[{"file":[{"date_updated":"2021-04-22T08:08:14Z","date_created":"2021-04-22T08:08:14Z","checksum":"1787baef1523d6d93753b90d0c109a6d","success":1,"relation":"main_file","file_id":"9346","file_size":3117435,"content_type":"application/pdf","creator":"mwintrae","file_name":"df_socg_final_version.pdf","access_level":"open_access"}],"oa_version":"Published Version","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","_id":"9345","intvolume":" 189","status":"public","ddc":["004","516"],"title":"The density fingerprint of a periodic point set","abstract":[{"text":"Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction.","lang":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"date_published":"2021-06-02T00:00:00Z","citation":{"ama":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. The density fingerprint of a periodic point set. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16. doi:10.4230/LIPIcs.SoCG.2021.32","ista":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. 2021. The density fingerprint of a periodic point set. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol. 189, 32:1-32:16.","ieee":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, and M. Wintraecken, “The density fingerprint of a periodic point set,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 32:1-32:16.","apa":"Edelsbrunner, H., Heiss, T., Kurlin , V., Smith, P., & Wintraecken, M. (2021). The density fingerprint of a periodic point set. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 32:1-32:16). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.32","mla":"Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:10.4230/LIPIcs.SoCG.2021.32.","short":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.","chicago":"Edelsbrunner, Herbert, Teresa Heiss, Vitaliy Kurlin , Philip Smith, and Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:32:1-32:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.32."},"publication":"37th International Symposium on Computational Geometry (SoCG 2021)","page":"32:1-32:16","has_accepted_license":"1","article_processing_charge":"No","day":"02","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"first_name":"Teresa","last_name":"Heiss","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"last_name":" Kurlin ","first_name":"Vitaliy","full_name":" Kurlin , Vitaliy"},{"full_name":"Smith, Philip","last_name":"Smith","first_name":"Philip"},{"full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken"}],"volume":189,"date_updated":"2023-02-23T13:55:40Z","date_created":"2021-04-22T08:09:58Z","acknowledgement":"The authors thank Janos Pach for insightful discussions on the topic of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.","year":"2021","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"publication_status":"published","ec_funded":1,"file_date_updated":"2021-04-22T08:08:14Z","doi":"10.4230/LIPIcs.SoCG.2021.32","conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2021-06-07","location":"Virtual","end_date":"2021-06-11"},"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,"project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Discretization in Geometry and Dynamics"},{"grant_number":"Z00312","_id":"25C5A090-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"},{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"quality_controlled":"1","publication_identifier":{"issn":["1868-8969"]},"month":"06"},{"file_date_updated":"2021-06-28T13:11:39Z","ec_funded":1,"article_number":"16","date_created":"2021-06-27T22:01:48Z","date_updated":"2023-02-23T14:02:28Z","volume":189,"author":[{"full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","first_name":"Ranita","last_name":"Biswas"},{"last_name":"Cultrera di Montesano","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"year":"2021","month":"06","publication_identifier":{"isbn":["9783959771849"],"issn":["18688969"]},"language":[{"iso":"eng"}],"conference":{"name":"SoCG: International Symposium on Computational Geometry","end_date":"2021-06-11","start_date":"2021-06-07","location":"Online"},"doi":"10.4230/LIPIcs.SoCG.2021.16","quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"},{"name":"Discretization in Geometry and Dynamics","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"}],"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"},"abstract":[{"text":"Generalizing Lee’s inductive argument for counting the cells of higher order Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse theoretic quantities for piecewise constant functions on planar arrangements. Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for 1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s first k-1 sublevel sets. We get similar expressions for the vertices, edges, and polygons of the order-k Voronoi tessellation.","lang":"eng"}],"alternative_title":["LIPIcs"],"type":"conference","file":[{"access_level":"open_access","file_name":"2021_LIPIcs_Biswas.pdf","file_size":727817,"content_type":"application/pdf","creator":"asandaue","relation":"main_file","file_id":"9611","checksum":"22b11a719018b22ecba2471b51f2eb40","success":1,"date_updated":"2021-06-28T13:11:39Z","date_created":"2021-06-28T13:11:39Z"}],"oa_version":"Published Version","status":"public","title":"Counting cells of order-k voronoi tessellations in ℝ3 with morse theory","ddc":["516"],"intvolume":" 189","_id":"9604","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","day":"02","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","date_published":"2021-06-02T00:00:00Z","publication":"Leibniz International Proceedings in Informatics","citation":{"short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","mla":"Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” Leibniz International Proceedings in Informatics, vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.16.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.16.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting cells of order-k voronoi tessellations in ℝ3 with morse theory,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2021). Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.16","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 16."}},{"_id":"9824","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","status":"public","intvolume":" 12708","oa_version":"None","type":"conference","alternative_title":["LNCS"],"abstract":[{"lang":"eng","text":"We define a new compact coordinate system in which each integer triplet addresses a voxel in the BCC grid, and we investigate some of its properties. We propose a characterization of 3D discrete analytical planes with their topological features (in the Cartesian and in the new coordinate system) such as the interrelation between the thickness of the plane and the separability constraint we aim to obtain."}],"publication":"Discrete Geometry and Mathematical Morphology","citation":{"ista":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered cubic grid - coordinate system and discrete analytical plane definition. Discrete Geometry and Mathematical Morphology. DGMM: International Conference on Discrete Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163.","ieee":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered cubic grid - coordinate system and discrete analytical plane definition,” in Discrete Geometry and Mathematical Morphology, Uppsala, Sweden, 2021, vol. 12708, pp. 152–163.","apa":"Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., & Andres, E. (2021). Body centered cubic grid - coordinate system and discrete analytical plane definition. In Discrete Geometry and Mathematical Morphology (Vol. 12708, pp. 152–163). Uppsala, Sweden: Springer Nature. https://doi.org/10.1007/978-3-030-76657-3_10","ama":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic grid - coordinate system and discrete analytical plane definition. In: Discrete Geometry and Mathematical Morphology. Vol 12708. Springer Nature; 2021:152-163. doi:10.1007/978-3-030-76657-3_10","chicago":"Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” In Discrete Geometry and Mathematical Morphology, 12708:152–63. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-76657-3_10.","mla":"Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” Discrete Geometry and Mathematical Morphology, vol. 12708, Springer Nature, 2021, pp. 152–63, doi:10.1007/978-3-030-76657-3_10.","short":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163."},"page":"152-163","date_published":"2021-05-16T00:00:00Z","scopus_import":"1","day":"16","article_processing_charge":"No","acknowledgement":"This work has been partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia through the project no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35 (RB).","year":"2021","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"author":[{"first_name":"Lidija","last_name":"Čomić","full_name":"Čomić, Lidija"},{"full_name":"Zrour, Rita","first_name":"Rita","last_name":"Zrour"},{"first_name":"Gaëlle","last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle"},{"full_name":"Biswas, Ranita","last_name":"Biswas","first_name":"Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Andres, Eric","last_name":"Andres","first_name":"Eric"}],"date_created":"2021-08-08T22:01:29Z","date_updated":"2022-05-31T06:58:21Z","volume":12708,"ec_funded":1,"quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","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"}],"conference":{"end_date":"2021-05-27","location":"Uppsala, Sweden","start_date":"2021-05-24","name":"DGMM: International Conference on Discrete Geometry and Mathematical Morphology"},"doi":"10.1007/978-3-030-76657-3_10","language":[{"iso":"eng"}],"month":"05","publication_identifier":{"issn":["03029743"],"isbn":["9783030766566"],"eissn":["16113349"]}},{"title":"Folding polyominoes with holes into a cube","status":"public","intvolume":" 93","_id":"8317","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability."}],"article_type":"original","publication":"Computational Geometry: Theory and Applications","citation":{"ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 2021;93. doi:10.1016/j.comgeo.2020.101700","ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2021. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 93, 101700.","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2020.101700","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications, vol. 93, 101700, Elsevier, 2021, doi:10.1016/j.comgeo.2020.101700.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, Computational Geometry: Theory and Applications 93 (2021).","chicago":"Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications. Elsevier, 2021. https://doi.org/10.1016/j.comgeo.2020.101700."},"date_published":"2021-02-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","publication_status":"published","publisher":"Elsevier","department":[{"_id":"HeEd"}],"acknowledgement":"This research was performed in part at the 33rd Bellairs Winter Workshop on Computational Geometry. We thank all other participants for a fruitful atmosphere. H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","year":"2021","date_created":"2020-08-30T22:01:09Z","date_updated":"2023-08-04T10:57:42Z","volume":93,"author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"full_name":"Akitaya, Hugo A.","first_name":"Hugo A.","last_name":"Akitaya"},{"full_name":"Cheung, Kenneth C.","first_name":"Kenneth C.","last_name":"Cheung"},{"first_name":"Erik D.","last_name":"Demaine","full_name":"Demaine, Erik D."},{"full_name":"Demaine, Martin L.","last_name":"Demaine","first_name":"Martin L."},{"first_name":"Sándor P.","last_name":"Fekete","full_name":"Fekete, Sándor P."},{"full_name":"Kleist, Linda","first_name":"Linda","last_name":"Kleist"},{"full_name":"Kostitsyna, Irina","last_name":"Kostitsyna","first_name":"Irina"},{"full_name":"Löffler, Maarten","last_name":"Löffler","first_name":"Maarten"},{"full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","first_name":"Zuzana","last_name":"Masárová"},{"full_name":"Mundilova, Klara","last_name":"Mundilova","first_name":"Klara"},{"first_name":"Christiane","last_name":"Schmidt","full_name":"Schmidt, Christiane"}],"related_material":{"record":[{"status":"public","relation":"shorter_version","id":"6989"}]},"article_number":"101700","isi":1,"quality_controlled":"1","project":[{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.09917v3"}],"external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2020.101700","month":"02","publication_identifier":{"issn":["09257721"]}},{"language":[{"iso":"eng"}],"doi":"10.1090/proc/15205","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.08286"}],"external_id":{"arxiv":["1910.08286"],"isi":["000600416300004"]},"publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]},"month":"01","volume":149,"date_updated":"2023-08-04T11:11:47Z","date_created":"2020-11-19T10:17:40Z","author":[{"last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","full_name":"Brown, Adam"},{"first_name":"Anna","last_name":"Romanov","full_name":"Romanov, Anna"}],"publisher":"American Mathematical Society","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2021","acknowledgement":"We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059.","ec_funded":1,"date_published":"2021-01-01T00:00:00Z","page":"37-52","article_type":"original","citation":{"chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/proc/15205.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52.","mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205.","apa":"Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15205","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings of the American Mathematical Society, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52.","ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205"},"publication":"Proceedings of the American Mathematical Society","article_processing_charge":"No","day":"01","keyword":["Applied Mathematics","General Mathematics"],"oa_version":"Preprint","intvolume":" 149","status":"public","title":"Contravariant forms on Whittaker modules","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"8773","issue":"1","abstract":[{"text":"Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.","lang":"eng"}],"type":"journal_article"},{"title":"Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic","status":"public","_id":"9253","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","type":"conference","abstract":[{"lang":"eng","text":"In March 2020, the Austrian government introduced a widespread lock-down in response to the COVID-19 pandemic. Based on subjective impressions and anecdotal evidence, Austrian public and private life came to a sudden halt. Here we assess the effect of the lock-down quantitatively for all regions in Austria and present an analysis of daily changes of human mobility throughout Austria using near-real-time anonymized mobile phone data. We describe an efficient data aggregation pipeline and analyze the mobility by quantifying mobile-phone traffic at specific point of interests (POIs), analyzing individual trajectories and investigating the cluster structure of the origin-destination graph. We found a reduction of commuters at Viennese metro stations of over 80% and the number of devices with a radius of gyration of less than 500 m almost doubled. The results of studying crowd-movement behavior highlight considerable changes in the structure of mobility networks, revealed by a higher modularity and an increase from 12 to 20 detected communities. We demonstrate the relevance of mobility data for epidemiological studies by showing a significant correlation of the outflow from the town of Ischgl (an early COVID-19 hotspot) and the reported COVID-19 cases with an 8-day time lag. This research indicates that mobile phone usage data permits the moment-by-moment quantification of mobility behavior for a whole country. We emphasize the need to improve the availability of such data in anonymized form to empower rapid response to combat COVID-19 and future pandemics."