[{"volume":189,"ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","file":[{"file_name":"df_socg_final_version.pdf","date_created":"2021-04-22T08:08:14Z","file_size":3117435,"date_updated":"2021-04-22T08:08:14Z","creator":"mwintrae","success":1,"file_id":"9346","checksum":"1787baef1523d6d93753b90d0c109a6d","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1868-8969"]},"publication_status":"published","month":"06","intvolume":" 189","alternative_title":["LIPIcs"],"oa_version":"Published Version","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"}],"department":[{"_id":"HeEd"}],"file_date_updated":"2021-04-22T08:08:14Z","ddc":["004","516"],"date_updated":"2023-02-23T13:55:40Z","status":"public","type":"conference","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2021-06-11","location":"Virtual","start_date":"2021-06-07"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"9345","doi":"10.4230/LIPIcs.SoCG.2021.32","date_published":"2021-06-02T00:00:00Z","date_created":"2021-04-22T08:09:58Z","page":"32:1-32:16","day":"02","publication":"37th International Symposium on Computational Geometry (SoCG 2021)","has_accepted_license":"1","year":"2021","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"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.","title":"The density fingerprint of a periodic point set","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689","last_name":"Heiss"},{"last_name":" Kurlin ","full_name":" Kurlin , Vitaliy","first_name":"Vitaliy"},{"last_name":"Smith","full_name":"Smith, Philip","first_name":"Philip"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"article_processing_charge":"No","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"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.","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.","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","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","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.","short":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.","mla":"Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:10.4230/LIPIcs.SoCG.2021.32."},"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"grant_number":"I4887","name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"name":"The Wittgenstein Prize","grant_number":"Z00312","call_identifier":"FWF","_id":"25C5A090-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}]},{"ddc":["516"],"date_updated":"2023-02-23T14:02:28Z","file_date_updated":"2021-06-28T13:11:39Z","department":[{"_id":"HeEd"}],"_id":"9604","status":"public","type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"start_date":"2021-06-07","location":"Online","end_date":"2021-06-11","name":"SoCG: International Symposium on Computational Geometry"},"file":[{"file_name":"2021_LIPIcs_Biswas.pdf","date_created":"2021-06-28T13:11:39Z","file_size":727817,"date_updated":"2021-06-28T13:11:39Z","creator":"asandaue","success":1,"file_id":"9611","checksum":"22b11a719018b22ecba2471b51f2eb40","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783959771849"],"issn":["18688969"]},"publication_status":"published","volume":189,"ec_funded":1,"oa_version":"Published Version","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"}],"month":"06","intvolume":" 189","scopus_import":"1","alternative_title":["LIPIcs"],"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"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.","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.","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.","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.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","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","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"},"title":"Counting cells of order-k voronoi tessellations in ℝ3 with morse theory","author":[{"orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza"}],"article_processing_charge":"No","article_number":"16","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","grant_number":"Z00342"},{"grant_number":"I4887","name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"}],"day":"02","publication":"Leibniz International Proceedings in Informatics","has_accepted_license":"1","year":"2021","date_published":"2021-06-02T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2021.16","date_created":"2021-06-27T22:01:48Z","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1},{"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).","quality_controlled":"1","publisher":"Springer Nature","year":"2021","day":"16","publication":"Discrete Geometry and Mathematical Morphology","page":"152-163","doi":"10.1007/978-3-030-76657-3_10","date_published":"2021-05-16T00:00:00Z","date_created":"2021-08-08T22:01:29Z","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"citation":{"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.","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.","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.","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"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Čomić","full_name":"Čomić, Lidija","first_name":"Lidija"},{"first_name":"Rita","last_name":"Zrour","full_name":"Zrour, Rita"},{"last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle","first_name":"Gaëlle"},{"last_name":"Biswas","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"first_name":"Eric","last_name":"Andres","full_name":"Andres, Eric"}],"article_processing_charge":"No","title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","abstract":[{"text":"We define a new compact coordinate system in which each integer triplet addresses a voxel in the BCC grid, and we investigate some of its properties. We propose a characterization of 3D discrete analytical planes with their topological features (in the Cartesian and in the new coordinate system) such as the interrelation between the thickness of the plane and the separability constraint we aim to obtain.","lang":"eng"}],"oa_version":"None","alternative_title":["LNCS"],"scopus_import":"1","month":"05","intvolume":" 12708","publication_identifier":{"issn":["03029743"],"eissn":["16113349"],"isbn":["9783030766566"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":12708,"ec_funded":1,"_id":"9824","type":"conference","conference":{"name":"DGMM: International Conference on Discrete Geometry and Mathematical Morphology","end_date":"2021-05-27","location":"Uppsala, Sweden","start_date":"2021-05-24"},"status":"public","date_updated":"2022-05-31T06:58:21Z","department":[{"_id":"HeEd"}]},{"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["09257721"]},"related_material":{"record":[{"id":"6989","status":"public","relation":"shorter_version"}]},"volume":93,"oa_version":"Preprint","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."}],"intvolume":" 93","month":"02","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.09917v3"}],"scopus_import":"1","date_updated":"2023-08-04T10:57:42Z","department":[{"_id":"HeEd"}],"_id":"8317","status":"public","article_type":"original","type":"journal_article","publication":"Computational Geometry: Theory and Applications","day":"01","year":"2021","isi":1,"date_created":"2020-08-30T22:01:09Z","date_published":"2021-02-01T00:00:00Z","doi":"10.1016/j.comgeo.2020.101700","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.","oa":1,"quality_controlled":"1","publisher":"Elsevier","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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).","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.","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","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.","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.","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."},"title":"Folding polyominoes with holes into a cube","article_processing_charge":"No","external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"last_name":"Akitaya","full_name":"Akitaya, Hugo A.","first_name":"Hugo A."},{"last_name":"Cheung","full_name":"Cheung, Kenneth C.","first_name":"Kenneth C."},{"full_name":"Demaine, Erik D.","last_name":"Demaine","first_name":"Erik D."},{"last_name":"Demaine","full_name":"Demaine, Martin L.","first_name":"Martin L."},{"full_name":"Fekete, Sándor P.","last_name":"Fekete","first_name":"Sándor P."},{"first_name":"Linda","full_name":"Kleist, Linda","last_name":"Kleist"},{"first_name":"Irina","last_name":"Kostitsyna","full_name":"Kostitsyna, Irina"},{"full_name":"Löffler, Maarten","last_name":"Löffler","first_name":"Maarten"},{"orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Klara","full_name":"Mundilova, Klara","last_name":"Mundilova"},{"full_name":"Schmidt, Christiane","last_name":"Schmidt","first_name":"Christiane"}],"article_number":"101700","project":[{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize"}]},{"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.","publisher":"American Mathematical Society","quality_controlled":"1","oa":1,"isi":1,"year":"2021","day":"01","publication":"Proceedings of the American Mathematical Society","page":"37-52","doi":"10.1090/proc/15205","date_published":"2021-01-01T00:00:00Z","date_created":"2020-11-19T10:17:40Z","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"citation":{"ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52.","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.","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","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","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Brown, Adam","last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"full_name":"Romanov, Anna","last_name":"Romanov","first_name":"Anna"}],"external_id":{"isi":["000600416300004"],"arxiv":["1910.08286"]},"article_processing_charge":"No","title":"Contravariant forms on Whittaker modules","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"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.08286"}],"month":"01","intvolume":" 149","publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"1","volume":149,"ec_funded":1,"_id":"8773","type":"journal_article","article_type":"original","status":"public","keyword":["Applied Mathematics","General Mathematics"],"date_updated":"2023-08-04T11:11:47Z","department":[{"_id":"HeEd"}]},{"_id":"9253","conference":{"name":"Big Data: International Conference on Big Data","start_date":"2020-12-10","end_date":"2020-12-13","location":"Atlanta, GA, United States"},"type":"conference","status":"public","date_updated":"2023-08-07T14:00:13Z","department":[{"_id":"HeEd"}],"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."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2008.10064"}],"scopus_import":"1","month":"03","publication_status":"published","publication_identifier":{"isbn":["9781728162515"]},"language":[{"iso":"eng"}],"citation":{"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.","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","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.","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.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000662554703032"],"arxiv":["2008.10064"]},"author":[{"first_name":"Georg","full_name":"Heiler, Georg","last_name":"Heiler"},{"last_name":"Reisch","full_name":"Reisch, Tobias","first_name":"Tobias"},{"full_name":"Hurt, Jan","last_name":"Hurt","first_name":"Jan"},{"last_name":"Forghani","full_name":"Forghani, Mohammad","first_name":"Mohammad"},{"last_name":"Omani","full_name":"Omani, Aida","first_name":"Aida"},{"last_name":"Hanbury","full_name":"Hanbury, Allan","first_name":"Allan"},{"first_name":"Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","last_name":"Karimipour","orcid":"0000-0001-6746-4174","full_name":"Karimipour, Farid"}],"title":"Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic","oa":1,"quality_controlled":"1","publisher":"IEEE","year":"2021","isi":1,"publication":"2020 IEEE International Conference on Big Data","day":"19","page":"3123-3132","date_created":"2021-03-21T11:34:07Z","doi":"10.1109/bigdata50022.2020.9378374","date_published":"2021-03-19T00:00:00Z"},{"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"citation":{"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.","short":"H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.","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","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.","ista":"Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 65, 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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000635460400001"]},"author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F","last_name":"Osang"}],"title":"The multi-cover persistence of Euclidean balls","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).","oa":1,"publisher":"Springer Nature","quality_controlled":"1","year":"2021","isi":1,"has_accepted_license":"1","publication":"Discrete and Computational Geometry","day":"31","page":"1296–1313","date_created":"2021-04-11T22:01:15Z","date_published":"2021-03-31T00:00:00Z","doi":"10.1007/s00454-021-00281-9","_id":"9317","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","date_updated":"2023-08-07T14:35:44Z","ddc":["516"],"file_date_updated":"2021-12-01T10:56:53Z","department":[{"_id":"HeEd"}],"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 65","month":"03","publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2021-12-01T10:56:53Z","file_name":"2021_DisCompGeo_Edelsbrunner_Osang.pdf","creator":"cchlebak","date_updated":"2021-12-01T10:56:53Z","file_size":677704,"file_id":"10394","checksum":"59b4e1e827e494209bcb4aae22e1d347","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"ec_funded":1,"related_material":{"record":[{"id":"187","status":"public","relation":"earlier_version"}]},"volume":65},{"department":[{"_id":"HeEd"}],"file_date_updated":"2021-06-28T13:33:23Z","ddc":["510"],"date_updated":"2023-08-10T13:38:00Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"9602","volume":151,"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"15fbc9064cd9d1c777ac0043b78c8f12","file_id":"9612","success":1,"date_updated":"2021-06-28T13:33:23Z","file_size":418168,"creator":"asandaue","date_created":"2021-06-28T13:33:23Z","file_name":"2021_JournalOfCombinatorialTheory_Pach.pdf"}],"publication_status":"published","publication_identifier":{"issn":["0095-8956"]},"intvolume":" 151","month":"06","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"title":"Erdős-Hajnal-type results for monotone paths","article_processing_charge":"No","external_id":{"isi":["000702280800002"]},"author":[{"full_name":"Pach, János","last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"first_name":"István","full_name":"Tomon, István","last_name":"Tomon"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","ista":"Pach J, Tomon I. 2021. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. 151, 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.","short":"J. Pach, I. Tomon, Journal of Combinatorial Theory. Series B 151 (2021) 21–37.","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.","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"},"project":[{"grant_number":"Z00342","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"date_created":"2021-06-27T22:01:47Z","date_published":"2021-06-09T00:00:00Z","doi":"10.1016/j.jctb.2021.05.004","page":"21-37","publication":"Journal of Combinatorial Theory. Series B","day":"09","year":"2021","has_accepted_license":"1","isi":1,"oa":1,"publisher":"Elsevier","quality_controlled":"1","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."},{"citation":{"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.","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.","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.","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.","short":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, K. Narkiewicz, PLoS ONE 16 (2021)."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Graff","full_name":"Graff, Grzegorz","first_name":"Grzegorz"},{"first_name":"Beata","full_name":"Graff, Beata","last_name":"Graff"},{"last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","last_name":"Jablonski"},{"last_name":"Gąsecki","full_name":"Gąsecki, Dariusz","first_name":"Dariusz"},{"full_name":"Narkiewicz, Krzysztof","last_name":"Narkiewicz","first_name":"Krzysztof"}],"external_id":{"isi":["000678124900050"],"pmid":["34292957"]},"article_processing_charge":"Yes","title":"Persistent homology as a new method of the assessment of heart rate variability","article_number":"e0253851","has_accepted_license":"1","isi":1,"year":"2021","day":"01","publication":"PLoS ONE","date_published":"2021-07-01T00:00:00Z","doi":"10.1371/journal.pone.0253851","date_created":"2021-08-08T22:01:28Z","acknowledgement":"We express our gratitude to the anonymous referees who provided constructive comments that helped us improve the quality of the paper.","quality_controlled":"1","publisher":"Public Library of Science","oa":1,"date_updated":"2023-08-10T14:21:42Z","ddc":["006"],"file_date_updated":"2021-08-09T09:25:41Z","department":[{"_id":"HeEd"}],"_id":"9821","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","publication_identifier":{"eissn":["19326203"]},"publication_status":"published","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"9832","checksum":"0277aa155d5db1febd2cb384768bba5f","success":1,"creator":"asandaue","date_updated":"2021-08-09T09:25:41Z","file_size":2706919,"date_created":"2021-08-09T09:25:41Z","file_name":"2021_PLoSONE_Graff.pdf"}],"language":[{"iso":"eng"}],"volume":16,"issue":"7","abstract":[{"lang":"eng","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."}],"pmid":1,"oa_version":"Published Version","scopus_import":"1","month":"07","intvolume":" 16"},{"ec_funded":1,"publication_status":"published","publication_identifier":{"issn":["1058-6458"],"eissn":["1944-950X"]},"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"14053","checksum":"3514382e3a1eb87fa6c61ad622874415","success":1,"creator":"dernst","date_updated":"2023-08-14T11:55:10Z","file_size":1966019,"date_created":"2023-08-14T11:55:10Z","file_name":"2023_ExperimentalMath_Akopyan.pdf"}],"scopus_import":"1","month":"10","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","department":[{"_id":"HeEd"}],"file_date_updated":"2023-08-14T11:55:10Z","date_updated":"2023-08-14T11:57:07Z","ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","_id":"10222","page":"1-15","date_created":"2021-11-07T23:01:25Z","doi":"10.1080/10586458.2021.1980459","date_published":"2021-10-25T00:00:00Z","year":"2021","isi":1,"has_accepted_license":"1","publication":"Experimental Mathematics","day":"25","oa":1,"publisher":"Taylor and Francis","quality_controlled":"1","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.","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000710893500001"],"arxiv":["2007.07783"]},"author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","last_name":"Nikitenko"}],"title":"The beauty of random polytopes inscribed in the 2-sphere","citation":{"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.","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","short":"A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 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.","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.","ista":"Akopyan A, Edelsbrunner H, Nikitenko A. 2021. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics., 1–15."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize"},{"name":"Discretization in Geometry and Dynamics","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}]},{"publication":"Discrete & Computational Geometry","day":"01","year":"2021","isi":1,"has_accepted_license":"1","date_created":"2020-12-12T11:07:02Z","date_published":"2021-07-01T00:00:00Z","doi":"10.1007/s00454-020-00250-8","page":"386-434","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).","oa":1,"publisher":"Springer Nature","quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational Geometry 66 (2021) 386–434.","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.","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","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","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.","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."},"title":"Triangulating submanifolds: An elementary and quantified version of Whitney’s method","external_id":{"isi":["000597770300001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat"},{"first_name":"Siargey","full_name":"Kachanovich, Siargey","last_name":"Kachanovich"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"language":[{"iso":"eng"}],"file":[{"date_created":"2021-08-06T09:52:29Z","file_name":"2021_DescreteCompGeopmetry_Boissonnat.pdf","creator":"kschuh","date_updated":"2021-08-06T09:52:29Z","file_size":983307,"checksum":"c848986091e56699dc12de85adb1e39c","file_id":"9795","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"ec_funded":1,"issue":"1","volume":66,"oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"intvolume":" 66","month":"07","ddc":["516"],"date_updated":"2023-09-05T15:02:40Z","department":[{"_id":"HeEd"}],"file_date_updated":"2021-08-06T09:52:29Z","_id":"8940","keyword":["Theoretical Computer Science","Computational Theory and Mathematics","Geometry and Topology","Discrete Mathematics and Combinatorics"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original"},{"ddc":["510"],"date_updated":"2023-09-05T15:37:56Z","file_date_updated":"2021-02-11T14:43:59Z","department":[{"_id":"HeEd"}],"_id":"9111","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"date_created":"2021-02-11T14:43:59Z","file_name":"2020_JourApplCompTopology_Brown.pdf","date_updated":"2021-02-11T14:43:59Z","file_size":2090265,"creator":"dernst","file_id":"9112","checksum":"3f02e9d47c428484733da0f588a3c069","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"publication_status":"published","issue":"1","volume":5,"ec_funded":1,"oa_version":"Published Version","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"}],"month":"03","intvolume":" 5","scopus_import":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","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.","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","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","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.","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.","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."},"title":"Probabilistic convergence and stability of random mapper graphs","author":[{"first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","full_name":"Brown, Adam","last_name":"Brown"},{"first_name":"Omer","last_name":"Bobrowski","full_name":"Bobrowski, Omer"},{"full_name":"Munch, Elizabeth","last_name":"Munch","first_name":"Elizabeth"},{"full_name":"Wang, Bei","last_name":"Wang","first_name":"Bei"}],"external_id":{"arxiv":["1909.03488"]},"article_processing_charge":"Yes (via OA deal)","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"day":"01","publication":"Journal of Applied and Computational Topology","has_accepted_license":"1","year":"2021","date_published":"2021-03-01T00:00:00Z","doi":"10.1007/s41468-020-00063-x","date_created":"2021-02-11T14:41:02Z","page":"99-140","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).","publisher":"Springer Nature","quality_controlled":"1","oa":1},{"file":[{"file_name":"thesis_source.zip","date_created":"2021-02-02T14:09:25Z","creator":"patrickd","file_size":13446994,"date_updated":"2021-02-03T10:37:28Z","file_id":"9063","checksum":"bcf27986147cab0533b6abadd74e7629","relation":"source_file","access_level":"closed","content_type":"application/zip"},{"success":1,"checksum":"9cc8af266579a464385bbe2aff6af606","file_id":"9064","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"thesis_pdfA2b.pdf","date_created":"2021-02-02T14:09:18Z","file_size":5210329,"date_updated":"2021-02-02T14:09:18Z","creator":"patrickd"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"187"},{"id":"8703","status":"public","relation":"part_of_dissertation"}]},"oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"place":"Klosterneuburg","month":"02","alternative_title":["ISTA Thesis"],"ddc":["006","514","516"],"supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"}],"date_updated":"2023-09-07T13:29:01Z","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"file_date_updated":"2021-02-03T10:37:28Z","_id":"9056","status":"public","type":"dissertation","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","has_accepted_license":"1","year":"2021","doi":"10.15479/AT:ISTA:9056","date_published":"2021-02-01T00:00:00Z","date_created":"2021-02-02T14:11:06Z","page":"134","publisher":"Institute of Science and Technology Austria","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg: Institute of Science and Technology Austria.","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.","ama":"Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056","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","ieee":"G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of Science and Technology Austria, Klosterneuburg, 2021.","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."},"title":"Multi-cover persistence and Delaunay mosaics","author":[{"orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"}],"article_processing_charge":"No"},{"quality_controlled":"1","publisher":"Royal Society of Chemistry ","oa":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.","page":"9107-9115","date_published":"2021-10-20T00:00:00Z","doi":"10.1039/d1sm00774b","date_created":"2021-10-31T23:01:30Z","isi":1,"has_accepted_license":"1","year":"2021","day":"20","publication":"Soft Matter","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"}],"author":[{"orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Saadatfar","full_name":"Saadatfar, Mohammad","first_name":"Mohammad"}],"external_id":{"pmid":["34569592"],"isi":["000700090000001"]},"article_processing_charge":"No","title":"Topological signatures and stability of hexagonal close packing and Barlow stackings","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","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","short":"G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 9107–9115.","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.","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.","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","month":"10","intvolume":" 17","abstract":[{"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.","lang":"eng"}],"oa_version":"Submitted Version","pmid":1,"issue":"40","volume":17,"ec_funded":1,"publication_identifier":{"eissn":["1744-6848"],"issn":["1744-683X"]},"publication_status":"published","file":[{"creator":"dernst","date_updated":"2023-10-03T09:21:42Z","file_size":4678788,"date_created":"2023-10-03T09:21:42Z","file_name":"2021_SoftMatter_acceptedversion_Osang.