 2020.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67."},"date_published":"2020-06-20T00:00:00Z","day":"20","has_accepted_license":"1","article_processing_charge":"No"},{"publisher":"De Gruyter","department":[{"_id":"HeEd"}],"publication_status":"published","acknowledgement":"The authors of this paper thank Roland Roth for suggesting the analysis of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis 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). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","year":"2020","volume":8,"date_updated":"2023-10-17T12:35:10Z","date_created":"2021-02-17T15:12:44Z","author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"ec_funded":1,"file_date_updated":"2021-02-19T13:33:19Z","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"quality_controlled":"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"},"external_id":{"arxiv":["1908.06777"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1515/cmb-2020-0101","publication_identifier":{"issn":["2544-7297"]},"month":"07","intvolume":" 8","status":"public","ddc":["510"],"title":"The weighted Gaussian curvature derivative of a space-filling diagram","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9156","oa_version":"Published Version","file":[{"file_id":"9170","relation":"main_file","success":1,"checksum":"ca43a7440834eab6bbea29c59b56ef3a","date_created":"2021-02-19T13:33:19Z","date_updated":"2021-02-19T13:33:19Z","access_level":"open_access","file_name":"2020_CompMathBiophysics_Akopyan.pdf","creator":"dernst","file_size":707452,"content_type":"application/pdf"}],"type":"journal_article","issue":"1","abstract":[{"text":"The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.","lang":"eng"}],"page":"74-88","article_type":"original","citation":{"chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.","apa":"Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0101","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.","ama":"Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88. doi:10.1515/cmb-2020-0101"},"publication":"Computational and Mathematical Biophysics","date_published":"2020-07-21T00:00:00Z","article_processing_charge":"No","has_accepted_license":"1","day":"21"},{"day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","scopus_import":"1","date_published":"2020-12-01T00:00:00Z","article_type":"original","page":"455-480","publication":"Journal of Applied and Computational Topology","citation":{"ista":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 4(4), 455–480.","ieee":"U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient flow and homology inference for self-maps,” Journal of Applied and Computational Topology, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.","apa":"Bauer, U., Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2020). Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00058-8","ama":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 2020;4(4):455-480. doi:10.1007/s41468-020-00058-8","chicago":"Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology. Springer Nature, 2020. https://doi.org/10.1007/s41468-020-00058-8.","mla":"Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:10.1007/s41468-020-00058-8.","short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480."},"abstract":[{"lang":"eng","text":"We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems."}],"issue":"4","type":"journal_article","oa_version":"Published Version","file":[{"file_size":851190,"content_type":"application/pdf","creator":"dernst","file_name":"2020_JourApplCompTopology_Bauer.pdf","access_level":"open_access","date_updated":"2024-03-04T10:52:42Z","date_created":"2024-03-04T10:52:42Z","checksum":"eed1168b6e66cd55272c19bb7fca8a1c","success":1,"relation":"main_file","file_id":"15065"}],"title":"Čech-Delaunay gradient flow and homology inference for self-maps","status":"public","ddc":["500"],"intvolume":" 4","_id":"15064","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"12","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"language":[{"iso":"eng"}],"doi":"10.1007/s41468-020-00058-8","quality_controlled":"1","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"},"file_date_updated":"2024-03-04T10:52:42Z","date_updated":"2024-03-04T10:54:04Z","date_created":"2024-03-04T10:47:49Z","volume":4,"author":[{"last_name":"Bauer","first_name":"U.","full_name":"Bauer, U."},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","last_name":"Jablonski","first_name":"Grzegorz","full_name":"Jablonski, Grzegorz"},{"first_name":"M.","last_name":"Mrozek","full_name":"Mrozek, M."}],"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"year":"2020","acknowledgement":"This research has been supported by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding provided by Projekt DEAL."},{"year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Carleton University","author":[{"full_name":"Dyer, Ramsay","first_name":"Ramsay","last_name":"Dyer"},{"full_name":"Vegter, Gert","first_name":"Gert","last_name":"Vegter"},{"last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs"}],"date_updated":"2021-01-12T08:07:50Z","date_created":"2019-06-03T09:35:33Z","volume":10,"file_date_updated":"2020-07-14T12:47:32Z","ec_funded":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"},"oa":1,"quality_controlled":"1","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"doi":"10.20382/jocg.v10i1a9","language":[{"iso":"eng"}],"month":"07","publication_identifier":{"issn":["1920-180X"]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"6515","ddc":["510"],"status":"public","title":"Simplices modelled on spaces of constant curvature","intvolume":" 10","file":[{"creator":"mwintrae","file_size":2170882,"content_type":"application/pdf","access_level":"open_access","file_name":"mainJournalFinal.pdf","checksum":"57b4df2f16a74eb499734ec8ee240178","date_created":"2019-06-03T09:30:01Z","date_updated":"2020-07-14T12:47:32Z","file_id":"6516","relation":"main_file"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"lang":"eng","text":"We give non-degeneracy criteria for Riemannian simplices based on simplices in spaces of constant sectional curvature. It extends previous work on Riemannian simplices, where we developed Riemannian simplices with respect to Euclidean reference simplices. The criteria we give in this article are in terms of quality measures for spaces of constant curvature that we develop here. We see that simplices in spaces that have nearly constant curvature, are already non-degenerate under very weak quality demands. This is of importance because it allows for sampling of Riemannian manifolds based on anisotropy of the manifold and not (absolute) curvature."}],"issue":"1","publication":"Journal of Computational Geometry ","citation":{"mla":"Dyer, Ramsay, et al. “Simplices Modelled on Spaces of Constant Curvature.” Journal of Computational Geometry , vol. 10, no. 1, Carleton University, 2019, pp. 223–256, doi:10.20382/jocg.v10i1a9.","short":"R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10 (2019) 223–256.","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.","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","ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","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","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."},"page":"223–256","date_published":"2019-07-01T00:00:00Z","scopus_import":1,"day":"01","has_accepted_license":"1"},{"oa_version":"Submitted Version","file":[{"date_created":"2019-07-12T08:32:46Z","date_updated":"2020-07-14T12:47:34Z","checksum":"ceabd152cfa55170d57763f9c6c60a53","file_id":"6629","relation":"main_file","creator":"mwintrae","content_type":"application/pdf","file_size":321176,"file_name":"IntrinsicExtrinsicCCCG2019.pdf","access_level":"open_access"}],"date_created":"2019-07-12T08:34:57Z","date_updated":"2021-01-12T08:08:16Z","author":[{"last_name":"Vegter","first_name":"Gert","full_name":"Vegter, Gert"},{"full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"department":[{"_id":"HeEd"}],"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","ddc":["004"],"publication_status":"published","status":"public","year":"2019","_id":"6628","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"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"}],"file_date_updated":"2020-07-14T12:47:34Z","type":"conference","language":[{"iso":"eng"}],"date_published":"2019-08-01T00:00:00Z","conference":{"end_date":"2019-08-10","location":"Edmonton, Canada","start_date":"2019-08-08","name":"CCCG: Canadian Conference in Computational Geometry"},"page":"275-279","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"quality_controlled":"1","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.","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.","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.","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.","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.","mla":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–79.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279."},"oa":1,"publication":"The 31st Canadian Conference in Computational Geometry","has_accepted_license":"1","month":"08","day":"01","scopus_import":1},{"day":"01","has_accepted_license":"1","scopus_import":1,"date_published":"2019-06-01T00:00:00Z","publication":"35th International Symposium on Computational Geometry","citation":{"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.","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.","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.","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","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","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."},"page":"31:1-31:14","abstract":[{"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.","lang":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2019_LIPICS_Edelsbrunner.pdf","creator":"dernst","content_type":"application/pdf","file_size":1355179,"file_id":"6666","relation":"main_file","checksum":"8ec8720730d4c789bf7b06540f1c29f4","date_created":"2019-07-24T06:40:01Z","date_updated":"2020-07-14T12:47:35Z"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"6648","ddc":["510"],"status":"public","title":"Topological data analysis in information space","intvolume":" 129","month":"06","publication_identifier":{"isbn":["9783959771047"]},"conference":{"location":"Portland, OR, United States","start_date":"2019-06-18","end_date":"2019-06-21","name":"SoCG 2019: Symposium on Computational Geometry"},"doi":"10.4230/LIPICS.SOCG.2019.31","language":[{"iso":"eng"}],"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"},"external_id":{"arxiv":["1903.08510"]},"oa":1,"quality_controlled":"1","project":[{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"file_date_updated":"2020-07-14T12:47:35Z","author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Hubert"}],"date_updated":"2021-01-12T08:08:23Z","date_created":"2019-07-17T10:36:09Z","volume":129,"year":"2019","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}]},{"language":[{"iso":"eng"}],"conference":{"end_date":"2019-08-10","start_date":"2019-08-08","location":"Edmonton, Canada","name":"CCCG: Canadian Conference in Computational Geometry"},"date_published":"2019-08-01T00:00:00Z","quality_controlled":"1","page":"164-170","publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","external_id":{"arxiv":["1910.09917"]},"main_file_link":[{"url":"https://cccg.ca/proceedings/2019/proceedings.pdf","open_access":"1"}],"citation":{"ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. In: Proceedings of the 31st Canadian Conference on Computational Geometry. Canadian Conference on Computational Geometry; 2019:164-170.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a cube. In Proceedings of the 31st Canadian Conference on Computational Geometry (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” in Proceedings of the 31st Canadian Conference on Computational Geometry, Edmonton, Canada, 2019, pp. 164–170.","ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference on Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 164–170.","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.","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.","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."