}],"page":"3123-3132","publication":"2020 IEEE International Conference on Big Data","citation":{"ista":"Heiler G, Reisch T, Hurt J, Forghani M, Omani A, Hanbury A, Karimipour F. 2021. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. 2020 IEEE International Conference on Big Data. Big Data: International Conference on Big Data, 3123–3132.","apa":"Heiler, G., Reisch, T., Hurt, J., Forghani, M., Omani, A., Hanbury, A., & Karimipour, F. (2021). Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In 2020 IEEE International Conference on Big Data (pp. 3123–3132). Atlanta, GA, United States: IEEE. https://doi.org/10.1109/bigdata50022.2020.9378374","ieee":"G. Heiler et al., “Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic,” in 2020 IEEE International Conference on Big Data, Atlanta, GA, United States, 2021, pp. 3123–3132.","ama":"Heiler G, Reisch T, Hurt J, et al. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In: 2020 IEEE International Conference on Big Data. IEEE; 2021:3123-3132. doi:10.1109/bigdata50022.2020.9378374","chicago":"Heiler, Georg, Tobias Reisch, Jan Hurt, Mohammad Forghani, Aida Omani, Allan Hanbury, and Farid Karimipour. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” In 2020 IEEE International Conference on Big Data, 3123–32. IEEE, 2021. https://doi.org/10.1109/bigdata50022.2020.9378374.","mla":"Heiler, Georg, et al. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–32, doi:10.1109/bigdata50022.2020.9378374.","short":"G. Heiler, T. Reisch, J. Hurt, M. Forghani, A. Omani, A. Hanbury, F. Karimipour, in:, 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–3132."},"date_published":"2021-03-19T00:00:00Z","scopus_import":"1","day":"19","article_processing_charge":"No","publication_status":"published","publisher":"IEEE","department":[{"_id":"HeEd"}],"year":"2021","date_created":"2021-03-21T11:34:07Z","date_updated":"2023-08-07T14:00:13Z","author":[{"full_name":"Heiler, Georg","first_name":"Georg","last_name":"Heiler"},{"first_name":"Tobias","last_name":"Reisch","full_name":"Reisch, Tobias"},{"last_name":"Hurt","first_name":"Jan","full_name":"Hurt, Jan"},{"last_name":"Forghani","first_name":"Mohammad","full_name":"Forghani, Mohammad"},{"first_name":"Aida","last_name":"Omani","full_name":"Omani, Aida"},{"first_name":"Allan","last_name":"Hanbury","full_name":"Hanbury, Allan"},{"orcid":"0000-0001-6746-4174","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","last_name":"Karimipour","first_name":"Farid","full_name":"Karimipour, Farid"}],"isi":1,"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2008.10064"}],"external_id":{"arxiv":["2008.10064"],"isi":["000662554703032"]},"oa":1,"language":[{"iso":"eng"}],"conference":{"name":"Big Data: International Conference on Big Data","start_date":"2020-12-10","location":"Atlanta, GA, United States","end_date":"2020-12-13"},"doi":"10.1109/bigdata50022.2020.9378374","month":"03","publication_identifier":{"isbn":["9781728162515"]}},{"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"quality_controlled":"1","isi":1,"external_id":{"isi":["000635460400001"]},"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":"10.1007/s00454-021-00281-9","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"month":"03","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2021","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha), and by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF)\r\nOpen Access funding provided by the Institute of Science and Technology (IST Austria).","volume":65,"date_updated":"2023-08-07T14:35:44Z","date_created":"2021-04-11T22:01:15Z","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"187"}]},"author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Osang, Georg F","first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"ec_funded":1,"file_date_updated":"2021-12-01T10:56:53Z","page":"1296–1313","article_type":"original","citation":{"ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 2021;65:1296–1313. doi:10.1007/s00454-021-00281-9","ista":"Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 65, 1296–1313.","ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” Discrete and Computational Geometry, vol. 65. Springer Nature, pp. 1296–1313, 2021.","apa":"Edelsbrunner, H., & Osang, G. F. (2021). The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00281-9","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “The Multi-Cover Persistence of Euclidean Balls.” Discrete and Computational Geometry, vol. 65, Springer Nature, 2021, pp. 1296–1313, doi:10.1007/s00454-021-00281-9.","short":"H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-021-00281-9."},"publication":"Discrete and Computational Geometry","date_published":"2021-03-31T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"31","intvolume":" 65","ddc":["516"],"title":"The multi-cover persistence of Euclidean balls","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9317","oa_version":"Published Version","file":[{"creator":"cchlebak","file_size":677704,"content_type":"application/pdf","file_name":"2021_DisCompGeo_Edelsbrunner_Osang.pdf","access_level":"open_access","date_created":"2021-12-01T10:56:53Z","date_updated":"2021-12-01T10:56:53Z","success":1,"checksum":"59b4e1e827e494209bcb4aae22e1d347","file_id":"10394","relation":"main_file"}],"type":"journal_article","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 of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers."}]},{"language":[{"iso":"eng"}],"doi":"10.1016/j.jctb.2021.05.004","isi":1,"quality_controlled":"1","project":[{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize"}],"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":{"isi":["000702280800002"]},"month":"06","publication_identifier":{"issn":["0095-8956"]},"date_created":"2021-06-27T22:01:47Z","date_updated":"2023-08-10T13:38:00Z","volume":151,"author":[{"full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","last_name":"Pach"},{"full_name":"Tomon, István","first_name":"István","last_name":"Tomon"}],"publication_status":"published","publisher":"Elsevier","department":[{"_id":"HeEd"}],"year":"2021","acknowledgement":"We would like to thank the anonymous referees for their useful comments and suggestions. János Pach is partially supported by Austrian Science Fund (FWF) grant Z 342-N31 and by ERC Advanced grant “GeoScape.” István Tomon is partially supported by Swiss National Science Foundation grant no. 200021_196965, and thanks the support of MIPT Moscow. Both authors are partially supported by The Russian Government in the framework of MegaGrant no. 075-15-2019-1926.","file_date_updated":"2021-06-28T13:33:23Z","date_published":"2021-06-09T00:00:00Z","article_type":"original","page":"21-37","publication":"Journal of Combinatorial Theory. Series B","citation":{"ama":"Pach J, Tomon I. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory Series B. 2021;151:21-37. doi:10.1016/j.jctb.2021.05.004","apa":"Pach, J., & Tomon, I. (2021). Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. Elsevier. https://doi.org/10.1016/j.jctb.2021.05.004","ieee":"J. Pach and I. Tomon, “Erdős-Hajnal-type results for monotone paths,” Journal of Combinatorial Theory. Series B, vol. 151. Elsevier, pp. 21–37, 2021.","ista":"Pach J, Tomon I. 2021. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. 151, 21–37.","short":"J. Pach, I. Tomon, Journal of Combinatorial Theory. Series B 151 (2021) 21–37.","mla":"Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” Journal of Combinatorial Theory. Series B, vol. 151, Elsevier, 2021, pp. 21–37, doi:10.1016/j.jctb.2021.05.004.","chicago":"Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” Journal of Combinatorial Theory. Series B. Elsevier, 2021. https://doi.org/10.1016/j.jctb.2021.05.004."},"day":"09","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","file":[{"date_created":"2021-06-28T13:33:23Z","date_updated":"2021-06-28T13:33:23Z","checksum":"15fbc9064cd9d1c777ac0043b78c8f12","success":1,"relation":"main_file","file_id":"9612","file_size":418168,"content_type":"application/pdf","creator":"asandaue","file_name":"2021_JournalOfCombinatorialTheory_Pach.pdf","access_level":"open_access"}],"oa_version":"Published Version","title":"Erdős-Hajnal-type results for monotone paths","status":"public","ddc":["510"],"intvolume":" 151","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9602","abstract":[{"text":"An ordered graph is a graph with a linear ordering on its vertex set. We prove that for every positive integer k, there exists a constant ck > 0 such that any ordered graph G on n vertices with the property that neither G nor its complement contains an induced monotone path of size k, has either a clique or an independent set of size at least n^ck . This strengthens a result of Bousquet, Lagoutte, and Thomassé, who proved the analogous result for unordered graphs.\r\nA key idea of the above paper was to show that any unordered graph on n vertices that does not contain an induced path of size k, and whose maximum degree is at most c(k)n for some small c(k) > 0, contains two disjoint linear size subsets with no edge between them. This approach fails for ordered graphs, because the analogous statement is false for k ≥ 3, by a construction of Fox. We provide some further examples showing that this statement also fails for ordered graphs avoiding other ordered trees.","lang":"eng"}],"type":"journal_article"},{"publication_identifier":{"eissn":["19326203"]},"month":"07","doi":"10.1371/journal.pone.0253851","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":{"pmid":["34292957"],"isi":["000678124900050"]},"oa":1,"isi":1,"quality_controlled":"1","file_date_updated":"2021-08-09T09:25:41Z","article_number":"e0253851","author":[{"full_name":"Graff, Grzegorz","last_name":"Graff","first_name":"Grzegorz"},{"full_name":"Graff, Beata","last_name":"Graff","first_name":"Beata"},{"last_name":"Pilarczyk","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel"},{"full_name":"Jablonski, Grzegorz","first_name":"Grzegorz","last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866"},{"last_name":"Gąsecki","first_name":"Dariusz","full_name":"Gąsecki, Dariusz"},{"full_name":"Narkiewicz, Krzysztof","first_name":"Krzysztof","last_name":"Narkiewicz"}],"volume":16,"date_updated":"2023-08-10T14:21:42Z","date_created":"2021-08-08T22:01:28Z","pmid":1,"acknowledgement":"We express our gratitude to the anonymous referees who provided constructive comments that helped us improve the quality of the paper.","year":"2021","publisher":"Public Library of Science","department":[{"_id":"HeEd"}],"publication_status":"published","has_accepted_license":"1","article_processing_charge":"Yes","day":"01","scopus_import":"1","date_published":"2021-07-01T00:00:00Z","citation":{"short":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, K. Narkiewicz, PLoS ONE 16 (2021).","mla":"Graff, Grzegorz, et al. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” PLoS ONE, vol. 16, no. 7, e0253851, Public Library of Science, 2021, doi:10.1371/journal.pone.0253851.","chicago":"Graff, Grzegorz, Beata Graff, Pawel Pilarczyk, Grzegorz Jablonski, Dariusz Gąsecki, and Krzysztof Narkiewicz. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” PLoS ONE. Public Library of Science, 2021. https://doi.org/10.1371/journal.pone.0253851.","ama":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 2021;16(7). doi:10.1371/journal.pone.0253851","apa":"Graff, G., Graff, B., Pilarczyk, P., Jablonski, G., Gąsecki, D., & Narkiewicz, K. (2021). Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. Public Library of Science. https://doi.org/10.1371/journal.pone.0253851","ieee":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, and K. Narkiewicz, “Persistent homology as a new method of the assessment of heart rate variability,” PLoS ONE, vol. 16, no. 7. Public Library of Science, 2021.","ista":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. 2021. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 16(7), e0253851."},"publication":"PLoS ONE","article_type":"original","issue":"7","abstract":[{"text":"Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent homology is a novel data analysis tool developed in the recent decades that is rooted at algebraic topology. The Topological Data Analysis (TDA) approach focuses on examining the shape of the data in terms of connectedness and holes, and has recently proved to be very effective in various fields of research. In this paper we propose the use of persistent homology to the hrv analysis. We recall selected topological descriptors used in the literature and we introduce some new topological descriptors that reflect the specificity of hrv, and we discuss their relation to the standard hrv measures. In particular, we show that this novel approach provides a collection of indices that might be at least as useful as the classical parameters in differentiating between series of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering from a stroke episode.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","file":[{"creator":"asandaue","content_type":"application/pdf","file_size":2706919,"file_name":"2021_PLoSONE_Graff.pdf","access_level":"open_access","date_updated":"2021-08-09T09:25:41Z","date_created":"2021-08-09T09:25:41Z","success":1,"checksum":"0277aa155d5db1febd2cb384768bba5f","file_id":"9832","relation":"main_file"}],"_id":"9821","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 16","status":"public","ddc":["006"],"title":"Persistent homology as a new method of the assessment of heart rate variability"},{"oa_version":"Published Version","file":[{"date_updated":"2023-08-14T11:55:10Z","date_created":"2023-08-14T11:55:10Z","checksum":"3514382e3a1eb87fa6c61ad622874415","success":1,"relation":"main_file","file_id":"14053","file_size":1966019,"content_type":"application/pdf","creator":"dernst","file_name":"2023_ExperimentalMath_Akopyan.pdf","access_level":"open_access"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"10222","ddc":["510"],"status":"public","title":"The beauty of random polytopes inscribed in the 2-sphere","abstract":[{"lang":"eng","text":"Consider a random set of points on the unit sphere in ℝd, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the case d = 3, for which there are elementary proofs and fascinating formulas for metric properties. In particular, we study the fraction of acute facets, the expected intrinsic volumes, the total edge length, and the distance to a fixed point. Finally we generalize the results to the ellipsoid with homeoid density."}],"type":"journal_article","date_published":"2021-10-25T00:00:00Z","citation":{"ista":"Akopyan A, Edelsbrunner H, Nikitenko A. 2021. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics., 1–15.","ieee":"A. Akopyan, H. Edelsbrunner, and A. Nikitenko, “The beauty of random polytopes inscribed in the 2-sphere,” Experimental Mathematics. Taylor and Francis, pp. 1–15, 2021.","apa":"Akopyan, A., Edelsbrunner, H., & Nikitenko, A. (2021). The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. Taylor and Francis. https://doi.org/10.1080/10586458.2021.1980459","ama":"Akopyan A, Edelsbrunner H, Nikitenko A. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. 2021:1-15. doi:10.1080/10586458.2021.1980459","chicago":"Akopyan, Arseniy, Herbert Edelsbrunner, and Anton Nikitenko. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics. Taylor and Francis, 2021. https://doi.org/10.1080/10586458.2021.1980459.","mla":"Akopyan, Arseniy, et al. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics, Taylor and Francis, 2021, pp. 1–15, doi:10.1080/10586458.2021.1980459.","short":"A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15."},"publication":"Experimental Mathematics","page":"1-15","article_type":"original","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"25","scopus_import":"1","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"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"}],"date_updated":"2023-08-14T11:57:07Z","date_created":"2021-11-07T23:01:25Z","year":"2021","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.\r\nWe are grateful to Dmitry Zaporozhets and Christoph Thäle for valuable comments and for directing us to relevant references. We also thank to Anton Mellit for a useful discussion on Bessel functions.","publisher":"Taylor and Francis","department":[{"_id":"HeEd"}],"publication_status":"published","ec_funded":1,"file_date_updated":"2023-08-14T11:55:10Z","doi":"10.1080/10586458.2021.1980459","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":["000710893500001"],"arxiv":["2007.07783"]},"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Discretization in Geometry and Dynamics"},{"_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","publication_identifier":{"issn":["1058-6458"],"eissn":["1944-950X"]},"month":"10"},{"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"month":"07","language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00250-8","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"isi":1,"quality_controlled":"1","external_id":{"isi":["000597770300001"]},"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,"ec_funded":1,"file_date_updated":"2021-08-06T09:52:29Z","volume":66,"date_created":"2020-12-12T11:07:02Z","date_updated":"2023-09-05T15:02:40Z","author":[{"full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel","last_name":"Boissonnat"},{"last_name":"Kachanovich","first_name":"Siargey","full_name":"Kachanovich, Siargey"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","first_name":"Mathijs"}],"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding provided by the Institute of Science and Technology (IST Austria).","year":"2021","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","keyword":["Theoretical Computer Science","Computational Theory and Mathematics","Geometry and Topology","Discrete Mathematics and Combinatorics"],"date_published":"2021-07-01T00:00:00Z","page":"386-434","article_type":"original","citation":{"chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00250-8.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational Geometry 66 (2021) 386–434.","mla":"Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry, vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds: An elementary and quantified version of Whitney’s method,” Discrete & Computational Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 66(1), 386–434.","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8"},"publication":"Discrete & Computational Geometry","issue":"1","abstract":[{"text":"We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","file":[{"creator":"kschuh","content_type":"application/pdf","file_size":983307,"file_name":"2021_DescreteCompGeopmetry_Boissonnat.pdf","access_level":"open_access","date_updated":"2021-08-06T09:52:29Z","date_created":"2021-08-06T09:52:29Z","success":1,"checksum":"c848986091e56699dc12de85adb1e39c","file_id":"9795","relation":"main_file"}],"intvolume":" 66","status":"public","ddc":["516"],"title":"Triangulating submanifolds: An elementary and quantified version of Whitney’s method","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"8940"},{"year":"2021","acknowledgement":"AB was supported in part by the European Union’s Horizon 2020 research and innovation\r\nprogramme under the Marie Sklodowska-Curie GrantAgreement No. 754411 and NSF IIS-1513616. OB was supported in part by the Israel Science Foundation, Grant 1965/19. BW was supported in part by NSF IIS-1513616 and DBI-1661375. EM was supported in part by NSF CMMI-1800466, DMS-1800446, and CCF-1907591.We would like to thank the Institute for Mathematics and its Applications for hosting a workshop titled Bridging Statistics and Sheaves in May 2018, where this work was conceived.\r\nOpen Access funding provided by Institute of Science and Technology (IST Austria).","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"author":[{"full_name":"Brown, Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","first_name":"Adam"},{"full_name":"Bobrowski, Omer","last_name":"Bobrowski","first_name":"Omer"},{"full_name":"Munch, Elizabeth","last_name":"Munch","first_name":"Elizabeth"},{"full_name":"Wang, Bei","first_name":"Bei","last_name":"Wang"}],"date_updated":"2023-09-05T15:37:56Z","date_created":"2021-02-11T14:41:02Z","volume":5,"file_date_updated":"2021-02-11T14:43:59Z","ec_funded":1,"external_id":{"arxiv":["1909.03488"]},"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":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"doi":"10.1007/s41468-020-00063-x","language":[{"iso":"eng"}],"month":"03","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"9111","status":"public","ddc":["510"],"title":"Probabilistic convergence and stability of random mapper graphs","intvolume":" 5","file":[{"file_id":"9112","relation":"main_file","date_updated":"2021-02-11T14:43:59Z","date_created":"2021-02-11T14:43:59Z","success":1,"checksum":"3f02e9d47c428484733da0f588a3c069","file_name":"2020_JourApplCompTopology_Brown.pdf","access_level":"open_access","creator":"dernst","file_size":2090265,"content_type":"application/pdf"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"text":"We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space X equipped with a continuous function f:X→R. We first give a categorification of the mapper graph and the Reeb graph by interpreting them in terms of cosheaves and stratified covers of the real line R. We then introduce a variant of the classic mapper graph of Singh et al. (in: Eurographics symposium on point-based graphics, 2007), referred to as the enhanced mapper graph, and demonstrate that such a construction approximates the Reeb graph of (X,f) when it is applied to points randomly sampled from a probability density function concentrated on (X,f). Our techniques are based on the interleaving distance of constructible cosheaves and topological estimation via kernel density estimates. Following Munch and Wang (In: 32nd international symposium on computational geometry, volume 51 of Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, Germany, pp 53:1–53:16, 2016), we first show that the mapper graph of (X,f), a constructible R-space (with a fixed open cover), approximates the Reeb graph of the same space. We then construct an isomorphism between the mapper of (X,f) to the mapper of a super-level set of a probability density function concentrated on (X,f). Finally, building on the approach of Bobrowski et al. (Bernoulli 23(1):288–328, 2017b), we show that, with high probability, we can recover the mapper of the super-level set given a sufficiently large sample. Our work is the first to consider the mapper construction using the theory of cosheaves in a probabilistic setting. It is part of an ongoing effort to combine sheaf theory, probability, and statistics, to support topological data analysis with random data.","lang":"eng"}],"issue":"1","publication":"Journal of Applied and Computational Topology","citation":{"mla":"Brown, Adam, et al. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology, vol. 5, no. 1, Springer Nature, 2021, pp. 99–140, doi:10.1007/s41468-020-00063-x.","short":"A. Brown, O. Bobrowski, E. Munch, B. Wang, Journal of Applied and Computational Topology 5 (2021) 99–140.","chicago":"Brown, Adam, Omer Bobrowski, Elizabeth Munch, and Bei Wang. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology. Springer Nature, 2021. https://doi.org/10.1007/s41468-020-00063-x.","ama":"Brown A, Bobrowski O, Munch E, Wang B. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 2021;5(1):99-140. doi:10.1007/s41468-020-00063-x","ista":"Brown A, Bobrowski O, Munch E, Wang B. 2021. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 5(1), 99–140.","ieee":"A. Brown, O. Bobrowski, E. Munch, and B. Wang, “Probabilistic convergence and stability of random mapper graphs,” Journal of Applied and Computational Topology, vol. 5, no. 1. Springer Nature, pp. 99–140, 2021.","apa":"Brown, A., Bobrowski, O., Munch, E., & Wang, B. (2021). Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00063-x"},"article_type":"original","page":"99-140","date_published":"2021-03-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1"},{"page":"134","citation":{"chicago":"Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9056.","short":"G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science and Technology Austria, 2021.","mla":"Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9056.","ieee":"G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of Science and Technology Austria, Klosterneuburg, 2021.","apa":"Osang, G. F. (2021). Multi-cover persistence and Delaunay mosaics. Institute of Science and Technology Austria, Klosterneuburg. https://doi.org/10.15479/AT:ISTA:9056","ista":"Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg: Institute of Science and Technology Austria.","ama":"Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056"},"date_published":"2021-02-01T00:00:00Z","article_processing_charge":"No","has_accepted_license":"1","day":"01","title":"Multi-cover persistence and Delaunay mosaics","ddc":["006","514","516"],"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"9056","oa_version":"Published Version","file":[{"file_id":"9063","relation":"source_file","date_created":"2021-02-02T14:09:25Z","date_updated":"2021-02-03T10:37:28Z","checksum":"bcf27986147cab0533b6abadd74e7629","file_name":"thesis_source.zip","access_level":"closed","creator":"patrickd","file_size":13446994,"content_type":"application/zip"},{"file_id":"9064","relation":"main_file","success":1,"checksum":"9cc8af266579a464385bbe2aff6af606","date_created":"2021-02-02T14:09:18Z","date_updated":"2021-02-02T14:09:18Z","access_level":"open_access","file_name":"thesis_pdfA2b.pdf","creator":"patrickd","content_type":"application/pdf","file_size":5210329}],"alternative_title":["ISTA Thesis"],"type":"dissertation","abstract":[{"lang":"eng","text":"In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations. The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,\r\nand thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics. We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss the implications on persistence for periodic data sets."}],"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"}],"degree_awarded":"PhD","supervisor":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"doi":"10.15479/AT:ISTA:9056","publication_identifier":{"issn":["2663-337X"]},"month":"02","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"publisher":"Institute of Science and Technology Austria","publication_status":"published","year":"2021","date_updated":"2023-09-07T13:29:01Z","date_created":"2021-02-02T14:11:06Z","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"187"},{"status":"public","relation":"part_of_dissertation","id":"8703"}]},"author":[{"first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F"}],"place":"Klosterneuburg","file_date_updated":"2021-02-03T10:37:28Z"},{"language":[{"iso":"eng"}],"doi":"10.1039/d1sm00774b","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"quality_controlled":"1","isi":1,"oa":1,"external_id":{"pmid":["34569592"],"isi":["000700090000001"]},"publication_identifier":{"eissn":["1744-6848"],"issn":["1744-683X"]},"month":"10","volume":17,"date_updated":"2023-10-03T09:24:27Z","date_created":"2021-10-31T23:01:30Z","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":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Mohammad","last_name":"Saadatfar","full_name":"Saadatfar, Mohammad"}],"publisher":"Royal Society of Chemistry ","department":[{"_id":"HeEd"}],"publication_status":"published","pmid":1,"acknowledgement":"MS acknowledges the support by Australian Research Council funding through the ARC Training Centre for M3D Innovation (IC180100008). MS thanks M. Hanifpour and N. Francois for their input and valuable discussions. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant no. 788183 and from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","year":"2021","ec_funded":1,"file_date_updated":"2023-10-03T09:21:42Z","date_published":"2021-10-20T00:00:00Z","page":"9107-9115","article_type":"original","citation":{"ama":"Osang GF, Edelsbrunner H, Saadatfar M. Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. 2021;17(40):9107-9115. doi:10.1039/d1sm00774b","ieee":"G. F. Osang, H. Edelsbrunner, and M. Saadatfar, “Topological signatures and stability of hexagonal close packing and Barlow stackings,” Soft Matter, vol. 17, no. 40. Royal Society of Chemistry , pp. 9107–9115, 2021.","apa":"Osang, G. F., Edelsbrunner, H., & Saadatfar, M. (2021). Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. Royal Society of Chemistry . https://doi.org/10.1039/d1sm00774b","ista":"Osang GF, Edelsbrunner H, Saadatfar M. 2021. Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. 17(40), 9107–9115.","short":"G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 9107–9115.","mla":"Osang, Georg F., et al. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft Matter, vol. 17, no. 40, Royal Society of Chemistry , 2021, pp. 9107–15, doi:10.1039/d1sm00774b.","chicago":"Osang, Georg F, Herbert Edelsbrunner, and Mohammad Saadatfar. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft Matter. Royal Society of Chemistry , 2021. https://doi.org/10.1039/d1sm00774b."},"publication":"Soft Matter","article_processing_charge":"No","has_accepted_license":"1","day":"20","scopus_import":"1","file":[{"checksum":"b4da0c420530295e61b153960f6cb350","success":1,"date_updated":"2023-10-03T09:21:42Z","date_created":"2023-10-03T09:21:42Z","relation":"main_file","file_id":"14385","content_type":"application/pdf","file_size":4678788,"creator":"dernst","access_level":"open_access","file_name":"2021_SoftMatter_acceptedversion_Osang.pdf"}],"oa_version":"Submitted Version","intvolume":" 17","ddc":["540"],"title":"Topological signatures and stability of hexagonal close packing and Barlow stackings","status":"public","_id":"10204","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"40","abstract":[{"lang":"eng","text":"Two common representations of close packings of identical spheres consisting of hexagonal layers, called Barlow stackings, appear abundantly in minerals and metals. These motifs, however, occupy an identical portion of space and bear identical first-order topological signatures as measured by persistent homology. Here we present a novel method based on k-fold covers that unambiguously distinguishes between these patterns. Moreover, our approach provides topological evidence that the FCC motif is the more stable of the two in the context of evolving experimental sphere packings during the transition from disordered to an ordered state. We conclude that our approach can be generalised to distinguish between various Barlow stackings manifested in minerals and metals."