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"b4da0c420530295e61b153960f6cb350","file_id":"14385","success":1}],"language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","status":"public","_id":"10204","department":[{"_id":"HeEd"}],"file_date_updated":"2023-10-03T09:21:42Z","date_updated":"2023-10-03T09:24:27Z","ddc":["540"]},{"month":"06","intvolume":" 189","scopus_import":"1","alternative_title":["LIPIcs"],"oa_version":"Published Version","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"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"12709"}],"link":[{"url":"https://arxiv.org/abs/2103.07823","relation":"extended_version"}]},"volume":189,"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"9610","checksum":"0de217501e7ba8b267d58deed0d51761","file_size":"1367983","date_updated":"2021-06-28T12:40:47Z","creator":"cziletti","file_name":"2021_LIPIcs_Corbet.pdf","date_created":"2021-06-28T12:40:47Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["18688969"],"isbn":["9783959771849"]},"publication_status":"published","status":"public","type":"conference","conference":{"name":"SoCG: International Symposium on Computational Geometry","start_date":"2021-06-07","location":"Online","end_date":"2021-06-11"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"9605","file_date_updated":"2021-06-28T12:40:47Z","department":[{"_id":"HeEd"}],"ddc":["516"],"date_updated":"2023-10-04T12:03:39Z","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"acknowledgement":"The authors want to thank the reviewers for many helpful comments and suggestions.","doi":"10.4230/LIPIcs.SoCG.2021.27","date_published":"2021-06-02T00:00:00Z","date_created":"2021-06-27T22:01:49Z","day":"02","publication":"Leibniz International Proceedings in Informatics","has_accepted_license":"1","year":"2021","article_number":"27","title":"Computing the multicover bifiltration","author":[{"first_name":"René","full_name":"Corbet, René","last_name":"Corbet"},{"last_name":"Kerber","full_name":"Kerber, Michael","first_name":"Michael"},{"full_name":"Lesnick, Michael","last_name":"Lesnick","first_name":"Michael"},{"last_name":"Osang","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"}],"article_processing_charge":"No","external_id":{"arxiv":["2103.07823"]},"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"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.","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","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","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","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.","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.","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."}},{"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations","article_processing_charge":"No","author":[{"last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel"},{"full_name":"Kachanovich, Siargey","last_name":"Kachanovich","first_name":"Siargey"},{"last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"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.","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.","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.","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","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.","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."},"oa":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","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.","date_created":"2021-06-02T10:10:55Z","doi":"10.4230/LIPIcs.SoCG.2021.17","date_published":"2021-06-02T00:00:00Z","page":"17:1-17:16","publication":"37th International Symposium on Computational Geometry (SoCG 2021)","day":"02","year":"2021","has_accepted_license":"1","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2021-06-11","location":"Virtual","start_date":"2021-06-07"},"type":"conference","series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","_id":"9441","department":[{"_id":"HeEd"}],"file_date_updated":"2021-06-02T10:22:33Z","ddc":["005","516","514"],"date_updated":"2023-10-10T07:34:34Z","intvolume":" 189","place":"Dagstuhl, Germany","month":"06","alternative_title":["LIPIcs"],"oa_version":"Published Version","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"}],"ec_funded":1,"volume":189,"related_material":{"record":[{"id":"12960","status":"public","relation":"later_version"}]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"c322aa48d5d35a35877896cc565705b6","file_id":"9442","file_size":1972902,"date_updated":"2021-06-02T10:22:33Z","creator":"mwintrae","file_name":"LIPIcs-SoCG-2021-17.pdf","date_created":"2021-06-02T10:22:33Z"}],"publication_status":"published","publication_identifier":{"isbn":["978-3-95977-184-9"],"issn":["1868-8969"]}},{"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).","oa":1,"publisher":"Springer Nature","quality_controlled":"1","year":"2021","isi":1,"publication":"Discrete and Computational Geometry","day":"01","page":"938-976","date_created":"2020-09-06T22:01:13Z","date_published":"2021-10-01T00:00:00Z","doi":"10.1007/s00454-020-00240-w","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"citation":{"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.","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.","short":"A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational Geometry 66 (2021) 938–976.","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.","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","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","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."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"arxiv":["1908.00856"],"isi":["000564488500002"]},"author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","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."},{"first_name":"Jan","last_name":"Techter","full_name":"Techter, Jan"}],"title":"On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs","abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1908.00856"}],"scopus_import":"1","intvolume":" 66","month":"10","publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":66,"_id":"8338","article_type":"original","type":"journal_article","status":"public","date_updated":"2024-03-07T14:51:11Z","department":[{"_id":"HeEd"}]},{"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"title":"Local conditions for triangulating submanifolds of Euclidean space","external_id":{"isi":["000558119300001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"first_name":"Ramsay","full_name":"Dyer, Ramsay","last_name":"Dyer"},{"last_name":"Ghosh","full_name":"Ghosh, Arijit","first_name":"Arijit"},{"first_name":"Andre","full_name":"Lieutier, Andre","last_name":"Lieutier"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, M. Wintraecken, Discrete and Computational Geometry 66 (2021) 666–686.","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","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","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.","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."},"oa":1,"quality_controlled":"1","publisher":"Springer Nature","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.","date_created":"2020-08-11T07:11:51Z","doi":"10.1007/s00454-020-00233-9","date_published":"2021-09-01T00:00:00Z","page":"666-686","publication":"Discrete and Computational Geometry","day":"01","year":"2021","has_accepted_license":"1","isi":1,"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"8248","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2024-03-07T14:54:59Z","intvolume":" 66","month":"09","main_file_link":[{"url":"https://doi.org/10.1007/s00454-020-00233-9","open_access":"1"}],"scopus_import":"1","oa_version":"Published Version","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."}],"ec_funded":1,"volume":66,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]}},{"file_date_updated":"2020-11-25T09:06:41Z","department":[{"_id":"HeEd"}],"date_updated":"2024-03-07T15:01:58Z","ddc":["510"],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"7905","volume":65,"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publication_status":"published","file":[{"checksum":"487a84ea5841b75f04f66d7ebd71b67e","file_id":"8803","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2020-11-25T09:06:41Z","file_name":"2020_DiscreteCompGeometry_Brown.pdf","date_updated":"2020-11-25T09:06:41Z","file_size":1013730,"creator":"dernst"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"06","intvolume":" 65","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","author":[{"full_name":"Brown, Adam","last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"last_name":"Wang","full_name":"Wang, Bei","first_name":"Bei"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000536324700001"],"arxiv":["1712.07734"]},"title":"Sheaf-theoretic stratification learning from geometric and topological perspectives","citation":{"ista":"Brown A, Wang B. 2021. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 65, 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.","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","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","short":"A. Brown, B. Wang, Discrete and Computational Geometry 65 (2021) 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.","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."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"page":"1166-1198","date_published":"2021-06-01T00:00:00Z","doi":"10.1007/s00454-020-00206-y","date_created":"2020-05-30T10:26:04Z","has_accepted_license":"1","isi":1,"year":"2021","day":"01","publication":"Discrete and Computational Geometry","publisher":"Springer Nature","quality_controlled":"1","oa":1,"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."},{"oa_version":"Published Version","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."}],"month":"03","intvolume":" 14","scopus_import":"1","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"8783","checksum":"1d145f3ab50ccee735983cb89236e609","file_size":872275,"date_updated":"2020-11-20T10:18:02Z","creator":"dernst","file_name":"2020_MathCompScie_Choudhary.pdf","date_created":"2020-11-20T10:18:02Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1661-8289"],"issn":["1661-8270"]},"publication_status":"published","volume":14,"ec_funded":1,"_id":"7567","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2021-01-12T08:14:13Z","file_date_updated":"2020-11-20T10:18:02Z","department":[{"_id":"HeEd"}],"quality_controlled":"1","publisher":"Springer Nature","oa":1,"day":"01","publication":"Mathematics in Computer Science","has_accepted_license":"1","year":"2020","date_published":"2020-03-01T00:00:00Z","doi":"10.1007/s11786-020-00461-5","date_created":"2020-03-05T13:30:18Z","page":"141-176","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","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.","short":"A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science 14 (2020) 141–176.","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","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","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.","ista":"Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have good quality. Mathematics in Computer Science. 14, 141–176."},"title":"Coxeter triangulations have good quality","author":[{"full_name":"Choudhary, Aruni","last_name":"Choudhary","first_name":"Aruni"},{"first_name":"Siargey","last_name":"Kachanovich","full_name":"Kachanovich, Siargey"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"article_processing_charge":"Yes (via OA deal)"},{"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).","quality_controlled":"1","publisher":"Springer Nature","oa":1,"day":"22","publication":"Topological Data Analysis","has_accepted_license":"1","year":"2020","doi":"10.1007/978-3-030-43408-3_8","date_published":"2020-06-22T00:00:00Z","date_created":"2020-07-19T22:00:59Z","page":"181-218","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"_id":"2533E772-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"638176","name":"Efficient Simulation of Natural Phenomena at Extremely Large Scales"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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.","short":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218.","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.","apa":"Edelsbrunner, H., Nikitenko, A., Ölsböck, K., & Synak, P. (2020). 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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."}],"month":"06","intvolume":" 15","alternative_title":["Abel Symposia"],"scopus_import":"1","file":[{"creator":"dernst","date_updated":"2020-10-08T08:56:14Z","file_size":2207071,"date_created":"2020-10-08T08:56:14Z","file_name":"2020-B-01-PoissonExperimentalSurvey.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"7b5e0de10675d787a2ddb2091370b8d8","file_id":"8628","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["21978549"],"isbn":["9783030434076"],"issn":["21932808"]},"publication_status":"published","volume":15,"ec_funded":1,"_id":"8135","status":"public","type":"conference","ddc":["510"],"date_updated":"2021-01-12T08:17:06Z","file_date_updated":"2020-10-08T08:56:14Z","department":[{"_id":"HeEd"}]},{"intvolume":" 4","month":"11","oa_version":"Published Version","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. 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Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 4(1), 143–158.","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.","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.","short":"R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.","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","apa":"Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2020). 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Crossings between non-homotopic edges. 28th International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network VisualizationLNCS vol. 12590, 359–371.","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.","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.","short":"J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 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. 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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"}],"volume":12590,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0302-9743"],"isbn":["9783030687656"],"eissn":["1611-3349"]},"publication_status":"published"},{"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.","ista":"Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. 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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).","publisher":"Carleton University","quality_controlled":"1","oa":1,"date_updated":"2021-08-11T12:26:34Z","ddc":["510","000"],"file_date_updated":"2021-08-11T11:55:11Z","department":[{"_id":"HeEd"}],"_id":"9630","type":"journal_article","article_type":"original","tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"status":"public","publication_identifier":{"eissn":["1920180X"]},"publication_status":"published","file":[{"success":1,"checksum":"f02d0b2b3838e7891a6c417fc34ffdcd","file_id":"9882","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2020_JournalOfComputationalGeometry_Edelsbrunner.pdf","date_created":"2021-08-11T11:55:11Z","creator":"asandaue","file_size":1449234,"date_updated":"2021-08-11T11:55:11Z"}],"language":[{"iso":"eng"}],"issue":"2","volume":11,"license":"https://creativecommons.org/licenses/by/3.0/","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 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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"12","intvolume":" 11"},{"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"mla":"Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” European Journal of Mathematics, Springer Nature, 2020, doi:10.1007/s40879-020-00426-9.","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","ieee":"A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,” European Journal of Mathematics. Springer Nature, 2020.","short":"A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics (2020).","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.","ista":"Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited. European Journal of Mathematics."},"title":"Billiards in ellipses revisited","article_processing_charge":"No","external_id":{"arxiv":["2001.02934"]},"author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Schwartz","full_name":"Schwartz, Richard","first_name":"Richard"},{"full_name":"Tabachnikov, Serge","last_name":"Tabachnikov","first_name":"Serge"}],"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"}],"publication":"European Journal of Mathematics","day":"09","year":"2020","date_created":"2020-09-20T22:01:38Z","date_published":"2020-09-09T00:00:00Z","doi":"10.1007/s40879-020-00426-9","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.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","date_updated":"2021-12-02T15:10:17Z","department":[{"_id":"HeEd"}],"_id":"8538","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"ec_funded":1,"oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"month":"09","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2001.02934"}],"scopus_import":"1"},{"date_created":"2020-06-09T07:24:11Z","date_published":"2020-06-01T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2020.20","publication":"36th International Symposium on Computational Geometry","day":"01","year":"2020","has_accepted_license":"1","oa":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","title":"The topological correctness of PL-approximations of isomanifolds","article_processing_charge":"No","author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","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","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","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.","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.","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."},"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"article_number":"20:1-20:18","ec_funded":1,"related_material":{"record":[{"relation":"later_version","id":"9649","status":"public"}]},"volume":164,"language":[{"iso":"eng"}],"file":[{"file_name":"2020_LIPIcsSoCG_Boissonnat.pdf","date_created":"2020-06-17T10:13:34Z","file_size":1009739,"date_updated":"2020-07-14T12:48:06Z","creator":"dernst","file_id":"7969","checksum":"38cbfa4f5d484d267a35d44d210df044","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"publication_status":"published","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-143-6"]},"intvolume":" 164","month":"06","alternative_title":["LIPIcs"],"scopus_import":"1","oa_version":"Published Version","abstract":[{"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. ","lang":"eng"}],"file_date_updated":"2020-07-14T12:48:06Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2023-08-02T06:49:16Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"start_date":"2020-06-22","end_date":"2020-06-26","location":"Zürich, Switzerland","name":"SoCG: Symposium on Computational Geometry"},"type":"conference","_id":"7952"},{"ec_funded":1,"volume":2256,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eisbn":["9783030360207"],"eissn":["16179692"],"isbn":["9783030360191"],"issn":["00758434"]},"intvolume":" 2256","month":"06","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07350"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"department":[{"_id":"HeEd"},{"_id":"JaMa"}],"date_updated":"2023-08-17T13:48:31Z","status":"public","type":"book_chapter","series_title":"LNM","_id":"74","date_created":"2018-12-11T11:44:29Z","date_published":"2020-06-21T00:00:00Z","doi":"10.1007/978-3-030-36020-7_1","page":"1-27","publication":"Geometric Aspects of Functional Analysis","day":"21","year":"2020","isi":1,"oa":1,"quality_controlled":"1","publisher":"Springer Nature","title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","editor":[{"first_name":"Bo'az","full_name":"Klartag, Bo'az","last_name":"Klartag"},{"first_name":"Emanuel","last_name":"Milman","full_name":"Milman, Emanuel"}],"article_processing_charge":"No","external_id":{"isi":["000557689300003"],"arxiv":["1808.07350"]},"author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Roman","last_name":"Karasev","full_name":"Karasev, Roman"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 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","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","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.","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.","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."},"project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}]},{"isi":1,"year":"2020","day":"13","publication":"Theory of Probability and its Applications","page":"595-614","doi":"10.1137/S0040585X97T989726","date_published":"2020-02-13T00:00:00Z","date_created":"2020-03-01T23:00:39Z","quality_controlled":"1","publisher":"SIAM","oa":1,"citation":{"chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications. SIAM, 2020. https://doi.org/10.1137/S0040585X97T989726.","ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614.","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.","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.","short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 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","ama":"Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 2020;64(4):595-614. doi:10.1137/S0040585X97T989726"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","last_name":"Nikitenko","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"isi":["000551393100007"],"arxiv":["1705.08735"]},"title":"Weighted Poisson–Delaunay mosaics","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"publication_identifier":{"issn":["0040585X"],"eissn":["10957219"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"4","volume":64,"ec_funded":1,"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 ${R}^n$."}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1705.08735","open_access":"1"}],"month":"02","intvolume":" 64","date_updated":"2023-08-18T06:45:48Z","department":[{"_id":"HeEd"}],"_id":"7554","article_type":"original","type":"journal_article","status":"public"},{"citation":{"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","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","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.","short":"H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.","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.","ista":"Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Ölsböck","orcid":"0000-0002-4672-8297","full_name":"Ölsböck, Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000520918800001"]},"title":"Tri-partitions and bases of an ordered complex","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"has_accepted_license":"1","isi":1,"year":"2020","day":"20","publication":"Discrete and Computational Geometry","page":"759-775","date_published":"2020-03-20T00:00:00Z","doi":"10.1007/s00454-020-00188-x","date_created":"2020-04-19T22:00:56Z","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).","quality_controlled":"1","publisher":"Springer Nature","oa":1,"date_updated":"2023-08-21T06:13:48Z","ddc":["510"],"file_date_updated":"2020-11-20T13:22:21Z","department":[{"_id":"HeEd"}],"_id":"7666","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"publication_status":"published","file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"8786","checksum":"f8cc96e497f00c38340b5dafe0cb91d7","creator":"dernst","file_size":701673,"date_updated":"2020-11-20T13:22:21Z","file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf","date_created":"2020-11-20T13:22:21Z"}],"language":[{"iso":"eng"}],"volume":64,"ec_funded":1,"abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","scopus_import":"1","month":"03","intvolume":" 64"},{"page":"888-917","date_created":"2020-06-14T22:00:51Z","doi":"10.1007/s00454-020-00213-z","date_published":"2020-06-05T00:00:00Z","year":"2020","isi":1,"publication":"Discrete and Computational Geometry","day":"05","oa":1,"quality_controlled":"1","publisher":"Springer Nature","external_id":{"arxiv":["1803.06710"],"isi":["000538229000001"]},"article_processing_charge":"No","author":[{"full_name":"Pach, János","last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János"},{"first_name":"Bruce","full_name":"Reed, Bruce","last_name":"Reed"},{"last_name":"Yuditsky","full_name":"Yuditsky, Yelena","first_name":"Yelena"}],"title":"Almost all string graphs are intersection graphs of plane convex sets","citation":{"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.","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.","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","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","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"name":"The Wittgenstein Prize","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"volume":63,"issue":"4","publication_status":"published","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1803.06710"}],"scopus_import":"1","intvolume":" 63","month":"06","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"}],"oa_version":"Preprint","department":[{"_id":"HeEd"}],"date_updated":"2023-08-21T08:49:18Z","type":"journal_article","article_type":"original","status":"public","_id":"7962"},{"_id":"8323","type":"journal_article","article_type":"letter_note","status":"public","date_updated":"2023-08-22T09:05:04Z","department":[{"_id":"HeEd"}],"oa_version":"None","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-020-00237-5"}],"month":"10","intvolume":" 64","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":64,"citation":{"short":"J. Pach, Discrete and Computational Geometry 64 (2020) 571–574.","ieee":"J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 571–574, 2020.","ama":"Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry. 2020;64:571-574. doi:10.1007/s00454-020-00237-5","apa":"Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5","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.","ista":"Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574.","chicago":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach","full_name":"Pach, János"}],"article_processing_charge":"No","external_id":{"isi":["000561483500001"]},"title":"A farewell to Ricky Pollack","publisher":"Springer Nature","oa":1,"isi":1,"year":"2020","day":"01","publication":"Discrete and Computational Geometry","page":"571-574","date_published":"2020-10-01T00:00:00Z","doi":"10.1007/s00454-020-00237-5","date_created":"2020-08-30T22:01:12Z"},{"conference":{"name":"ESGCO: European Study Group on Cardiovascular Oscillations","location":"Pisa, Italy","end_date":"2020-07-15","start_date":"2020-07-15"},"type":"conference","status":"public","_id":"8580","article_number":"9158054","external_id":{"isi":["000621172600045"]},"article_processing_charge":"No","author":[{"first_name":"Grzegorz","full_name":"Graff, Grzegorz","last_name":"Graff"},{"first_name":"Beata","last_name":"Graff","full_name":"Graff, Beata"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz","last_name":"Jablonski","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866"},{"first_name":"Krzysztof","full_name":"Narkiewicz, Krzysztof","last_name":"Narkiewicz"}],"department":[{"_id":"HeEd"}],"title":"The application of persistent homology in the analysis of heart rate variability","date_updated":"2023-08-22T09:33:34Z","citation":{"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.","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.","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.","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","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","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","publisher":"IEEE","scopus_import":"1","month":"08","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"}],"oa_version":"None","date_created":"2020-09-28T08:59:27Z","doi":"10.1109/ESGCO49734.2020.9158054","date_published":"2020-08-01T00:00:00Z","publication_status":"published","year":"2020","publication_identifier":{"isbn":["9781728157511"]},"isi":1,"language":[{"iso":"eng"}],"publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ","day":"01"},{"publication_status":"published","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"language":[{"iso":"eng"}],"issue":"3","volume":2020,"abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1702.07513","open_access":"1"}],"scopus_import":"1","intvolume":" 2020","month":"02","date_updated":"2023-08-24T14:19:55Z","department":[{"_id":"HeEd"}],"_id":"10867","article_type":"original","type":"journal_article","keyword":["General Mathematics"],"status":"public","year":"2020","isi":1,"publication":"International Mathematics Research Notices","day":"01","page":"669-697","date_created":"2022-03-18T11:39:30Z","doi":"10.1093/imrn/rny037","date_published":"2020-02-01T00:00:00Z","acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","oa":1,"quality_controlled":"1","publisher":"Oxford University Press","citation":{"ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","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.","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","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.","short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]},"article_processing_charge":"No","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"title":"Waist of balls in hyperbolic and spherical spaces"},{"page":"155","date_published":"2020-02-10T00:00:00Z","doi":"10.15479/AT:ISTA:7460","date_created":"2020-02-06T14:56:53Z","has_accepted_license":"1","year":"2020","day":"10","publisher":"Institute of Science and Technology Austria","oa":1,"author":[{"first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","last_name":"Ölsböck","orcid":"0000-0002-4672-8297","full_name":"Ölsböck, Katharina"}],"article_processing_charge":"No","title":"The hole system of triangulated shapes","citation":{"chicago":"Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460.","ista":"Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria.","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.","ieee":"K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science and Technology Austria, 2020.","ama":"Ölsböck K. The hole system of triangulated shapes. 