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Pach, Discrete and Computational Geometry 64 (2020) 571–574.","mla":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 571–74, doi:10.1007/s00454-020-00237-5.","chicago":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5.","ama":"Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry. 2020;64:571-574. doi:10.1007/s00454-020-00237-5","ieee":"J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 571–574, 2020.","apa":"Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5","ista":"Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574."},"article_type":"letter_note","page":"571-574","date_published":"2020-10-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","_id":"8323","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"A farewell to Ricky Pollack","intvolume":" 64","oa_version":"None","type":"journal_article"},{"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","author":[{"full_name":"Graff, Grzegorz","last_name":"Graff","first_name":"Grzegorz"},{"full_name":"Graff, Beata","first_name":"Beata","last_name":"Graff"},{"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","first_name":"Krzysztof","last_name":"Narkiewicz"}],"date_updated":"2023-08-22T09:33:34Z","date_created":"2020-09-28T08:59:27Z","oa_version":"None","year":"2020","_id":"8580","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","title":"The application of persistent homology in the analysis of heart rate variability","status":"public","publisher":"IEEE","department":[{"_id":"HeEd"}],"month":"08","day":"01","article_processing_charge":"No","publication_identifier":{"isbn":["9781728157511"]},"scopus_import":"1","conference":{"name":"ESGCO: European Study Group on Cardiovascular Oscillations","end_date":"2020-07-15","location":"Pisa, Italy","start_date":"2020-07-15"},"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, ","citation":{"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","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.","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","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.","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.","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."},"external_id":{"isi":["000621172600045"]},"isi":1,"quality_controlled":"1"},{"type":"journal_article","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."}],"issue":"3","status":"public","title":"Waist of balls in hyperbolic and spherical spaces","intvolume":" 2020","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10867","oa_version":"Preprint","keyword":["General Mathematics"],"scopus_import":"1","day":"01","article_processing_charge":"No","article_type":"original","page":"669-697","publication":"International Mathematics Research Notices","citation":{"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","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","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.","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","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. 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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."}],"page":"155","citation":{"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.","chicago":"Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460.","ama":"Ölsböck K. The hole system of triangulated shapes. 2020. doi:10.15479/AT:ISTA:7460","ista":"Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria.","apa":"Ölsböck, K. (2020). The hole system of triangulated shapes. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7460","ieee":"K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science and Technology Austria, 2020."},"date_published":"2020-02-10T00:00:00Z","keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"],"day":"10","has_accepted_license":"1","article_processing_charge":"No"},{"publication_identifier":{"isbn":["978-3-99078-005-3"],"issn":["2663-337X"]},"month":"06","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"},"language":[{"iso":"eng"}],"supervisor":[{"full_name":"Wagner, Uli","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"degree_awarded":"PhD","doi":"10.15479/AT:ISTA:7944","license":"https://creativecommons.org/licenses/by-sa/4.0/","file_date_updated":"2020-07-14T12:48:05Z","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"publication_status":"published","year":"2020","date_created":"2020-06-08T00:49:46Z","date_updated":"2023-09-07T13:17:37Z","related_material":{"record":[{"id":"7950","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"5986"}]},"author":[{"orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana","full_name":"Masárová, Zuzana"}],"keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"has_accepted_license":"1","article_processing_charge":"No","day":"09","page":"160","citation":{"chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944.","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.","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.","ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944"},"date_published":"2020-06-09T00:00:00Z","alternative_title":["ISTA Thesis"],"type":"dissertation","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."