}],"type":"journal_article"},{"date_created":"2021-06-27T22:01:49Z","date_updated":"2023-10-04T12:03:39Z","volume":189,"author":[{"last_name":"Corbet","first_name":"René","full_name":"Corbet, René"},{"last_name":"Kerber","first_name":"Michael","full_name":"Kerber, Michael"},{"full_name":"Lesnick, Michael","last_name":"Lesnick","first_name":"Michael"},{"full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","first_name":"Georg F","last_name":"Osang"}],"related_material":{"link":[{"url":"https://arxiv.org/abs/2103.07823","relation":"extended_version"}],"record":[{"relation":"later_version","status":"public","id":"12709"}]},"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"year":"2021","acknowledgement":"The authors want to thank the reviewers for many helpful comments and suggestions.","file_date_updated":"2021-06-28T12:40:47Z","article_number":"27","language":[{"iso":"eng"}],"conference":{"name":"SoCG: International Symposium on Computational Geometry","end_date":"2021-06-11","start_date":"2021-06-07","location":"Online"},"doi":"10.4230/LIPIcs.SoCG.2021.27","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":{"arxiv":["2103.07823"]},"month":"06","publication_identifier":{"issn":["18688969"],"isbn":["9783959771849"]},"oa_version":"Published Version","file":[{"date_created":"2021-06-28T12:40:47Z","date_updated":"2021-06-28T12:40:47Z","success":1,"checksum":"0de217501e7ba8b267d58deed0d51761","file_id":"9610","relation":"main_file","creator":"cziletti","file_size":"1367983","content_type":"application/pdf","file_name":"2021_LIPIcs_Corbet.pdf","access_level":"open_access"}],"ddc":["516"],"status":"public","title":"Computing the multicover bifiltration","intvolume":" 189","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","_id":"9605","abstract":[{"text":"Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness. ","lang":"eng"}],"alternative_title":["LIPIcs"],"type":"conference","date_published":"2021-06-02T00:00:00Z","publication":"Leibniz International Proceedings in Informatics","citation":{"ama":"Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.27","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2021. Computing the multicover bifiltration. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 27.","apa":"Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2021). Computing the multicover bifiltration. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.27","ieee":"R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.","mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” Leibniz International Proceedings in Informatics, vol. 189, 27, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.27.","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","chicago":"Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.27."},"day":"02","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1"},{"day":"02","article_processing_charge":"No","has_accepted_license":"1","series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","date_published":"2021-06-02T00:00:00Z","publication":"37th International Symposium on Computational Geometry (SoCG 2021)","citation":{"ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 17:1-17:16.","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 17:1-17:16). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.17","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational GeometryLeibniz International Proceedings in Informatics (LIPIcs), LIPIcs, vol. 189, 17:1-17:16.","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:17:1-17:16. doi:10.4230/LIPIcs.SoCG.2021.17","chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn Triangulations.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:17:1-17:16. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.17.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2021, p. 17:1-17:16.","mla":"Boissonnat, Jean-Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn Triangulations.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 17:1-17:16, doi:10.4230/LIPIcs.SoCG.2021.17."},"page":"17:1-17:16","abstract":[{"text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. submanifolds of ℝ^d defined as the zero set of some multivariate multivalued smooth function f: ℝ^d → ℝ^{d-n}, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M is to consider its Piecewise-Linear (PL) approximation M̂ based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ = 1/D (and unavoidably exponential in n). Since it is known that for δ = Ω (d^{2.5}), M̂ is O(D²)-close and isotopic to M, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M̂ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. ","lang":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"file":[{"date_updated":"2021-06-02T10:22:33Z","date_created":"2021-06-02T10:22:33Z","checksum":"c322aa48d5d35a35877896cc565705b6","success":1,"relation":"main_file","file_id":"9442","file_size":1972902,"content_type":"application/pdf","creator":"mwintrae","file_name":"LIPIcs-SoCG-2021-17.pdf","access_level":"open_access"}],"oa_version":"Published Version","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","_id":"9441","ddc":["005","516","514"],"title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations","status":"public","intvolume":" 189","month":"06","publication_identifier":{"isbn":["978-3-95977-184-9"],"issn":["1868-8969"]},"conference":{"start_date":"2021-06-07","location":"Virtual","end_date":"2021-06-11","name":"SoCG: Symposium on Computational Geometry"},"doi":"10.4230/LIPIcs.SoCG.2021.17","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,"quality_controlled":"1","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"file_date_updated":"2021-06-02T10:22:33Z","ec_funded":1,"place":"Dagstuhl, Germany","author":[{"full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel","last_name":"Boissonnat"},{"first_name":"Siargey","last_name":"Kachanovich","full_name":"Kachanovich, Siargey"},{"full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"related_material":{"record":[{"id":"12960","relation":"later_version","status":"public"}]},"date_updated":"2023-10-10T07:34:34Z","date_created":"2021-06-02T10:10:55Z","volume":189,"year":"2021","acknowledgement":"We thank Dominique Attali, Guilherme de Fonseca, Arijit Ghosh, Vincent Pilaud and Aurélien Alvarez for their comments and suggestions. We also acknowledge the reviewers.","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}]},{"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"month":"10","language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00240-w","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"}],"quality_controlled":"1","isi":1,"oa":1,"external_id":{"arxiv":["1908.00856"],"isi":["000564488500002"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1908.00856"}],"ec_funded":1,"volume":66,"date_created":"2020-09-06T22:01:13Z","date_updated":"2024-03-07T14:51:11Z","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"first_name":"Alexander I.","last_name":"Bobenko","full_name":"Bobenko, Alexander I."},{"full_name":"Schief, Wolfgang K.","last_name":"Schief","first_name":"Wolfgang K."},{"last_name":"Techter","first_name":"Jan","full_name":"Techter, Jan"}],"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","year":"2021","acknowledgement":"This research was supported by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”. W.K.S. was also supported by the Australian Research Council (DP1401000851). A.V.A. was also supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha).","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2021-10-01T00:00:00Z","page":"938-976","article_type":"original","citation":{"chicago":"Akopyan, Arseniy, Alexander I. Bobenko, Wolfgang K. Schief, and Jan Techter. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00240-w.","mla":"Akopyan, Arseniy, et al. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete and Computational Geometry, vol. 66, Springer Nature, 2021, pp. 938–76, doi:10.1007/s00454-020-00240-w.","short":"A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational Geometry 66 (2021) 938–976.","ista":"Akopyan A, Bobenko AI, Schief WK, Techter J. 2021. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. 66, 938–976.","apa":"Akopyan, A., Bobenko, A. I., Schief, W. K., & Techter, J. (2021). On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00240-w","ieee":"A. Akopyan, A. I. Bobenko, W. K. Schief, and J. Techter, “On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs,” Discrete and Computational Geometry, vol. 66. Springer Nature, pp. 938–976, 2021.","ama":"Akopyan A, Bobenko AI, Schief WK, Techter J. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. 2021;66:938-976. doi:10.1007/s00454-020-00240-w"},"publication":"Discrete and Computational Geometry","abstract":[{"lang":"eng","text":"Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics and systems of confocal quadrics. Intimate connections with classical deformations of quadrics that are isometric along asymptotic lines and circular cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces of Blaschke type generated by asymptotic and characteristic lines that are diagonally related to lines of curvature is proved theoretically and established constructively. Appropriate samplings (grids) of these webs lead to three-dimensional extensions of non-planar IC nets. Three-dimensional octahedral grids composed of planes and spatially extending (checkerboard) IC-nets are shown to arise in connection with systems of confocal quadrics in Minkowski space. In this context, the Laguerre geometric notion of conical octahedral grids of planes is introduced. The latter generalise the octahedral grids derived from systems of confocal quadrics in Minkowski space. An explicit construction of conical octahedral grids is presented. The results are accompanied by various illustrations which are based on the explicit formulae provided by the theory."}],"type":"journal_article","oa_version":"Preprint","intvolume":" 66","title":"On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs","status":"public","_id":"8338","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"oa_version":"Published Version","_id":"8248","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","ddc":["510"],"title":"Local conditions for triangulating submanifolds of Euclidean space","intvolume":" 66","abstract":[{"lang":"eng","text":"We consider the following setting: suppose that we are given a manifold M in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is, they are homeomorphic."}],"type":"journal_article","date_published":"2021-09-01T00:00:00Z","publication":"Discrete and Computational Geometry","citation":{"ama":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. 2021;66:666-686. doi:10.1007/s00454-020-00233-9","ista":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. 2021. Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. 66, 666–686.","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, and M. Wintraecken, “Local conditions for triangulating submanifolds of Euclidean space,” Discrete and Computational Geometry, vol. 66. Springer Nature, pp. 666–686, 2021.","apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., Lieutier, A., & Wintraecken, M. (2021). Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00233-9","mla":"Boissonnat, Jean-Daniel, et al. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” Discrete and Computational Geometry, vol. 66, Springer Nature, 2021, pp. 666–86, doi:10.1007/s00454-020-00233-9.","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, M. Wintraecken, Discrete and Computational Geometry 66 (2021) 666–686.","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, Andre Lieutier, and Mathijs Wintraecken. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00233-9."},"article_type":"original","page":"666-686","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"full_name":"Dyer, Ramsay","first_name":"Ramsay","last_name":"Dyer"},{"first_name":"Arijit","last_name":"Ghosh","full_name":"Ghosh, Arijit"},{"first_name":"Andre","last_name":"Lieutier","full_name":"Lieutier, Andre"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","first_name":"Mathijs"}],"date_created":"2020-08-11T07:11:51Z","date_updated":"2024-03-07T14:54:59Z","volume":66,"year":"2021","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria). Arijit Ghosh is supported by the Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India.\r\nThis work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India. The fifth author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"ec_funded":1,"doi":"10.1007/s00454-020-00233-9","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"},"main_file_link":[{"url":"https://doi.org/10.1007/s00454-020-00233-9","open_access":"1"}],"external_id":{"isi":["000558119300001"]},"quality_controlled":"1","isi":1,"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"month":"09","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]}},{"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"month":"06","language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00206-y","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","isi":1,"external_id":{"arxiv":["1712.07734"],"isi":["000536324700001"]},"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":"2020-11-25T09:06:41Z","volume":65,"date_created":"2020-05-30T10:26:04Z","date_updated":"2024-03-07T15:01:58Z","author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam","last_name":"Brown","full_name":"Brown, Adam"},{"first_name":"Bei","last_name":"Wang","full_name":"Wang, Bei"}],"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). This work was partially supported by NSF IIS-1513616 and NSF ABI-1661375. The authors would like to thank the anonymous referees for their insightful comments.","year":"2021","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","scopus_import":"1","date_published":"2021-06-01T00:00:00Z","page":"1166-1198","article_type":"original","citation":{"ama":"Brown A, Wang B. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 2021;65:1166-1198. doi:10.1007/s00454-020-00206-y","ista":"Brown A, Wang B. 2021. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 65, 1166–1198.","ieee":"A. Brown and B. Wang, “Sheaf-theoretic stratification learning from geometric and topological perspectives,” Discrete and Computational Geometry, vol. 65. Springer Nature, pp. 1166–1198, 2021.","apa":"Brown, A., & Wang, B. (2021). Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00206-y","mla":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” Discrete and Computational Geometry, vol. 65, Springer Nature, 2021, pp. 1166–98, doi:10.1007/s00454-020-00206-y.","short":"A. Brown, B. Wang, Discrete and Computational Geometry 65 (2021) 1166–1198.","chicago":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00206-y."