2020. doi:10.15479/AT:ISTA:7460","apa":"Ölsböck, K. (2020). The hole system of triangulated shapes. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7460"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","related_material":{"record":[{"id":"6608","status":"public","relation":"part_of_dissertation"}]},"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","file":[{"file_size":76195184,"date_updated":"2020-07-14T12:47:58Z","creator":"koelsboe","file_name":"thesis_ist-final_noack.pdf","date_created":"2020-02-06T14:43:54Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"7461","checksum":"1df9f8c530b443c0e63a3f2e4fde412e"},{"access_level":"closed","relation":"source_file","description":"latex source files, figures","content_type":"application/x-zip-compressed","checksum":"7a52383c812b0be64d3826546509e5a4","file_id":"7462","creator":"koelsboe","date_updated":"2020-07-14T12:47:58Z","file_size":122103715,"date_created":"2020-02-06T14:52:45Z","file_name":"latex-files.zip"}],"language":[{"iso":"eng"}],"alternative_title":["ISTA Thesis"],"month":"02","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."}],"oa_version":"Published Version","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"file_date_updated":"2020-07-14T12:47:58Z","supervisor":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"date_updated":"2023-09-07T13:15:30Z","ddc":["514"],"type":"dissertation","tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)"},"status":"public","keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"],"_id":"7460"},{"department":[{"_id":"HeEd"},{"_id":"UlWa"}],"file_date_updated":"2020-07-14T12:48:05Z","supervisor":[{"last_name":"Wagner","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"date_updated":"2023-09-07T13:17:37Z","ddc":["516","514"],"type":"dissertation","tmp":{"short":"CC BY-SA (4.0)","image":"/images/cc_by_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)"},"status":"public","keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"_id":"7944","related_material":{"record":[{"status":"public","id":"7950","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"5986"}]},"license":"https://creativecommons.org/licenses/by-sa/4.0/","publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-005-3"]},"degree_awarded":"PhD","publication_status":"published","file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"7945","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","date_updated":"2020-07-14T12:48:05Z","file_size":13661779,"creator":"zmasarov","date_created":"2020-06-08T00:34:00Z","file_name":"THESIS_Zuzka_Masarova.pdf"},{"content_type":"application/zip","relation":"source_file","access_level":"closed","file_id":"7946","checksum":"45341a35b8f5529c74010b7af43ac188","file_size":32184006,"date_updated":"2020-07-14T12:48:05Z","creator":"zmasarov","file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","date_created":"2020-06-08T00:35:30Z"}],"language":[{"iso":"eng"}],"alternative_title":["ISTA Thesis"],"month":"06","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","author":[{"last_name":"Masárová","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana"}],"article_processing_charge":"No","title":"Reconfiguration problems","citation":{"ieee":"Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020.","short":"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","ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944","mla":"Masárová, Zuzana. Reconfiguration Problems. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7944.","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria.","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","page":"160","date_published":"2020-06-09T00:00:00Z","doi":"10.15479/AT:ISTA:7944","date_created":"2020-06-08T00:49:46Z","has_accepted_license":"1","year":"2020","day":"09","publisher":"Institute of Science and Technology Austria","oa":1},{"_id":"8703","status":"public","type":"conference","tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"conference":{"name":"ESA: Annual European Symposium on Algorithms","location":"Virtual, Online; Pisa, Italy","end_date":"2020-09-09","start_date":"2020-09-07"},"ddc":["000"],"date_updated":"2023-09-07T13:29:00Z","department":[{"_id":"HeEd"}],"file_date_updated":"2020-10-27T14:31:52Z","oa_version":"Published Version","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. "}],"month":"08","intvolume":" 173","scopus_import":"1","alternative_title":["LIPIcs"],"file":[{"creator":"cziletti","date_updated":"2020-10-27T14:31:52Z","file_size":733291,"date_created":"2020-10-27T14:31:52Z","file_name":"2020_LIPIcs_Osang.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"8712","checksum":"fe0f7c49a99ed870c671b911e10d5496","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["18688969"],"isbn":["9783959771627"]},"publication_status":"published","volume":173,"related_material":{"record":[{"relation":"dissertation_contains","id":"9056","status":"public"}]},"ec_funded":1,"article_number":"75","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","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.","ama":"Osang GF, Rouxel-Labbé M, Teillaud M. Generalizing CGAL periodic Delaunay triangulations. In: 28th Annual European Symposium on Algorithms. Vol 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.ESA.2020.75","apa":"Osang, G. F., Rouxel-Labbé, M., & Teillaud, M. (2020). Generalizing CGAL periodic Delaunay triangulations. In 28th Annual European Symposium on Algorithms (Vol. 173). Virtual, Online; Pisa, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2020.75","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.","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.","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."},"title":"Generalizing CGAL periodic Delaunay triangulations","author":[{"full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"},{"first_name":"Mael","full_name":"Rouxel-Labbé, Mael","last_name":"Rouxel-Labbé"},{"last_name":"Teillaud","full_name":"Teillaud, Monique","first_name":"Monique"}],"article_processing_charge":"No","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"day":"26","publication":"28th Annual European Symposium on Algorithms","has_accepted_license":"1","year":"2020","date_published":"2020-08-26T00:00:00Z","doi":"10.4230/LIPIcs.ESA.2020.75","date_created":"2020-10-25T23:01:18Z"},{"_id":"8163","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)"},"status":"public","date_updated":"2023-10-10T13:05:27Z","ddc":["510"],"file_date_updated":"2020-07-24T07:09:06Z","department":[{"_id":"HeEd"}],"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"}],"oa_version":"Published Version","scopus_import":"1","month":"07","intvolume":" 57","publication_identifier":{"eissn":["1588-2896"],"issn":["0081-6906"]},"publication_status":"published","file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"8164","creator":"mwintrae","file_size":1476072,"date_updated":"2020-07-24T07:09:06Z","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","date_created":"2020-07-24T07:09:06Z"}],"language":[{"iso":"eng"}],"volume":57,"issue":"2","license":"https://creativecommons.org/licenses/by-nc/4.0/","ec_funded":1,"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","grant_number":"Z00342"}],"citation":{"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.","short":"G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199.","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","ama":"Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 2020;57(2):193-199. doi:10.1556/012.2020.57.2.1454","chicago":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó, 2020. https://doi.org/10.1556/012.2020.57.2.1454.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Gert","full_name":"Vegter, Gert","last_name":"Vegter"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000570978400005"]},"article_processing_charge":"No","title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","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.","quality_controlled":"1","publisher":"Akadémiai Kiadó","oa":1,"has_accepted_license":"1","isi":1,"year":"2020","day":"24","publication":"Studia Scientiarum Mathematicarum Hungarica","page":"193-199","date_published":"2020-07-24T00:00:00Z","doi":"10.1556/012.2020.57.2.1454","date_created":"2020-07-24T07:09:18Z"},{"oa_version":"Published Version","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"}],"month":"06","intvolume":" 8","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"9171","checksum":"cea41de9937d07a3b927d71ee8b4e432","file_size":562359,"date_updated":"2021-02-19T13:56:24Z","creator":"dernst","file_name":"2020_CompMathBiophysics_Akopyan2.pdf","date_created":"2021-02-19T13:56:24Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2544-7297"]},"publication_status":"published","volume":8,"issue":"1","ec_funded":1,"_id":"9157","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2023-10-17T12:34:51Z","file_date_updated":"2021-02-19T13:56:24Z","department":[{"_id":"HeEd"}],"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).","publisher":"De Gruyter","quality_controlled":"1","oa":1,"day":"20","publication":"Computational and Mathematical Biophysics","has_accepted_license":"1","year":"2020","date_published":"2020-06-20T00:00:00Z","doi":"10.1515/cmb-2020-0100","date_created":"2021-02-17T15:13:01Z","page":"51-67","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0100.","ama":"Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):51-67. doi:10.1515/cmb-2020-0100","apa":"Akopyan, A., & Edelsbrunner, H. (2020). The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0100","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 51–67, 2020.","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."},"title":"The weighted mean curvature derivative of a space-filling diagram","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"article_processing_charge":"No"},{"month":"07","intvolume":" 8","oa_version":"Published Version","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"}],"volume":8,"issue":"1","ec_funded":1,"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"ca43a7440834eab6bbea29c59b56ef3a","file_id":"9170","creator":"dernst","file_size":707452,"date_updated":"2021-02-19T13:33:19Z","file_name":"2020_CompMathBiophysics_Akopyan.pdf","date_created":"2021-02-19T13:33:19Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2544-7297"]},"publication_status":"published","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"9156","file_date_updated":"2021-02-19T13:33:19Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2023-10-17T12:35:10Z","publisher":"De Gruyter","quality_controlled":"1","oa":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).","doi":"10.1515/cmb-2020-0101","date_published":"2020-07-21T00:00:00Z","date_created":"2021-02-17T15:12:44Z","page":"74-88","day":"21","publication":"Computational and Mathematical Biophysics","has_accepted_license":"1","year":"2020","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"title":"The weighted Gaussian curvature derivative of a space-filling diagram","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["1908.06777"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.","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","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","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 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.","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."}},{"publication":"Journal of Applied and Computational Topology","day":"01","year":"2020","has_accepted_license":"1","date_created":"2024-03-04T10:47:49Z","doi":"10.1007/s41468-020-00058-8","date_published":"2020-12-01T00:00:00Z","page":"455-480","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.","oa":1,"quality_controlled":"1","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 4(4), 455–480.","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.","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.","short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480.","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","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","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."},"title":"Čech-Delaunay gradient flow and homology inference for self-maps","article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"U.","full_name":"Bauer, U.","last_name":"Bauer"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866","last_name":"Jablonski"},{"full_name":"Mrozek, M.","last_name":"Mrozek","first_name":"M."}],"language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":851190,"date_updated":"2024-03-04T10:52:42Z","file_name":"2020_JourApplCompTopology_Bauer.pdf","date_created":"2024-03-04T10:52:42Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"eed1168b6e66cd55272c19bb7fca8a1c","file_id":"15065"}],"publication_status":"published","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"volume":4,"issue":"4","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems."}],"intvolume":" 4","month":"12","scopus_import":"1","ddc":["500"],"date_updated":"2024-03-04T10:54:04Z","file_date_updated":"2024-03-04T10:52:42Z","department":[{"_id":"HeEd"}],"_id":"15064","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original"},{"_id":"6515","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2021-01-12T08:07:50Z","ddc":["510"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:32Z","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."}],"oa_version":"Published Version","scopus_import":1,"month":"07","intvolume":" 10","publication_identifier":{"issn":["1920-180X"]},"publication_status":"published","file":[{"file_size":2170882,"date_updated":"2020-07-14T12:47:32Z","creator":"mwintrae","file_name":"mainJournalFinal.pdf","date_created":"2019-06-03T09:30:01Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","checksum":"57b4df2f16a74eb499734ec8ee240178","file_id":"6516"}],"language":[{"iso":"eng"}],"volume":10,"issue":"1","ec_funded":1,"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"citation":{"short":"R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10 (2019) 223–256.","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.","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","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","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.","ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","chicago":"Dyer, Ramsay, Gert Vegter, and Mathijs Wintraecken. “Simplices Modelled on Spaces of Constant Curvature.” Journal of Computational Geometry . Carleton University, 2019. https://doi.org/10.20382/jocg.v10i1a9."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Dyer, Ramsay","last_name":"Dyer","first_name":"Ramsay"},{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"title":"Simplices modelled on spaces of constant curvature","publisher":"Carleton University","quality_controlled":"1","oa":1,"has_accepted_license":"1","year":"2019","day":"01","publication":"Journal of Computational Geometry ","page":"223–256","date_published":"2019-07-01T00:00:00Z","doi":"10.20382/jocg.v10i1a9","date_created":"2019-06-03T09:35:33Z"},{"type":"conference","conference":{"name":"CCCG: Canadian Conference in Computational Geometry","start_date":"2019-08-08","end_date":"2019-08-10","location":"Edmonton, Canada"},"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"status":"public","_id":"6628","author":[{"last_name":"Vegter","full_name":"Vegter, Gert","first_name":"Gert"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220"}],"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","file_date_updated":"2020-07-14T12:47:34Z","department":[{"_id":"HeEd"}],"citation":{"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.","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.","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.","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.","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.","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.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279."},"date_updated":"2021-01-12T08:08:16Z","ddc":["004"],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","scopus_import":1,"oa":1,"month":"08","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."}],"oa_version":"Submitted Version","page":"275-279","date_published":"2019-08-01T00:00:00Z","ec_funded":1,"date_created":"2019-07-12T08:34:57Z","has_accepted_license":"1","year":"2019","publication_status":"published","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"ceabd152cfa55170d57763f9c6c60a53","file_id":"6629","creator":"mwintrae","date_updated":"2020-07-14T12:47:34Z","file_size":321176,"date_created":"2019-07-12T08:32:46Z","file_name":"IntrinsicExtrinsicCCCG2019.pdf"}],"day":"01","language":[{"iso":"eng"}],"publication":"The 31st Canadian Conference in Computational Geometry"},{"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:35Z","ddc":["510"],"date_updated":"2021-01-12T08:08:23Z","status":"public","type":"conference","conference":{"name":"SoCG 2019: Symposium on Computational Geometry","start_date":"2019-06-18","end_date":"2019-06-21","location":"Portland, OR, United States"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"6648","volume":129,"file":[{"file_id":"6666","checksum":"8ec8720730d4c789bf7b06540f1c29f4","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2019-07-24T06:40:01Z","file_name":"2019_LIPICS_Edelsbrunner.pdf","creator":"dernst","date_updated":"2020-07-14T12:47:35Z","file_size":1355179}],"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783959771047"]},"publication_status":"published","month":"06","intvolume":" 129","scopus_import":1,"alternative_title":["LIPIcs"],"oa_version":"Published Version","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"}],"title":"Topological data analysis in information space","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","full_name":"Wagner, Hubert","last_name":"Wagner"}],"external_id":{"arxiv":["1903.08510"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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","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.","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.","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."},"project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"date_published":"2019-06-01T00:00:00Z","doi":"10.4230/LIPICS.SOCG.2019.31","date_created":"2019-07-17T10:36:09Z","page":"31:1-31:14","day":"01","publication":"35th International Symposium on Computational Geometry","has_accepted_license":"1","year":"2019","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","oa":1},{"author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"last_name":"Akitaya","full_name":"Akitaya, Hugo A","first_name":"Hugo A"},{"first_name":"Kenneth C","last_name":"Cheung","full_name":"Cheung, Kenneth C"},{"full_name":"Demaine, Erik D","last_name":"Demaine","first_name":"Erik D"},{"full_name":"Demaine, Martin L","last_name":"Demaine","first_name":"Martin L"},{"full_name":"Fekete, Sandor P","last_name":"Fekete","first_name":"Sandor P"},{"first_name":"Linda","full_name":"Kleist, Linda","last_name":"Kleist"},{"first_name":"Irina","last_name":"Kostitsyna","full_name":"Kostitsyna, Irina"},{"last_name":"Löffler","full_name":"Löffler, Maarten","first_name":"Maarten"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"first_name":"Christiane","last_name":"Schmidt","full_name":"Schmidt, Christiane"}],"article_processing_charge":"No","external_id":{"arxiv":["1910.09917"]},"department":[{"_id":"HeEd"}],"title":"Folding polyominoes with holes into a cube","citation":{"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.","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.","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–70.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, in:, Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–170.","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.","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.","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."},"date_updated":"2023-08-04T10:57:42Z","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","type":"conference","conference":{"name":"CCCG: Canadian Conference in Computational Geometry","start_date":"2019-08-08","end_date":"2019-08-10","location":"Edmonton, Canada"},"status":"public","_id":"6989","page":"164-170","related_material":{"record":[{"id":"8317","status":"public","relation":"extended_version"}]},"date_published":"2019-08-01T00:00:00Z","date_created":"2019-11-04T16:46:11Z","year":"2019","publication_status":"published","day":"01","publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","language":[{"iso":"eng"}],"quality_controlled":"1","publisher":"Canadian Conference on Computational Geometry","scopus_import":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://cccg.ca/proceedings/2019/proceedings.pdf"}],"month":"08","abstract":[{"lang":"eng","text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability. "}],"oa_version":"Published Version","acknowledgement":"This research was performed in part at the 33rd BellairsWinter Workshop on Computational Geometry. Wethank all other participants for a fruitful atmosphere."},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","_id":"6671","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:36Z","date_updated":"2023-08-22T12:37:47Z","ddc":["000"],"intvolume":" 3","month":"06","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","ec_funded":1,"issue":"1-2","volume":3,"publication_status":"published","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"language":[{"iso":"eng"}],"file":[{"file_size":2215157,"date_updated":"2020-07-14T12:47:36Z","creator":"dernst","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf","date_created":"2019-07-31T08:09:56Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"6741","checksum":"a5b244db9f751221409cf09c97ee0935"}],"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","citation":{"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.","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.","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.","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.","short":"J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58.","apa":"Boissonnat, J.