},"oa":1,"day":"01","month":"08","article_processing_charge":"No","scopus_import":"1","date_created":"2019-11-04T16:46:11Z","date_updated":"2023-08-04T10:57:42Z","oa_version":"Published Version","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"full_name":"Akitaya, Hugo A","first_name":"Hugo A","last_name":"Akitaya"},{"full_name":"Cheung, Kenneth C","first_name":"Kenneth C","last_name":"Cheung"},{"full_name":"Demaine, Erik D","last_name":"Demaine","first_name":"Erik D"},{"full_name":"Demaine, Martin L","first_name":"Martin L","last_name":"Demaine"},{"last_name":"Fekete","first_name":"Sandor P","full_name":"Fekete, Sandor P"},{"full_name":"Kleist, Linda","last_name":"Kleist","first_name":"Linda"},{"full_name":"Kostitsyna, Irina","first_name":"Irina","last_name":"Kostitsyna"},{"last_name":"Löffler","first_name":"Maarten","full_name":"Löffler, Maarten"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","first_name":"Zuzana","last_name":"Masárová","full_name":"Masárová, Zuzana"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"last_name":"Schmidt","first_name":"Christiane","full_name":"Schmidt, Christiane"}],"related_material":{"record":[{"relation":"extended_version","status":"public","id":"8317"}]},"status":"public","title":"Folding polyominoes with holes into a cube","publication_status":"published","publisher":"Canadian Conference on Computational Geometry","department":[{"_id":"HeEd"}],"year":"2019","_id":"6989","acknowledgement":"This research was performed in part at the 33rd BellairsWinter Workshop on Computational Geometry. Wethank all other participants for a fruitful atmosphere.","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","abstract":[{"lang":"eng","text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability. "}],"type":"conference"},{"type":"journal_article","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."}],"issue":"1-2","status":"public","title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","ddc":["000"],"intvolume":" 3","_id":"6671","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_id":"6741","relation":"main_file","date_updated":"2020-07-14T12:47:36Z","date_created":"2019-07-31T08:09:56Z","checksum":"a5b244db9f751221409cf09c97ee0935","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":2215157}],"oa_version":"Published Version","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","article_type":"original","page":"29–58","publication":"Journal of Applied and Computational Topology","citation":{"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","ista":"Boissonnat J-D, Lieutier A, Wintraecken M. 2019. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. 3(1–2), 29–58.","ama":"Boissonnat J-D, Lieutier A, Wintraecken M. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. 2019;3(1-2):29–58. doi:10.1007/s41468-019-00029-8","chicago":"Boissonnat, Jean-Daniel, André Lieutier, and Mathijs Wintraecken. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” Journal of Applied and Computational Topology. Springer Nature, 2019. https://doi.org/10.1007/s41468-019-00029-8.","short":"J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58.","mla":"Boissonnat, Jean-Daniel, et al. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” Journal of Applied and Computational Topology, vol. 3, no. 1–2, Springer Nature, 2019, pp. 29–58, doi:10.1007/s41468-019-00029-8."},"date_published":"2019-06-01T00:00:00Z","file_date_updated":"2020-07-14T12:47:36Z","ec_funded":1,"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"year":"2019","date_created":"2019-07-24T08:37:29Z","date_updated":"2023-08-22T12:37:47Z","volume":3,"author":[{"full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel","last_name":"Boissonnat"},{"last_name":"Lieutier","first_name":"André","full_name":"Lieutier, André"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs"}],"month":"06","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"quality_controlled":"1","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"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"},"language":[{"iso":"eng"}],"doi":"10.1007/s41468-019-00029-8"},{"doi":"10.1090/proc/14240","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1709.02562","open_access":"1"}],"oa":1,"external_id":{"arxiv":["1709.02562"],"isi":["000450363900008"]},"isi":1,"quality_controlled":"1","month":"01","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"},{"first_name":"Roman","last_name":"Fedorov","full_name":"Fedorov, Roman"}],"volume":147,"date_created":"2019-02-24T22:59:19Z","date_updated":"2023-08-24T14:48:59Z","year":"2019","publisher":"AMS","department":[{"_id":"HeEd"}],"publication_status":"published","date_published":"2019-01-01T00:00:00Z","citation":{"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","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.","ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","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","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.","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102.","mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society, vol. 147, AMS, 2019, pp. 91–102, doi:10.1090/proc/14240."},"publication":"Proceedings of the American Mathematical Society","page":"91-102","article_processing_charge":"No","day":"01","scopus_import":"1","oa_version":"Preprint","_id":"6050","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 147","status":"public","title":"Two circles and only a straightedge","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"}],"type":"journal_article"},{"ec_funded":1,"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"first_name":"Alfredo","last_name":"Hubard","full_name":"Hubard, Alfredo"},{"first_name":"Roman","last_name":"Karasev","full_name":"Karasev, Roman"}],"volume":53,"date_updated":"2023-08-29T06:32:48Z","date_created":"2019-07-14T21:59:19Z","year":"2019","publisher":"Akademicka Platforma Czasopism","department":[{"_id":"HeEd"}],"publication_status":"published","month":"06","doi":"10.12775/TMNA.2019.008","language":[{"iso":"eng"}],"oa":1,"external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.06926"}],"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"quality_controlled":"1","isi":1,"issue":"2","abstract":[{"lang":"eng","text":"In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure."}],"type":"journal_article","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6634","intvolume":" 53","status":"public","title":"Lower and upper bounds for the waists of different spaces","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2019-06-01T00:00:00Z","citation":{"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","ieee":"A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.","ista":"Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.","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","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.","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."},"publication":"Topological Methods in Nonlinear Analysis","page":"457-490"},{"citation":{"mla":"Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627, A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916.","short":"P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).","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.","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","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.","ieee":"P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 2019.","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"},"publication":"Astronomy and Astrophysics","article_type":"original","date_published":"2019-07-17T00:00:00Z","scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"17","_id":"6756","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 627","ddc":["520","530"],"status":"public","title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","oa_version":"Published Version","file":[{"date_updated":"2020-07-14T12:47:39Z","date_created":"2019-08-05T08:08:59Z","checksum":"83b9209ed9eefbdcefd89019c5a97805","file_id":"6766","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":14420451,"file_name":"2019_AstronomyAstrophysics_Pranav.pdf","access_level":"open_access"}],"type":"journal_article","abstract":[{"lang":"eng","text":"We study the topology generated by the temperature fluctuations of the cosmic microwave background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over 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."}],"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"},"external_id":{"arxiv":["1812.07678"],"isi":["000475839300003"]},"project":[{"_id":"265683E4-B435-11E9-9278-68D0E5697425","grant_number":"M62909-18-1-2038","name":"Toward Computational Information Topology"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"quality_controlled":"1","isi":1,"doi":"10.1051/0004-6361/201834916","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["14320746"],"issn":["00046361"]},"month":"07","year":"2019","publisher":"EDP Sciences","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"first_name":"Pratyush","last_name":"Pranav","full_name":"Pranav, Pratyush"},{"last_name":"Adler","first_name":"Robert J.","full_name":"Adler, Robert J."},{"full_name":"Buchert, Thomas","first_name":"Thomas","last_name":"Buchert"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Jones, Bernard J.T.","first_name":"Bernard J.T.","last_name":"Jones"},{"full_name":"Schwartzman, Armin","first_name":"Armin","last_name":"Schwartzman"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Hubert"},{"full_name":"Van De Weygaert, Rien","last_name":"Van De Weygaert","first_name":"Rien"}],"volume":627,"date_created":"2019-08-04T21:59:18Z","date_updated":"2023-08-29T07:01:48Z","article_number":"A163","file_date_updated":"2020-07-14T12:47:39Z"},{"article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2019-10-01T00:00:00Z","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.","short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 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.","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.","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","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.","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"},"publication":"Bulletin of the London Mathematical Society","page":"765-775","article_type":"original","issue":"5","abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","_id":"6793","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 51","status":"public","title":"The Regge symmetry, confocal conics, and the Schläfli formula","publication_identifier":{"eissn":["14692120"],"issn":["00246093"]},"month":"10","doi":"10.1112/blms.12276","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1903.04929","open_access":"1"}],"external_id":{"arxiv":["1903.04929"],"isi":["000478560200001"]},"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"}],"isi":1,"quality_controlled":"1","ec_funded":1,"author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"first_name":"Ivan","last_name":"Izmestiev","full_name":"Izmestiev, Ivan"}],"volume":51,"date_updated":"2023-08-29T07:08:34Z","date_created":"2019-08-11T21:59:23Z","year":"2019","department":[{"_id":"HeEd"}],"publisher":"London Mathematical Society","publication_status":"published"},{"language":[{"iso":"eng"}],"doi":"10.1016/j.jalgebra.2019.07.027","quality_controlled":"1","isi":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.04676"}],"external_id":{"isi":["000487176300011"],"arxiv":["1805.04676"]},"oa":1,"publication_identifier":{"issn":["0021-8693"]},"month":"11","volume":538,"date_created":"2019-08-22T07:54:13Z","date_updated":"2023-08-29T07:11:47Z","author":[{"first_name":"Adam","last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425","full_name":"Brown, Adam"}],"department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","year":"2019","date_published":"2019-11-15T00:00:00Z","page":"261-289","article_type":"original","citation":{"short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","mla":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027.","chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/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","ieee":"A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra, vol. 538. Elsevier, pp. 261–289, 2019.","apa":"Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. Elsevier. 