}],"title":"Reconfiguration problems","status":"public","ddc":["516","514"],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"7944","file":[{"creator":"zmasarov","file_size":13661779,"content_type":"application/pdf","access_level":"open_access","file_name":"THESIS_Zuzka_Masarova.pdf","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","date_updated":"2020-07-14T12:48:05Z","date_created":"2020-06-08T00:34:00Z","file_id":"7945","relation":"main_file"},{"file_id":"7946","relation":"source_file","checksum":"45341a35b8f5529c74010b7af43ac188","date_created":"2020-06-08T00:35:30Z","date_updated":"2020-07-14T12:48:05Z","access_level":"closed","file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","creator":"zmasarov","content_type":"application/zip","file_size":32184006}],"oa_version":"Published Version"},{"license":"https://creativecommons.org/licenses/by/3.0/","ec_funded":1,"file_date_updated":"2020-10-27T14:31:52Z","article_number":"75","volume":173,"date_created":"2020-10-25T23:01:18Z","date_updated":"2023-09-07T13:29:00Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"9056"}]},"author":[{"full_name":"Osang, Georg F","last_name":"Osang","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Rouxel-Labbé, Mael","first_name":"Mael","last_name":"Rouxel-Labbé"},{"last_name":"Teillaud","first_name":"Monique","full_name":"Teillaud, Monique"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2020","publication_identifier":{"issn":["18688969"],"isbn":["9783959771627"]},"month":"08","language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.ESA.2020.75","conference":{"name":"ESA: Annual European Symposium on Algorithms","start_date":"2020-09-07","location":"Virtual, Online; Pisa, Italy","end_date":"2020-09-09"},"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","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"},"abstract":[{"lang":"eng","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. "}],"alternative_title":["LIPIcs"],"type":"conference","oa_version":"Published Version","file":[{"success":1,"checksum":"fe0f7c49a99ed870c671b911e10d5496","date_created":"2020-10-27T14:31:52Z","date_updated":"2020-10-27T14:31:52Z","file_id":"8712","relation":"main_file","creator":"cziletti","content_type":"application/pdf","file_size":733291,"access_level":"open_access","file_name":"2020_LIPIcs_Osang.pdf"}],"intvolume":" 173","ddc":["000"],"status":"public","title":"Generalizing CGAL periodic Delaunay triangulations","_id":"8703","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","has_accepted_license":"1","day":"26","scopus_import":"1","date_published":"2020-08-26T00:00:00Z","citation":{"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.","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.","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","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","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.","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.","short":"G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020."},"publication":"28th Annual European Symposium on Algorithms"},{"ec_funded":1,"file_date_updated":"2020-07-24T07:09:06Z","license":"https://creativecommons.org/licenses/by-nc/4.0/","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.","department":[{"_id":"HeEd"}],"publisher":"Akadémiai Kiadó","publication_status":"published","author":[{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken"}],"volume":57,"date_created":"2020-07-24T07:09:18Z","date_updated":"2023-10-10T13:05:27Z","publication_identifier":{"eissn":["1588-2896"],"issn":["0081-6906"]},"month":"07","oa":1,"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"]},"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"isi":1,"quality_controlled":"1","doi":"10.1556/012.2020.57.2.1454","language":[{"iso":"eng"}],"type":"journal_article","issue":"2","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."}],"_id":"8163","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 57","title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","status":"public","ddc":["510"],"file":[{"access_level":"open_access","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","creator":"mwintrae","file_size":1476072,"content_type":"application/pdf","file_id":"8164","relation":"main_file","date_created":"2020-07-24T07:09:06Z","date_updated":"2020-07-24T07:09:06Z"}],"oa_version":"Published Version","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"No","day":"24","citation":{"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.","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","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.","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"},"publication":"Studia Scientiarum Mathematicarum Hungarica","page":"193-199","article_type":"original","date_published":"2020-07-24T00:00:00Z"},{"file_date_updated":"2021-02-19T13:56:24Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","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).","publication_status":"published","publisher":"De Gruyter","department":[{"_id":"HeEd"}],"author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"}],"date_created":"2021-02-17T15:13:01Z","date_updated":"2023-10-17T12:34:51Z","volume":8,"month":"06","publication_identifier":{"issn":["2544-7297"]},"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"},"quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"doi":"10.1515/cmb-2020-0100","language":[{"iso":"eng"}],"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","_id":"9157","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"The weighted mean curvature derivative of a space-filling diagram","status":"public","ddc":["510"],"intvolume":" 