-D., Lieutier, A., & Wintraecken, M. (2019). The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-019-00029-8","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"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publisher":"Springer Nature","quality_controlled":"1","page":"29–58","date_created":"2019-07-24T08:37:29Z","doi":"10.1007/s41468-019-00029-8","date_published":"2019-06-01T00:00:00Z","year":"2019","has_accepted_license":"1","publication":"Journal of Applied and Computational Topology","day":"01"},{"volume":147,"publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1709.02562","open_access":"1"}],"scopus_import":"1","intvolume":" 147","month":"01","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. "}],"oa_version":"Preprint","department":[{"_id":"HeEd"}],"date_updated":"2023-08-24T14:48:59Z","type":"journal_article","status":"public","_id":"6050","page":"91-102","date_created":"2019-02-24T22:59:19Z","date_published":"2019-01-01T00:00:00Z","doi":"10.1090/proc/14240","year":"2019","isi":1,"publication":"Proceedings of the American Mathematical Society","day":"01","oa":1,"publisher":"AMS","quality_controlled":"1","external_id":{"arxiv":["1709.02562"],"isi":["000450363900008"]},"article_processing_charge":"No","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"full_name":"Fedorov, Roman","last_name":"Fedorov","first_name":"Roman"}],"title":"Two circles and only a straightedge","citation":{"ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 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.","apa":"Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240","ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240","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.","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102.","mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society, vol. 147, AMS, 2019, pp. 91–102, doi:10.1090/proc/14240."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","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.","mla":"Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008.","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","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.","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","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"},"title":"Lower and upper bounds for the waists of different spaces","author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"first_name":"Alfredo","full_name":"Hubard, Alfredo","last_name":"Hubard"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"article_processing_charge":"No","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"day":"01","publication":"Topological Methods in Nonlinear Analysis","isi":1,"year":"2019","doi":"10.12775/TMNA.2019.008","date_published":"2019-06-01T00:00:00Z","date_created":"2019-07-14T21:59:19Z","page":"457-490","quality_controlled":"1","publisher":"Akademicka Platforma Czasopism","oa":1,"date_updated":"2023-08-29T06:32:48Z","department":[{"_id":"HeEd"}],"_id":"6634","status":"public","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","volume":53,"issue":"2","ec_funded":1,"oa_version":"Preprint","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"}],"month":"06","intvolume":" 53","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.06926"}]},{"ddc":["520","530"],"date_updated":"2023-08-29T07:01:48Z","file_date_updated":"2020-07-14T12:47:39Z","department":[{"_id":"HeEd"}],"_id":"6756","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":14420451,"date_updated":"2020-07-14T12:47:39Z","file_name":"2019_AstronomyAstrophysics_Pranav.pdf","date_created":"2019-08-05T08:08:59Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"6766","checksum":"83b9209ed9eefbdcefd89019c5a97805"}],"publication_status":"published","publication_identifier":{"issn":["00046361"],"eissn":["14320746"]},"volume":627,"oa_version":"Published Version","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."}],"intvolume":" 627","month":"07","scopus_import":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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","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","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).","ieee":"P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 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.","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.","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."},"title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","external_id":{"arxiv":["1812.07678"],"isi":["000475839300003"]},"article_processing_charge":"No","author":[{"first_name":"Pratyush","last_name":"Pranav","full_name":"Pranav, Pratyush"},{"full_name":"Adler, Robert J.","last_name":"Adler","first_name":"Robert J."},{"first_name":"Thomas","last_name":"Buchert","full_name":"Buchert, Thomas"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Jones","full_name":"Jones, Bernard J.T.","first_name":"Bernard J.T."},{"first_name":"Armin","last_name":"Schwartzman","full_name":"Schwartzman, Armin"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","full_name":"Wagner, Hubert","last_name":"Wagner"},{"first_name":"Rien","last_name":"Van De Weygaert","full_name":"Van De Weygaert, Rien"}],"article_number":"A163","project":[{"grant_number":"M62909-18-1-2038","name":"Toward Computational Information Topology","_id":"265683E4-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"publication":"Astronomy and Astrophysics","day":"17","year":"2019","isi":1,"has_accepted_license":"1","date_created":"2019-08-04T21:59:18Z","date_published":"2019-07-17T00:00:00Z","doi":"10.1051/0004-6361/201834916","oa":1,"publisher":"EDP Sciences","quality_controlled":"1"},{"date_updated":"2023-08-29T07:08:34Z","department":[{"_id":"HeEd"}],"_id":"6793","type":"journal_article","article_type":"original","status":"public","publication_identifier":{"eissn":["14692120"],"issn":["00246093"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"5","volume":51,"ec_funded":1,"abstract":[{"lang":"eng","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."}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1903.04929","open_access":"1"}],"month":"10","intvolume":" 51","citation":{"short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","ieee":"A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019.","apa":"Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12276","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","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.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X"},{"first_name":"Ivan","full_name":"Izmestiev, Ivan","last_name":"Izmestiev"}],"external_id":{"arxiv":["1903.04929"],"isi":["000478560200001"]},"article_processing_charge":"No","title":"The Regge symmetry, confocal conics, and the Schläfli formula","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"isi":1,"year":"2019","day":"01","publication":"Bulletin of the London Mathematical Society","page":"765-775","date_published":"2019-10-01T00:00:00Z","doi":"10.1112/blms.12276","date_created":"2019-08-11T21:59:23Z","quality_controlled":"1","publisher":"London Mathematical Society","oa":1},{"citation":{"ieee":"A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra, vol. 538. Elsevier, pp. 261–289, 2019.","short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","ama":"Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027","apa":"Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. Elsevier. 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.","ista":"Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289.","chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam","full_name":"Brown, Adam","last_name":"Brown"}],"article_processing_charge":"No","external_id":{"isi":["000487176300011"],"arxiv":["1805.04676"]},"title":"Arakawa-Suzuki functors for Whittaker modules","isi":1,"year":"2019","day":"15","publication":"Journal of Algebra","page":"261-289","doi":"10.1016/j.jalgebra.2019.07.027","date_published":"2019-11-15T00:00:00Z","date_created":"2019-08-22T07:54:13Z","quality_controlled":"1","publisher":"Elsevier","oa":1,"date_updated":"2023-08-29T07:11:47Z","department":[{"_id":"HeEd"}],"_id":"6828","type":"journal_article","article_type":"original","status":"public","publication_identifier":{"issn":["0021-8693"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":538,"abstract":[{"lang":"eng","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 ."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.04676"}],"month":"11","intvolume":" 538"},{"status":"public","type":"conference","conference":{"end_date":"2019-10-30","location":"Auckland, New Zealand","start_date":"2019-10-27","name":"ITSC: Intelligent Transportation Systems Conference"},"article_number":"8917514","_id":"7216","department":[{"_id":"HeEd"}],"title":"LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale","author":[{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","last_name":"Osang","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F"},{"last_name":"Cook","full_name":"Cook, James","first_name":"James"},{"full_name":"Fabrikant, Alex","last_name":"Fabrikant","first_name":"Alex"},{"first_name":"Marco","full_name":"Gruteser, Marco","last_name":"Gruteser"}],"external_id":{"isi":["000521238102050"]},"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Osang, Georg F, James Cook, Alex Fabrikant, and Marco Gruteser. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” In 2019 IEEE Intelligent Transportation Systems Conference. IEEE, 2019. https://doi.org/10.1109/ITSC.2019.8917514.","ista":"Osang GF, Cook J, Fabrikant A, Gruteser M. 2019. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. 2019 IEEE Intelligent Transportation Systems Conference. ITSC: Intelligent Transportation Systems Conference, 8917514.","mla":"Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” 2019 IEEE Intelligent Transportation Systems Conference, 8917514, IEEE, 2019, doi:10.1109/ITSC.2019.8917514.","apa":"Osang, G. F., Cook, J., Fabrikant, A., & Gruteser, M. (2019). LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In 2019 IEEE Intelligent Transportation Systems Conference. Auckland, New Zealand: IEEE. https://doi.org/10.1109/ITSC.2019.8917514","ama":"Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In: 2019 IEEE Intelligent Transportation Systems Conference. IEEE; 2019. doi:10.1109/ITSC.2019.8917514","ieee":"G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale,” in 2019 IEEE Intelligent Transportation Systems Conference, Auckland, New Zealand, 2019.","short":"G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019."},"date_updated":"2023-09-06T14:50:28Z","month":"11","quality_controlled":"1","publisher":"IEEE","scopus_import":"1","oa_version":"None","abstract":[{"lang":"eng","text":"We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system to label a stream of noisy observations of transit vehicle trajectories with the transit routes they are serving (e.g., northbound bus #5). In order to scale efficiently to large transit networks, our system first retrieves a small set of candidate routes from a geometrically indexed data structure, then applies a fine-grained scoring step to choose the best match. Given that real-time data remains unavailable for the majority of the world’s transit agencies, these inferences can help feed a real-time map of a transit system’s trips, infer transit trip delays in real time, or measure and correct noisy transit tracking data. This system can run on vehicle observations from a variety of sources that don’t attach route information to vehicle observations, such as public imagery streams or user-contributed transit vehicle sightings.We abstract away the specifics of the sensing system and demonstrate the effectiveness of our system on a \"semisynthetic\" dataset of all New York City buses, where we simulate sensed trajectories by starting with fully labeled vehicle trajectories reported via the GTFS-Realtime protocol, removing the transit route IDs, and perturbing locations with synthetic noise. Using just the geometric shapes of the trajectories, we demonstrate that our system converges on the correct route ID within a few minutes, even after a vehicle switches from serving one trip to the next."}],"date_published":"2019-11-28T00:00:00Z","doi":"10.1109/ITSC.2019.8917514","date_created":"2019-12-29T23:00:47Z","day":"28","language":[{"iso":"eng"}],"publication":"2019 IEEE Intelligent Transportation Systems Conference","isi":1,"publication_identifier":{"isbn":["9781538670248"]},"publication_status":"published","year":"2019"},{"_id":"5678","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","date_updated":"2023-09-07T12:07:12Z","ddc":["516"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:10Z","abstract":[{"text":"The order-k Voronoi tessellation of a locally finite set 𝑋⊆ℝ𝑛 decomposes ℝ𝑛 into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 62","month":"12","publication_status":"published","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","date_created":"2019-02-06T10:10:46Z","creator":"dernst","file_size":599339,"date_updated":"2020-07-14T12:47:10Z","file_id":"5932","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"ec_funded":1,"volume":62,"issue":"4","related_material":{"record":[{"status":"public","id":"6287","relation":"dissertation_contains"}]},"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"citation":{"short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.","ieee":"H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019.","apa":"Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2","ama":"Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2.","ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["1709.09380"],"isi":["000494042900008"]},"author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","last_name":"Nikitenko","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton"}],"title":"Poisson–Delaunay Mosaics of Order k","oa":1,"quality_controlled":"1","publisher":"Springer","year":"2019","isi":1,"has_accepted_license":"1","publication":"Discrete and Computational Geometry","day":"01","page":"865–878","date_created":"2018-12-16T22:59:20Z","date_published":"2019-12-01T00:00:00Z","doi":"10.1007/s00454-018-0049-2"},{"quality_controlled":"1","publisher":"Elsevier","oa":1,"day":"01","publication":"Computer Aided Geometric Design","has_accepted_license":"1","isi":1,"year":"2019","doi":"10.1016/j.cagd.2019.06.003","date_published":"2019-08-01T00:00:00Z","date_created":"2019-07-07T21:59:20Z","page":"1-15","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019, pp. 1–15, doi:10.1016/j.cagd.2019.06.003.","apa":"Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered complex. Computer Aided Geometric Design. Elsevier. https://doi.org/10.1016/j.cagd.2019.06.003","ama":"Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003","ieee":"H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” Computer Aided Geometric Design, vol. 73. Elsevier, pp. 1–15, 2019.","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design. Elsevier, 2019. https://doi.org/10.1016/j.cagd.2019.06.003.","ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15."},"title":"Holes and dependences in an ordered complex","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Ölsböck","orcid":"0000-0002-4672-8297","full_name":"Ölsböck, Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina"}],"external_id":{"isi":["000485207800001"]},"article_processing_charge":"No","oa_version":"Published Version","abstract":[{"text":"We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram.","lang":"eng"}],"month":"08","intvolume":" 73","scopus_import":"1","file":[{"file_id":"6624","checksum":"7c99be505dc7533257d42eb1830cef04","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2019-07-08T15:24:26Z","file_name":"Elsevier_2019_Edelsbrunner.pdf","date_updated":"2020-07-14T12:47:34Z","file_size":2665013,"creator":"kschuh"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":73,"related_material":{"record":[{"relation":"dissertation_contains","id":"7460","status":"public"}]},"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","ec_funded":1,"_id":"6608","status":"public","type":"journal_article","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"ddc":["000"],"date_updated":"2023-09-07T13:15:29Z","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:34Z"},{"article_number":"1903.06981","_id":"7950","status":"public","type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-01-04T12:42:08Z","citation":{"apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. arXiv.","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv.","ieee":"A. Biniaz et al., “Token swapping on trees,” arXiv. .","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.).","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981.","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981.","chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” ArXiv, n.d."},"department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"title":"Token swapping on trees","external_id":{"arxiv":["1903.06981"]},"article_processing_charge":"No","author":[{"first_name":"Ahmad","last_name":"Biniaz","full_name":"Biniaz, Ahmad"},{"first_name":"Kshitij","full_name":"Jain, Kshitij","last_name":"Jain"},{"full_name":"Lubiw, Anna","last_name":"Lubiw","first_name":"Anna"},{"first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","last_name":"Masárová"},{"first_name":"Tillmann","last_name":"Miltzow","full_name":"Miltzow, Tillmann"},{"full_name":"Mondal, Debajyoti","last_name":"Mondal","first_name":"Debajyoti"},{"first_name":"Anurag Murty","full_name":"Naredla, Anurag Murty","last_name":"Naredla"},{"id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef","last_name":"Tkadlec"},{"first_name":"Alexi","last_name":"Turcotte","full_name":"Turcotte, Alexi"}],"oa_version":"Preprint","abstract":[{"text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:\r\n1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.","lang":"eng"}],"month":"03","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.06981"}],"language":[{"iso":"eng"}],"publication":"arXiv","day":"16","year":"2019","publication_status":"submitted","date_created":"2020-06-08T12:25:25Z","date_published":"2019-03-16T00:00:00Z","related_material":{"record":[{"status":"public","id":"7944","relation":"dissertation_contains"},{"relation":"later_version","status":"public","id":"12833"}]}},{"author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga"},{"last_name":"Wagner","full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert"}],"publist_id":"7733","title":"Smallest enclosing spheres and Chernoff points in Bregman geometry","citation":{"chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.35.","ista":"Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13.","mla":"Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35","ama":"Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:35:1-35:13. doi:10.4230/LIPIcs.SoCG.2018.35"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"page":"35:1 - 35:13","date_created":"2018-12-11T11:45:05Z","doi":"10.4230/LIPIcs.SoCG.2018.35","date_published":"2018-06-11T00:00:00Z","year":"2018","has_accepted_license":"1","day":"11","oa":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","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","file_date_updated":"2020-07-14T12:45:20Z","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T06:53:48Z","ddc":["000"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"start_date":"2018-06-11","end_date":"2018-06-14","location":"Budapest, Hungary","name":"SoCG: Symposium on Computational Geometry"},"type":"conference","status":"public","_id":"188","volume":99,"publication_status":"published","language":[{"iso":"eng"}],"file":[{"file_id":"5724","checksum":"7509403803b3ac1aee94bbc2ad293d21","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2018-12-17T16:31:31Z","file_name":"2018_LIPIcs_Edelsbrunner.pdf","date_updated":"2020-07-14T12:45:20Z","file_size":489080,"creator":"dernst"}],"alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"scopus_import":1,"intvolume":" 99","month":"06","abstract":[{"text":"Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex.","lang":"eng"}],"oa_version":"Published Version"},{"day":"11","has_accepted_license":"1","year":"2018","date_published":"2018-06-11T00:00:00Z","doi":"10.15479/AT:ISTA:th_1026","date_created":"2018-12-11T11:45:10Z","page":"171","publisher":"Institute of Science and Technology Austria","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"apa":"Iglesias Ham, M. (2018). Multiple covers with balls. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1026","ama":"Iglesias Ham M. Multiple covers with balls. 2018. doi:10.15479/AT:ISTA:th_1026","ieee":"M. Iglesias Ham, “Multiple covers with balls,” Institute of Science and Technology Austria, 2018.","short":"M. Iglesias Ham, Multiple Covers with Balls, Institute of Science and Technology Austria, 2018.","mla":"Iglesias Ham, Mabel. Multiple Covers with Balls. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1026.","ista":"Iglesias Ham M. 2018. Multiple covers with balls. Institute of Science and Technology Austria.","chicago":"Iglesias Ham, Mabel. “Multiple Covers with Balls.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1026."},"title":"Multiple covers with balls","author":[{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel","last_name":"Iglesias Ham","full_name":"Iglesias Ham, Mabel"}],"publist_id":"7712","article_processing_charge":"No","file":[{"access_level":"closed","relation":"source_file","content_type":"application/zip","file_id":"5918","checksum":"dd699303623e96d1478a6ae07210dd05","creator":"kschuh","date_updated":"2020-07-14T12:45:24Z","file_size":11827713,"date_created":"2019-02-05T07:43:31Z","file_name":"IST-2018-1025-v2+5_ist-thesis-iglesias-11June2018(1).zip"},{"checksum":"ba163849a190d2b41d66fef0e4983294","file_id":"5919","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2019-02-05T07:43:45Z","file_name":"IST-2018-1025-v2+4_ThesisIglesiasFinal11June2018.pdf","creator":"kschuh","date_updated":"2020-07-14T12:45:24Z","file_size":4783846}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","oa_version":"Published Version","abstract":[{"text":"We describe arrangements of three-dimensional spheres from a geometrical and topological point of view. Real data (fitting this setup) often consist of soft spheres which show certain degree of deformation while strongly packing against each other. In this context, we answer the following questions: If we model a soft packing of spheres by hard spheres that are allowed to overlap, can we measure the volume in the overlapped areas? Can we be more specific about the overlap volume, i.e. quantify how much volume is there covered exactly twice, three times, or k times? What would be a good optimization criteria that rule the arrangement of soft spheres while making a good use of the available space? Fixing a particular criterion, what would be the optimal sphere configuration? The first result of this thesis are short formulas for the computation of volumes covered by at least k of the balls. The formulas exploit information contained in the order-k Voronoi diagrams and its closely related Level-k complex. The used complexes lead to a natural generalization into poset diagrams, a theoretical formalism that contains the order-k and degree-k diagrams as special cases. In parallel, we define different criteria to determine what could be considered an optimal arrangement from a geometrical point of view. Fixing a criterion, we find optimal soft packing configurations in 2D and 3D where the ball centers lie on a lattice. As a last step, we use tools from computational topology on real physical data, to show the potentials of higher-order diagrams in the description of melting crystals. The results of the experiments leaves us with an open window to apply the theories developed in this thesis in real applications.","lang":"eng"}],"month":"06","alternative_title":["ISTA Thesis"],"ddc":["514","516"],"supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"date_updated":"2023-09-07T12:25:32Z","file_date_updated":"2020-07-14T12:45:24Z","department":[{"_id":"HeEd"}],"_id":"201","status":"public","pubrep_id":"1026","type":"dissertation"},{"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","oa":1,"acknowledgement":"This work is partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","doi":"10.4230/LIPIcs.SoCG.2018.34","date_published":"2018-06-11T00:00:00Z","date_created":"2018-12-11T11:45:05Z","has_accepted_license":"1","year":"2018","day":"11","project":[{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"article_number":"34","publist_id":"7732","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","last_name":"Osang"}],"title":"The multi-cover persistence of Euclidean balls","citation":{"ista":"Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.34.","apa":"Edelsbrunner, H., & Osang, G. F. (2018). The multi-cover persistence of Euclidean balls (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.34","ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.34","short":"H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. The Multi-Cover Persistence of Euclidean Balls. Vol. 99, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.34."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","alternative_title":["LIPIcs"],"scopus_import":1,"month":"06","intvolume":" 99","abstract":[{"text":"Given a locally finite X ⊆ ℝd and a radius r ≥ 0, the k-fold cover of X and r consists of all points in ℝd that have k or more points of X within distance r. We consider two filtrations - one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k - and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in ℝd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. ","lang":"eng"}],"oa_version":"Published Version","volume":99,"related_material":{"record":[{"relation":"later_version","status":"public","id":"9317"},{"relation":"dissertation_contains","status":"public","id":"9056"}]},"publication_status":"published","file":[{"date_created":"2018-12-18T09:27:22Z","file_name":"2018_LIPIcs_Edelsbrunner_Osang.pdf","creator":"dernst","date_updated":"2020-07-14T12:45:19Z","file_size":528018,"file_id":"5738","checksum":"d8c0533ad0018eb4ed1077475eb8fc18","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Budapest, Hungary","end_date":"2018-06-14","start_date":"2018-06-11"},"status":"public","_id":"187","file_date_updated":"2020-07-14T12:45:19Z","department":[{"_id":"HeEd"}],"date_updated":"2023-09-07T13:29:00Z","ddc":["516"]},{"publisher":"Springer","quality_controlled":"1","oa":1,"date_published":"2018-06-01T00:00:00Z","doi":"10.1007/s10711-017-0265-6","date_created":"2018-12-11T11:47:57Z","page":"55 - 64","day":"01","publication":"Geometriae Dedicata","isi":1,"has_accepted_license":"1","year":"2018","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"title":"3-Webs generated by confocal conics and circles","publist_id":"7014","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"}],"external_id":{"isi":["000431418800004"]},"article_processing_charge":"Yes (via OA deal)","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata, vol. 194, no. 1, Springer, 2018, pp. 55–64, doi:10.1007/s10711-017-0265-6.","apa":"Akopyan, A. (2018). 