},"publication":"Discrete and Computational Geometry","abstract":[{"lang":"eng","text":"We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the given sheaf is constructible. In particular, when we choose to work with the local homology sheaf, our algorithm gives an alternative to the local homology transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2), 195–222, 2020). Additionally, we give examples of stratifications based on the geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018), illustrating how the sheaf-theoretic approach can be used to study stratifications from both topological and geometric perspectives. This approach also points toward future applications of sheaf theory in the study of topological data analysis by illustrating the utility of the language of sheaf theory in generalizing existing algorithms."}],"type":"journal_article","file":[{"file_name":"2020_DiscreteCompGeometry_Brown.pdf","access_level":"open_access","content_type":"application/pdf","file_size":1013730,"creator":"dernst","relation":"main_file","file_id":"8803","date_updated":"2020-11-25T09:06:41Z","date_created":"2020-11-25T09:06:41Z","checksum":"487a84ea5841b75f04f66d7ebd71b67e","success":1}],"oa_version":"Published Version","intvolume":" 65","status":"public","ddc":["510"],"title":"Sheaf-theoretic stratification learning from geometric and topological perspectives","_id":"7905","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"language":[{"iso":"eng"}],"doi":"10.1007/s11786-020-00461-5","quality_controlled":"1","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"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":"03","publication_identifier":{"eissn":["1661-8289"],"issn":["1661-8270"]},"date_created":"2020-03-05T13:30:18Z","date_updated":"2021-01-12T08:14:13Z","volume":14,"author":[{"full_name":"Choudhary, Aruni","last_name":"Choudhary","first_name":"Aruni"},{"full_name":"Kachanovich, Siargey","last_name":"Kachanovich","first_name":"Siargey"},{"full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken"}],"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"year":"2020","file_date_updated":"2020-11-20T10:18:02Z","ec_funded":1,"date_published":"2020-03-01T00:00:00Z","article_type":"original","page":"141-176","publication":"Mathematics in Computer Science","citation":{"mla":"Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” Mathematics in Computer Science, vol. 14, Springer Nature, 2020, pp. 141–76, doi:10.1007/s11786-020-00461-5.","short":"A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science 14 (2020) 141–176.","chicago":"Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter Triangulations Have Good Quality.” Mathematics in Computer Science. Springer Nature, 2020. https://doi.org/10.1007/s11786-020-00461-5.","ama":"Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good quality. Mathematics in Computer Science. 2020;14:141-176. doi:10.1007/s11786-020-00461-5","ista":"Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have good quality. Mathematics in Computer Science. 14, 141–176.","apa":"Choudhary, A., Kachanovich, S., & Wintraecken, M. (2020). Coxeter triangulations have good quality. Mathematics in Computer Science. Springer Nature. https://doi.org/10.1007/s11786-020-00461-5","ieee":"A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations have good quality,” Mathematics in Computer Science, vol. 14. Springer Nature, pp. 141–176, 2020."},"day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","file":[{"relation":"main_file","file_id":"8783","checksum":"1d145f3ab50ccee735983cb89236e609","success":1,"date_created":"2020-11-20T10:18:02Z","date_updated":"2020-11-20T10:18:02Z","access_level":"open_access","file_name":"2020_MathCompScie_Choudhary.pdf","content_type":"application/pdf","file_size":872275,"creator":"dernst"}],"oa_version":"Published Version","title":"Coxeter triangulations have good quality","ddc":["510"],"status":"public","intvolume":" 14","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7567","abstract":[{"lang":"eng","text":"Coxeter triangulations are triangulations of Euclidean space based on a single simplex. By this we mean that given an individual simplex we can recover the entire triangulation of Euclidean space by inductively reflecting in the faces of the simplex. In this paper we establish that the quality of the simplices in all Coxeter triangulations is O(1/d−−√) of the quality of regular simplex. We further investigate the Delaunay property for these triangulations. Moreover, we consider an extension of the Delaunay property, namely protection, which is a measure of non-degeneracy of a Delaunay triangulation. In particular, one family of Coxeter triangulations achieves the protection O(1/d2). We conjecture that both bounds are optimal for triangulations in Euclidean space."}],"type":"journal_article"},{"oa":1,"quality_controlled":"1","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"name":"Efficient Simulation of Natural Phenomena at Extremely Large Scales","call_identifier":"H2020","grant_number":"638176","_id":"2533E772-B435-11E9-9278-68D0E5697425"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"doi":"10.1007/978-3-030-43408-3_8","language":[{"iso":"eng"}],"month":"06","publication_identifier":{"issn":["21932808"],"eissn":["21978549"],"isbn":["9783030434076"]},"year":"2020","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 78818 Alpha and No 638176). 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":"Springer Nature","department":[{"_id":"HeEd"}],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Nikitenko, Anton","last_name":"Nikitenko","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Ölsböck, Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","last_name":"Ölsböck","first_name":"Katharina"},{"id":"331776E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Synak","full_name":"Synak, Peter"}],"date_updated":"2021-01-12T08:17:06Z","date_created":"2020-07-19T22:00:59Z","volume":15,"file_date_updated":"2020-10-08T08:56:14Z","ec_funded":1,"publication":"Topological Data Analysis","citation":{"apa":"Edelsbrunner, H., Nikitenko, A., Ölsböck, K., & Synak, P. (2020). Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In Topological Data Analysis (Vol. 15, pp. 181–218). Springer Nature. https://doi.org/10.1007/978-3-030-43408-3_8","ieee":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions on Poisson–Delaunay mosaics and related complexes experimentally,” in Topological Data Analysis, 2020, vol. 15, pp. 181–218.","ista":"Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. 2020. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. Topological Data Analysis. , Abel Symposia, vol. 15, 181–218.","ama":"Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In: Topological Data Analysis. Vol 15. Springer Nature; 2020:181-218. doi:10.1007/978-3-030-43408-3_8","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” In Topological Data Analysis, 15:181–218. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-43408-3_8.","short":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218.","mla":"Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” Topological Data Analysis, vol. 15, Springer Nature, 2020, pp. 181–218, doi:10.1007/978-3-030-43408-3_8."},"page":"181-218","date_published":"2020-06-22T00:00:00Z","scopus_import":"1","day":"22","article_processing_charge":"No","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8135","title":"Radius functions on Poisson–Delaunay mosaics and related complexes experimentally","ddc":["510"],"status":"public","intvolume":" 15","file":[{"relation":"main_file","file_id":"8628","date_updated":"2020-10-08T08:56:14Z","date_created":"2020-10-08T08:56:14Z","checksum":"7b5e0de10675d787a2ddb2091370b8d8","success":1,"file_name":"2020-B-01-PoissonExperimentalSurvey.pdf","access_level":"open_access","content_type":"application/pdf","file_size":2207071,"creator":"dernst"}],"oa_version":"Submitted Version","type":"conference","alternative_title":["Abel Symposia"],"abstract":[{"lang":"eng","text":"Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics."}]},{"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":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","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"}],"doi":"10.1515/mathm-2020-0106","language":[{"iso":"eng"}],"month":"11","publication_identifier":{"issn":["2353-3390"]},"acknowledgement":"This work has been partially supported by the European Research Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. ","year":"2020","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"De Gruyter","author":[{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita"},{"first_name":"Gaëlle","last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle"},{"full_name":"Zrour, Rita","first_name":"Rita","last_name":"Zrour"},{"full_name":"Andres, Eric","first_name":"Eric","last_name":"Andres"}],"date_updated":"2021-03-22T09:01:50Z","date_created":"2021-03-16T08:55:19Z","volume":4,"file_date_updated":"2021-03-22T08:56:37Z","ec_funded":1,"publication":"Mathematical Morphology - Theory and Applications","citation":{"short":"R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.","mla":"Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and Applications, vol. 4, no. 1, De Gruyter, 2020, pp. 143–58, doi:10.1515/mathm-2020-0106.","chicago":"Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and Applications. De Gruyter, 2020. https://doi.org/10.1515/mathm-2020-0106.","ama":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 2020;4(1):143-158. doi:10.1515/mathm-2020-0106","ieee":"R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects in rhombic dodecahedron grid,” Mathematical Morphology - Theory and Applications, vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.","apa":"Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2020). Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. De Gruyter. https://doi.org/10.1515/mathm-2020-0106","ista":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 4(1), 143–158."},"article_type":"original","page":"143-158","date_published":"2020-11-17T00:00:00Z","day":"17","has_accepted_license":"1","article_processing_charge":"No","_id":"9249","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","ddc":["510"],"title":"Digital objects in rhombic dodecahedron grid","intvolume":" 4","file":[{"creator":"dernst","content_type":"application/pdf","file_size":3668725,"access_level":"open_access","file_name":"2020_MathMorpholTheoryAppl_Biswas.pdf","success":1,"checksum":"4a1043fa0548a725d464017fe2483ce0","date_updated":"2021-03-22T08:56:37Z","date_created":"2021-03-22T08:56:37Z","file_id":"9272","relation":"main_file"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"lang":"eng","text":"Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system."}],"issue":"1"},{"abstract":[{"text":"We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on n>1 vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and m>4n edges is larger than cm2n for some constant c>0 , and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and m⟶∞ .","lang":"eng"}],"type":"conference","oa_version":"Preprint","intvolume":" 12590","title":"Crossings between non-homotopic edges","status":"public","_id":"9299","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","day":"20","series_title":"LNCS","scopus_import":"1","date_published":"2020-09-20T00:00:00Z","page":"359-371","citation":{"chicago":"Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic Edges.” In 28th International Symposium on Graph Drawing and Network Visualization, 12590:359–71. LNCS. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-68766-3_28.","short":"J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 359–371.","mla":"Pach, János, et al. “Crossings between Non-Homotopic Edges.” 28th International Symposium on Graph Drawing and Network Visualization, vol. 12590, Springer Nature, 2020, pp. 359–71, doi:10.1007/978-3-030-68766-3_28.","apa":"Pach, J., Tardos, G., & Tóth, G. (2020). Crossings between non-homotopic edges. In 28th International Symposium on Graph Drawing and Network Visualization (Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. https://doi.org/10.1007/978-3-030-68766-3_28","ieee":"J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,” in 28th International Symposium on Graph Drawing and Network Visualization, Virtual, Online, 2020, vol. 12590, pp. 359–371.","ista":"Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network VisualizationLNCS vol. 12590, 359–371.","ama":"Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: 28th International Symposium on Graph Drawing and Network Visualization. Vol 12590. LNCS. Springer Nature; 2020:359-371. doi:10.1007/978-3-030-68766-3_28"},"publication":"28th International Symposium on Graph Drawing and Network Visualization","volume":12590,"date_created":"2021-03-28T22:01:44Z","date_updated":"2021-04-06T11:32:32Z","author":[{"full_name":"Pach, János","first_name":"János","last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"full_name":"Tardos, Gábor","first_name":"Gábor","last_name":"Tardos"},{"full_name":"Tóth, Géza","first_name":"Géza","last_name":"Tóth"}],"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","year":"2020","acknowledgement":"Supported by the National Research, Development and Innovation Office, NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full version can be found at https://arxiv.org/abs/2006.14908.","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783030687656"]},"month":"09","language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-68766-3_28","conference":{"name":"GD: Graph Drawing and Network Visualization","end_date":"2020-09-18","start_date":"2020-09-16","location":"Virtual, Online"},"project":[{"call_identifier":"FWF","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"}],"quality_controlled":"1","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2006.14908","open_access":"1"}],"external_id":{"arxiv":["2006.14908"]}},{"intvolume":" 11","title":"Topological data analysis in information space","status":"public","ddc":["510","000"],"_id":"9630","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","oa_version":"Published Version","file":[{"date_created":"2021-08-11T11:55:11Z","date_updated":"2021-08-11T11:55:11Z","checksum":"f02d0b2b3838e7891a6c417fc34ffdcd","success":1,"relation":"main_file","file_id":"9882","file_size":1449234,"content_type":"application/pdf","creator":"asandaue","file_name":"2020_JournalOfComputationalGeometry_Edelsbrunner.pdf","access_level":"open_access"}],"type":"journal_article","issue":"2","abstract":[{"lang":"eng","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 needed 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."}],"page":"162-182","article_type":"original","citation":{"chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” Journal of Computational Geometry. Carleton University, 2020. https://doi.org/10.20382/jocg.v11i2a7.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11 (2020) 162–182.","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” Journal of Computational Geometry, vol. 11, no. 2, Carleton University, 2020, pp. 162–82, doi:10.20382/jocg.v11i2a7.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University, pp. 162–182, 2020.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis in information space. Journal of Computational Geometry. Carleton University. https://doi.org/10.20382/jocg.v11i2a7","ista":"Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. Journal of Computational Geometry. 