8","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}],"oa_version":"Published Version","day":"20","article_processing_charge":"No","has_accepted_license":"1","publication":"Computational and Mathematical Biophysics","citation":{"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.","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.","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.","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","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","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"},"article_type":"original","page":"51-67","date_published":"2020-06-20T00:00:00Z"},{"file":[{"content_type":"application/pdf","file_size":707452,"creator":"dernst","file_name":"2020_CompMathBiophysics_Akopyan.pdf","access_level":"open_access","date_created":"2021-02-19T13:33:19Z","date_updated":"2021-02-19T13:33:19Z","checksum":"ca43a7440834eab6bbea29c59b56ef3a","success":1,"relation":"main_file","file_id":"9170"}],"oa_version":"Published Version","intvolume":" 8","title":"The weighted Gaussian curvature derivative of a space-filling diagram","ddc":["510"],"status":"public","_id":"9156","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","abstract":[{"lang":"eng","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."}],"type":"journal_article","date_published":"2020-07-21T00:00:00Z","page":"74-88","article_type":"original","citation":{"ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.","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.","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","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","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."},"publication":"Computational and Mathematical Biophysics","article_processing_charge":"No","has_accepted_license":"1","day":"21","volume":8,"date_created":"2021-02-17T15:12:44Z","date_updated":"2023-10-17T12:35:10Z","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}],"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","ec_funded":1,"file_date_updated":"2021-02-19T13:33:19Z","language":[{"iso":"eng"}],"doi":"10.1515/cmb-2020-0101","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"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":["1908.06777"]},"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,"publication_identifier":{"issn":["2544-7297"]},"month":"07"},{"month":"12","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"doi":"10.1007/s41468-020-00058-8","language":[{"iso":"eng"}],"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"},"quality_controlled":"1","file_date_updated":"2024-03-04T10:52:42Z","author":[{"first_name":"U.","last_name":"Bauer","full_name":"Bauer, U."},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","first_name":"Grzegorz","last_name":"Jablonski","full_name":"Jablonski, Grzegorz"},{"first_name":"M.","last_name":"Mrozek","full_name":"Mrozek, M."}],"date_created":"2024-03-04T10:47:49Z","date_updated":"2024-03-04T10:54:04Z","volume":4,"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.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","scopus_import":"1","date_published":"2020-12-01T00:00:00Z","publication":"Journal of Applied and Computational Topology","citation":{"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.","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.","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","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.","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"},"article_type":"original","page":"455-480","abstract":[{"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.","lang":"eng"}],"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"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"15064","title":"Čech-Delaunay gradient flow and homology inference for self-maps","status":"public","ddc":["500"],"intvolume":" 4"},{"month":"07","publication_identifier":{"issn":["1920-180X"]},"language":[{"iso":"eng"}],"doi":"10.20382/jocg.v10i1a9","quality_controlled":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"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":"2020-07-14T12:47:32Z","ec_funded":1,"date_created":"2019-06-03T09:35:33Z","date_updated":"2021-01-12T08:07:50Z","volume":10,"author":[{"first_name":"Ramsay","last_name":"Dyer","full_name":"Dyer, Ramsay"},{"first_name":"Gert","last_name":"Vegter","full_name":"Vegter, Gert"},{"first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Carleton University","year":"2019","day":"01","has_accepted_license":"1","scopus_import":1,"date_published":"2019-07-01T00:00:00Z","page":"223–256","publication":"Journal of Computational Geometry ","citation":{"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.","ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","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","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.","short":"R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10 (2019) 223–256.","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."