3-Webs generated by confocal conics and circles. Geometriae Dedicata. Springer. https://doi.org/10.1007/s10711-017-0265-6","ama":"Akopyan A. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 2018;194(1):55-64. doi:10.1007/s10711-017-0265-6","ieee":"A. Akopyan, “3-Webs generated by confocal conics and circles,” Geometriae Dedicata, vol. 194, no. 1. Springer, pp. 55–64, 2018.","short":"A. Akopyan, Geometriae Dedicata 194 (2018) 55–64.","chicago":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0265-6.","ista":"Akopyan A. 2018. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 194(1), 55–64."},"month":"06","intvolume":" 194","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider families of confocal conics and two pencils of Apollonian circles having the same foci. We will show that these families of curves generate trivial 3-webs and find the exact formulas describing them."}],"issue":"1","volume":194,"ec_funded":1,"file":[{"creator":"kschuh","file_size":1140860,"date_updated":"2020-07-14T12:47:44Z","file_name":"2018_Springer_Akopyan.pdf","date_created":"2020-01-03T11:35:08Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"7222","checksum":"1febcfc1266486053a069e3425ea3713"}],"language":[{"iso":"eng"}],"publication_status":"published","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"692","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:44Z","ddc":["510"],"date_updated":"2023-09-08T11:40:29Z"},{"date_updated":"2023-09-11T12:48:39Z","department":[{"_id":"HeEd"}],"_id":"58","type":"journal_article","status":"public","publication_status":"published","language":[{"iso":"eng"}],"issue":"3","volume":32,"ec_funded":1,"abstract":[{"lang":"eng","text":"Inside a two-dimensional region (``cake""), there are m nonoverlapping tiles of a certain kind (``toppings""). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,"" such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks."}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1604.00960","open_access":"1"}],"month":"09","intvolume":" 32","citation":{"ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.","chicago":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M110407X.","ama":"Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 2018;32(3):2242-2257. doi:10.1137/16M110407X","apa":"Akopyan, A., & Segal Halevi, E. (2018). Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M110407X","ieee":"A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,” SIAM Journal on Discrete Mathematics, vol. 32, no. 3. Society for Industrial and Applied Mathematics , pp. 2242–2257, 2018.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257.","mla":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics, vol. 32, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 2242–57, doi:10.1137/16M110407X."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"first_name":"Erel","full_name":"Segal Halevi, Erel","last_name":"Segal Halevi"}],"publist_id":"7996","external_id":{"arxiv":["1604.00960"],"isi":["000450810500036"]},"article_processing_charge":"No","title":"Counting blanks in polygonal arrangements","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"isi":1,"year":"2018","day":"06","publication":"SIAM Journal on Discrete Mathematics","page":"2242 - 2257","doi":"10.1137/16M110407X","date_published":"2018-09-06T00:00:00Z","date_created":"2018-12-11T11:44:24Z","quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics ","oa":1},{"year":"2018","isi":1,"publication":"Transactions of the American Mathematical Society","day":"01","page":"2825 - 2854","date_created":"2018-12-11T11:46:35Z","date_published":"2018-04-01T00:00:00Z","doi":"10.1090/tran/7292","acknowledgement":"DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”; People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) REA grant agreement n◦[291734]","oa":1,"quality_controlled":"1","publisher":"American Mathematical Society","citation":{"chicago":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” Transactions of the American Mathematical Society. American Mathematical Society, 2018. https://doi.org/10.1090/tran/7292.","ista":"Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 370(4), 2825–2854.","mla":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” Transactions of the American Mathematical Society, vol. 370, no. 4, American Mathematical Society, 2018, pp. 2825–54, doi:10.1090/tran/7292.","short":"A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society 370 (2018) 2825–2854.","ieee":"A. Akopyan and A. Bobenko, “Incircular nets and confocal conics,” Transactions of the American Mathematical Society, vol. 370, no. 4. American Mathematical Society, pp. 2825–2854, 2018.","apa":"Akopyan, A., & Bobenko, A. (2018). Incircular nets and confocal conics. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/7292","ama":"Akopyan A, Bobenko A. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 2018;370(4):2825-2854. doi:10.1090/tran/7292"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000423197800019"]},"article_processing_charge":"No","publist_id":"7363","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"full_name":"Bobenko, Alexander","last_name":"Bobenko","first_name":"Alexander"}],"title":"Incircular nets and confocal conics","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"issue":"4","volume":370,"abstract":[{"lang":"eng","text":"We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics. Our main new results are on checkerboard IC-nets in the plane. These are congruences of straight lines in the plane with the combinatorics of the square grid, combinatorially colored as a checkerboard, such that all black coordinate quadrilaterals possess inscribed circles. We show how this larger class of IC-nets appears quite naturally in Laguerre geometry of oriented planes and spheres and leads to new remarkable incidence theorems. Most of our results are valid in hyperbolic and spherical geometries as well. We present also generalizations in spaces of higher dimension, called checkerboard IS-nets. The construction of these nets is based on a new 9 inspheres incidence theorem."}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1602.04637","open_access":"1"}],"scopus_import":"1","intvolume":" 370","month":"04","date_updated":"2023-09-11T14:19:12Z","department":[{"_id":"HeEd"}],"_id":"458","type":"journal_article","status":"public"},{"oa_version":"Preprint","abstract":[{"text":"The goal of this article is to introduce the reader to the theory of intrinsic geometry of convex surfaces. We illustrate the power of the tools by proving a theorem on convex surfaces containing an arbitrarily long closed simple geodesic. Let us remind ourselves that a curve in a surface is called geodesic if every sufficiently short arc of the curve is length minimizing; if, in addition, it has no self-intersections, we call it simple geodesic. A tetrahedron with equal opposite edges is called isosceles. The axiomatic method of Alexandrov geometry allows us to work with the metrics of convex surfaces directly, without approximating it first by a smooth or polyhedral metric. Such approximations destroy the closed geodesics on the surface; therefore it is difficult (if at all possible) to apply approximations in the proof of our theorem. On the other hand, a proof in the smooth or polyhedral case usually admits a translation into Alexandrov’s language; such translation makes the result more general. In fact, our proof resembles a translation of the proof given by Protasov. Note that the main theorem implies in particular that a smooth convex surface does not have arbitrarily long simple closed geodesics. However we do not know a proof of this corollary that is essentially simpler than the one presented below.","lang":"eng"}],"month":"09","intvolume":" 40","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.05172"}],"language":[{"iso":"eng"}],"publication_status":"published","issue":"3","volume":40,"_id":"106","status":"public","type":"journal_article","date_updated":"2023-09-13T08:49:16Z","department":[{"_id":"HeEd"}],"publisher":"Springer","quality_controlled":"1","oa":1,"day":"01","publication":"Mathematical Intelligencer","isi":1,"year":"2018","doi":"10.1007/s00283-018-9795-5","date_published":"2018-09-01T00:00:00Z","date_created":"2018-12-11T11:44:40Z","page":"26 - 31","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer, vol. 40, no. 3, Springer, 2018, pp. 26–31, doi:10.1007/s00283-018-9795-5.","short":"A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31.","ieee":"A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” Mathematical Intelligencer, vol. 40, no. 3. Springer, pp. 26–31, 2018.","apa":"Akopyan, A., & Petrunin, A. (2018). Long geodesics on convex surfaces. Mathematical Intelligencer. Springer. https://doi.org/10.1007/s00283-018-9795-5","ama":"Akopyan A, Petrunin A. Long geodesics on convex surfaces. Mathematical Intelligencer. 2018;40(3):26-31. doi:10.1007/s00283-018-9795-5","chicago":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer. Springer, 2018. https://doi.org/10.1007/s00283-018-9795-5.","ista":"Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical Intelligencer. 40(3), 26–31."},"title":"Long geodesics on convex surfaces","publist_id":"7948","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"first_name":"Anton","last_name":"Petrunin","full_name":"Petrunin, Anton"}],"external_id":{"arxiv":["1702.05172"],"isi":["000444141200005"]},"article_processing_charge":"No"},{"citation":{"mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications, vol. 68, Elsevier, 2018, pp. 119–33, doi:10.1016/j.comgeo.2017.06.014.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” Computational Geometry: Theory and Applications, vol. 68. Elsevier, pp. 119–133, 2018.","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 2018;68:119-133. doi:10.1016/j.comgeo.2017.06.014","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.014","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications. Elsevier, 2018. https://doi.org/10.1016/j.comgeo.2017.06.014.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"isi":["000415778300010"]},"publist_id":"7289","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham"}],"title":"Multiple covers with balls I: Inclusion–exclusion","project":[{"name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"year":"2018","isi":1,"has_accepted_license":"1","publication":"Computational Geometry: Theory and Applications","day":"01","page":"119 - 133","date_created":"2018-12-11T11:46:59Z","date_published":"2018-03-01T00:00:00Z","doi":"10.1016/j.comgeo.2017.06.014","oa":1,"quality_controlled":"1","publisher":"Elsevier","date_updated":"2023-09-13T08:59:00Z","ddc":["000"],"file_date_updated":"2020-07-14T12:46:38Z","department":[{"_id":"HeEd"}],"_id":"530","type":"journal_article","status":"public","publication_status":"published","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","file_id":"5953","date_updated":"2020-07-14T12:46:38Z","file_size":708357,"creator":"dernst","date_created":"2019-02-12T06:47:52Z","file_name":"2018_Edelsbrunner.pdf"}],"ec_funded":1,"volume":68,"abstract":[{"lang":"eng","text":"Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of Rn covered by at least k balls in a finite set. We implement two of the formulas in dimension n=3 and report on results obtained with our software."}],"oa_version":"Preprint","scopus_import":"1","intvolume":" 68","month":"03"},{"oa":1,"publisher":"ACM","quality_controlled":"1","acknowledgement":"Leonid Reyzin was supported in part by IST Austria and by US NSF grants 1012910, 1012798, and 1422965; this research was performed while he was visiting IST Austria.","page":"51 - 65","date_created":"2018-12-11T11:45:07Z","doi":"10.1145/3196494.3196534","date_published":"2018-06-01T00:00:00Z","year":"2018","isi":1,"publication":"Proceedings of the 2018 on Asia Conference on Computer and Communication Security","day":"01","project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"},{"call_identifier":"H2020","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","grant_number":"682815","name":"Teaching Old Crypto New Tricks"}],"article_processing_charge":"No","external_id":{"isi":["000516620100005"]},"author":[{"first_name":"Joel F","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87","last_name":"Alwen","full_name":"Alwen, Joel F"},{"first_name":"Peter","full_name":"Gazi, Peter","last_name":"Gazi"},{"first_name":"Chethan","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","full_name":"Kamath Hosdurg, Chethan","last_name":"Kamath Hosdurg"},{"last_name":"Klein","full_name":"Klein, Karen","id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87","first_name":"Karen"},{"last_name":"Osang","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","last_name":"Pietrzak","orcid":"0000-0002-9139-1654","full_name":"Pietrzak, Krzysztof Z"},{"last_name":"Reyzin","full_name":"Reyzin, Lenoid","first_name":"Lenoid"},{"last_name":"Rolinek","full_name":"Rolinek, Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","first_name":"Michal"},{"full_name":"Rybar, Michal","last_name":"Rybar","id":"2B3E3DE8-F248-11E8-B48F-1D18A9856A87","first_name":"Michal"}],"publist_id":"7723","title":"On the memory hardness of data independent password hashing functions","citation":{"short":"J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak, L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65.","ieee":"J. F. Alwen et al., “On the memory hardness of data independent password hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65.","ama":"Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data independent password hashing functions. In: Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534","apa":"Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak, K. Z., … Rybar, M. (2018). On the memory hardness of data independent password hashing functions. In Proceedings of the 2018 on Asia Conference on Computer and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534","mla":"Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534.","ista":"Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password hashing functions. Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ASIACCS: Asia Conference on Computer and Communications Security , 51–65.","chicago":"Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar. “On the Memory Hardness of Data Independent Password Hashing Functions.” In Proceedings of the 2018 on Asia Conference on Computer and Communication Security, 51–65. ACM, 2018. https://doi.org/10.1145/3196494.3196534."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2016/783"}],"scopus_import":"1","month":"06","abstract":[{"lang":"eng","text":"We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki'16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block'16] for analyzing the hardware costs of an iMHF."}],"oa_version":"Submitted Version","ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}],"conference":{"location":"Incheon, Republic of Korea","end_date":"2018-06-08","start_date":"2018-06-04","name":"ASIACCS: Asia Conference on Computer and Communications Security "},"type":"conference","status":"public","_id":"193","department":[{"_id":"KrPi"},{"_id":"HeEd"},{"_id":"VlKo"}],"date_updated":"2023-09-13T09:13:12Z"},{"quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics ","oa":1,"acknowledgement":"This work was partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics,” through grant I02979-N35 of the Austrian Science Fund (FWF).","page":"750 - 782","doi":"10.1137/16M1097201","date_published":"2018-03-29T00:00:00Z","date_created":"2018-12-11T11:45:46Z","isi":1,"year":"2018","day":"29","publication":"SIAM J Discrete Math","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7553","article_processing_charge":"No","external_id":{"isi":["000428958900038"]},"title":"On the optimality of the FCC lattice for soft sphere packing","citation":{"mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math, vol. 32, no. 1, Society for Industrial and Applied Mathematics , 2018, pp. 750–82, doi:10.1137/16M1097201.","ama":"Edelsbrunner H, Iglesias Ham M. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 2018;32(1):750-782. doi:10.1137/16M1097201","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M1097201","short":"H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “On the optimality of the FCC lattice for soft sphere packing,” SIAM J Discrete Math, vol. 32, no. 1. Society for Industrial and Applied Mathematics , pp. 750–782, 2018.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1097201.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 32(1), 750–782."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","scopus_import":"1","main_file_link":[{"url":"http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf","open_access":"1"}],"month":"03","intvolume":" 32","abstract":[{"lang":"eng","text":"Motivated by biological questions, we study configurations of equal spheres that neither pack nor cover. Placing their centers on a lattice, we define the soft density of the configuration by penalizing multiple overlaps. Considering the 1-parameter family of diagonally distorted 3-dimensional integer lattices, we show that the soft density is maximized at the FCC lattice."}],"oa_version":"Submitted Version","volume":32,"issue":"1","publication_identifier":{"issn":["08954801"]},"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","status":"public","_id":"312","department":[{"_id":"HeEd"}],"date_updated":"2023-09-13T09:34:38Z"},{"date_updated":"2023-09-13T09:34:12Z","department":[{"_id":"HeEd"}],"_id":"409","status":"public","type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1631073X"]},"publication_status":"published","issue":"4","volume":356,"oa_version":"Preprint","abstract":[{"text":"We give a simple proof of T. Stehling's result [4], whereby in any normal tiling of the plane with convex polygons with number of sides not less than six, all tiles except a finite number are hexagons.","lang":"eng"}],"month":"04","intvolume":" 356","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1805.01652","open_access":"1"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"apa":"Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. Elsevier. https://doi.org/10.1016/j.crma.2018.03.005","ama":"Akopyan A. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 2018;356(4):412-414. doi:10.1016/j.crma.2018.03.005","ieee":"A. Akopyan, “On the number of non-hexagons in a planar tiling,” Comptes Rendus Mathematique, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.","short":"A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.","mla":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:10.1016/j.crma.2018.03.005.","ista":"Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 356(4), 412–414.","chicago":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique. Elsevier, 2018. https://doi.org/10.1016/j.crma.2018.03.005."},"title":"On the number of non-hexagons in a planar tiling","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7420","external_id":{"isi":["000430402700009"],"arxiv":["1805.01652"]},"article_processing_charge":"No","day":"01","publication":"Comptes Rendus Mathematique","isi":1,"year":"2018","doi":"10.1016/j.crma.2018.03.005","date_published":"2018-04-01T00:00:00Z","date_created":"2018-12-11T11:46:19Z","page":"412-414","quality_controlled":"1","publisher":"Elsevier","oa":1},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability. Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/18-AAP1389.","ista":"Edelsbrunner H, Nikitenko A. 2018. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 28(5), 3215–3238.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability, vol. 28, no. 5, Institute of Mathematical Statistics, 2018, pp. 3215–38, doi:10.1214/18-AAP1389.","ama":"Edelsbrunner H, Nikitenko A. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 2018;28(5):3215-3238. doi:10.1214/18-AAP1389","apa":"Edelsbrunner, H., & Nikitenko, A. (2018). Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AAP1389","ieee":"H. Edelsbrunner and A. Nikitenko, “Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics,” Annals of Applied Probability, vol. 28, no. 5. Institute of Mathematical Statistics, pp. 3215–3238, 2018.","short":"H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238."},"title":"Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics","article_processing_charge":"No","external_id":{"isi":["000442893500018"],"arxiv":["1705.02870"]},"author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","last_name":"Nikitenko","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton"}],"publist_id":"7967","project":[{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"publication":"Annals of Applied Probability","day":"01","year":"2018","isi":1,"date_created":"2018-12-11T11:44:33Z","doi":"10.1214/18-AAP1389","date_published":"2018-10-01T00:00:00Z","page":"3215 - 3238","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","date_updated":"2023-09-15T12:10:35Z","department":[{"_id":"HeEd"}],"_id":"87","status":"public","type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"publication_status":"published","issue":"5","related_material":{"record":[{"id":"6287","status":"public","relation":"dissertation_contains"}]},"volume":28,"oa_version":"Preprint","abstract":[{"text":"Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. We find that the expectations are essentially the same as for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to the boundary complex of the convex hull in Rn+1, so we also get the expected number of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric to the standard n-simplex equipped with the Fisher information metric. It follows that the latter space has similar stochastic properties as the n-dimensional Euclidean space. Our results are therefore relevant in information geometry and in population genetics.","lang":"eng"}],"intvolume":" 28","month":"10","main_file_link":[{"url":"https://arxiv.org/abs/1705.02870","open_access":"1"}],"scopus_import":"1"},{"publication_status":"published","publication_identifier":{"issn":["2050-5094"]},"language":[{"iso":"eng"}],"file":[{"file_id":"6356","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2019-04-30T06:14:58Z","file_name":"2018_ForumMahtematics_Akopyan.pdf","date_updated":"2020-07-14T12:47:28Z","file_size":249246,"creator":"dernst"}],"ec_funded":1,"volume":6,"related_material":{"record":[{"relation":"dissertation_contains","id":"8156","status":"public"}]},"abstract":[{"lang":"eng","text":"We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle."}],"oa_version":"Published Version","intvolume":" 6","month":"05","date_updated":"2023-09-19T14:50:12Z","ddc":["510"],"department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:47:28Z","_id":"6355","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","status":"public","year":"2018","has_accepted_license":"1","isi":1,"publication":"Forum of Mathematics, Sigma","day":"31","date_created":"2019-04-30T06:09:57Z","doi":"10.1017/fms.2018.7","date_published":"2018-05-31T00:00:00Z","oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","citation":{"mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6, e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7","apa":"Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2018.7","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge University Press, 2018.","chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma. Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7.","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Avvakumov","full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey"}],"title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","article_number":"e7","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}]},{"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"1064","file_date_updated":"2019-01-18T09:27:36Z","department":[{"_id":"HeEd"}],"ddc":["516","000"],"date_updated":"2023-09-20T12:08:51Z","intvolume":" 59","month":"06","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets.","lang":"eng"}],"ec_funded":1,"issue":"4","volume":59,"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"5844","creator":"dernst","file_size":482518,"date_updated":"2019-01-18T09:27:36Z","file_name":"2018_DiscreteComp_Akopyan.pdf","date_created":"2019-01-18T09:27:36Z"}],"publication_status":"published","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"title":"On the circle covering theorem by A.W. Goodman and R.E. Goodman","external_id":{"isi":["000432205500011"]},"article_processing_charge":"Yes (via OA deal)","publist_id":"6324","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Balitskiy","full_name":"Balitskiy, Alexey","first_name":"Alexey"},{"full_name":"Grigorev, Mikhail","last_name":"Grigorev","first_name":"Mikhail"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ama":"Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 2018;59(4):1001-1009. doi:10.1007/s00454-017-9883-x","apa":"Akopyan, A., Balitskiy, A., & Grigorev, M. (2018). On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-017-9883-x","short":"A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry 59 (2018) 1001–1009.","ieee":"A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem by A.W. Goodman and R.E. Goodman,” Discrete & Computational Geometry, vol. 59, no. 4. Springer, pp. 1001–1009, 2018.","mla":"Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry, vol. 59, no. 4, Springer, 2018, pp. 1001–09, doi:10.1007/s00454-017-9883-x.","ista":"Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 59(4), 1001–1009.","chicago":"Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry. Springer, 2018. https://doi.org/10.1007/s00454-017-9883-x."},"oa":1,"publisher":"Springer","quality_controlled":"1","date_created":"2018-12-11T11:49:57Z","doi":"10.1007/s00454-017-9883-x","date_published":"2018-06-01T00:00:00Z","page":"1001-1009","publication":"Discrete & Computational Geometry","day":"01","year":"2018","has_accepted_license":"1","isi":1},{"related_material":{"record":[{"status":"public","id":"8156","relation":"dissertation_contains"}]},"date_published":"2018-09-13T00:00:00Z","doi":"10.48550/arXiv.1804.03057","date_created":"2018-12-11T11:44:30Z","ec_funded":1,"year":"2018","publication_status":"published","day":"13","language":[{"iso":"eng"}],"publisher":"arXiv","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.03057"}],"month":"09","abstract":[{"lang":"eng","text":"We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥2; this result was previously known for prime powers m=pk. We also give a higher-dimensional generalization."