11(2), 162–182.","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7"},"publication":"Journal of Computational Geometry","date_published":"2020-12-14T00:00:00Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes","day":"14","department":[{"_id":"HeEd"}],"publisher":"Carleton University","publication_status":"published","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 (FWF).","year":"2020","volume":11,"date_created":"2021-07-04T22:01:26Z","date_updated":"2021-08-11T12:26:34Z","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner"}],"file_date_updated":"2021-08-11T11:55:11Z","project":[{"grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Discretization in Geometry and Dynamics"}],"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"},"language":[{"iso":"eng"}],"doi":"10.20382/jocg.v11i2a7","publication_identifier":{"eissn":["1920180X"]},"month":"12"},{"date_published":"2020-09-09T00:00:00Z","publication":"European Journal of Mathematics","citation":{"ista":"Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited. European Journal of Mathematics.","ieee":"A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,” European Journal of Mathematics. Springer Nature, 2020.","apa":"Akopyan, A., Schwartz, R., & Tabachnikov, S. (2020). Billiards in ellipses revisited. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00426-9","ama":"Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. European Journal of Mathematics. 2020. doi:10.1007/s40879-020-00426-9","chicago":"Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in Ellipses Revisited.” European Journal of Mathematics. Springer Nature, 2020. https://doi.org/10.1007/s40879-020-00426-9.","mla":"Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” European Journal of Mathematics, Springer Nature, 2020, doi:10.1007/s40879-020-00426-9.","short":"A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics (2020)."},"article_type":"original","day":"09","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"8538","status":"public","title":"Billiards in ellipses revisited","abstract":[{"text":"We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.","lang":"eng"}],"type":"journal_article","doi":"10.1007/s40879-020-00426-9","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2001.02934","open_access":"1"}],"external_id":{"arxiv":["2001.02934"]},"quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"}],"month":"09","publication_identifier":{"eissn":["2199-6768"],"issn":["2199-675X"]},"author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"full_name":"Schwartz, Richard","last_name":"Schwartz","first_name":"Richard"},{"first_name":"Serge","last_name":"Tabachnikov","full_name":"Tabachnikov, Serge"}],"date_created":"2020-09-20T22:01:38Z","date_updated":"2021-12-02T15:10:17Z","acknowledgement":" This paper would not be written if not for Dan Reznik’s curiosity and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller for interesting discussions. It is a pleasure to thank the Mathematical Institute of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality. AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR 191.","year":"2020","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","ec_funded":1},{"date_published":"2020-06-01T00:00:00Z","publication":"36th International Symposium on Computational Geometry","citation":{"mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” 36th International Symposium on Computational Geometry, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.20.","short":"J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.20.","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations of isomanifolds. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.20","ista":"Boissonnat J-D, Wintraecken M. 2020. The topological correctness of PL-approximations of isomanifolds. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 20:1-20:18.","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations of isomanifolds,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.","apa":"Boissonnat, J.-D., & Wintraecken, M. (2020). The topological correctness of PL-approximations of isomanifolds. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.20"},"day":"01","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","oa_version":"Published Version","file":[{"file_id":"7969","relation":"main_file","date_updated":"2020-07-14T12:48:06Z","date_created":"2020-06-17T10:13:34Z","checksum":"38cbfa4f5d484d267a35d44d210df044","file_name":"2020_LIPIcsSoCG_Boissonnat.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":1009739}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7952","ddc":["510"],"status":"public","title":"The topological correctness of PL-approximations of isomanifolds","intvolume":" 164","abstract":[{"lang":"eng","text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine triangulation 𝒯. This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary. "}],"type":"conference","alternative_title":["LIPIcs"],"conference":{"end_date":"2020-06-26","start_date":"2020-06-22","location":"Zürich, Switzerland","name":"SoCG: Symposium on Computational Geometry"},"doi":"10.4230/LIPIcs.SoCG.2020.20","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","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"month":"06","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-143-6"]},"author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs"}],"related_material":{"record":[{"id":"9649","relation":"later_version","status":"public"}]},"date_updated":"2023-08-02T06:49:16Z","date_created":"2020-06-09T07:24:11Z","volume":164,"year":"2020","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","file_date_updated":"2020-07-14T12:48:06Z","ec_funded":1,"article_number":"20:1-20:18"},{"month":"06","publication_identifier":{"eisbn":["9783030360207"],"issn":["00758434"],"eissn":["16179692"],"isbn":["9783030360191"]},"external_id":{"isi":["000557689300003"],"arxiv":["1808.07350"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07350"}],"oa":1,"quality_controlled":"1","isi":1,"project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"}],"doi":"10.1007/978-3-030-36020-7_1","language":[{"iso":"eng"}],"ec_funded":1,"year":"2020","publication_status":"published","editor":[{"full_name":"Klartag, Bo'az","first_name":"Bo'az","last_name":"Klartag"},{"first_name":"Emanuel","last_name":"Milman","full_name":"Milman, Emanuel"}],"department":[{"_id":"HeEd"},{"_id":"JaMa"}],"publisher":"Springer Nature","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"date_created":"2018-12-11T11:44:29Z","date_updated":"2023-08-17T13:48:31Z","volume":2256,"scopus_import":"1","series_title":"LNM","day":"21","article_processing_charge":"No","publication":"Geometric Aspects of Functional Analysis","citation":{"mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1.","ama":"Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1","ista":"Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis. vol. 2256, 1–27.","ieee":"A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.","apa":"Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.), Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer Nature. https://doi.org/10.1007/978-3-030-36020-7_1"},"page":"1-27","date_published":"2020-06-21T00:00:00Z","type":"book_chapter","abstract":[{"text":"We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about the waist of radially symmetric Gaussian measures. In particular, it turns our possible to extend Gromov’s original result to the case of not necessarily radially symmetric Gaussian measure. We also provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument to produce some estimates of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures.","lang":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"74","status":"public","title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","intvolume":" 2256","oa_version":"Preprint"},{"date_created":"2020-03-01T23:00:39Z","date_updated":"2023-08-18T06:45:48Z","volume":64,"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"first_name":"Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton"}],"publication_status":"published","publisher":"SIAM","department":[{"_id":"HeEd"}],"year":"2020","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1137/S0040585X97T989726","quality_controlled":"1","isi":1,"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"external_id":{"isi":["000551393100007"],"arxiv":["1705.08735"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.08735"}],"month":"02","publication_identifier":{"issn":["0040585X"],"eissn":["10957219"]},"oa_version":"Preprint","title":"Weighted Poisson–Delaunay mosaics","status":"public","intvolume":" 64","_id":"7554","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"lang":"eng","text":"Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the smallest empty circumscribed sphere whose center lies in the $k$-plane gives a generalized discrete Morse function. Assuming the Voronoi tessellation is generated by a Poisson point process in ${R}^n$, we study the expected number of simplices in the $k$-dimensional weighted Delaunay mosaic as well as the expected number of intervals of the Morse function, both as functions of a radius threshold. As a by-product, we obtain a new proof for the expected number of connected components (clumps) in a line section of a circular Boolean model in ${R}^n$."}],"issue":"4","type":"journal_article","date_published":"2020-02-13T00:00:00Z","article_type":"original","page":"595-614","publication":"Theory of Probability and its Applications","citation":{"mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications, vol. 64, no. 4, SIAM, 2020, pp. 595–614, doi:10.1137/S0040585X97T989726.","short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications. SIAM, 2020. https://doi.org/10.1137/S0040585X97T989726.","ama":"Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 2020;64(4):595-614. doi:10.1137/S0040585X97T989726","ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614.","apa":"Edelsbrunner, H., & Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics. Theory of Probability and Its Applications. SIAM. https://doi.org/10.1137/S0040585X97T989726","ieee":"H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” Theory of Probability and its Applications, vol. 64, no. 4. SIAM, pp. 595–614, 2020."},"day":"13","article_processing_charge":"No","scopus_import":"1"},{"citation":{"chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00188-x.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 759–75, doi:10.1007/s00454-020-00188-x.","short":"H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.","ista":"Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775.","ieee":"H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 759–775, 2020.","apa":"Edelsbrunner, H., & Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00188-x","ama":"Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 2020;64:759-775. doi:10.1007/s00454-020-00188-x"},"publication":"Discrete and Computational Geometry","page":"759-775","article_type":"original","date_published":"2020-03-20T00:00:00Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"20","_id":"7666","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 64","title":"Tri-partitions and bases of an ordered complex","ddc":["510"],"status":"public","oa_version":"Published Version","file":[{"creator":"dernst","content_type":"application/pdf","file_size":701673,"access_level":"open_access","file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf","success":1,"checksum":"f8cc96e497f00c38340b5dafe0cb91d7","date_created":"2020-11-20T13:22:21Z","date_updated":"2020-11-20T13:22:21Z","file_id":"8786","relation":"main_file"}],"type":"journal_article","abstract":[{"text":"Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups.","lang":"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":["000520918800001"]},"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"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"}],"isi":1,"quality_controlled":"1","doi":"10.1007/s00454-020-00188-x","language":[{"iso":"eng"}],"publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"month":"03","acknowledgement":"This project has received funding from the European Research Council 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","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","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"},{"full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","last_name":"Ölsböck","first_name":"Katharina"}],"volume":64,"date_updated":"2023-08-21T06:13:48Z","date_created":"2020-04-19T22:00:56Z","ec_funded":1,"file_date_updated":"2020-11-20T13:22:21Z"},{"year":"2020","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"author":[{"first_name":"János","last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János"},{"full_name":"Reed, Bruce","last_name":"Reed","first_name":"Bruce"},{"full_name":"Yuditsky, Yelena","last_name":"Yuditsky","first_name":"Yelena"}],"date_updated":"2023-08-21T08:49:18Z","date_created":"2020-06-14T22:00:51Z","volume":63,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1803.06710"}],"external_id":{"arxiv":["1803.06710"],"isi":["000538229000001"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"}],"doi":"10.1007/s00454-020-00213-z","language":[{"iso":"eng"}],"month":"06","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7962","status":"public","title":"Almost all string graphs are intersection graphs of plane convex sets","intvolume":" 63","oa_version":"Preprint","type":"journal_article","abstract":[{"text":"A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n→∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.","lang":"eng"}],"issue":"4","publication":"Discrete and Computational Geometry","citation":{"ieee":"J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection graphs of plane convex sets,” Discrete and Computational Geometry, vol. 63, no. 4. Springer Nature, pp. 888–917, 2020.","apa":"Pach, J., Reed, B., & Yuditsky, Y. (2020). Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00213-z","ista":"Pach J, Reed B, Yuditsky Y. 2020. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 63(4), 888–917.","ama":"Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 2020;63(4):888-917. doi:10.1007/s00454-020-00213-z","chicago":"Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00213-z.","short":"J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917.","mla":"Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry, vol. 63, no. 4, Springer Nature, 2020, pp. 888–917, doi:10.1007/s00454-020-00213-z."},"article_type":"original","page":"888-917","date_published":"2020-06-05T00:00:00Z","scopus_import":"1","day":"05","article_processing_charge":"No"},{"type":"journal_article","intvolume":" 64","status":"public","title":"A farewell to Ricky Pollack","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"8323","oa_version":"None","scopus_import":"1","article_processing_charge":"No","day":"01","page":"571-574","article_type":"letter_note","citation":{"chicago":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5.","short":"J. 