},"abstract":[{"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.","lang":"eng"}],"issue":"1","type":"journal_article","file":[{"date_updated":"2020-07-14T12:47:32Z","date_created":"2019-06-03T09:30:01Z","checksum":"57b4df2f16a74eb499734ec8ee240178","relation":"main_file","file_id":"6516","file_size":2170882,"content_type":"application/pdf","creator":"mwintrae","file_name":"mainJournalFinal.pdf","access_level":"open_access"}],"oa_version":"Published Version","status":"public","ddc":["510"],"title":"Simplices modelled on spaces of constant curvature","intvolume":" 10","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"6515"},{"file":[{"relation":"main_file","file_id":"6629","date_created":"2019-07-12T08:32:46Z","date_updated":"2020-07-14T12:47:34Z","checksum":"ceabd152cfa55170d57763f9c6c60a53","file_name":"IntrinsicExtrinsicCCCG2019.pdf","access_level":"open_access","file_size":321176,"content_type":"application/pdf","creator":"mwintrae"}],"oa_version":"Submitted Version","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","last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"HeEd"}],"status":"public","title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","publication_status":"published","ddc":["004"],"year":"2019","_id":"6628","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"abstract":[{"lang":"eng","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."}],"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","start_date":"2019-08-08","location":"Edmonton, Canada","name":"CCCG: Canadian Conference in Computational Geometry"},"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"page":"275-279","quality_controlled":"1","citation":{"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.","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.","ieee":"G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds,” in The 31st Canadian Conference in Computational Geometry, Edmonton, Canada, 2019, pp. 275–279.","apa":"Vegter, G., & Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In The 31st Canadian Conference in Computational Geometry (pp. 275–279). Edmonton, Canada.","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.","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."},"oa":1,"publication":"The 31st Canadian Conference in Computational Geometry","has_accepted_license":"1","day":"01","month":"08","scopus_import":1},{"type":"conference","alternative_title":["LIPIcs"],"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"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"6648","status":"public","title":"Topological data analysis in information space","ddc":["510"],"intvolume":" 129","file":[{"checksum":"8ec8720730d4c789bf7b06540f1c29f4","date_updated":"2020-07-14T12:47:35Z","date_created":"2019-07-24T06:40:01Z","file_id":"6666","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":1355179,"access_level":"open_access","file_name":"2019_LIPICS_Edelsbrunner.pdf"}],"oa_version":"Published Version","scopus_import":1,"day":"01","has_accepted_license":"1","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","date_published":"2019-06-01T00:00:00Z","file_date_updated":"2020-07-14T12:47:35Z","year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga"},{"first_name":"Hubert","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert"}],"date_updated":"2021-01-12T08:08:23Z","date_created":"2019-07-17T10:36:09Z","volume":129,"month":"06","publication_identifier":{"isbn":["9783959771047"]},"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":{"arxiv":["1903.08510"]},"quality_controlled":"1","project":[{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"conference":{"end_date":"2019-06-21","location":"Portland, OR, United States","start_date":"2019-06-18","name":"SoCG 2019: Symposium on Computational Geometry"},"doi":"10.4230/LIPICS.SOCG.2019.31","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"date_published":"2019-08-01T00:00:00Z","conference":{"name":"CCCG: Canadian Conference in Computational Geometry","end_date":"2019-08-10","start_date":"2019-08-08","location":"Edmonton, Canada"},"page":"164-170","quality_controlled":"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.","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.","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.","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.","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.","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."},"main_file_link":[{"url":"https://cccg.ca/proceedings/2019/proceedings.pdf","open_access":"1"}],"external_id":{"arxiv":["1910.09917"]},"oa":1,"publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","article_processing_charge":"No","day":"01","month":"08","scopus_import":"1","oa_version":"Published Version","date_created":"2019-11-04T16:46:11Z","date_updated":"2023-08-04T10:57:42Z","related_material":{"record":[{"id":"8317","relation":"extended_version","status":"public"}]},"author":[{"last_name":"Aichholzer","first_name":"Oswin","full_name":"Aichholzer, Oswin"},{"first_name":"Hugo A","last_name":"Akitaya","full_name":"Akitaya, Hugo A"},{"last_name":"Cheung","first_name":"Kenneth C","full_name":"Cheung, Kenneth C"},{"first_name":"Erik D","last_name":"Demaine","full_name":"Demaine, Erik D"},{"first_name":"Martin L","last_name":"Demaine","full_name":"Demaine, Martin L"},{"last_name":"Fekete","first_name":"Sandor P","full_name":"Fekete, Sandor P"},{"full_name":"Kleist, Linda","first_name":"Linda","last_name":"Kleist"},{"last_name":"Kostitsyna","first_name":"Irina","full_name":"Kostitsyna, Irina"},{"first_name":"Maarten","last_name":"Löffler","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"},{"full_name":"Mundilova, Klara","last_name":"Mundilova","first_name":"Klara"},{"full_name":"Schmidt, Christiane","last_name":"Schmidt","first_name":"Christiane"}],"department":[{"_id":"HeEd"}],"publisher":"Canadian Conference on Computational Geometry","title":"Folding polyominoes with holes into a