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."},"publication":"Journal of Algebra","article_processing_charge":"No","day":"15","oa_version":"Preprint","intvolume":" 538","title":"Arakawa-Suzuki functors for Whittaker modules","status":"public","_id":"6828","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"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 .","lang":"eng"}],"type":"journal_article"},{"year":"2019","_id":"7216","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"IEEE","department":[{"_id":"HeEd"}],"status":"public","title":"LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale","publication_status":"published","author":[{"orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","first_name":"Georg F","full_name":"Osang, Georg F"},{"last_name":"Cook","first_name":"James","full_name":"Cook, James"},{"last_name":"Fabrikant","first_name":"Alex","full_name":"Fabrikant, Alex"},{"full_name":"Gruteser, Marco","last_name":"Gruteser","first_name":"Marco"}],"oa_version":"None","date_updated":"2023-09-06T14:50:28Z","date_created":"2019-12-29T23:00:47Z","type":"conference","article_number":"8917514","abstract":[{"lang":"eng","text":"We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system to label a stream of noisy observations of transit vehicle trajectories with the transit routes they are serving (e.g., northbound bus #5). In order to scale efficiently to large transit networks, our system first retrieves a small set of candidate routes from a geometrically indexed data structure, then applies a fine-grained scoring step to choose the best match. Given that real-time data remains unavailable for the majority of the world’s transit agencies, these inferences can help feed a real-time map of a transit system’s trips, infer transit trip delays in real time, or measure and correct noisy transit tracking data. This system can run on vehicle observations from a variety of sources that don’t attach route information to vehicle observations, such as public imagery streams or user-contributed transit vehicle sightings.We abstract away the specifics of the sensing system and demonstrate the effectiveness of our system on a \"semisynthetic\" dataset of all New York City buses, where we simulate sensed trajectories by starting with fully labeled vehicle trajectories reported via the GTFS-Realtime protocol, removing the transit route IDs, and perturbing locations with synthetic noise. Using just the geometric shapes of the trajectories, we demonstrate that our system converges on the correct route ID within a few minutes, even after a vehicle switches from serving one trip to the next."}],"citation":{"ama":"Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In: 2019 IEEE Intelligent Transportation Systems Conference. IEEE; 2019. doi:10.1109/ITSC.2019.8917514","apa":"Osang, G. F., Cook, J., Fabrikant, A., & Gruteser, M. (2019). LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In 2019 IEEE Intelligent Transportation Systems Conference. Auckland, New Zealand: IEEE. https://doi.org/10.1109/ITSC.2019.8917514","ieee":"G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale,” in 2019 IEEE Intelligent Transportation Systems Conference, Auckland, New Zealand, 2019.","ista":"Osang GF, Cook J, Fabrikant A, Gruteser M. 2019. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. 2019 IEEE Intelligent Transportation Systems Conference. ITSC: Intelligent Transportation Systems Conference, 8917514.","short":"G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019.","mla":"Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” 2019 IEEE Intelligent Transportation Systems Conference, 8917514, IEEE, 2019, doi:10.1109/ITSC.2019.8917514.","chicago":"Osang, Georg F, James Cook, Alex Fabrikant, and Marco Gruteser. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” In 2019 IEEE Intelligent Transportation Systems Conference. IEEE, 2019. https://doi.org/10.1109/ITSC.2019.8917514."},"external_id":{"isi":["000521238102050"]},"publication":"2019 IEEE Intelligent Transportation Systems Conference","isi":1,"quality_controlled":"1","date_published":"2019-11-28T00:00:00Z","doi":"10.1109/ITSC.2019.8917514","conference":{"name":"ITSC: Intelligent Transportation Systems Conference","end_date":"2019-10-30","start_date":"2019-10-27","location":"Auckland, New Zealand"},"language":[{"iso":"eng"}],"scopus_import":"1","publication_identifier":{"isbn":["9781538670248"]},"article_processing_charge":"No","month":"11","day":"28"},{"date_published":"2019-12-01T00:00:00Z","page":"865–878","article_type":"original","citation":{"ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.","ieee":"H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019.","apa":"Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2","ama":"Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2.","short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878."},"publication":"Discrete and Computational Geometry","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","file":[{"file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","access_level":"open_access","file_size":599339,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"5932","date_created":"2019-02-06T10:10:46Z","date_updated":"2020-07-14T12:47:10Z","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4"}],"oa_version":"Published Version","intvolume":" 62","title":"Poisson–Delaunay Mosaics of Order k","ddc":["516"],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"5678","issue":"4","abstract":[{"text":"The order-k Voronoi tessellation of a locally finite set 𝑋⊆ℝ𝑛 decomposes ℝ𝑛 into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold.","lang":"eng"}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s00454-018-0049-2","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","isi":1,"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"},"external_id":{"arxiv":["1709.09380"],"isi":["000494042900008"]},"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"month":"12","volume":62,"date_created":"2018-12-16T22:59:20Z","date_updated":"2023-09-07T12:07:12Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6287"}]},"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","first_name":"Anton"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2019","ec_funded":1,"file_date_updated":"2020-07-14T12:47:10Z"},{"intvolume":" 73","ddc":["000"],"status":"public","title":"Holes and dependences in an ordered complex","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6608","file":[{"file_name":"Elsevier_2019_Edelsbrunner.pdf","access_level":"open_access","content_type":"application/pdf","file_size":2665013,"creator":"kschuh","relation":"main_file","file_id":"6624","date_created":"2019-07-08T15:24:26Z","date_updated":"2020-07-14T12:47:34Z","checksum":"7c99be505dc7533257d42eb1830cef04"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"text":"We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram.","lang":"eng"}],"page":"1-15","citation":{"apa":"Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered complex. Computer Aided Geometric Design. Elsevier. https://doi.org/10.1016/j.cagd.2019.06.003","ieee":"H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” Computer Aided Geometric Design, vol. 73. Elsevier, pp. 1–15, 2019.","ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.","ama":"Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design. Elsevier, 2019. https://doi.org/10.1016/j.cagd.2019.06.003.","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019, pp. 1–15, doi:10.1016/j.cagd.2019.06.003."},"publication":"Computer Aided Geometric Design","date_published":"2019-08-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"01","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2019","volume":73,"date_updated":"2023-09-07T13:15:29Z","date_created":"2019-07-07T21:59:20Z","related_material":{"record":[{"id":"7460","relation":"dissertation_contains","status":"public"}]},"author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Ölsböck, Katharina","last_name":"Ölsböck","first_name":"Katharina","orcid":"0000-0002-4672-8297","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87"}],"ec_funded":1,"file_date_updated":"2020-07-14T12:47:34Z","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"isi":1,"quality_controlled":"1","external_id":{"isi":["000485207800001"]},"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.cagd.2019.06.003","month":"08"},{"abstract":[{"lang":"eng","text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:\r\n1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved."}],"article_number":"1903.06981","type":"preprint","date_created":"2020-06-08T12:25:25Z","date_updated":"2024-01-04T12:42:08Z","oa_version":"Preprint","author":[{"first_name":"Ahmad","last_name":"Biniaz","full_name":"Biniaz, Ahmad"},{"full_name":"Jain, Kshitij","first_name":"Kshitij","last_name":"Jain"},{"full_name":"Lubiw, Anna","last_name":"Lubiw","first_name":"Anna"},{"full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana"},{"full_name":"Miltzow, Tillmann","last_name":"Miltzow","first_name":"Tillmann"},{"full_name":"Mondal, Debajyoti","last_name":"Mondal","first_name":"Debajyoti"},{"last_name":"Naredla","first_name":"Anurag Murty","full_name":"Naredla, Anurag Murty"},{"full_name":"Tkadlec, Josef","first_name":"Josef","last_name":"Tkadlec","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684"},{"full_name":"Turcotte, Alexi","first_name":"Alexi","last_name":"Turcotte"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"7944"},{"id":"12833","relation":"later_version","status":"public"}]},"publication_status":"submitted","status":"public","title":"Token swapping on trees","department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7950","year":"2019","month":"03","day":"16","article_processing_charge":"No","language":[{"iso":"eng"}],"date_published":"2019-03-16T00:00:00Z","publication":"arXiv","external_id":{"arxiv":["1903.06981"]},"citation":{"mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981.","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.).","chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” ArXiv, n.d.","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv.","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981.","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. arXiv.","ieee":"A. Biniaz et al., “Token swapping on trees,” arXiv. ."},"main_file_link":[{"url":"https://arxiv.org/abs/1903.06981","open_access":"1"}],"oa":1},{"day":"11","has_accepted_license":"1","scopus_import":1,"date_published":"2018-06-11T00:00:00Z","page":"35:1 - 35:13","citation":{"short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13.","mla":"Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.35.","ama":"Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:35:1-35:13. doi:10.4230/LIPIcs.SoCG.2018.35","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35","ista":"Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13."},"abstract":[{"lang":"eng","text":"Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex."}],"alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"type":"conference","file":[{"date_created":"2018-12-17T16:31:31Z","date_updated":"2020-07-14T12:45:20Z","checksum":"7509403803b3ac1aee94bbc2ad293d21","relation":"main_file","file_id":"5724","content_type":"application/pdf","file_size":489080,"creator":"dernst","file_name":"2018_LIPIcs_Edelsbrunner.pdf","access_level":"open_access"}],"oa_version":"Published Version","status":"public","ddc":["000"],"title":"Smallest enclosing spheres and Chernoff points in Bregman geometry","intvolume":" 99","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"188","month":"06","language":[{"iso":"eng"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2018-06-14","location":"Budapest, Hungary","start_date":"2018-06-11"},"doi":"10.4230/LIPIcs.SoCG.2018.35","quality_controlled":"1","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"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"},"oa":1,"file_date_updated":"2020-07-14T12:45:20Z","publist_id":"7733","date_created":"2018-12-11T11:45:05Z","date_updated":"2021-01-12T06:53:48Z","volume":99,"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Virk","first_name":"Ziga","full_name":"Virk, Ziga"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner"}],"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"year":"2018","acknowledgement":"This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund"},{"article_processing_charge":"No","has_accepted_license":"1","day":"11","page":"171","citation":{"ama":"Iglesias Ham M. Multiple covers with balls. 2018. doi:10.15479/AT:ISTA:th_1026","ista":"Iglesias Ham M. 2018. Multiple covers with balls. Institute of Science and Technology Austria.","apa":"Iglesias Ham, M. (2018). Multiple covers with balls. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1026","ieee":"M. Iglesias Ham, “Multiple covers with balls,” Institute of Science and Technology Austria, 2018.","mla":"Iglesias Ham, Mabel. Multiple Covers with Balls. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1026.","short":"M. Iglesias Ham, Multiple Covers with Balls, Institute of Science and Technology Austria, 2018.","chicago":"Iglesias Ham, Mabel. “Multiple Covers with Balls.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1026."},"date_published":"2018-06-11T00:00:00Z","alternative_title":["ISTA Thesis"],"type":"dissertation","abstract":[{"text":"We describe arrangements of three-dimensional spheres from a geometrical and topological point of view. Real data (fitting this setup) often consist of soft spheres which show certain degree of deformation while strongly packing against each other. In this context, we answer the following questions: If we model a soft packing of spheres by hard spheres that are allowed to overlap, can we measure the volume in the overlapped areas? Can we be more specific about the overlap volume, i.e. quantify how much volume is there covered exactly twice, three times, or k times? What would be a good optimization criteria that rule the arrangement of soft spheres while making a good use of the available space? Fixing a particular criterion, what would be the optimal sphere configuration? The first result of this thesis are short formulas for the computation of volumes covered by at least k of the balls. The formulas exploit information contained in the order-k Voronoi diagrams and its closely related Level-k complex. The used complexes lead to a natural generalization into poset diagrams, a theoretical formalism that contains the order-k and degree-k diagrams as special cases. In parallel, we define different criteria to determine what could be considered an optimal arrangement from a geometrical point of view. Fixing a criterion, we find optimal soft packing configurations in 2D and 3D where the ball centers lie on a lattice. As a last step, we use tools from computational topology on real physical data, to show the potentials of higher-order diagrams in the description of melting crystals. The results of the experiments leaves us with an open window to apply the theories developed in this thesis in real applications.","lang":"eng"}],"title":"Multiple covers with balls","ddc":["514","516"],"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"201","file":[{"file_name":"IST-2018-1025-v2+5_ist-thesis-iglesias-11June2018(1).zip","access_level":"closed","creator":"kschuh","file_size":11827713,"content_type":"application/zip","file_id":"5918","relation":"source_file","date_created":"2019-02-05T07:43:31Z","date_updated":"2020-07-14T12:45:24Z","checksum":"dd699303623e96d1478a6ae07210dd05"},{"creator":"kschuh","content_type":"application/pdf","file_size":4783846,"file_name":"IST-2018-1025-v2+4_ThesisIglesiasFinal11June2018.pdf","access_level":"open_access","date_updated":"2020-07-14T12:45:24Z","date_created":"2019-02-05T07:43:45Z","checksum":"ba163849a190d2b41d66fef0e4983294","file_id":"5919","relation":"main_file"}],"oa_version":"Published Version","pubrep_id":"1026","publication_identifier":{"issn":["2663-337X"]},"month":"06","oa":1,"language":[{"iso":"eng"}],"degree_awarded":"PhD","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}],"doi":"10.15479/AT:ISTA:th_1026","publist_id":"7712","file_date_updated":"2020-07-14T12:45:24Z","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2018","date_created":"2018-12-11T11:45:10Z","date_updated":"2023-09-07T12:25:32Z","author":[{"first_name":"Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel"}]},{"scopus_import":1,"has_accepted_license":"1","day":"11","citation":{"chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.34.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. The Multi-Cover Persistence of Euclidean Balls. Vol. 99, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.34.","short":"H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","ista":"Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.","ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.","apa":"Edelsbrunner, H., & Osang, G. F. (2018). The multi-cover persistence of Euclidean balls (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.34","ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.34"},"date_published":"2018-06-11T00:00:00Z","type":"conference","alternative_title":["LIPIcs"],"abstract":[{"lang":"eng","text":"Given a locally finite X ⊆ ℝd and a radius r ≥ 0, the k-fold cover of X and r consists of all points in ℝd that have k or more points of X within distance r. We consider two filtrations - one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k - and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in ℝd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. "}],"_id":"187","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 99","status":"public","title":"The multi-cover persistence of Euclidean balls","ddc":["516"],"file":[{"file_name":"2018_LIPIcs_Edelsbrunner_Osang.pdf","access_level":"open_access","content_type":"application/pdf","file_size":528018,"creator":"dernst","relation":"main_file","file_id":"5738","date_created":"2018-12-18T09:27:22Z","date_updated":"2020-07-14T12:45:19Z","checksum":"d8c0533ad0018eb4ed1077475eb8fc18"}],"oa_version":"Published Version","month":"06","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"},"oa":1,"project":[{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","doi":"10.4230/LIPIcs.SoCG.2018.34","conference":{"location":"Budapest, Hungary","start_date":"2018-06-11","end_date":"2018-06-14","name":"SoCG: Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"article_number":"34","publist_id":"7732","file_date_updated":"2020-07-14T12:45:19Z","acknowledgement":"This work is partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","year":"2018","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","related_material":{"record":[{"relation":"later_version","status":"public","id":"9317"},{"id":"9056","status":"public","relation":"dissertation_contains"}]},"author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Osang","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F"}],"volume":99,"date_created":"2018-12-11T11:45:05Z","date_updated":"2023-09-07T13:29:00Z"},{"publist_id":"7014","ec_funded":1,"file_date_updated":"2020-07-14T12:47:44Z","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","year":"2018","volume":194,"date_updated":"2023-09-08T11:40:29Z","date_created":"2018-12-11T11:47:57Z","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"}],"month":"06","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"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"},"oa":1,"external_id":{"isi":["000431418800004"]},"language":[{"iso":"eng"}],"doi":"10.1007/s10711-017-0265-6","type":"journal_article","issue":"1","abstract":[{"text":"We consider families of confocal conics and two pencils of Apollonian circles having the same foci. We will show that these families of curves generate trivial 3-webs and find the exact formulas describing them.","lang":"eng"}],"intvolume":" 194","ddc":["510"],"status":"public","title":"3-Webs generated by confocal conics and circles","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"692","oa_version":"Published Version","file":[{"file_id":"7222","relation":"main_file","date_created":"2020-01-03T11:35:08Z","date_updated":"2020-07-14T12:47:44Z","checksum":"1febcfc1266486053a069e3425ea3713","file_name":"2018_Springer_Akopyan.pdf","access_level":"open_access","creator":"kschuh","content_type":"application/pdf","file_size":1140860}],"scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","page":"55 - 64","article_type":"original","citation":{"ieee":"A. Akopyan, “3-Webs generated by confocal conics and circles,” Geometriae Dedicata, vol. 194, no. 1. Springer, pp. 55–64, 2018.","apa":"Akopyan, A. (2018). 3-Webs generated by confocal conics and circles. Geometriae Dedicata. Springer. https://doi.org/10.1007/s10711-017-0265-6","ista":"Akopyan A. 2018. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 194(1), 55–64.","ama":"Akopyan A. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 2018;194(1):55-64. doi:10.1007/s10711-017-0265-6","chicago":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0265-6.","short":"A. Akopyan, Geometriae Dedicata 194 (2018) 55–64.","mla":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata, vol. 194, no. 1, Springer, 2018, pp. 55–64, doi:10.1007/s10711-017-0265-6."},"publication":"Geometriae Dedicata","date_published":"2018-06-01T00:00:00Z"},{"date_published":"2018-09-06T00:00:00Z","publication":"SIAM Journal on Discrete Mathematics","citation":{"ama":"Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 2018;32(3):2242-2257. doi:10.1137/16M110407X","apa":"Akopyan, A., & Segal Halevi, E. (2018). Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M110407X","ieee":"A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,” SIAM Journal on Discrete Mathematics, vol. 32, no. 3. Society for Industrial and Applied Mathematics , pp. 2242–2257, 2018.","ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257.","mla":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics, vol. 32, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 2242–57, doi:10.1137/16M110407X.","chicago":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M110407X."},"page":"2242 - 2257","day":"06","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"58","title":"Counting blanks in polygonal arrangements","status":"public","intvolume":" 32","abstract":[{"lang":"eng","text":"Inside a two-dimensional region (``cake""), there are m nonoverlapping tiles of a certain kind (``toppings""). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,"" such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks."}],"issue":"3","type":"journal_article","doi":"10.1137/16M110407X","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1604.00960","open_access":"1"}],"external_id":{"isi":["000450810500036"],"arxiv":["1604.00960"]},"quality_controlled":"1","isi":1,"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"month":"09","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"},{"first_name":"Erel","last_name":"Segal Halevi","full_name":"Segal Halevi, Erel"}],"date_created":"2018-12-11T11:44:24Z","date_updated":"2023-09-11T12:48:39Z","volume":32,"year":"2018","publication_status":"published","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"HeEd"}],"publist_id":"7996","ec_funded":1},{"acknowledgement":"DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”; People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) REA grant agreement n◦[291734]","year":"2018","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"American Mathematical Society","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Bobenko","first_name":"Alexander","full_name":"Bobenko, Alexander"}],"date_updated":"2023-09-11T14:19:12Z","date_created":"2018-12-11T11:46:35Z","volume":370,"ec_funded":1,"publist_id":"7363","external_id":{"isi":["000423197800019"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1602.04637","open_access":"1"}],"quality_controlled":"1","isi":1,"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"doi":"10.1090/tran/7292","language":[{"iso":"eng"}],"month":"04","_id":"458","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Incircular nets and confocal conics","status":"public","intvolume":" 370","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics. Our main new results are on checkerboard IC-nets in the plane. These are congruences of straight lines in the plane with the combinatorics of the square grid, combinatorially colored as a checkerboard, such that all black coordinate quadrilaterals possess inscribed circles. We show how this larger class of IC-nets appears quite naturally in Laguerre geometry of oriented planes and spheres and leads to new remarkable incidence theorems. Most of our results are valid in hyperbolic and spherical geometries as well. We present also generalizations in spaces of higher dimension, called checkerboard IS-nets. The construction of these nets is based on a new 9 inspheres incidence theorem."}],"issue":"4","publication":"Transactions of the American Mathematical Society","citation":{"mla":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” Transactions of the American Mathematical Society, vol. 370, no. 4, American Mathematical Society, 2018, pp. 2825–54, doi:10.1090/tran/7292.","short":"A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society 370 (2018) 2825–2854.","chicago":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” Transactions of the American Mathematical Society. American Mathematical Society, 2018. https://doi.org/10.1090/tran/7292.","ama":"Akopyan A, Bobenko A. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 2018;370(4):2825-2854. doi:10.1090/tran/7292","ista":"Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 370(4), 2825–2854.","apa":"Akopyan, A., & Bobenko, A. (2018). Incircular nets and confocal conics. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/7292","ieee":"A. Akopyan and A. Bobenko, “Incircular nets and confocal conics,” Transactions of the American Mathematical Society, vol. 370, no. 4. American Mathematical Society, pp. 2825–2854, 2018."},"page":"2825 - 2854","date_published":"2018-04-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No"},{"type":"journal_article","abstract":[{"text":"The goal of this article is to introduce the reader to the theory of intrinsic geometry of convex surfaces. We illustrate the power of the tools by proving a theorem on convex surfaces containing an arbitrarily long closed simple geodesic. Let us remind ourselves that a curve in a surface is called geodesic if every sufficiently short arc of the curve is length minimizing; if, in addition, it has no self-intersections, we call it simple geodesic. A tetrahedron with equal opposite edges is called isosceles. The axiomatic method of Alexandrov geometry allows us to work with the metrics of convex surfaces directly, without approximating it first by a smooth or polyhedral metric. Such approximations destroy the closed geodesics on the surface; therefore it is difficult (if at all possible) to apply approximations in the proof of our theorem. On the other hand, a proof in the smooth or polyhedral case usually admits a translation into Alexandrov’s language; such translation makes the result more general. In fact, our proof resembles a translation of the proof given by Protasov. Note that the main theorem implies in particular that a smooth convex surface does not have arbitrarily long simple closed geodesics. However we do not know a proof of this corollary that is essentially simpler than the one presented below.","lang":"eng"}],"issue":"3","_id":"106","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Long geodesics on convex surfaces","status":"public","intvolume":" 40","oa_version":"Preprint","scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Mathematical Intelligencer","citation":{"short":"A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31.","mla":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer, vol. 40, no. 3, Springer, 2018, pp. 26–31, doi:10.1007/s00283-018-9795-5.","chicago":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer. Springer, 2018. https://doi.org/10.1007/s00283-018-9795-5.","ama":"Akopyan A, Petrunin A. Long geodesics on convex surfaces. Mathematical Intelligencer. 2018;40(3):26-31. doi:10.1007/s00283-018-9795-5","ieee":"A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” Mathematical Intelligencer, vol. 40, no. 3. Springer, pp. 26–31, 2018.","apa":"Akopyan, A., & Petrunin, A. (2018). Long geodesics on convex surfaces. Mathematical Intelligencer. Springer. https://doi.org/10.1007/s00283-018-9795-5","ista":"Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical Intelligencer. 40(3), 26–31."},"page":"26 - 31","date_published":"2018-09-01T00:00:00Z","publist_id":"7948","year":"2018","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"first_name":"Anton","last_name":"Petrunin","full_name":"Petrunin, Anton"}],"date_created":"2018-12-11T11:44:40Z","date_updated":"2023-09-13T08:49:16Z","volume":40,"month":"09","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.05172"}],"oa":1,"external_id":{"isi":["000444141200005"],"arxiv":["1702.05172"]},"quality_controlled":"1","isi":1,"doi":"10.1007/s00283-018-9795-5","language":[{"iso":"eng"}]},{"file":[{"checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","date_updated":"2020-07-14T12:46:38Z","date_created":"2019-02-12T06:47:52Z","file_id":"5953","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":708357,"access_level":"open_access","file_name":"2018_Edelsbrunner.pdf"}],"oa_version":"Preprint","title":"Multiple covers with balls I: Inclusion–exclusion","ddc":["000"],"status":"public","intvolume":" 68","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"530","abstract":[{"lang":"eng","text":"Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of Rn covered by at least k balls in a finite set. We implement two of the formulas in dimension n=3 and report on results obtained with our software."}],"type":"journal_article","date_published":"2018-03-01T00:00:00Z","page":"119 - 133","publication":"Computational Geometry: Theory and Applications","citation":{"chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications. Elsevier, 2018. https://doi.org/10.1016/j.comgeo.2017.06.014.","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications, vol. 68, Elsevier, 2018, pp. 119–33, doi:10.1016/j.comgeo.2017.06.014.","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.014","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” Computational Geometry: Theory and Applications, vol. 68. Elsevier, pp. 119–133, 2018.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 2018;68:119-133. doi:10.1016/j.comgeo.2017.06.014"},"day":"01","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","date_created":"2018-12-11T11:46:59Z","date_updated":"2023-09-13T08:59:00Z","volume":68,"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel"}],"publication_status":"published","publisher":"Elsevier","department":[{"_id":"HeEd"}],"year":"2018","file_date_updated":"2020-07-14T12:46:38Z","ec_funded":1,"publist_id":"7289","language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2017.06.014","quality_controlled":"1","isi":1,"project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7"}],"oa":1,"external_id":{"isi":["000415778300010"]},"month":"03"},{"page":"51 - 65","publication":"Proceedings of the 2018 on Asia Conference on Computer and Communication Security","citation":{"ama":"Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data independent password hashing functions. In: Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534","ista":"Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password hashing functions. Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ASIACCS: Asia Conference on Computer and Communications Security , 51–65.","ieee":"J. F. Alwen et al., “On the memory hardness of data independent password hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65.","apa":"Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak, K. Z., … Rybar, M. (2018). On the memory hardness of data independent password hashing functions. In Proceedings of the 2018 on Asia Conference on Computer and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534","mla":"Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534.","short":"J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak, L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65.","chicago":"Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar. “On the Memory Hardness of Data Independent Password Hashing Functions.” In Proceedings of the 2018 on Asia Conference on Computer and Communication Security, 51–65. ACM, 2018. https://doi.org/10.1145/3196494.3196534."},"date_published":"2018-06-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","status":"public","title":"On the memory hardness of data independent password hashing functions","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"193","oa_version":"Submitted Version","type":"conference","abstract":[{"lang":"eng","text":"We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki'16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block'16] for analyzing the hardware costs of an iMHF."}],"isi":1,"quality_controlled":"1","project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7"},{"call_identifier":"H2020","name":"Teaching Old Crypto New Tricks","grant_number":"682815","_id":"258AA5B2-B435-11E9-9278-68D0E5697425"}],"oa":1,"external_id":{"isi":["000516620100005"]},"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2016/783"}],"language":[{"iso":"eng"}],"conference":{"name":"ASIACCS: Asia Conference on Computer and Communications Security ","end_date":"2018-06-08","start_date":"2018-06-04","location":"Incheon, Republic of Korea"},"doi":"10.1145/3196494.3196534","month":"06","publication_status":"published","publisher":"ACM","department":[{"_id":"KrPi"},{"_id":"HeEd"},{"_id":"VlKo"}],"acknowledgement":"Leonid Reyzin was supported in part by IST Austria and by US NSF grants 1012910, 1012798, and 1422965; this research was performed while he was visiting IST Austria.","year":"2018","date_updated":"2023-09-13T09:13:12Z","date_created":"2018-12-11T11:45:07Z","author":[{"full_name":"Alwen, Joel F","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87","first_name":"Joel F","last_name":"Alwen"},{"full_name":"Gazi, Peter","last_name":"Gazi","first_name":"Peter"},{"full_name":"Kamath Hosdurg, Chethan","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","last_name":"Kamath Hosdurg","first_name":"Chethan"},{"id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87","last_name":"Klein","first_name":"Karen","full_name":"Klein, Karen"},{"full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","first_name":"Georg F","last_name":"Osang"},{"orcid":"0000-0002-9139-1654","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","last_name":"Pietrzak","first_name":"Krzysztof Z","full_name":"Pietrzak, Krzysztof Z"},{"first_name":"Lenoid","last_name":"Reyzin","full_name":"Reyzin, Lenoid"},{"full_name":"Rolinek, Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","first_name":"Michal","last_name":"Rolinek"},{"full_name":"Rybar, Michal","last_name":"Rybar","first_name":"Michal","id":"2B3E3DE8-F248-11E8-B48F-1D18A9856A87"}],"ec_funded":1,"publist_id":"7723"},{"publication_identifier":{"issn":["08954801"]},"month":"03","doi":"10.1137/16M1097201","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf","open_access":"1"}],"external_id":{"isi":["000428958900038"]},"project":[{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"quality_controlled":"1","isi":1,"publist_id":"7553","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"first_name":"Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel"}],"volume":32,"date_created":"2018-12-11T11:45:46Z","date_updated":"2023-09-13T09:34:38Z","year":"2018","acknowledgement":"This work was partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics,” through grant I02979-N35 of the Austrian Science Fund (FWF).","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"HeEd"}],"publication_status":"published","article_processing_charge":"No","day":"29","scopus_import":"1","date_published":"2018-03-29T00:00:00Z","citation":{"mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math, vol. 32, no. 1, Society for Industrial and Applied Mathematics , 2018, pp. 750–82, doi:10.1137/16M1097201.","short":"H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1097201.","ama":"Edelsbrunner H, Iglesias Ham M. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 2018;32(1):750-782. doi:10.1137/16M1097201","ista":"Edelsbrunner H, Iglesias Ham M. 2018. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 32(1), 750–782.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M1097201","ieee":"H. Edelsbrunner and M. Iglesias Ham, “On the optimality of the FCC lattice for soft sphere packing,” SIAM J Discrete Math, vol. 32, no. 1. Society for Industrial and Applied Mathematics , pp. 750–782, 2018."},"publication":"SIAM J Discrete Math","page":"750 - 782","article_type":"original","issue":"1","abstract":[{"lang":"eng","text":"Motivated by biological questions, we study configurations of equal spheres that neither pack nor cover. Placing their centers on a lattice, we define the soft density of the configuration by penalizing multiple overlaps. Considering the 1-parameter family of diagonally distorted 3-dimensional integer lattices, we show that the soft density is maximized at the FCC lattice."}],"type":"journal_article","oa_version":"Submitted Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"312","intvolume":" 32","status":"public","title":"On the optimality of the FCC lattice for soft sphere packing"},{"issue":"4","abstract":[{"lang":"eng","text":"We give a simple proof of T. Stehling's result [4], whereby in any normal tiling of the plane with convex polygons with number of sides not less than six, all tiles except a finite number are hexagons."}],"type":"journal_article","oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"409","intvolume":" 356","status":"public","title":"On the number of non-hexagons in a planar tiling","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2018-04-01T00:00:00Z","citation":{"ama":"Akopyan A. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 2018;356(4):412-414. doi:10.1016/j.crma.2018.03.005","ieee":"A. Akopyan, “On the number of non-hexagons in a planar tiling,” Comptes Rendus Mathematique, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.","apa":"Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. Elsevier. https://doi.org/10.1016/j.crma.2018.03.005","ista":"Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 356(4), 412–414.","short":"A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.","mla":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:10.1016/j.crma.2018.03.005.","chicago":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique. Elsevier, 2018. https://doi.org/10.1016/j.crma.2018.03.005."},"publication":"Comptes Rendus Mathematique","page":"412-414","article_type":"original","publist_id":"7420","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"}],"volume":356,"date_created":"2018-12-11T11:46:19Z","date_updated":"2023-09-13T09:34:12Z","year":"2018","department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","publication_identifier":{"issn":["1631073X"]},"month":"04","doi":"10.1016/j.crma.2018.03.005","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1805.01652","open_access":"1"}],"external_id":{"isi":["000430402700009"],"arxiv":["1805.01652"]},"isi":1,"quality_controlled":"1"},{"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.02870"}],"external_id":{"isi":["000442893500018"],"arxiv":["1705.02870"]},"project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"isi":1,"quality_controlled":"1","doi":"10.1214/18-AAP1389","language":[{"iso":"eng"}],"month":"10","year":"2018","department":[{"_id":"HeEd"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6287"}]},"author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","first_name":"Anton","full_name":"Nikitenko, Anton"}],"volume":28,"date_created":"2018-12-11T11:44:33Z","date_updated":"2023-09-15T12:10:35Z","publist_id":"7967","citation":{"mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability, vol. 28, no. 5, Institute of Mathematical Statistics, 2018, pp. 3215–38, doi:10.1214/18-AAP1389.","short":"H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability. Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/18-AAP1389.","ama":"Edelsbrunner H, Nikitenko A. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 2018;28(5):3215-3238. doi:10.1214/18-AAP1389","ista":"Edelsbrunner H, Nikitenko A. 2018. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 28(5), 3215–3238.","ieee":"H. Edelsbrunner and A. Nikitenko, “Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics,” Annals of Applied Probability, vol. 28, no. 5. Institute of Mathematical Statistics, pp. 3215–3238, 2018.","apa":"Edelsbrunner, H., & Nikitenko, A. (2018). Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AAP1389"},"publication":"Annals of Applied Probability","page":"3215 - 3238","article_type":"original","date_published":"2018-10-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"87","intvolume":" 28","status":"public","title":"Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics","oa_version":"Preprint","type":"journal_article","issue":"5","abstract":[{"lang":"eng","text":"Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. We find that the expectations are essentially the same as for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to the boundary complex of the convex hull in Rn+1, so we also get the expected number of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric to the standard n-simplex equipped with the Fisher information metric. It follows that the latter space has similar stochastic properties as the n-dimensional Euclidean space. Our results are therefore relevant in information geometry and in population genetics."}]},{"month":"05","publication_identifier":{"issn":["2050-5094"]},"language":[{"iso":"eng"}],"doi":"10.1017/fms.2018.7","quality_controlled":"1","isi":1,"project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"}],"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"},"external_id":{"isi":["000433915500001"],"arxiv":["1712.10205"]},"oa":1,"file_date_updated":"2020-07-14T12:47:28Z","ec_funded":1,"article_number":"e7","date_updated":"2023-09-19T14:50:12Z","date_created":"2019-04-30T06:09:57Z","volume":6,"author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"},{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey","last_name":"Avvakumov","full_name":"Avvakumov, Sergey"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"8156"}]},"publication_status":"published","publisher":"Cambridge University Press","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"year":"2018","day":"31","has_accepted_license":"1","article_processing_charge":"No","date_published":"2018-05-31T00:00:00Z","publication":"Forum of Mathematics, Sigma","citation":{"chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma. Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7.","mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6, e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","apa":"Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2018.7","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge University Press, 2018.","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7"},"abstract":[{"lang":"eng","text":"We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle."}],"type":"journal_article","oa_version":"Published Version","file":[{"file_size":249246,"content_type":"application/pdf","creator":"dernst","file_name":"2018_ForumMahtematics_Akopyan.pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:28Z","date_created":"2019-04-30T06:14:58Z","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","relation":"main_file","file_id":"6356"}],"title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","status":"public","ddc":["510"],"intvolume":" 6","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"6355"},{"isi":1,"quality_controlled":"1","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"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"},"external_id":{"isi":["000432205500011"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00454-017-9883-x","month":"06","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"publication_status":"published","publisher":"Springer","department":[{"_id":"HeEd"}],"year":"2018","date_updated":"2023-09-20T12:08:51Z","date_created":"2018-12-11T11:49:57Z","volume":59,"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"full_name":"Balitskiy, Alexey","last_name":"Balitskiy","first_name":"Alexey"},{"first_name":"Mikhail","last_name":"Grigorev","full_name":"Grigorev, Mikhail"}],"file_date_updated":"2019-01-18T09:27:36Z","publist_id":"6324","ec_funded":1,"article_type":"original","page":"1001-1009","publication":"Discrete & Computational Geometry","citation":{"ista":"Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 59(4), 1001–1009.","apa":"Akopyan, A., Balitskiy, A., & Grigorev, M. (2018). On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-017-9883-x","ieee":"A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem by A.W. Goodman and R.E. Goodman,” Discrete & Computational Geometry, vol. 59, no. 4. Springer, pp. 1001–1009, 2018.","ama":"Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 2018;59(4):1001-1009. doi:10.1007/s00454-017-9883-x","chicago":"Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry. Springer, 2018. https://doi.org/10.1007/s00454-017-9883-x.","mla":"Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry, vol. 59, no. 4, Springer, 2018, pp. 1001–09, doi:10.1007/s00454-017-9883-x.","short":"A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry 59 (2018) 1001–1009."},"date_published":"2018-06-01T00:00:00Z","scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","title":"On the circle covering theorem by A.W. Goodman and R.E. Goodman","status":"public","ddc":["516","000"],"intvolume":" 59","_id":"1064","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"relation":"main_file","file_id":"5844","date_created":"2019-01-18T09:27:36Z","date_updated":"2019-01-18T09:27:36Z","success":1,"file_name":"2018_DiscreteComp_Akopyan.pdf","access_level":"open_access","content_type":"application/pdf","file_size":482518,"creator":"dernst"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"text":"In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets.","lang":"eng"}],"issue":"4"},{"month":"09","day":"13","article_processing_charge":"No","language":[{"iso":"eng"}],"doi":"10.48550/arXiv.1804.03057","date_published":"2018-09-13T00:00:00Z","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.03057"}],"oa":1,"citation":{"ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:10.48550/arXiv.1804.03057","ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","apa":"Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018).","mla":"Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.","chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057."},"external_id":{"arxiv":["1804.03057"]},"abstract":[{"lang":"eng","text":"We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥2; this result was previously known for prime powers m=pk. We also give a higher-dimensional generalization."