}],"oa_version":"Preprint","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X"},{"first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey","last_name":"Avvakumov"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"external_id":{"arxiv":["1804.03057"]},"article_processing_charge":"No","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"title":"Convex fair partitions into arbitrary number of pieces","citation":{"mla":"Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018).","ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","apa":"Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057","ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:10.48550/arXiv.1804.03057","chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057.","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057."},"date_updated":"2023-12-18T10:51:02Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"preprint","status":"public","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"_id":"75","article_number":"1804.03057"},{"oa":1,"quality_controlled":"1","publisher":"World Scientific Publishing","acknowledgement":"Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.","date_created":"2018-12-11T11:46:43Z","doi":"10.1142/S0218195916600050","date_published":"2017-04-13T00:00:00Z","page":"211 - 229","publication":"International Journal of Computational Geometry and Applications","day":"13","year":"2017","has_accepted_license":"1","title":"Planar matchings for weighted straight skeletons","publist_id":"7338","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber"},{"first_name":"Peter","last_name":"Palfrader","full_name":"Palfrader, Peter"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050.","ista":"Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 26(3–4), 211–229.","mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050.","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229. doi:10.1142/S0218195916600050","apa":"Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195916600050","short":"T. Biedl, S. Huber, P. Palfrader, International Journal of Computational Geometry and Applications 26 (2017) 211–229.","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017."},"intvolume":" 26","month":"04","scopus_import":1,"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist. Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings."}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"10892"}]},"volume":26,"issue":"3-4","language":[{"iso":"eng"}],"file":[{"file_size":769296,"date_updated":"2020-07-14T12:46:35Z","creator":"system","file_name":"IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf","date_created":"2018-12-12T10:09:34Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"4758","checksum":"f79e8558bfe4b368dfefeb8eec2e3a5e"}],"publication_status":"published","pubrep_id":"949","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","_id":"481","file_date_updated":"2020-07-14T12:46:35Z","department":[{"_id":"HeEd"}],"ddc":["004","514","516"],"date_updated":"2023-02-21T16:06:22Z"},{"date_updated":"2021-01-12T08:01:21Z","citation":{"chicago":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.","ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57.","mla":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.","short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.","apa":"Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005","ama":"Austin K, Virk Z. Higson compactification and dimension raising. Topology and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Austin","full_name":"Austin, Kyle","first_name":"Kyle"},{"first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","full_name":"Virk, Ziga","last_name":"Virk"}],"publist_id":"7299","title":"Higson compactification and dimension raising","department":[{"_id":"HeEd"}],"_id":"521","type":"journal_article","status":"public","publication_identifier":{"issn":["01668641"]},"year":"2017","publication_status":"published","day":"01","language":[{"iso":"eng"}],"publication":"Topology and its Applications","page":"45 - 57","volume":215,"date_published":"2017-01-01T00:00:00Z","doi":"10.1016/j.topol.2016.10.005","date_created":"2018-12-11T11:46:56Z","abstract":[{"lang":"eng","text":"Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension."}],"oa_version":"Submitted Version","publisher":"Elsevier","quality_controlled":"1","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1608.03954v1","open_access":"1"}],"month":"01","intvolume":" 215"},{"status":"public","type":"journal_article","_id":"568","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_updated":"2021-01-12T08:03:12Z","intvolume":" 19","month":"01","main_file_link":[{"url":"https://arxiv.org/abs/1507.04310","open_access":"1"}],"scopus_import":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C)."}],"ec_funded":1,"issue":"2","volume":19,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["15320073"]},"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"2590DB08-B435-11E9-9278-68D0E5697425","name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)","grant_number":"701309"}],"title":"Persistence of zero sets","publist_id":"7246","author":[{"first_name":"Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87","full_name":"Franek, Peter","last_name":"Franek"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","full_name":"Krcál, Marek","last_name":"Krcál"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16.","ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","mla":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.","apa":"Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16","ama":"Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications. 2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.","short":"P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342."},"oa":1,"quality_controlled":"1","publisher":"International Press","date_created":"2018-12-11T11:47:14Z","date_published":"2017-01-01T00:00:00Z","doi":"10.4310/HHA.2017.v19.n2.a16","page":"313 - 342","publication":"Homology, Homotopy and Applications","day":"01","year":"2017"},{"title":"Construction of persistent Voronoi diagram on 3D digital plane","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas"},{"first_name":"Partha","last_name":"Bhowmick","full_name":"Bhowmick, Partha"}],"article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"mla":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.","ieee":"R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104.","short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104.","ama":"Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature; 2017:93-104. doi:10.1007/978-3-319-59108-7_8","apa":"Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256, pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8","chicago":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104. Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.","ista":"Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104."},"date_published":"2017-05-17T00:00:00Z","doi":"10.1007/978-3-319-59108-7_8","date_created":"2019-01-08T20:42:56Z","page":"93-104","day":"17","publication":"Combinatorial image analysis","year":"2017","quality_controlled":"1","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"extern":"1","date_updated":"2022-01-28T07:48:24Z","status":"public","type":"book_chapter","conference":{"location":"Plovdiv, Bulgaria","end_date":"2017-06-21","start_date":"2017-06-19","name":"IWCIA: International Workshop on Combinatorial Image Analysis"},"_id":"5803","volume":10256,"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-3-319-59107-0","978-3-319-59108-7"],"issn":["0302-9743","1611-3349"]},"publication_status":"published","month":"05","place":"Cham","intvolume":" 10256","alternative_title":["LNCS"],"oa_version":"None","abstract":[{"lang":"eng","text":"Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept."}]},{"title":"Topological data analysis with Bregman divergences","publist_id":"7021","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,” presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia, 2017, vol. 77, pp. 391–3916.","short":"H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916.","ama":"Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916. doi:10.4230/LIPIcs.SoCG.2017.39","apa":"Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2017.39","mla":"Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.","ista":"Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.","chicago":"Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39."},"date_created":"2018-12-11T11:47:56Z","doi":"10.4230/LIPIcs.SoCG.2017.39","date_published":"2017-06-01T00:00:00Z","page":"391-3916","day":"01","year":"2017","has_accepted_license":"1","oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"file_date_updated":"2020-07-14T12:47:42Z","ddc":["514","516"],"date_updated":"2021-01-12T08:09:26Z","pubrep_id":"895","status":"public","conference":{"location":"Brisbane, Australia","end_date":"2017-07-07","start_date":"2017-07-04","name":"Symposium on Computational Geometry, SoCG"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"conference","_id":"688","volume":77,"language":[{"iso":"eng"}],"file":[{"file_id":"4856","checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2018-12-12T10:11:03Z","file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf","date_updated":"2020-07-14T12:47:42Z","file_size":990546,"creator":"system"}],"publication_status":"published","publication_identifier":{"issn":["18688969"]},"intvolume":" 77","month":"06","alternative_title":["LIPIcs"],"scopus_import":1,"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. "}]},{"publication_status":"published","publication_identifier":{"issn":["00246093"]},"language":[{"iso":"eng"}],"ec_funded":1,"issue":"4","volume":49,"abstract":[{"text":"We answer a question of M. Gromov on the waist of the unit ball.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.06279"}],"scopus_import":1,"intvolume":" 49","month":"08","date_updated":"2021-01-12T08:11:41Z","department":[{"_id":"HeEd"}],"_id":"707","type":"journal_article","status":"public","year":"2017","publication":"Bulletin of the London Mathematical Society","day":"01","page":"690 - 693","date_created":"2018-12-11T11:48:02Z","date_published":"2017-08-01T00:00:00Z","doi":"10.1112/blms.12062","oa":1,"quality_controlled":"1","publisher":"Wiley-Blackwell","citation":{"ista":"Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 49(4), 690–693.","chicago":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society. Wiley-Blackwell, 2017. https://doi.org/10.1112/blms.12062.","apa":"Akopyan, A., & Karasev, R. (2017). A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. Wiley-Blackwell. https://doi.org/10.1112/blms.12062","ama":"Akopyan A, Karasev R. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 2017;49(4):690-693. doi:10.1112/blms.12062","short":"A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693.","ieee":"A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,” Bulletin of the London Mathematical Society, vol. 49, no. 4. Wiley-Blackwell, pp. 690–693, 2017.","mla":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society, vol. 49, no. 4, Wiley-Blackwell, 2017, pp. 690–93, doi:10.1112/blms.12062."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"first_name":"Roman","last_name":"Karasev","full_name":"Karasev, Roman"}],"publist_id":"6982","title":"A tight estimate for the waist of the ball ","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}]},{"project":[{"name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"citation":{"mla":"Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability, vol. 49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20.","ama":"Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 2017;49(3):745-767. doi:10.1017/apr.2017.20","apa":"Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20","ieee":"H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson Delaunay mosaics and their discrete Morse functions,” Advances in Applied Probability, vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017.","short":"H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767.","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability. Cambridge University Press, 2017. https://doi.org/10.1017/apr.2017.20.","ista":"Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3), 745–767."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1607.05915"]},"publist_id":"6962","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","last_name":"Nikitenko"},{"first_name":"Matthias","last_name":"Reitzner","full_name":"Reitzner, Matthias"}],"title":"Expected sizes of poisson Delaunay mosaics and their discrete Morse functions","oa":1,"quality_controlled":"1","publisher":"Cambridge University Press","year":"2017","publication":"Advances in Applied Probability","day":"01","page":"745 - 767","date_created":"2018-12-11T11:48:07Z","doi":"10.1017/apr.2017.20","date_published":"2017-09-01T00:00:00Z","_id":"718","type":"journal_article","status":"public","date_updated":"2023-09-07T12:07:12Z","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from a Poisson point process in ℝ n , we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and nonsingular intervals in the corresponding generalized discrete gradient. Observing connections with other probabilistic models, we obtain precise expressions for the expected numbers in low dimensions. In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4."}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1607.05915","open_access":"1"}],"scopus_import":1,"intvolume":" 49","month":"09","publication_status":"published","publication_identifier":{"issn":["00018678"]},"language":[{"iso":"eng"}],"ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6287"}]},"issue":"3","volume":49},{"date_created":"2019-04-09T15:04:32Z","doi":"10.15479/AT:ISTA:th_873","date_published":"2017-10-27T00:00:00Z","page":"86","day":"27","year":"2017","has_accepted_license":"1","oa":1,"publisher":"Institute of Science and Technology Austria","title":"Discrete Morse theory for random complexes ","article_processing_charge":"No","author":[{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_873.","ista":"Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute of Science and Technology Austria.","mla":"Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873.","ieee":"A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of Science and Technology Austria, 2017.","short":"A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science and Technology Austria, 2017.","apa":"Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873","ama":"Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873"},"related_material":{"record":[{"id":"718","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"5678","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"87","status":"public"}]},"language":[{"iso":"eng"}],"file":[{"file_id":"6289","checksum":"ece7e598a2f060b263c2febf7f3fe7f9","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2017_Thesis_Nikitenko.pdf","date_created":"2019-04-09T14:54:51Z","creator":"dernst","file_size":2324870,"date_updated":"2020-07-14T12:47:26Z"},{"content_type":"application/zip","relation":"source_file","access_level":"closed","file_id":"6290","checksum":"99b7ad76e317efd447af60f91e29b49b","file_size":2863219,"date_updated":"2020-07-14T12:47:26Z","creator":"dernst","file_name":"2017_Thesis_Nikitenko_source.zip","date_created":"2019-04-09T14:54:51Z"}],"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"month":"10","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","abstract":[{"text":"The main objects considered in the present work are simplicial and CW-complexes with vertices forming a random point cloud. In particular, we consider a Poisson point process in R^n and study Delaunay and Voronoi complexes of the first and higher orders and weighted Delaunay complexes obtained as sections of Delaunay complexes, as well as the Čech complex. Further, we examine theDelaunay complex of a Poisson point process on the sphere S^n, as well as of a uniform point cloud, which is equivalent to the convex hull, providing a connection to the theory of random polytopes. Each of the complexes in question can be endowed with a radius function, which maps its cells to the radii of appropriately chosen circumspheres, called the radius of the cell. Applying and developing discrete Morse theory for these functions, joining it together with probabilistic and sometimes analytic machinery, and developing several integral geometric tools, we aim at getting the distributions of circumradii of typical cells. For all considered complexes, we are able to generalize and obtain up to constants the distribution of radii of typical intervals of all types. In low dimensions the constants can be computed explicitly, thus providing the explicit expressions for the expected numbers of cells. In particular, it allows to find the expected density of simplices of every dimension for a Poisson point process in R^4, whereas the result for R^3 was known already in 1970's.","lang":"eng"}],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:26Z","ddc":["514","516","519"],"date_updated":"2023-09-15T12:10:34Z","supervisor":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"pubrep_id":"873","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"dissertation","_id":"6287"},{"project":[{"grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"title":"Phat - Persistent homology algorithms toolbox","external_id":{"isi":["000384396000005"]},"article_processing_charge":"No","author":[{"last_name":"Bauer","full_name":"Bauer, Ulrich","first_name":"Ulrich"},{"first_name":"Michael","full_name":"Kerber, Michael","last_name":"Kerber"},{"first_name":"Jan","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","full_name":"Wagner, Hubert","last_name":"Wagner"}],"publist_id":"5765","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation. Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008.","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. Academic Press. https://doi.org/10.1016/j.jsc.2016.03.008","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90.","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic Press, pp. 76–90, 2017.","mla":"Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008."},"oa":1,"publisher":"Academic Press","quality_controlled":"1","date_created":"2018-12-11T11:51:59Z","date_published":"2017-01-01T00:00:00Z","doi":"10.1016/j.jsc.2016.03.008","page":"76 - 90","publication":"Journal of Symbolic Computation","day":"01","year":"2017","isi":1,"status":"public","article_type":"original","type":"journal_article","_id":"1433","department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T09:42:40Z","intvolume":" 78","month":"01","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jsc.2016.03.008"}],"scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"Phat is an open-source C. ++ library for the computation of persistent homology by matrix reduction, targeted towards developers of software for topological data analysis. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. We provide numerous different reduction strategies as well as data types to store and manipulate the boundary matrix. We compare the different combinations through extensive experimental evaluation and identify optimization techniques that work well in practical situations. We also compare our software with various other publicly available libraries for persistent homology.","lang":"eng"}],"ec_funded":1,"volume":78,"related_material":{"record":[{"id":"10894","status":"public","relation":"earlier_version"}]},"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":[" 07477171"]}},{"department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T11:21:27Z","type":"journal_article","status":"public","_id":"1180","ec_funded":1,"volume":308,"publication_status":"published","publication_identifier":{"issn":["00018708"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1508.07594","open_access":"1"}],"scopus_import":"1","intvolume":" 308","month":"02","abstract":[{"text":"In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform.","lang":"eng"}],"oa_version":"Submitted Version","article_processing_charge":"No","external_id":{"isi":["000409292900015"]},"author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"first_name":"Imre","last_name":"Bárány","full_name":"Bárány, Imre"},{"last_name":"Robins","full_name":"Robins, Sinai","first_name":"Sinai"}],"publist_id":"6173","title":"Algebraic vertices of non-convex polyhedra","citation":{"mla":"Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.","apa":"Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026","ama":"Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026","ieee":"A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.","short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.","chicago":"Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.","ista":"Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"page":"627 - 644","date_created":"2018-12-11T11:50:34Z","doi":"10.1016/j.aim.2016.12.026","date_published":"2017-02-21T00:00:00Z","year":"2017","isi":1,"publication":"Advances in Mathematics","day":"21","oa":1,"publisher":"Academic Press","quality_controlled":"1"},{"_id":"1173","status":"public","type":"journal_article","date_updated":"2023-09-20T11:23:53Z","department":[{"_id":"HeEd"}],"oa_version":"Submitted Version","abstract":[{"text":"We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions.","lang":"eng"}],"month":"10","intvolume":" 37","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1411.6337","open_access":"1"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["02099683"]},"publication_status":"published","volume":37,"issue":"5","ec_funded":1,"project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ama":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910. doi:10.1007/s00493-016-3308-y","apa":"Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The Voronoi functional is maximized by the Delaunay triangulation in the plane. 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Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y."},"title":"The Voronoi functional is maximized by the Delaunay triangulation in the plane","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alexey","last_name":"Glazyrin","full_name":"Glazyrin, Alexey"},{"last_name":"Musin","full_name":"Musin, Oleg","first_name":"Oleg"},{"last_name":"Nikitenko","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton"}],"publist_id":"6182","article_processing_charge":"No","external_id":{"isi":["000418056000005"]},"acknowledgement":"This research is partially supported by the Russian Government under the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by NSF grants DMS-1101688, DMS-1400876.","publisher":"Springer","quality_controlled":"1","oa":1,"day":"01","publication":"Combinatorica","isi":1,"year":"2017","doi":"10.1007/s00493-016-3308-y","date_published":"2017-10-01T00:00:00Z","date_created":"2018-12-11T11:50:32Z","page":"887 - 910"},{"_id":"1072","status":"public","article_type":"original","type":"journal_article","date_updated":"2023-09-20T12:05:56Z","department":[{"_id":"HeEd"}],"oa_version":"Preprint","abstract":[{"text":"Given a finite set of points in Rn and a radius parameter, we study the Čech, Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four complexes are simple-homotopy equivalent by a sequence of simplicial collapses, which are explicitly described by a single discrete gradient field.","lang":"eng"}],"month":"05","intvolume":" 369","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1312.1231","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":369,"issue":"5","ec_funded":1,"project":[{"grant_number":"318493","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” Transactions of the American Mathematical Society, vol. 369, no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:10.1090/tran/6991.","short":"U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society 369 (2017) 3741–3762.","ieee":"U. Bauer and H. Edelsbrunner, “The Morse theory of Čech and delaunay complexes,” Transactions of the American Mathematical Society, vol. 369, no. 5. American Mathematical Society, pp. 3741–3762, 2017.","apa":"Bauer, U., & Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/6991","ama":"Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 2017;369(5):3741-3762. doi:10.1090/tran/6991","chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” Transactions of the American Mathematical Society. American Mathematical Society, 2017. https://doi.org/10.1090/tran/6991.","ista":"Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 369(5), 3741–3762."},"title":"The Morse theory of Čech and delaunay complexes","author":[{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich","last_name":"Bauer","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"publist_id":"6311","article_processing_charge":"No","external_id":{"arxiv":["1312.1231"],"isi":["000398030400024"]},"acknowledgement":"This research has been supported by the EU project Toposys(FP7-ICT-318493-STREP), by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”.","publisher":"American Mathematical Society","quality_controlled":"1","oa":1,"day":"01","publication":"Transactions of the American Mathematical Society","isi":1,"year":"2017","doi":"10.1090/tran/6991","date_published":"2017-05-01T00:00:00Z","date_created":"2018-12-11T11:49:59Z","page":"3741 - 3762"},{"ddc":["000"],"date_updated":"2023-09-20T12:08:18Z","department":[{"_id":"KrCh"},{"_id":"HeEd"}],"file_date_updated":"2019-10-15T07:44:51Z","_id":"1065","status":"public","pubrep_id":"991","type":"journal_article","file":[{"file_name":"IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf","date_created":"2018-12-12T10:13:17Z","creator":"system","file_size":247657,"date_updated":"2019-10-15T07:44:51Z","file_id":"4998","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["00200190"]},"publication_status":"published","volume":122,"ec_funded":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We consider the problem of reachability in pushdown graphs. We study the problem for pushdown graphs with constant treewidth. Even for pushdown graphs with treewidth 1, for the reachability problem we establish the following: (i) the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem would contradict the k-clique conjecture and imply faster combinatorial algorithms for cliques in graphs."}],"month":"06","intvolume":" 122","scopus_import":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"apa":"Chatterjee, K., & Osang, G. F. (2017). Pushdown reachability with constant treewidth. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2017.02.003","ama":"Chatterjee K, Osang GF. Pushdown reachability with constant treewidth. Information Processing Letters. 