cube","status":"public","publication_status":"published","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","_id":"6989","year":"2019","acknowledgement":"This research was performed in part at the 33rd BellairsWinter Workshop on Computational Geometry. Wethank all other participants for a fruitful atmosphere.","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"},{"language":[{"iso":"eng"}],"doi":"10.1007/s41468-019-00029-8","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"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"},"publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"month":"06","volume":3,"date_updated":"2023-08-22T12:37:47Z","date_created":"2019-07-24T08:37:29Z","author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"},{"full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken"}],"publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2019","ec_funded":1,"file_date_updated":"2020-07-14T12:47:36Z","date_published":"2019-06-01T00:00:00Z","page":"29–58","article_type":"original","citation":{"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.","short":"J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58.","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.","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","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.","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","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."},"publication":"Journal of Applied and Computational Topology","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"6741","date_created":"2019-07-31T08:09:56Z","date_updated":"2020-07-14T12:47:36Z","checksum":"a5b244db9f751221409cf09c97ee0935","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf","access_level":"open_access","content_type":"application/pdf","file_size":2215157,"creator":"dernst"}],"intvolume":" 3","title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","status":"public","ddc":["000"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"6671","issue":"1-2","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."}],"type":"journal_article"},{"page":"91-102","publication":"Proceedings of the American Mathematical Society","citation":{"ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.","apa":"Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240","ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240","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.","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.","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102."},"date_published":"2019-01-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","title":"Two circles and only a straightedge","status":"public","intvolume":" 147","_id":"6050","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","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. "}],"isi":1,"quality_controlled":"1","external_id":{"isi":["000450363900008"],"arxiv":["1709.02562"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1709.02562"}],"language":[{"iso":"eng"}],"doi":"10.1090/proc/14240","month":"01","publication_status":"published","publisher":"AMS","department":[{"_id":"HeEd"}],"year":"2019","date_created":"2019-02-24T22:59:19Z","date_updated":"2023-08-24T14:48:59Z","volume":147,"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"last_name":"Fedorov","first_name":"Roman","full_name":"Fedorov, Roman"}]},{"publication":"Topological Methods in Nonlinear Analysis","citation":{"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","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.","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.","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.","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","chicago":"Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008."},"page":"457-490","date_published":"2019-06-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","_id":"6634","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"Lower and upper bounds for the waists of different spaces","intvolume":" 53","oa_version":"Preprint","type":"journal_article","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."}],"issue":"2","external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.06926"}],"isi":1,"quality_controlled":"1","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"doi":"10.12775/TMNA.2019.008","language":[{"iso":"eng"}],"month":"06","year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Akademicka Platforma Czasopism","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Hubard","first_name":"Alfredo","full_name":"Hubard, Alfredo"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"date_updated":"2023-08-29T06:32:48Z","date_created":"2019-07-14T21:59:19Z","volume":53,"ec_funded":1},{"day":"17","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","date_published":"2019-07-17T00:00:00Z","publication":"Astronomy and Astrophysics","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.","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","ieee":"P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 2019."