}],"ec_funded":1,"article_number":"1804.03057","type":"preprint","date_created":"2018-12-11T11:44:30Z","date_updated":"2023-12-18T10:51:02Z","oa_version":"Preprint","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","last_name":"Avvakumov","first_name":"Sergey"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"8156"}]},"status":"public","publication_status":"published","title":"Convex fair partitions into arbitrary number of pieces","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"publisher":"arXiv","_id":"75","year":"2018","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"department":[{"_id":"HeEd"}],"publisher":"World Scientific Publishing","publication_status":"published","year":"2017","acknowledgement":"Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.","volume":26,"date_created":"2018-12-11T11:46:43Z","date_updated":"2023-02-21T16:06:22Z","related_material":{"record":[{"id":"10892","status":"public","relation":"earlier_version"}]},"author":[{"last_name":"Biedl","first_name":"Therese","full_name":"Biedl, Therese"},{"last_name":"Huber","first_name":"Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","full_name":"Huber, Stefan"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"}],"publist_id":"7338","file_date_updated":"2020-07-14T12:46:35Z","quality_controlled":"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"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1142/S0218195916600050","month":"04","intvolume":" 26","ddc":["004","514","516"],"title":"Planar matchings for weighted straight skeletons","status":"public","_id":"481","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","file":[{"date_updated":"2020-07-14T12:46:35Z","date_created":"2018-12-12T10:09:34Z","checksum":"f79e8558bfe4b368dfefeb8eec2e3a5e","relation":"main_file","file_id":"4758","file_size":769296,"content_type":"application/pdf","creator":"system","file_name":"IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf","access_level":"open_access"}],"oa_version":"Published Version","pubrep_id":"949","type":"journal_article","issue":"3-4","abstract":[{"lang":"eng","text":"We introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist. Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings."}],"page":"211 - 229","citation":{"chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050.","mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050.","short":"T. Biedl, S. Huber, P. Palfrader, International Journal of Computational Geometry and Applications 26 (2017) 211–229.","ista":"Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 26(3–4), 211–229.","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017.","apa":"Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195916600050","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229. doi:10.1142/S0218195916600050"},"publication":"International Journal of Computational Geometry and Applications","date_published":"2017-04-13T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"13"},{"day":"01","month":"01","publication_identifier":{"issn":["01668641"]},"language":[{"iso":"eng"}],"date_published":"2017-01-01T00:00:00Z","doi":"10.1016/j.topol.2016.10.005","quality_controlled":"1","page":"45 - 57","publication":"Topology and its Applications","main_file_link":[{"url":"https://arxiv.org/abs/1608.03954v1","open_access":"1"}],"oa":1,"citation":{"ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57.","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.","apa":"Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005","ama":"Austin K, Virk Z. Higson compactification and dimension raising. Topology and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005","chicago":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.","mla":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.","short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57."},"abstract":[{"text":"Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension.","lang":"eng"}],"publist_id":"7299","type":"journal_article","date_updated":"2021-01-12T08:01:21Z","date_created":"2018-12-11T11:46:56Z","oa_version":"Submitted Version","volume":215,"author":[{"full_name":"Austin, Kyle","last_name":"Austin","first_name":"Kyle"},{"full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","status":"public","title":"Higson compactification and dimension raising","publisher":"Elsevier","department":[{"_id":"HeEd"}],"intvolume":" 215","year":"2017","_id":"521","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"publist_id":"7246","ec_funded":1,"volume":19,"date_updated":"2021-01-12T08:03:12Z","date_created":"2018-12-11T11:47:14Z","author":[{"first_name":"Peter","last_name":"Franek","id":"473294AE-F248-11E8-B48F-1D18A9856A87","full_name":"Franek, Peter"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","first_name":"Marek","full_name":"Krcál, Marek"}],"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"International Press","publication_status":"published","year":"2017","publication_identifier":{"issn":["15320073"]},"month":"01","language":[{"iso":"eng"}],"doi":"10.4310/HHA.2017.v19.n2.a16","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"},{"grant_number":"701309","_id":"2590DB08-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)"}],"quality_controlled":"1","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1507.04310","open_access":"1"}],"issue":"2","abstract":[{"text":"We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C).","lang":"eng"}],"type":"journal_article","oa_version":"Submitted Version","intvolume":" 19","title":"Persistence of zero sets","status":"public","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"568","day":"01","scopus_import":1,"date_published":"2017-01-01T00:00:00Z","page":"313 - 342","citation":{"ama":"Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications. 2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16","ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.","apa":"Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16","mla":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.","short":"P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.","chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16."},"publication":"Homology, Homotopy and Applications"},{"month":"05","publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["978-3-319-59107-0","978-3-319-59108-7"]},"quality_controlled":"1","language":[{"iso":"eng"}],"conference":{"name":"IWCIA: International Workshop on Combinatorial Image Analysis","start_date":"2017-06-19","location":"Plovdiv, Bulgaria","end_date":"2017-06-21"},"doi":"10.1007/978-3-319-59108-7_8","place":"Cham","extern":"1","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","year":"2017","date_created":"2019-01-08T20:42:56Z","date_updated":"2022-01-28T07:48:24Z","volume":10256,"author":[{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita"},{"full_name":"Bhowmick, Partha","first_name":"Partha","last_name":"Bhowmick"}],"day":"17","article_processing_charge":"No","page":"93-104","publication":"Combinatorial image analysis","citation":{"ama":"Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature; 2017:93-104. doi:10.1007/978-3-319-59108-7_8","apa":"Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256, pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8","ieee":"R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104.","ista":"Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.","short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104.","mla":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.","chicago":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104. Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8."},"date_published":"2017-05-17T00:00:00Z","alternative_title":["LNCS"],"type":"book_chapter","abstract":[{"text":"Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept.","lang":"eng"}],"status":"public","title":"Construction of persistent Voronoi diagram on 3D digital plane","intvolume":" 10256","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"5803","oa_version":"None"},{"date_updated":"2021-01-12T08:09:26Z","date_created":"2018-12-11T11:47:56Z","volume":77,"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert"}],"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"year":"2017","file_date_updated":"2020-07-14T12:47:42Z","publist_id":"7021","language":[{"iso":"eng"}],"conference":{"end_date":"2017-07-07","location":"Brisbane, Australia","start_date":"2017-07-04","name":"Symposium on Computational Geometry, SoCG"},"doi":"10.4230/LIPIcs.SoCG.2017.39","quality_controlled":"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"},"oa":1,"month":"06","publication_identifier":{"issn":["18688969"]},"oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":990546,"creator":"system","access_level":"open_access","file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf","checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","date_updated":"2020-07-14T12:47:42Z","date_created":"2018-12-12T10:11:03Z","relation":"main_file","file_id":"4856"}],"pubrep_id":"895","ddc":["514","516"],"status":"public","title":"Topological data analysis with Bregman divergences","intvolume":" 77","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"688","abstract":[{"text":"We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. ","lang":"eng"}],"alternative_title":["LIPIcs"],"type":"conference","date_published":"2017-06-01T00:00:00Z","page":"391-3916","citation":{"short":"H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916.","mla":"Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.","chicago":"Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39.","ama":"Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916. doi:10.4230/LIPIcs.SoCG.2017.39","ieee":"H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,” presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia, 2017, vol. 77, pp. 391–3916.","apa":"Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2017.39","ista":"Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916."},"day":"01","has_accepted_license":"1","scopus_import":1},{"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.06279"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1112/blms.12062","month":"08","publication_identifier":{"issn":["00246093"]},"publication_status":"published","publisher":"Wiley-Blackwell","department":[{"_id":"HeEd"}],"year":"2017","date_updated":"2021-01-12T08:11:41Z","date_created":"2018-12-11T11:48:02Z","volume":49,"author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"publist_id":"6982","ec_funded":1,"page":"690 - 693","publication":"Bulletin of the London Mathematical Society","citation":{"ama":"Akopyan A, Karasev R. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 2017;49(4):690-693. doi:10.1112/blms.12062","ista":"Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 49(4), 690–693.","ieee":"A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,” Bulletin of the London Mathematical Society, vol. 49, no. 4. Wiley-Blackwell, pp. 690–693, 2017.","apa":"Akopyan, A., & Karasev, R. (2017). A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. Wiley-Blackwell. https://doi.org/10.1112/blms.12062","mla":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society, vol. 49, no. 4, Wiley-Blackwell, 2017, pp. 690–93, doi:10.1112/blms.12062.","short":"A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693.","chicago":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society. Wiley-Blackwell, 2017. https://doi.org/10.1112/blms.12062."},"date_published":"2017-08-01T00:00:00Z","scopus_import":1,"day":"01","status":"public","title":"A tight estimate for the waist of the ball ","intvolume":" 49","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"707","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"We answer a question of M. Gromov on the waist of the unit ball."