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.","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.","ama":"Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry. 2020;64:571-574. doi:10.1007/s00454-020-00237-5"},"publication":"Discrete and Computational Geometry","date_published":"2020-10-01T00:00:00Z","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","year":"2020","volume":64,"date_updated":"2023-08-22T09:05:04Z","date_created":"2020-08-30T22:01:12Z","author":[{"full_name":"Pach, János","last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"}],"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"month":"10","isi":1,"main_file_link":[{"url":"https://doi.org/10.1007/s00454-020-00237-5","open_access":"1"}],"oa":1,"external_id":{"isi":["000561483500001"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00237-5"},{"day":"01","month":"08","article_processing_charge":"No","publication_identifier":{"isbn":["9781728157511"]},"scopus_import":"1","language":[{"iso":"eng"}],"conference":{"end_date":"2020-07-15","start_date":"2020-07-15","location":"Pisa, Italy","name":"ESGCO: European Study Group on Cardiovascular Oscillations"},"date_published":"2020-08-01T00:00:00Z","doi":"10.1109/ESGCO49734.2020.9158054","quality_controlled":"1","isi":1,"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":{"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","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.","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."},"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","date_created":"2020-09-28T08:59:27Z","date_updated":"2023-08-22T09:33:34Z","oa_version":"None","author":[{"full_name":"Graff, Grzegorz","last_name":"Graff","first_name":"Grzegorz"},{"full_name":"Graff, Beata","last_name":"Graff","first_name":"Beata"},{"full_name":"Jablonski, Grzegorz","last_name":"Jablonski","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Narkiewicz","first_name":"Krzysztof","full_name":"Narkiewicz, Krzysztof"}],"title":"The application of persistent homology in the analysis of heart rate variability","status":"public","publication_status":"published","publisher":"IEEE","department":[{"_id":"HeEd"}],"_id":"8580","year":"2020","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"date_created":"2022-03-18T11:39:30Z","date_updated":"2023-08-24T14:19:55Z","volume":2020,"author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Oxford University Press","acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","year":"2020","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rny037","isi":1,"quality_controlled":"1","oa":1,"external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.07513"}],"month":"02","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"oa_version":"Preprint","status":"public","title":"Waist of balls in hyperbolic and spherical spaces","intvolume":" 2020","_id":"10867","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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","type":"journal_article","date_published":"2020-02-01T00:00:00Z","article_type":"original","page":"669-697","publication":"International Mathematics Research Notices","citation":{"ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","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","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","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.","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.","short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697."},"day":"01","article_processing_charge":"No","keyword":["General Mathematics"],"scopus_import":"1"},{"author":[{"full_name":"Ölsböck, Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4672-8297","first_name":"Katharina","last_name":"Ölsböck"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"6608"}]},"date_created":"2020-02-06T14:56:53Z","date_updated":"2023-09-07T13:15:30Z","year":"2020","publication_status":"published","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"publisher":"Institute of Science and Technology Austria","file_date_updated":"2020-07-14T12:47:58Z","doi":"10.15479/AT:ISTA:7460","degree_awarded":"PhD","supervisor":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"}],"language":[{"iso":"eng"}],"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)"},"oa":1,"month":"02","publication_identifier":{"issn":["2663-337X"]},"file":[{"file_size":76195184,"content_type":"application/pdf","creator":"koelsboe","access_level":"open_access","file_name":"thesis_ist-final_noack.pdf","checksum":"1df9f8c530b443c0e63a3f2e4fde412e","date_updated":"2020-07-14T12:47:58Z","date_created":"2020-02-06T14:43:54Z","relation":"main_file","file_id":"7461"},{"date_created":"2020-02-06T14:52:45Z","date_updated":"2020-07-14T12:47:58Z","checksum":"7a52383c812b0be64d3826546509e5a4","relation":"source_file","file_id":"7462","file_size":122103715,"content_type":"application/x-zip-compressed","creator":"koelsboe","file_name":"latex-files.zip","description":"latex source files, figures","access_level":"closed"}],"oa_version":"Published Version","_id":"7460","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["514"],"status":"public","title":"The hole system of triangulated shapes","abstract":[{"lang":"eng","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."}],"type":"dissertation","alternative_title":["ISTA Thesis"],"date_published":"2020-02-10T00:00:00Z","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."},"page":"155","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"]},{"date_published":"2020-06-09T00:00:00Z","page":"160","citation":{"mla":"Masárová, Zuzana. Reconfiguration Problems. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7944.","short":"Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020.","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944.","ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria.","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"},"day":"09","article_processing_charge":"No","has_accepted_license":"1","keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"file":[{"content_type":"application/pdf","file_size":13661779,"creator":"zmasarov","access_level":"open_access","file_name":"THESIS_Zuzka_Masarova.pdf","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","date_created":"2020-06-08T00:34:00Z","date_updated":"2020-07-14T12:48:05Z","relation":"main_file","file_id":"7945"},{"file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","access_level":"closed","file_size":32184006,"content_type":"application/zip","creator":"zmasarov","relation":"source_file","file_id":"7946","date_updated":"2020-07-14T12:48:05Z","date_created":"2020-06-08T00:35:30Z","checksum":"45341a35b8f5529c74010b7af43ac188"}],"oa_version":"Published Version","status":"public","title":"Reconfiguration problems","ddc":["516","514"],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"7944","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","supervisor":[{"full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"degree_awarded":"PhD","language":[{"iso":"eng"}],"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"},"month":"06","publication_identifier":{"isbn":["978-3-99078-005-3"],"issn":["2663-337X"]},"date_created":"2020-06-08T00:49:46Z","date_updated":"2023-09-07T13:17:37Z","author":[{"full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana"}],"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"7950"},{"id":"5986","status":"public","relation":"part_of_dissertation"}]},"publication_status":"published","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"publisher":"Institute of Science and Technology Austria","year":"2020","license":"https://creativecommons.org/licenses/by-sa/4.0/","file_date_updated":"2020-07-14T12:48:05Z"},{"article_number":"75","ec_funded":1,"file_date_updated":"2020-10-27T14:31:52Z","year":"2020","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"publication_status":"published","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"9056"}]},"author":[{"full_name":"Osang, Georg F","first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116"},{"first_name":"Mael","last_name":"Rouxel-Labbé","full_name":"Rouxel-Labbé, Mael"},{"first_name":"Monique","last_name":"Teillaud","full_name":"Teillaud, Monique"}],"volume":173,"date_created":"2020-10-25T23:01:18Z","date_updated":"2023-09-07T13:29:00Z","publication_identifier":{"issn":["18688969"],"isbn":["9783959771627"]},"month":"08","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"},"oa":1,"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"}],"quality_controlled":"1","doi":"10.4230/LIPIcs.ESA.2020.75","conference":{"start_date":"2020-09-07","location":"Virtual, Online; Pisa, Italy","end_date":"2020-09-09","name":"ESA: Annual European Symposium on Algorithms"},"language":[{"iso":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"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. "}],"_id":"8703","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 173","status":"public","ddc":["000"],"title":"Generalizing CGAL periodic Delaunay triangulations","oa_version":"Published Version","file":[{"date_updated":"2020-10-27T14:31:52Z","date_created":"2020-10-27T14:31:52Z","checksum":"fe0f7c49a99ed870c671b911e10d5496","success":1,"relation":"main_file","file_id":"8712","content_type":"application/pdf","file_size":733291,"creator":"cziletti","file_name":"2020_LIPIcs_Osang.pdf","access_level":"open_access"}],"scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"26","citation":{"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.","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"},"publication":"28th Annual European Symposium on Algorithms","date_published":"2020-08-26T00:00:00Z"},{"file":[{"date_updated":"2020-07-24T07:09:06Z","date_created":"2020-07-24T07:09:06Z","relation":"main_file","file_id":"8164","content_type":"application/pdf","file_size":1476072,"creator":"mwintrae","access_level":"open_access","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8163","status":"public","ddc":["510"],"title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","intvolume":" 57","abstract":[{"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.","lang":"eng"}],"issue":"2","type":"journal_article","date_published":"2020-07-24T00:00:00Z","publication":"Studia Scientiarum Mathematicarum Hungarica","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.","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"},"article_type":"original","page":"193-199","day":"24","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","author":[{"first_name":"Gert","last_name":"Vegter","full_name":"Vegter, Gert"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs"}],"date_created":"2020-07-24T07:09:18Z","date_updated":"2023-10-10T13:05:27Z","volume":57,"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.","year":"2020","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Akadémiai Kiadó","file_date_updated":"2020-07-24T07:09:06Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc/4.0/","doi":"10.1556/012.2020.57.2.1454","language":[{"iso":"eng"}],"external_id":{"isi":["000570978400005"]},"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)"},"oa":1,"quality_controlled":"1","isi":1,"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"call_identifier":"FWF","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"}],"month":"07","publication_identifier":{"eissn":["1588-2896"],"issn":["0081-6906"]}},{"publication_identifier":{"issn":["2544-7297"]},"month":"06","language":[{"iso":"eng"}],"doi":"10.1515/cmb-2020-0100","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","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"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"},"ec_funded":1,"file_date_updated":"2021-02-19T13:56:24Z","volume":8,"date_updated":"2023-10-17T12:34:51Z","date_created":"2021-02-17T15:13:01Z","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","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 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).","year":"2020","article_processing_charge":"No","has_accepted_license":"1","day":"20","date_published":"2020-06-20T00:00:00Z","page":"51-67","article_type":"original","citation":{"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.","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","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."},"publication":"Computational and Mathematical Biophysics","issue":"1","abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","file":[{"file_name":"2020_CompMathBiophysics_Akopyan2.pdf","access_level":"open_access","creator":"dernst","file_size":562359,"content_type":"application/pdf","file_id":"9171","relation":"main_file","date_created":"2021-02-19T13:56:24Z","date_updated":"2021-02-19T13:56:24Z","success":1,"checksum":"cea41de9937d07a3b927d71ee8b4e432"}],"intvolume":" 8","title":"The weighted mean curvature derivative of a space-filling diagram","status":"public","ddc":["510"],"_id":"9157","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"month":"07","publication_identifier":{"issn":["2544-7297"]},"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,"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"}],"doi":"10.1515/cmb-2020-0101","language":[{"iso":"eng"}],"file_date_updated":"2021-02-19T13:33:19Z","ec_funded":1,"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","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"De Gruyter","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"date_updated":"2023-10-17T12:35:10Z","date_created":"2021-02-17T15:12:44Z","volume":8,"day":"21","article_processing_charge":"No","has_accepted_license":"1","publication":"Computational and Mathematical Biophysics","citation":{"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.","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.","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","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"},"article_type":"original","page":"74-88","date_published":"2020-07-21T00:00:00Z","type":"journal_article","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"}],"issue":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9156","ddc":["510"],"title":"The weighted Gaussian curvature derivative of a space-filling diagram","status":"public","intvolume":" 8","oa_version":"Published Version","file":[{"file_id":"9170","relation":"main_file","date_created":"2021-02-19T13:33:19Z","date_updated":"2021-02-19T13:33:19Z","success":1,"checksum":"ca43a7440834eab6bbea29c59b56ef3a","file_name":"2020_CompMathBiophysics_Akopyan.pdf","access_level":"open_access","creator":"dernst","file_size":707452,"content_type":"application/pdf"}]},{"issue":"4","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"}],"type":"journal_article","oa_version":"Published Version","file":[{"success":1,"checksum":"eed1168b6e66cd55272c19bb7fca8a1c","date_updated":"2024-03-04T10:52:42Z","date_created":"2024-03-04T10:52:42Z","file_id":"15065","relation":"main_file","creator":"dernst","file_size":851190,"content_type":"application/pdf","access_level":"open_access","file_name":"2020_JourApplCompTopology_Bauer.pdf"}],"_id":"15064","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 4","status":"public","title":"Čech-Delaunay gradient flow and homology inference for self-maps","ddc":["500"],"has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","scopus_import":"1","date_published":"2020-12-01T00:00:00Z","citation":{"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","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","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.","short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480.","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.","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."