},"article_type":"original","abstract":[{"text":"We study the topology generated by the temperature fluctuations of the cosmic microwave background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over 𝕊2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of “masks” is of importance, we introduce the concept of relative homology. The parametric χ2-test shows differences between observations and simulations, yielding p-values at percent to less than permil levels roughly between 2 and 7°, with the difference in the number of components and holes peaking at more than 3σ sporadically at these scales. The highest observed deviation between the observations and simulations for b0 and b1 is approximately between 3σ and 4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66° in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and first Betti numbers, respectively. Further, since these topological descriptors show consistent anomalous behaviour over independent measurements of Planck and WMAP, instrumental and systematic errors may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations based on power-spectrum matching the characteristics of the observed dipped power spectrum are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB, whether cosmological in nature or arising due to late-time effects, is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate the study of primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology, including topological defect models.","lang":"eng"}],"type":"journal_article","file":[{"file_name":"2019_AstronomyAstrophysics_Pranav.pdf","access_level":"open_access","file_size":14420451,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"6766","date_updated":"2020-07-14T12:47:39Z","date_created":"2019-08-05T08:08:59Z","checksum":"83b9209ed9eefbdcefd89019c5a97805"}],"oa_version":"Published Version","_id":"6756","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["520","530"],"title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","status":"public","intvolume":" 627","month":"07","publication_identifier":{"issn":["00046361"],"eissn":["14320746"]},"doi":"10.1051/0004-6361/201834916","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"},"oa":1,"external_id":{"isi":["000475839300003"],"arxiv":["1812.07678"]},"isi":1,"quality_controlled":"1","project":[{"name":"Toward Computational Information Topology","grant_number":"M62909-18-1-2038","_id":"265683E4-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"file_date_updated":"2020-07-14T12:47:39Z","article_number":"A163","author":[{"full_name":"Pranav, Pratyush","last_name":"Pranav","first_name":"Pratyush"},{"last_name":"Adler","first_name":"Robert J.","full_name":"Adler, Robert J."},{"first_name":"Thomas","last_name":"Buchert","full_name":"Buchert, Thomas"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Jones","first_name":"Bernard J.T.","full_name":"Jones, Bernard J.T."},{"last_name":"Schwartzman","first_name":"Armin","full_name":"Schwartzman, Armin"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner"},{"last_name":"Van De Weygaert","first_name":"Rien","full_name":"Van De Weygaert, Rien"}],"date_created":"2019-08-04T21:59:18Z","date_updated":"2023-08-29T07:01:48Z","volume":627,"year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"EDP Sciences"},{"_id":"6793","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 51","title":"The Regge symmetry, confocal conics, and the Schläfli formula","status":"public","oa_version":"Preprint","type":"journal_article","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"}],"citation":{"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","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.","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.","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."},"publication":"Bulletin of the London Mathematical Society","page":"765-775","article_type":"original","date_published":"2019-10-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","year":"2019","department":[{"_id":"HeEd"}],"publisher":"London Mathematical Society","publication_status":"published","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"first_name":"Ivan","last_name":"Izmestiev","full_name":"Izmestiev, Ivan"}],"volume":51,"date_created":"2019-08-11T21:59:23Z","date_updated":"2023-08-29T07:08:34Z","ec_funded":1,"oa":1,"external_id":{"isi":["000478560200001"],"arxiv":["1903.04929"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.04929"}],"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"doi":"10.1112/blms.12276","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["14692120"],"issn":["00246093"]},"month":"10"},{"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","oa_version":"Preprint","_id":"6828","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"Arakawa-Suzuki functors for Whittaker modules","intvolume":" 538","day":"15","article_processing_charge":"No","date_published":"2019-11-15T00:00:00Z","publication":"Journal of Algebra","citation":{"mla":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027.","short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027.","ama":"Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027","ista":"Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289.","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"},"article_type":"original","page":"261-289","author":[{"full_name":"Brown, Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","first_name":"Adam"}],"date_created":"2019-08-22T07:54:13Z","date_updated":"2023-08-29T07:11:47Z","volume":538,"year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier","month":"11","publication_identifier":{"issn":["0021-8693"]},"doi":"10.1016/j.jalgebra.2019.07.027","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1805.04676","open_access":"1"}],"external_id":{"isi":["000487176300011"],"arxiv":["1805.04676"]},"oa":1,"isi":1,"quality_controlled":"1"}]