2017;122:25-29. doi:10.1016/j.ipl.2017.02.003","ieee":"K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,” Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017.","short":"K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29.","mla":"Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters, vol. 122, Elsevier, 2017, pp. 25–29, doi:10.1016/j.ipl.2017.02.003.","ista":"Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth. Information Processing Letters. 122, 25–29.","chicago":"Chatterjee, Krishnendu, and Georg F Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters. Elsevier, 2017. https://doi.org/10.1016/j.ipl.2017.02.003."},"title":"Pushdown reachability with constant treewidth","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang"}],"publist_id":"6323","article_processing_charge":"No","external_id":{"isi":["000399506600005"]},"project":[{"name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"grant_number":"S11407","name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications"}],"day":"01","publication":"Information Processing Letters","has_accepted_license":"1","isi":1,"year":"2017","doi":"10.1016/j.ipl.2017.02.003","date_published":"2017-06-01T00:00:00Z","date_created":"2018-12-11T11:49:57Z","page":"25 - 29","publisher":"Elsevier","quality_controlled":"1","oa":1},{"_id":"1022","status":"public","type":"journal_article","date_updated":"2023-09-22T09:40:55Z","department":[{"_id":"HeEd"}],"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its multiscale arrangement of matter and galaxies. Emanating from algebraic topology and Morse theory, Betti numbers and persistence diagrams represent an extension and deepening of the cosmologically familiar topological genus measure and the related geometric Minkowski functionals. In addition to a description of the mathematical background, this study presents the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations. The field may be computed starting from a discrete spatial distribution of galaxies or simulation particles. The main emphasis of this study concerns an extensive and systematic exploration of the imprint of different web-like morphologies and different levels of multiscale clustering in the corresponding computed Betti numbers and persistence diagrams. To this end, we use Voronoi clustering models as templates for a rich variety of web-like configurations and the fractal-like Soneira-Peebles models exemplify a range of multiscale configurations. We have identified the clear imprint of cluster nodes, filaments, walls, and voids in persistence diagrams, along with that of the nested hierarchy of structures in multiscale point distributions. We conclude by outlining the potential of persistent topology for understanding the connectivity structure of the cosmic web, in large simulations of cosmic structure formation and in the challenging context of the observed galaxy distribution in large galaxy surveys."}],"intvolume":" 465","month":"01","main_file_link":[{"url":"https://arxiv.org/abs/1608.04519","open_access":"1"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["00358711"]},"volume":465,"issue":"4","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ama":"Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. 2017;465(4):4281-4310. doi:10.1093/mnras/stw2862","apa":"Pranav, P., Edelsbrunner, H., Van De Weygaert, R., Vegter, G., Kerber, M., Jones, B., & Wintraecken, M. (2017). 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Oxford University Press, 2017. https://doi.org/10.1093/mnras/stw2862."},"title":"The topology of the cosmic web in terms of persistent Betti numbers","article_processing_charge":"No","external_id":{"isi":["000395170200039"]},"publist_id":"6373","author":[{"last_name":"Pranav","full_name":"Pranav, Pratyush","first_name":"Pratyush"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Rien","full_name":"Van De Weygaert, Rien","last_name":"Van De Weygaert"},{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"full_name":"Jones, Bernard","last_name":"Jones","first_name":"Bernard"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken"}],"acknowledgement":"Part of this work has been supported by the 7th Framework Programme for Research of the European Commission, under FETOpen grant number 255827 (CGL Computational Geometry Learning) and ERC advanced grant, URSAT (Understanding Random Systems via Algebraic Topology) number 320422.","oa":1,"quality_controlled":"1","publisher":"Oxford University Press","publication":"Monthly Notices of the Royal Astronomical Society","day":"01","year":"2017","isi":1,"date_created":"2018-12-11T11:49:44Z","date_published":"2017-01-01T00:00:00Z","doi":"10.1093/mnras/stw2862","page":"4281 - 4310"},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196.","chicago":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2017.09.015.","short":"Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.","ieee":"Z. Virk and A. Zastrow, “A new topology on the universal path space,” Topology and its Applications, vol. 231. Elsevier, pp. 186–196, 2017.","ama":"Virk Z, Zastrow A. A new topology on the universal path space. Topology and its Applications. 2017;231:186-196. doi:10.1016/j.topol.2017.09.015","apa":"Virk, Z., & Zastrow, A. (2017). A new topology on the universal path space. Topology and Its Applications. 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We develop basic properties of the new notion and provide a complete comparison of the obtained topology with the established topologies, in particular with the Lasso topology and the CO topology, i.e., the topology that is induced by the compact-open topology. It turns out that the new topology is the finest topology contained in the CO topology, for which the action of the fundamental group on the universal path space is a continuous group action.","lang":"eng"}],"intvolume":" 231","month":"11","scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["01668641"]},"volume":231},{"intvolume":" 198","month":"07","alternative_title":["PROMS"],"scopus_import":"1","oa_version":"None","abstract":[{"text":"Recent research has examined how to study the topological features of a continuous self-map by means of the persistence of the eigenspaces, for given eigenvalues, of the endomorphism induced in homology over a field. This raised the question of how to select dynamically significant eigenvalues. The present paper aims to answer this question, giving an algorithm that computes the persistence of eigenspaces for every eigenvalue simultaneously, also expressing said eigenspaces as direct sums of “finite” and “singular” subspaces.","lang":"eng"}],"ec_funded":1,"volume":198,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"isbn":["978-331956930-7"]},"status":"public","conference":{"start_date":"2015-07-20","location":"Kalamata, Greece","end_date":"2015-07-23","name":"ACA: Applications of Computer Algebra"},"type":"conference","_id":"836","department":[{"_id":"HeEd"}],"date_updated":"2023-09-26T15:50:52Z","publisher":"Springer","quality_controlled":"1","date_created":"2018-12-11T11:48:46Z","date_published":"2017-07-27T00:00:00Z","doi":"10.1007/978-3-319-56932-1_8","page":"119 - 136","publication":"Special Sessions in Applications of Computer Algebra","day":"27","year":"2017","isi":1,"project":[{"grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"title":"Finding eigenvalues of self-maps with the Kronecker canonical form","external_id":{"isi":["000434088200008"]},"article_processing_charge":"No","author":[{"first_name":"Marc","last_name":"Ethier","full_name":"Ethier, Marc"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz","last_name":"Jablonski","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866"},{"full_name":"Mrozek, Marian","last_name":"Mrozek","first_name":"Marian"}],"publist_id":"6812","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Ethier, Marc, Grzegorz Jablonski, and Marian Mrozek. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” In Special Sessions in Applications of Computer Algebra, 198:119–36. 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The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams.","lang":"eng"}],"volume":10424,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["03029743"]},"status":"public","conference":{"name":"CAIP: Computer Analysis of Images and Patterns","end_date":"2017-08-24","location":"Ystad, Sweden","start_date":"2017-08-22"},"type":"conference","_id":"833","department":[{"_id":"HeEd"}],"date_updated":"2023-09-26T16:10:03Z","oa":1,"quality_controlled":"1","publisher":"Springer","date_created":"2018-12-11T11:48:45Z","date_published":"2017-07-28T00:00:00Z","doi":"10.1007/978-3-319-64689-3_32","page":"397 - 409","day":"28","year":"2017","isi":1,"title":"Streaming algorithm for Euler characteristic curves of multidimensional images","editor":[{"first_name":"Michael","last_name":"Felsberg","full_name":"Felsberg, Michael"},{"first_name":"Anders","full_name":"Heyden, Anders","last_name":"Heyden"},{"full_name":"Krüger, Norbert","last_name":"Krüger","first_name":"Norbert"}],"external_id":{"isi":["000432085900032"]},"article_processing_charge":"No","publist_id":"6815","author":[{"last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","full_name":"Wagner, Hubert","last_name":"Wagner"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS, vol. 10424, 397–409.","chicago":"Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden, and Norbert Krüger, 10424:397–409. Springer, 2017. https://doi.org/10.1007/978-3-319-64689-3_32.","short":"T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer, 2017, pp. 397–409.","ieee":"T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves of multidimensional images,” presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.","apa":"Heiss, T., & Wagner, H. (2017). Streaming algorithm for Euler characteristic curves of multidimensional images. In M. Felsberg, A. Heyden, & N. Krüger (Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden: Springer. https://doi.org/10.1007/978-3-319-64689-3_32","ama":"Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer; 2017:397-409. doi:10.1007/978-3-319-64689-3_32","mla":"Heiss, Teresa, and Hubert Wagner. Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images. Edited by Michael Felsberg et al., vol. 10424, Springer, 2017, pp. 397–409, doi:10.1007/978-3-319-64689-3_32."}},{"status":"public","type":"book_chapter","series_title":"Handbook of Discrete and Computational Geometry","_id":"84","editor":[{"first_name":"Csaba","last_name":"Toth","full_name":"Toth, Csaba"},{"first_name":"Joseph","full_name":"O'Rourke, Joseph","last_name":"O'Rourke"},{"first_name":"Jacob","full_name":"Goodman, Jacob","last_name":"Goodman"}],"department":[{"_id":"HeEd"}],"title":"Computational topology for structural molecular biology","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Patrice","full_name":"Koehl, Patrice","last_name":"Koehl"}],"publist_id":"7970","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth et al., Taylor & Francis, 2017, pp. 1709–35, doi:10.1201/9781315119601.","ama":"Edelsbrunner H, Koehl P. Computational topology for structural molecular biology. In: Toth C, O’Rourke J, Goodman J, eds. Handbook of Discrete and Computational Geometry, Third Edition. Handbook of Discrete and Computational Geometry. Taylor & Francis; 2017:1709-1735. doi:10.1201/9781315119601","apa":"Edelsbrunner, H., & Koehl, P. (2017). Computational topology for structural molecular biology. In C. Toth, J. O’Rourke, & J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition (pp. 1709–1735). Taylor & Francis. https://doi.org/10.1201/9781315119601","short":"H. Edelsbrunner, P. Koehl, in:, C. Toth, J. O’Rourke, J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition, Taylor & Francis, 2017, pp. 1709–1735.","ieee":"H. Edelsbrunner and P. Koehl, “Computational topology for structural molecular biology,” in Handbook of Discrete and Computational Geometry, Third Edition, C. Toth, J. O’Rourke, and J. Goodman, Eds. Taylor & Francis, 2017, pp. 1709–1735.","chicago":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” In Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth, Joseph O’Rourke, and Jacob Goodman, 1709–35. Handbook of Discrete and Computational Geometry. Taylor & Francis, 2017. https://doi.org/10.1201/9781315119601.","ista":"Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular biology. In: Handbook of Discrete and Computational Geometry, Third Edition. , 1709–1735."},"date_updated":"2023-10-16T11:15:22Z","month":"11","publisher":"Taylor & Francis","scopus_import":"1","quality_controlled":"1","oa_version":"None","abstract":[{"text":"The advent of high-throughput technologies and the concurrent advances in information sciences have led to a data revolution in biology. This revolution is most significant in molecular biology, with an increase in the number and scale of the “omics” projects over the last decade. Genomics projects, for example, have produced impressive advances in our knowledge of the information concealed into genomes, from the many genes that encode for the proteins that are responsible for most if not all cellular functions, to the noncoding regions that are now known to provide regulatory functions. Proteomics initiatives help to decipher the role of post-translation modifications on the protein structures and provide maps of protein-protein interactions, while functional genomics is the field that attempts to make use of the data produced by these projects to understand protein functions. The biggest challenge today is to assimilate the wealth of information provided by these initiatives into a conceptual framework that will help us decipher life. For example, the current views of the relationship between protein structure and function remain fragmented. We know of their sequences, more and more about their structures, we have information on their biological activities, but we have difficulties connecting this dotted line into an informed whole. We lack the experimental and computational tools for directly studying protein structure, function, and dynamics at the molecular and supra-molecular levels. In this chapter, we review some of the current developments in building the computational tools that are needed, focusing on the role that geometry and topology play in these efforts. One of our goals is to raise the general awareness about the importance of geometric methods in elucidating the mysterious foundations of our very existence. Another goal is the broadening of what we consider a geometric algorithm. There is plenty of valuable no-man’s-land between combinatorial and numerical algorithms, and it seems opportune to explore this land with a computational-geometric frame of mind.","lang":"eng"}],"doi":"10.1201/9781315119601","date_published":"2017-11-09T00:00:00Z","date_created":"2018-12-11T11:44:32Z","page":"1709 - 1735","day":"09","publication":"Handbook of Discrete and Computational Geometry, Third Edition","language":[{"iso":"eng"}],"publication_identifier":{"eisbn":["9781498711425"]},"year":"2017","publication_status":"published"},{"date_created":"2018-12-11T11:49:09Z","date_published":"2017-01-01T00:00:00Z","doi":"10.4169/amer.math.monthly.124.7.588","page":"588 - 596","publication":"The American Mathematical Monthly","day":"01","year":"2017","isi":1,"oa":1,"publisher":"Mathematical Association of America","quality_controlled":"1","title":"On the lengths of curves passing through boundary points of a planar convex shape","article_processing_charge":"No","external_id":{"arxiv":["1605.07997"],"isi":["000413947300002"]},"publist_id":"6534","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"first_name":"Vladislav","last_name":"Vysotsky","full_name":"Vysotsky, Vladislav"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly. Mathematical Association of America, 2017. https://doi.org/10.4169/amer.math.monthly.124.7.588.","ista":"Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.","mla":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96, doi:10.4169/amer.math.monthly.124.7.588.","ieee":"A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary points of a planar convex shape,” The American Mathematical Monthly, vol. 124, no. 7. Mathematical Association of America, pp. 588–596, 2017.","short":"A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.","ama":"Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 2017;124(7):588-596. doi:10.4169/amer.math.monthly.124.7.588","apa":"Akopyan, A., & Vysotsky, V. (2017). On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. Mathematical Association of America. https://doi.org/10.4169/amer.math.monthly.124.7.588"},"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"volume":124,"issue":"7","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["00029890"]},"intvolume":" 124","month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.07997"}],"scopus_import":"1","oa_version":"Submitted Version","abstract":[{"text":"We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor ½ cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape.","lang":"eng"}],"department":[{"_id":"HeEd"}],"date_updated":"2023-10-17T11:24:57Z","status":"public","article_type":"original","type":"journal_article","_id":"909"},{"publisher":"Elsevier","quality_controlled":"1","scopus_import":1,"month":"09","intvolume":" 107","abstract":[{"text":"We study the usefulness of two most prominent publicly available rigorous ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable of handling entire sets of initial conditions and provide tight rigorous outer enclosures of the images under a time-T map. We conduct extensive benchmark computations using the well-known Lorenz system, and compare the computation time against the final accuracy achieved. We also discuss the effect of a few technical parameters, such as the order of the numerical integration method, the value of T, and the phase space resolution. We conclude that COSY may provide more precise results due to its ability of avoiding the variable dependency problem. However, the overall cost of computations conducted using CAPD is typically lower, especially when intervals of parameters are involved. Moreover, access to COSY is limited (registration required) and the rigorous ODE integrators are not publicly available, while CAPD is an open source free software project. Therefore, we recommend the latter integrator for this kind of computations. Nevertheless, proper choice of the various integration parameters turns out to be of even greater importance than the choice of the integrator itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved.","lang":"eng"}],"oa_version":"None","acknowledgement":"MG was partially supported by FAPESP grants 2013/07460-7 and 2010/00875-9, and by CNPq grants 305860/2013-5 and 306453/2009-6, Brazil. The work of HK was partially supported by Grant-in-Aid for Scientific Research (Nos.24654022, 25287029), Ministry of Education, Science, Technology, Culture and Sports, Japan. KM was supported by NSF grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR and DARPA. TM was supported by Grant-in-Aid for JSPS Fellows No. 245312. A part of the research of TM and HK was also supported by JST, CREST.\r\n\r\nResearch conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE – Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (Ref. FCT PTDC/MAT/098871/2008); from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement No. 622033; and from the same sources as HK.\r\n\r\nThe authors express their gratitude to the Department of Mathematics of Kyoto University for making their server available for conducting the computations described in the paper, and to the reviewers for helpful comments that contributed towards increasing the quality of the paper.","page":"34 - 47","volume":107,"doi":"10.1016/j.apnum.2016.04.005","date_published":"2016-09-01T00:00:00Z","ec_funded":1,"date_created":"2018-12-11T11:50:25Z","year":"2016","publication_status":"published","day":"01","language":[{"iso":"eng"}],"publication":"Applied Numerical Mathematics","type":"journal_article","project":[{"call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425","name":"Persistent Homology - Images, Data and Maps","grant_number":"622033"}],"status":"public","_id":"1149","publist_id":"6209","author":[{"first_name":"Tomoyuki","full_name":"Miyaji, Tomoyuki","last_name":"Miyaji"},{"full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel"},{"full_name":"Gameiro, Marcio","last_name":"Gameiro","first_name":"Marcio"},{"full_name":"Kokubu, Hiroshi","last_name":"Kokubu","first_name":"Hiroshi"},{"first_name":"Konstantin","full_name":"Mischaikow, Konstantin","last_name":"Mischaikow"}],"title":"A study of rigorous ODE integrators for multi scale set oriented computations","department":[{"_id":"HeEd"}],"citation":{"ama":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 2016;107:34-47. doi:10.1016/j.apnum.2016.04.005","apa":"Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., & Mischaikow, K. (2016). A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2016.04.005","short":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical Mathematics 107 (2016) 34–47.","ieee":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study of rigorous ODE integrators for multi scale set oriented computations,” Applied Numerical Mathematics, vol. 107. Elsevier, pp. 34–47, 2016.","mla":"Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics, vol. 107, Elsevier, 2016, pp. 34–47, doi:10.1016/j.apnum.2016.04.005.","ista":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 107, 34–47.","chicago":"Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.apnum.2016.04.005."},"date_updated":"2021-01-12T06:48:38Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"page":"55 - 80","issue":"1","volume":68,"date_published":"2016-01-01T00:00:00Z","date_created":"2018-12-11T11:50:46Z","year":"2016","publication_status":"published","day":"01","publication":"Archives of Mechanics","language":[{"iso":"eng"}],"quality_controlled":"1","publisher":"Polish Academy of Sciences Publishing House","scopus_import":1,"oa":1,"main_file_link":[{"open_access":"1","url":"http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf"}],"month":"01","intvolume":" 68","abstract":[{"text":"A framework fo r extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance is proposed in this paper. The minima of the acceleration magnitude (a superset of acceleration zeros) are extracted and discriminated into vortices and saddle points, based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These feature points are tracked in time with a robust algorithm for tracking features. Thus, a space-time hierarchy of the minima is built and vortex merging events are detected. We apply the acceleration feature extraction strategy to three two-dimensional shear flows: (1) an incompressible periodic cylinder wake, (2) an incompressible planar mixing layer and (3) a weakly compressible planar jet. The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of the pressure field and minima of λ2.","lang":"eng"}],"oa_version":"Published Version","acknowledgement":"The authors acknowledge funding of the German Re-\r\nsearch Foundation (DFG) via the Collaborative Re-\r\nsearch Center (SFB 557) \\Control of Complex Turbu-\r\nlent Shear Flows\" and the Emmy Noether Program.\r\nFurther funding was provided by the Zuse Institute\r\nBerlin (ZIB), the DFG-CNRS research group \\Noise\r\nGeneration in Turbulent Flows\" (2003{2010), the Chaire\r\nd'Excellence 'Closed-loop control of turbulent shear ows\r\nusing reduced-order models' (TUCOROM) of the French\r\nAgence Nationale de la Recherche (ANR), and the Eu-\r\nropean Social Fund (ESF App. No. 100098251). We\r\nthank the Ambrosys Ltd. Society for Complex Sys-\r\ntems Management and the Bernd R. Noack Cybernet-\r\nics Foundation for additional support. A part of this\r\nwork was performed using HPC resources from GENCI-[CCRT/CINES/IDRIS] supported by the Grant 2011-\r\n[x2011020912","author":[{"full_name":"Kasten, Jens","last_name":"Kasten","first_name":"Jens"},{"last_name":"Reininghaus","full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"first_name":"Ingrid","full_name":"Hotz, Ingrid","last_name":"Hotz"},{"last_name":"Hege","full_name":"Hege, Hans","first_name":"Hans"},{"full_name":"Noack, Bernd","last_name":"Noack","first_name":"Bernd"},{"last_name":"Daviller","full_name":"Daviller, Guillaume","first_name":"Guillaume"},{"first_name":"Marek","full_name":"Morzyński, Marek","last_name":"Morzyński"}],"publist_id":"6118","title":"Acceleration feature points of unsteady shear flows","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T06:49:09Z","citation":{"apa":"Kasten, J., Reininghaus, J., Hotz, I., Hege, H., Noack, B., Daviller, G., & Morzyński, M. (2016). Acceleration feature points of unsteady shear flows. Archives of Mechanics. Polish Academy of Sciences Publishing House.","ama":"Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 2016;68(1):55-80.","ieee":"J. Kasten et al., “Acceleration feature points of unsteady shear flows,” Archives of Mechanics, vol. 68, no. 1. Polish Academy of Sciences Publishing House, pp. 55–80, 2016.","short":"J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński, Archives of Mechanics 68 (2016) 55–80.","mla":"Kasten, Jens, et al. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics, vol. 68, no. 1, Polish Academy of Sciences Publishing House, 2016, pp. 55–80.","ista":"Kasten J, Reininghaus J, Hotz I, Hege H, Noack B, Daviller G, Morzyński M. 2016. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 68(1), 55–80.","chicago":"Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics. Polish Academy of Sciences Publishing House, 2016."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","type":"journal_article","status":"public","_id":"1216"},{"_id":"1222","status":"public","type":"journal_article","date_updated":"2021-01-12T06:49:11Z","department":[{"_id":"HeEd"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason—the problem of “super resolution of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly, for the case N=7 there are three different optimal arrangements. Our proof is based on a computer enumeration of toroidal irreducible contact graphs."}],"month":"01","intvolume":" 55","scopus_import":1,"main_file_link":[{"url":"https://arxiv.org/abs/1212.0649","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","issue":"1","volume":55,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 2016;55(1):1-20. doi:10.1007/s00454-015-9742-6","apa":"Musin, O., & Nikitenko, A. (2016). Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-015-9742-6","short":"O. Musin, A. Nikitenko, Discrete & Computational Geometry 55 (2016) 1–20.","ieee":"O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square flat torus,” Discrete & Computational Geometry, vol. 55, no. 1. Springer, pp. 1–20, 2016.","mla":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry, vol. 55, no. 1, Springer, 2016, pp. 1–20, doi:10.1007/s00454-015-9742-6.","ista":"Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 55(1), 1–20.","chicago":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-015-9742-6."},"title":"Optimal packings of congruent circles on a square flat torus","publist_id":"6111","author":[{"last_name":"Musin","full_name":"Musin, Oleg","first_name":"Oleg"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","last_name":"Nikitenko","full_name":"Nikitenko, Anton"}],"acknowledgement":"We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy for some useful comments and remarks, and especially Thom Sulanke for modifying surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant DMS-1400876 and by the RFBR Grant 15-01-99563. Anton V. Nikitenko was supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government Grant 11.G34.31.0026.","publisher":"Springer","quality_controlled":"1","oa":1,"day":"01","publication":"Discrete & Computational Geometry","year":"2016","doi":"10.1007/s00454-015-9742-6","date_published":"2016-01-01T00:00:00Z","date_created":"2018-12-11T11:50:48Z","page":"1 - 20"},{"_id":"1237","status":"public","conference":{"start_date":"2016-06-15","end_date":"2016-06-17","location":"Marseille, France","name":"CTIC: Computational Topology in Image Context"},"type":"conference","date_updated":"2021-01-12T06:49:18Z","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"oa_version":"None","abstract":[{"text":"Bitmap images of arbitrary dimension may be formally perceived as unions of m-dimensional boxes aligned with respect to a rectangular grid in ℝm. Cohomology and homology groups are well known topological invariants of such sets. Cohomological operations, such as the cup product, provide higher-order algebraic topological invariants, especially important for digital images of dimension higher than 3. If such an operation is determined at the level of simplicial chains [see e.g. González-Díaz, Real, Homology, Homotopy Appl, 2003, 83-93], then it is effectively computable. However, decomposing a cubical complex into a simplicial one deleteriously affects the efficiency of such an approach. In order to avoid this overhead, a direct cubical approach was applied in [Pilarczyk, Real, Adv. Comput. Math., 2015, 253-275] for the cup product in cohomology, and implemented in the ChainCon software package [http://www.pawelpilarczyk.com/chaincon/]. We establish a formula for the Steenrod square operations [see Steenrod, Annals of Mathematics. Second Series, 1947, 290-320] directly at the level of cubical chains, and we prove the correctness of this formula. An implementation of this formula is programmed in C++ within the ChainCon software framework. We provide a few examples and discuss the effectiveness of this approach. One specific application follows from the fact that Steenrod squares yield tests for the topological extension problem: Can a given map A → Sd to a sphere Sd be extended to a given super-complex X of A? In particular, the ROB-SAT problem, which is to decide for a given function f: X → ℝm and a value r > 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the extension problem.","lang":"eng"}],"intvolume":" 9667","month":"06","alternative_title":["LNCS"],"scopus_import":1,"language":[{"iso":"eng"}],"publication_status":"published","ec_funded":1,"volume":9667,"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"},{"name":"Persistent Homology - Images, Data and Maps","grant_number":"622033","call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"short":"M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.","ieee":"M. Krcál and P. Pilarczyk, “Computation of cubical Steenrod squares,” presented at the CTIC: Computational Topology in Image Context, Marseille, France, 2016, vol. 9667, pp. 140–151.","ama":"Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667. Springer; 2016:140-151. doi:10.1007/978-3-319-39441-1_13","apa":"Krcál, M., & Pilarczyk, P. (2016). Computation of cubical Steenrod squares (Vol. 9667, pp. 140–151). Presented at the CTIC: Computational Topology in Image Context, Marseille, France: Springer. https://doi.org/10.1007/978-3-319-39441-1_13","mla":"Krcál, Marek, and Pawel Pilarczyk. Computation of Cubical Steenrod Squares. Vol. 9667, Springer, 2016, pp. 140–51, doi:10.1007/978-3-319-39441-1_13.","ista":"Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC: Computational Topology in Image Context, LNCS, vol. 9667, 140–151.","chicago":"Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,” 9667:140–51. Springer, 2016. https://doi.org/10.1007/978-3-319-39441-1_13."},"title":"Computation of cubical Steenrod squares","author":[{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","full_name":"Krcál, Marek","last_name":"Krcál"},{"last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6096","acknowledgement":"The research conducted by both authors has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreements no. 291734 (for M. K.) and no. 622033 (for P. P.).","quality_controlled":"1","publisher":"Springer","day":"02","year":"2016","date_created":"2018-12-11T11:50:52Z","doi":"10.1007/978-3-319-39441-1_13","date_published":"2016-06-02T00:00:00Z","page":"140 - 151"},{"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1088-6826"]},"ec_funded":1,"volume":144,"issue":"4","oa_version":"Preprint","abstract":[{"text":"We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism induced by an outer approximation of a continuous map coincides with the homomorphism induced in homology by the map. In contrast to more classical results we do not require that the projection to the domain have acyclic preimages. Moreover, we show that it is possible to retrieve correct homological information from a correspondence even if some data is missing or perturbed. Finally, we describe an application to combinatorial maps that are either outer approximations of continuous maps or reconstructions of such maps from a finite set of data points.","lang":"eng"}],"intvolume":" 144","month":"04","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1411.7563"}],"scopus_import":"1","date_updated":"2022-05-24T09:35:58Z","department":[{"_id":"HeEd"}],"_id":"1252","status":"public","type":"journal_article","article_type":"original","publication":"Proceedings of the American Mathematical Society","day":"01","year":"2016","date_created":"2018-12-11T11:50:57Z","doi":"10.1090/proc/12812","date_published":"2016-04-01T00:00:00Z","page":"1787 - 1801","acknowledgement":"The authors gratefully acknowledge the support of the Lorenz Center which\r\nprovided an opportunity for us to discuss in depth the work of this paper. Research leading to these results has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT) in the framework of the research\r\nproject FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008),\r\nas well as from the People Programme (Marie Curie Actions) of the European\r\nUnion’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033 (supporting PP). The work of the first and third author has\r\nbeen partially supported by NSF grants NSF-DMS-0835621, 0915019, 1125174,\r\n1248071, and contracts from AFOSR and DARPA. The work of the second author\r\nwas supported by Grant-in-Aid for Scientific Research (No. 25287029), Ministry of\r\nEducation, Science, Technology, Culture and Sports, Japan.","oa":1,"publisher":"American Mathematical Society","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. 2016. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 144(4), 1787–1801.","chicago":"Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk. “Inducing a Map on Homology from a Correspondence.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/12812.","ama":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 2016;144(4):1787-1801. doi:10.1090/proc/12812","apa":"Harker, S., Kokubu, H., Mischaikow, K., & Pilarczyk, P. (2016). Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/12812","short":"S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American Mathematical Society 144 (2016) 1787–1801.","ieee":"S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on homology from a correspondence,” Proceedings of the American Mathematical Society, vol. 144, no. 4. American Mathematical Society, pp. 1787–1801, 2016.","mla":"Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” Proceedings of the American Mathematical Society, vol. 144, no. 4, American Mathematical Society, 2016, pp. 1787–801, doi:10.1090/proc/12812."},"title":"Inducing a map on homology from a correspondence","article_processing_charge":"No","external_id":{"arxiv":["1411.7563"]},"publist_id":"6075","author":[{"first_name":"Shaun","full_name":"Harker, Shaun","last_name":"Harker"},{"first_name":"Hiroshi","last_name":"Kokubu","full_name":"Kokubu, Hiroshi"},{"first_name":"Konstantin","full_name":"Mischaikow, Konstantin","last_name":"Mischaikow"},{"first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel"}],"project":[{"name":"Persistent Homology - Images, Data and Maps","grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}]},{"type":"journal_article","status":"public","_id":"1254","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T06:49:25Z","main_file_link":[{"url":"https://arxiv.org/abs/1504.00116","open_access":"1"}],"scopus_import":1,"intvolume":" 25","month":"04","abstract":[{"lang":"eng","text":"We use rigorous numerical techniques to compute a lower bound for the exponent of expansivity outside a neighborhood of the critical point for thousands of intervals of parameter values in the quadratic family. We first compute a radius of the critical neighborhood outside which the map is uniformly expanding. This radius is taken as small as possible, yet large enough for our numerical procedure to succeed in proving that the expansivity exponent outside this neighborhood is positive. Then, for each of the intervals, we compute a lower bound for this expansivity exponent, valid for all the parameters in that interval. We illustrate and study the distribution of the radii and the expansivity exponents. The results of our computations are mathematically rigorous. The source code of the software and the results of the computations are made publicly available at http://www.pawelpilarczyk.com/quadratic/."}],"oa_version":"Preprint","ec_funded":1,"issue":"2","volume":25,"publication_status":"published","language":[{"iso":"eng"}],"project":[{"name":"Persistent Homology - Images, Data and Maps","grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"author":[{"first_name":"Ali","last_name":"Golmakani","full_name":"Golmakani, Ali"},{"last_name":"Luzzatto","full_name":"Luzzatto, Stefano","first_name":"Stefano"},{"last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel"}],"publist_id":"6071","title":"Uniform expansivity outside a critical neighborhood in the quadratic family","citation":{"ista":"Golmakani A, Luzzatto S, Pilarczyk P. 2016. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 25(2), 116–124.","chicago":"Golmakani, Ali, Stefano Luzzatto, and Pawel Pilarczyk. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics. Taylor and Francis, 2016. https://doi.org/10.1080/10586458.2015.1048011.","apa":"Golmakani, A., Luzzatto, S., & Pilarczyk, P. (2016). Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. Taylor and Francis. https://doi.org/10.1080/10586458.2015.1048011","ama":"Golmakani A, Luzzatto S, Pilarczyk P. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 2016;25(2):116-124. doi:10.1080/10586458.2015.1048011","short":"A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016) 116–124.","ieee":"A. Golmakani, S. Luzzatto, and P. Pilarczyk, “Uniform expansivity outside a critical neighborhood in the quadratic family,” Experimental Mathematics, vol. 25, no. 2. Taylor and Francis, pp. 116–124, 2016.","mla":"Golmakani, Ali, et al. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics, vol. 25, no. 2, Taylor and Francis, 2016, pp. 116–24, doi:10.1080/10586458.2015.1048011."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa":1,"publisher":"Taylor and Francis","quality_controlled":"1","acknowledgement":"AG and PP were partially supported by Abdus Salam International Centre for Theoretical Physics (ICTP). Additionally, AG was supported by BREUDS, and research conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008); and from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033. The authors gratefully acknowledge the Department of\r\nMathematics of Kyoto University for providing access\r\nto their server for conducting computations for this\r\nproject.","page":"116 - 124","date_created":"2018-12-11T11:50:58Z","doi":"10.1080/10586458.2015.1048011","date_published":"2016-04-02T00:00:00Z","year":"2016","publication":"Experimental Mathematics","day":"02"},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Held, M., Huber, S., & Palfrader, P. (2016). Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. Taylor and Francis. https://doi.org/10.1080/16864360.2016.1150718","ama":"Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 2016;13(5):712-721. doi:10.1080/16864360.2016.1150718","ieee":"M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures using skeletons,” Computer-Aided Design and Applications, vol. 13, no. 5. Taylor and Francis, pp. 712–721, 2016.","short":"M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13 (2016) 712–721.","mla":"Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications, vol. 13, no. 5, Taylor and Francis, 2016, pp. 712–21, doi:10.1080/16864360.2016.1150718.","ista":"Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 13(5), 712–721.","chicago":"Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications. Taylor and Francis, 2016. https://doi.org/10.1080/16864360.2016.1150718."},"title":"Generalized offsetting of planar structures using skeletons","author":[{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","last_name":"Huber","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"publist_id":"6048","publication":"Computer-Aided Design and Applications","day":"02","year":"2016","has_accepted_license":"1","date_created":"2018-12-11T11:51:04Z","doi":"10.1080/16864360.2016.1150718","date_published":"2016-09-02T00:00:00Z","page":"712 - 721","acknowledgement":"This work was supported by Austrian Science Fund (FWF): P25816-N15.","oa":1,"quality_controlled":"1","publisher":"Taylor and Francis","ddc":["004","516"],"date_updated":"2021-01-12T06:49:32Z","file_date_updated":"2020-07-14T12:44:42Z","department":[{"_id":"HeEd"}],"_id":"1272","pubrep_id":"694","status":"public","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"type":"journal_article","language":[{"iso":"eng"}],"file":[{"date_created":"2018-12-12T10:16:20Z","file_name":"IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf","date_updated":"2020-07-14T12:44:42Z","file_size":1678369,"creator":"system","checksum":"c746f3a48edb62b588d92ea5d0fd2c0e","file_id":"5206","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","volume":13,"issue":"5","oa_version":"Published Version","abstract":[{"text":"We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a new geometric structure, called variable-radius Voronoi diagram, which supports the computation of variable-radius offsets, i.e., offsets whose distance to the input is allowed to vary along the input. We discuss properties of this structure and sketch a prototype implementation that supports the computation of variable-radius offsets based on this new variant of Voronoi diagrams.","lang":"eng"}],"intvolume":" 13","month":"09","scopus_import":1},{"citation":{"ista":"Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 54, 169–174.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.endm.2016.09.030.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted averages,” Electronic Notes in Discrete Mathematics, vol. 54. Elsevier, pp. 169–174, 2016.","short":"H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics 54 (2016) 169–174.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2016). Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2016.09.030","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 2016;54:169-174. doi:10.1016/j.endm.2016.09.030","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics, vol. 54, Elsevier, 2016, pp. 169–74, doi:10.1016/j.endm.2016.09.030."},"date_updated":"2021-01-12T06:49:41Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel"}],"publist_id":"5976","title":"Multiple covers with balls II: Weighted averages","department":[{"_id":"HeEd"}],"_id":"1295","type":"journal_article","project":[{"name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"status":"public","year":"2016","publication_status":"published","day":"01","publication":"Electronic Notes in Discrete Mathematics","language":[{"iso":"eng"}],"page":"169 - 174","date_published":"2016-10-01T00:00:00Z","volume":54,"doi":"10.1016/j.endm.2016.09.030","date_created":"2018-12-11T11:51:12Z","ec_funded":1,"abstract":[{"lang":"eng","text":"Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voronoi diagrams of average balls."}],"oa_version":"None","acknowledgement":"This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.","scopus_import":1,"publisher":"Elsevier","quality_controlled":"1","month":"10","intvolume":" 54"},{"_id":"1292","status":"public","type":"journal_article","date_updated":"2021-01-12T06:49:40Z","department":[{"_id":"HeEd"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We give explicit formulas and algorithms for the computation of the Thurston–Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on Heegaard surfaces in convex position. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds."}],"intvolume":" 150","month":"12","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.00794"}],"scopus_import":1,"language":[{"iso":"eng"}],"publication_status":"published","volume":150,"issue":"2","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 150(2), 441–455.","chicago":"Durst, Sebastian, Marc Kegel, and Mirko D Klukas. “Computing the Thurston–Bennequin Invariant in Open Books.” Acta Mathematica Hungarica. Springer, 2016. https://doi.org/10.1007/s10474-016-0648-4.","short":"S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455.","ieee":"S. Durst, M. Kegel, and M. D. Klukas, “Computing the Thurston–Bennequin invariant in open books,” Acta Mathematica Hungarica, vol. 150, no. 2. Springer, pp. 441–455, 2016.","ama":"Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 2016;150(2):441-455. doi:10.1007/s10474-016-0648-4","apa":"Durst, S., Kegel, M., & Klukas, M. D. (2016). Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. Springer. https://doi.org/10.1007/s10474-016-0648-4","mla":"Durst, Sebastian, et al. “Computing the Thurston–Bennequin Invariant in Open Books.” Acta Mathematica Hungarica, vol. 150, no. 2, Springer, 2016, pp. 441–55, doi:10.1007/s10474-016-0648-4."},"title":"Computing the Thurston–Bennequin invariant in open books","publist_id":"6023","author":[{"first_name":"Sebastian","full_name":"Durst, Sebastian","last_name":"Durst"},{"first_name":"Marc","full_name":"Kegel, Marc","last_name":"Kegel"},{"full_name":"Klukas, Mirko D","last_name":"Klukas","id":"34927512-F248-11E8-B48F-1D18A9856A87","first_name":"Mirko D"}],"acknowledgement":"The authors are veryg rateful to Hansj ̈org Geiges \r\nfor fruitful discussions and advice and Christian Evers for helpful remarks on a draft version.","oa":1,"quality_controlled":"1","publisher":"Springer","publication":"Acta Mathematica Hungarica","day":"01","year":"2016","date_created":"2018-12-11T11:51:11Z","date_published":"2016-12-01T00:00:00Z","doi":"10.1007/s10474-016-0648-4","page":"441 - 455"},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016, pp. 833–45, doi:10.1007/s11856-016-1429-z.","short":"A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.","ieee":"A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,” Israel Journal of Mathematics, vol. 216, no. 2. Springer, pp. 833–845, 2016.","ama":"Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 2016;216(2):833-845. doi:10.1007/s11856-016-1429-z","apa":"Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute angles. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1429-z","chicago":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics. Springer, 2016. https://doi.org/10.1007/s11856-016-1429-z.","ista":"Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845."},"title":"Billiards in convex bodies with acute angles","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"last_name":"Balitskiy","full_name":"Balitskiy, Alexey","first_name":"Alexey"}],"publist_id":"5938","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"day":"15","publication":"Israel Journal of Mathematics","year":"2016","doi":"10.1007/s11856-016-1429-z","date_published":"2016-10-15T00:00:00Z","date_created":"2018-12-11T11:51:24Z","page":"833 - 845","acknowledgement":"Supported by People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734]. Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part by the Moebius Contest Foundation for Young Scientists, and in part by the Simons Foundation.","publisher":"Springer","quality_controlled":"1","oa":1,"date_updated":"2021-01-12T06:49:56Z","department":[{"_id":"HeEd"}],"_id":"1330","status":"public","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","volume":216,"issue":"2","ec_funded":1,"oa_version":"Preprint","abstract":[{"text":"In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K is acute (in a certain sense), then there is a closed billiard trajectory in K.","lang":"eng"}],"month":"10","intvolume":" 216","scopus_import":1,"main_file_link":[{"url":"https://arxiv.org/abs/1506.06014","open_access":"1"}]},{"date_updated":"2021-01-12T06:50:09Z","department":[{"_id":"HeEd"}],"_id":"1360","status":"public","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","ec_funded":1,"volume":144,"issue":"10","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results. "}],"intvolume":" 144","month":"10","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1401.0442"}],"scopus_import":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"short":"A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513.","ieee":"A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,” Proceedings of the American Mathematical Society, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016.","ama":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062","apa":"Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062","mla":"Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society, vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062.","ista":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 144(10), 4501–4513.","chicago":"Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/13062."},"title":"Elementary approach to closed billiard trajectories in asymmetric normed spaces","article_processing_charge":"No","publist_id":"5885","author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alexey","full_name":"Balitskiy, Alexey","last_name":"Balitskiy"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"},{"last_name":"Sharipova","full_name":"Sharipova, Anastasia","first_name":"Anastasia"}],"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"publication":"Proceedings of the American Mathematical Society","day":"01","year":"2016","date_created":"2018-12-11T11:51:34Z","doi":"10.1090/proc/13062","date_published":"2016-10-01T00:00:00Z","page":"4501 - 4513","acknowledgement":"The first and third authors were supported by the Dynasty Foundation. The first, second and third authors were supported by the Russian Foundation for Basic Re- search grant 15-31-20403 (mol a ved).","oa":1,"quality_controlled":"1","publisher":"American Mathematical Society"},{"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","quality_controlled":"1","publisher":"Springer","oa":1,"day":"01","publication":"Discrete & Computational Geometry","has_accepted_license":"1","year":"2016","date_published":"2016-07-01T00:00:00Z","doi":"10.1007/s00454-016-9794-2","date_created":"2018-12-11T11:51:51Z","page":"126 - 164","project":[{"name":"Robust invariants of Nonlinear Systems","grant_number":"M01980","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete & Computational Geometry. 56(1), 126–164.","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-016-9794-2.","short":"P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164.","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” Discrete & Computational Geometry, vol. 56, no. 1. Springer, pp. 126–164, 2016.","apa":"Franek, P., & Krcál, M. (2016). On computability and triviality of well groups. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9794-2","ama":"Franek P, Krcál M. On computability and triviality of well groups. Discrete & Computational Geometry. 2016;56(1):126-164. doi:10.1007/s00454-016-9794-2","mla":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016, pp. 126–64, doi:10.1007/s00454-016-9794-2."},"title":"On computability and triviality of well groups","publist_id":"5799","author":[{"id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Franek","full_name":"Franek, Peter"},{"first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek","last_name":"Krcál"}],"article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","abstract":[{"lang":"eng","text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map (Formula presented.) on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within (Formula presented.) distance r from f for a given (Formula presented.). The main drawback of the approach is that the computability of well groups was shown only when (Formula presented.) or (Formula presented.). Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of (Formula presented.) by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and (Formula presented.), our approximation of the (Formula presented.)th well group is exact. For the second part, we find examples of maps (Formula presented.) with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status."}],"month":"07","intvolume":" 56","scopus_import":1,"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"4846","checksum":"e0da023abf6b72abd8c6a8c76740d53c","file_size":905303,"date_updated":"2020-07-14T12:44:53Z","creator":"system","file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","date_created":"2018-12-12T10:10:55Z"}],"language":[{"iso":"eng"}],"publication_status":"published","related_material":{"record":[{"id":"1510","status":"public","relation":"earlier_version"}]},"issue":"1","volume":56,"ec_funded":1,"_id":"1408","status":"public","pubrep_id":"614","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2023-02-23T10:02:11Z","file_date_updated":"2020-07-14T12:44:53Z","department":[{"_id":"UlWa"},{"_id":"HeEd"}]}]