}],"issue":"4"},{"oa_version":"Preprint","intvolume":" 49","status":"public","title":"Expected sizes of poisson Delaunay mosaics and their discrete Morse functions","_id":"718","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"3","abstract":[{"text":"Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from a Poisson point process in ℝ n , we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and nonsingular intervals in the corresponding generalized discrete gradient. Observing connections with other probabilistic models, we obtain precise expressions for the expected numbers in low dimensions. In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4.","lang":"eng"}],"type":"journal_article","date_published":"2017-09-01T00:00:00Z","page":"745 - 767","citation":{"ama":"Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 2017;49(3):745-767. doi:10.1017/apr.2017.20","apa":"Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20","ieee":"H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson Delaunay mosaics and their discrete Morse functions,” Advances in Applied Probability, vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017.","ista":"Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3), 745–767.","short":"H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767.","mla":"Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability, vol. 49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20.","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability. Cambridge University Press, 2017. https://doi.org/10.1017/apr.2017.20."},"publication":"Advances in Applied Probability","day":"01","scopus_import":1,"volume":49,"date_created":"2018-12-11T11:48:07Z","date_updated":"2023-09-07T12:07:12Z","related_material":{"record":[{"id":"6287","status":"public","relation":"dissertation_contains"}]},"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Nikitenko, Anton","first_name":"Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201"},{"full_name":"Reitzner, Matthias","first_name":"Matthias","last_name":"Reitzner"}],"department":[{"_id":"HeEd"}],"publisher":"Cambridge University Press","publication_status":"published","year":"2017","publist_id":"6962","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1017/apr.2017.20","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"quality_controlled":"1","external_id":{"arxiv":["1607.05915"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1607.05915"}],"oa":1,"publication_identifier":{"issn":["00018678"]},"month":"09"},{"_id":"6287","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","ddc":["514","516","519"],"title":"Discrete Morse theory for random complexes ","pubrep_id":"873","oa_version":"Published Version","file":[{"file_size":2324870,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2017_Thesis_Nikitenko.pdf","checksum":"ece7e598a2f060b263c2febf7f3fe7f9","date_updated":"2020-07-14T12:47:26Z","date_created":"2019-04-09T14:54:51Z","relation":"main_file","file_id":"6289"},{"file_id":"6290","relation":"source_file","checksum":"99b7ad76e317efd447af60f91e29b49b","date_created":"2019-04-09T14:54:51Z","date_updated":"2020-07-14T12:47:26Z","access_level":"closed","file_name":"2017_Thesis_Nikitenko_source.zip","creator":"dernst","content_type":"application/zip","file_size":2863219}],"type":"dissertation","alternative_title":["ISTA Thesis"],"abstract":[{"lang":"eng","text":"The main objects considered in the present work are simplicial and CW-complexes with vertices forming a random point cloud. In particular, we consider a Poisson point process in R^n and study Delaunay and Voronoi complexes of the first and higher orders and weighted Delaunay complexes obtained as sections of Delaunay complexes, as well as the Čech complex. Further, we examine theDelaunay complex of a Poisson point process on the sphere S^n, as well as of a uniform point cloud, which is equivalent to the convex hull, providing a connection to the theory of random polytopes. Each of the complexes in question can be endowed with a radius function, which maps its cells to the radii of appropriately chosen circumspheres, called the radius of the cell. Applying and developing discrete Morse theory for these functions, joining it together with probabilistic and sometimes analytic machinery, and developing several integral geometric tools, we aim at getting the distributions of circumradii of typical cells. For all considered complexes, we are able to generalize and obtain up to constants the distribution of radii of typical intervals of all types. In low dimensions the constants can be computed explicitly, thus providing the explicit expressions for the expected numbers of cells. In particular, it allows to find the expected density of simplices of every dimension for a Poisson point process in R^4, whereas the result for R^3 was known already in 1970's."}],"citation":{"chicago":"Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_873.","mla":"Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873.","short":"A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science and Technology Austria, 2017.","ista":"Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute of Science and Technology Austria.","apa":"Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873","ieee":"A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of Science and Technology Austria, 2017.","ama":"Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873"},"page":"86","date_published":"2017-10-27T00:00:00Z","day":"27","article_processing_charge":"No","has_accepted_license":"1","year":"2017","publication_status":"published","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"}],"author":[{"last_name":"Nikitenko","first_name":"Anton","orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"718"},{"status":"public","relation":"part_of_dissertation","id":"5678"},{"status":"public","relation":"part_of_dissertation","id":"87"}]},"date_created":"2019-04-09T15:04:32Z","date_updated":"2023-09-15T12:10:34Z","file_date_updated":"2020-07-14T12:47:26Z","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"},"doi":"10.15479/AT:ISTA:th_873","degree_awarded":"PhD","supervisor":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"}],"language":[{"iso":"eng"}],"month":"10","publication_identifier":{"issn":["2663-337X"]}},{"citation":{"ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic Press, pp. 76–90, 2017.","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. Academic Press. https://doi.org/10.1016/j.jsc.2016.03.008","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation. Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008.","mla":"Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90."},"publication":"Journal of Symbolic Computation","page":"76 - 90","article_type":"original","date_published":"2017-01-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1433","intvolume":" 78","title":"Phat - Persistent homology algorithms toolbox","status":"public","oa_version":"Published Version","type":"journal_article","abstract":[{"lang":"eng","text":"Phat is an open-source C. ++ library for the computation of persistent homology by matrix reduction, targeted towards developers of software for topological data analysis. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. We provide numerous different reduction strategies as well as data types to store and manipulate the boundary matrix. We compare the different combinations through extensive experimental evaluation and identify optimization techniques that work well in practical situations. We also compare our software with various other publicly available libraries for persistent homology."}],"external_id":{"isi":["000384396000005"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jsc.2016.03.008"}],"project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"quality_controlled":"1","isi":1,"doi":"10.1016/j.jsc.2016.03.008","language":[{"iso":"eng"}],"publication_identifier":{"issn":[" 07477171"]},"month":"01","year":"2017","department":[{"_id":"HeEd"}],"publisher":"Academic Press","publication_status":"published","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"10894"}]},"author":[{"last_name":"Bauer","first_name":"Ulrich","full_name":"Bauer, Ulrich"},{"last_name":"Kerber","first_name":"Michael","full_name":"Kerber, Michael"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner"}],"volume":78,"date_created":"2018-12-11T11:51:59Z","date_updated":"2023-09-20T09:42:40Z","ec_funded":1,"publist_id":"5765"},{"publication_identifier":{"issn":["00018708"]},"month":"02","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"isi":1,"quality_controlled":"1","external_id":{"isi":["000409292900015"]},"main_file_link":[{"url":"https://arxiv.org/abs/1508.07594","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.aim.2016.12.026","ec_funded":1,"publist_id":"6173","publisher":"Academic Press","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2017","volume":308,"date_updated":"2023-09-20T11:21:27Z","date_created":"2018-12-11T11:50:34Z","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"last_name":"Bárány","first_name":"Imre","full_name":"Bárány, Imre"},{"full_name":"Robins, Sinai","last_name":"Robins","first_name":"Sinai"}],"scopus_import":"1","article_processing_charge":"No","day":"21","page":"627 - 644","citation":{"short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.","mla":"Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.","chicago":"Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.","ama":"Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026","ieee":"A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.","apa":"Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026","ista":"Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644."},"publication":"Advances in Mathematics","date_published":"2017-02-21T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","text":"In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform."}],"intvolume":" 308","status":"public","title":"Algebraic vertices of non-convex polyhedra","_id":"1180","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Submitted Version"},{"ec_funded":1,"publist_id":"6182","year":"2017","acknowledgement":"This research is partially supported by the Russian Government under the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by NSF grants DMS-1101688, DMS-1400876.","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"first_name":"Alexey","last_name":"Glazyrin","full_name":"Glazyrin, Alexey"},{"first_name":"Oleg","last_name":"Musin","full_name":"Musin, Oleg"},{"full_name":"Nikitenko, Anton","first_name":"Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201"}],"volume":37,"date_created":"2018-12-11T11:50:32Z","date_updated":"2023-09-20T11:23:53Z","publication_identifier":{"issn":["02099683"]},"month":"10","main_file_link":[{"url":"https://arxiv.org/abs/1411.6337","open_access":"1"}],"oa":1,"external_id":{"isi":["000418056000005"]},"project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"quality_controlled":"1","isi":1,"doi":"10.1007/s00493-016-3308-y","language":[{"iso":"eng"}],"type":"journal_article","issue":"5","abstract":[{"text":"We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions.","lang":"eng"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1173","intvolume":" 37","status":"public","title":"The Voronoi functional is maximized by the Delaunay triangulation in the plane","oa_version":"Submitted Version","scopus_import":"1","article_processing_charge":"No","day":"01","citation":{"ama":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910. doi:10.1007/s00493-016-3308-y","ista":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5), 887–910.","ieee":"H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional is maximized by the Delaunay triangulation in the plane,” Combinatorica, vol. 37, no. 5. Springer, pp. 887–910, 2017.","apa":"Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. Springer. https://doi.org/10.1007/s00493-016-3308-y","mla":"Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017, pp. 887–910, doi:10.1007/s00493-016-3308-y.","short":"H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017) 887–910.","chicago":"Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y."},"publication":"Combinatorica","page":"887 - 910","date_published":"2017-10-01T00:00:00Z"}]