},"publication":"Journal of Applied and Computational Topology","page":"455-480","article_type":"original","file_date_updated":"2024-03-04T10:52:42Z","author":[{"full_name":"Bauer, U.","last_name":"Bauer","first_name":"U."},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Grzegorz","last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz"},{"first_name":"M.","last_name":"Mrozek","full_name":"Mrozek, M."}],"volume":4,"date_created":"2024-03-04T10:47:49Z","date_updated":"2024-03-04T10:54:04Z","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.","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"month":"12","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"},{"scopus_import":1,"day":"01","has_accepted_license":"1","publication":"Journal of Computational Geometry ","citation":{"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.","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"},"page":"223–256","date_published":"2019-07-01T00:00:00Z","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","_id":"6515","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","ddc":["510"],"title":"Simplices modelled on spaces of constant curvature","intvolume":" 10","file":[{"file_id":"6516","relation":"main_file","checksum":"57b4df2f16a74eb499734ec8ee240178","date_created":"2019-06-03T09:30:01Z","date_updated":"2020-07-14T12:47:32Z","access_level":"open_access","file_name":"mainJournalFinal.pdf","creator":"mwintrae","content_type":"application/pdf","file_size":2170882}],"oa_version":"Published Version","month":"07","publication_identifier":{"issn":["1920-180X"]},"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":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"doi":"10.20382/jocg.v10i1a9","language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:47:32Z","ec_funded":1,"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"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs"}],"date_created":"2019-06-03T09:35:33Z","date_updated":"2021-01-12T08:07:50Z","volume":10},{"file_date_updated":"2020-07-14T12:47:34Z","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."}],"ec_funded":1,"type":"conference","date_updated":"2021-01-12T08:08:16Z","date_created":"2019-07-12T08:34:57Z","oa_version":"Submitted Version","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","content_type":"application/pdf","file_size":321176,"creator":"mwintrae"}],"author":[{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","first_name":"Mathijs","full_name":"Wintraecken, Mathijs"}],"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","ddc":["004"],"publication_status":"published","status":"public","department":[{"_id":"HeEd"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"6628","year":"2019","month":"08","day":"01","has_accepted_license":"1","scopus_import":1,"language":[{"iso":"eng"}],"conference":{"end_date":"2019-08-10","location":"Edmonton, Canada","start_date":"2019-08-08","name":"CCCG: Canadian Conference in Computational Geometry"},"date_published":"2019-08-01T00:00:00Z","quality_controlled":"1","page":"275-279","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"publication":"The 31st Canadian Conference in Computational Geometry","oa":1,"citation":{"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.","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.","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.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279.","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."}},{"publication_identifier":{"isbn":["9783959771047"]},"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"},"external_id":{"arxiv":["1903.08510"]},"oa":1,"project":[{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"quality_controlled":"1","doi":"10.4230/LIPICS.SOCG.2019.31","conference":{"end_date":"2019-06-21","location":"Portland, OR, United States","start_date":"2019-06-18","name":"SoCG 2019: Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:47:35Z","year":"2019","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Hubert"}],"volume":129,"date_created":"2019-07-17T10:36:09Z","date_updated":"2021-01-12T08:08:23Z","scopus_import":1,"has_accepted_license":"1","day":"01","citation":{"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.","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.","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","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.","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.","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"},"publication":"35th International Symposium on Computational Geometry","page":"31:1-31:14","date_published":"2019-06-01T00:00:00Z","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","intvolume":" 129","status":"public","title":"Topological data analysis in information space","ddc":["510"],"file":[{"file_name":"2019_LIPICS_Edelsbrunner.pdf","access_level":"open_access","creator":"dernst","file_size":1355179,"content_type":"application/pdf","file_id":"6666","relation":"main_file","date_updated":"2020-07-14T12:47:35Z","date_created":"2019-07-24T06:40:01Z","checksum":"8ec8720730d4c789bf7b06540f1c29f4"}],"oa_version":"Published Version"},{"article_processing_charge":"No","month":"08","day":"01","scopus_import":"1","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"},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://cccg.ca/proceedings/2019/proceedings.pdf","open_access":"1"}],"citation":{"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.","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.","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.","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."},"external_id":{"arxiv":["1910.09917"]},"oa":1,"publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","page":"164-170","quality_controlled":"1","abstract":[{"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. ","lang":"eng"}],"type":"conference","related_material":{"record":[{"id":"8317","relation":"extended_version","status":"public"}]},"author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"last_name":"Akitaya","first_name":"Hugo A","full_name":"Akitaya, Hugo A"},{"full_name":"Cheung, Kenneth C","last_name":"Cheung","first_name":"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"},{"full_name":"Fekete, Sandor P","first_name":"Sandor P","last_name":"Fekete"},{"full_name":"Kleist, Linda","last_name":"Kleist","first_name":"Linda"},{"first_name":"Irina","last_name":"Kostitsyna","full_name":"Kostitsyna, Irina"},{"full_name":"Löffler, Maarten","last_name":"Löffler","first_name":"Maarten"},{"full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana"},{"full_name":"Mundilova, Klara","last_name":"Mundilova","first_name":"Klara"},{"full_name":"Schmidt, Christiane","last_name":"Schmidt","first_name":"Christiane"}],"oa_version":"Published Version","date_updated":"2023-08-04T10:57:42Z","date_created":"2019-11-04T16:46:11Z","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","publisher":"Canadian Conference on Computational Geometry","department":[{"_id":"HeEd"}],"status":"public","publication_status":"published","title":"Folding polyominoes with holes into a cube"},{"ec_funded":1,"file_date_updated":"2020-07-14T12:47:36Z","author":[{"full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel","last_name":"Boissonnat"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"},{"full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"volume":3,"date_created":"2019-07-24T08:37:29Z","date_updated":"2023-08-22T12:37:47Z","year":"2019","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"month":"06","doi":"10.1007/s41468-019-00029-8","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,"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","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","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","file_size":2215157,"content_type":"application/pdf"}],"oa_version":"Published Version","_id":"6671","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 3","ddc":["000"],"status":"public","title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","date_published":"2019-06-01T00:00:00Z","citation":{"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.","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","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."},"publication":"Journal of Applied and Computational Topology","page":"29–58","article_type":"original"},{"publisher":"AMS","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2019","volume":147,"date_updated":"2023-08-24T14:48:59Z","date_created":"2019-02-24T22:59:19Z","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"full_name":"Fedorov, Roman","first_name":"Roman","last_name":"Fedorov"}],"isi":1,"quality_controlled":"1","oa":1,"external_id":{"arxiv":["1709.02562"],"isi":["000450363900008"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1709.02562"}],"language":[{"iso":"eng"}],"doi":"10.1090/proc/14240","month":"01","intvolume":" 147","status":"public","title":"Two circles and only a straightedge","_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. "}],"page":"91-102","citation":{"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.","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.","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","ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","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."},"publication":"Proceedings of the American Mathematical Society","date_published":"2019-01-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01"},{"issue":"2","abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","_id":"6634","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 53","title":"Lower and upper bounds for the waists of different spaces","status":"public","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2019-06-01T00:00:00Z","citation":{"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.","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"},"publication":"Topological Methods in Nonlinear Analysis","page":"457-490","ec_funded":1,"author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"last_name":"Hubard","first_name":"Alfredo","full_name":"Hubard, Alfredo"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"volume":53,"date_created":"2019-07-14T21:59:19Z","date_updated":"2023-08-29T06:32:48Z","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,"main_file_link":[{"url":"https://arxiv.org/abs/1612.06926","open_access":"1"}],"external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"quality_controlled":"1","isi":1},{"day":"17","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","date_published":"2019-07-17T00:00:00Z","publication":"Astronomy and Astrophysics","citation":{"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.","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.","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","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.","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).","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."},"article_type":"original","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."}],"type":"journal_article","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2019_AstronomyAstrophysics_Pranav.pdf","creator":"dernst","file_size":14420451,"content_type":"application/pdf","file_id":"6766","relation":"main_file","checksum":"83b9209ed9eefbdcefd89019c5a97805","date_created":"2019-08-05T08:08:59Z","date_updated":"2020-07-14T12:47:39Z"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6756","status":"public","ddc":["520","530"],"title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","intvolume":" 627","month":"07","publication_identifier":{"issn":["00046361"],"eissn":["14320746"]},"doi":"10.1051/0004-6361/201834916","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"},"external_id":{"isi":["000475839300003"],"arxiv":["1812.07678"]},"quality_controlled":"1","isi":1,"project":[{"name":"Toward Computational Information Topology","_id":"265683E4-B435-11E9-9278-68D0E5697425","grant_number":"M62909-18-1-2038"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"file_date_updated":"2020-07-14T12:47:39Z","article_number":"A163","author":[{"full_name":"Pranav, Pratyush","first_name":"Pratyush","last_name":"Pranav"},{"full_name":"Adler, Robert J.","last_name":"Adler","first_name":"Robert J."},{"last_name":"Buchert","first_name":"Thomas","full_name":"Buchert, Thomas"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"last_name":"Jones","first_name":"Bernard J.T.","full_name":"Jones, Bernard J.T."},{"first_name":"Armin","last_name":"Schwartzman","full_name":"Schwartzman, Armin"},{"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"}],"date_updated":"2023-08-29T07:01:48Z","date_created":"2019-08-04T21:59:18Z","volume":627,"year":"2019","publication_status":"published","publisher":"EDP Sciences","department":[{"_id":"HeEd"}]},{"language":[{"iso":"eng"}],"doi":"10.1112/blms.12276","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"}],"isi":1,"quality_controlled":"1","oa":1,"external_id":{"isi":["000478560200001"],"arxiv":["1903.04929"]},"main_file_link":[{"url":"https://arxiv.org/abs/1903.04929","open_access":"1"}],"publication_identifier":{"eissn":["14692120"],"issn":["00246093"]},"month":"10","volume":51,"date_updated":"2023-08-29T07:08:34Z","date_created":"2019-08-11T21:59:23Z","author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"last_name":"Izmestiev","first_name":"Ivan","full_name":"Izmestiev, Ivan"}],"department":[{"_id":"HeEd"}],"publisher":"London Mathematical Society","publication_status":"published","year":"2019","ec_funded":1,"date_published":"2019-10-01T00:00:00Z","page":"765-775","article_type":"original","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","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","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.","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","article_processing_charge":"No","day":"01","scopus_import":"1","oa_version":"Preprint","intvolume":" 51","title":"The Regge symmetry, confocal conics, and the Schläfli formula","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6793","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"},{"author":[{"first_name":"Adam","last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425","full_name":"Brown, Adam"}],"volume":538,"date_updated":"2023-08-29T07:11:47Z","date_created":"2019-08-22T07:54:13Z","year":"2019","department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","doi":"10.1016/j.jalgebra.2019.07.027","language":[{"iso":"eng"}],"external_id":{"arxiv":["1805.04676"],"isi":["000487176300011"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.04676"}],"oa":1,"quality_controlled":"1","isi":1,"publication_identifier":{"issn":["0021-8693"]},"month":"11","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6828","intvolume":" 538","status":"public","title":"Arakawa-Suzuki functors for Whittaker modules","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","date_published":"2019-11-15T00:00:00Z","citation":{"chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027.","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.","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","ama":"Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027"},"publication":"Journal of Algebra","page":"261-289","article_type":"original","article_processing_charge":"No","day":"15"}]