[{"type":"journal_article","status":"public","_id":"1578","publist_id":"5593","author":[{"first_name":"Thanhtung","last_name":"Cao","full_name":"Cao, Thanhtung"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Tan","full_name":"Tan, Tiowseng","first_name":"Tiowseng"}],"title":"Triangulations from topologically correct digital Voronoi diagrams","department":[{"_id":"HeEd"}],"citation":{"ista":"Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519.","chicago":"Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.04.001.","ama":"Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 2015;48(7):507-519. doi:10.1016/j.comgeo.2015.04.001","apa":"Cao, T., Edelsbrunner, H., & Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2015.04.001","short":"T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.","ieee":"T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct digital Voronoi diagrams,” Computational Geometry, vol. 48, no. 7. Elsevier, pp. 507–519, 2015.","mla":"Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry, vol. 48, no. 7, Elsevier, 2015, pp. 507–19, doi:10.1016/j.comgeo.2015.04.001."},"date_updated":"2021-01-12T06:51:43Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"quality_controlled":"1","publisher":"Elsevier","month":"08","intvolume":" 48","abstract":[{"lang":"eng","text":"We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations."}],"oa_version":"None","acknowledgement":"The research of the second author is partially supported by NSF under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n","page":"507 - 519","doi":"10.1016/j.comgeo.2015.04.001","date_published":"2015-08-01T00:00:00Z","volume":48,"issue":"7","date_created":"2018-12-11T11:52:49Z","year":"2015","publication_status":"published","day":"01","publication":"Computational Geometry","language":[{"iso":"eng"}]},{"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights."}],"month":"07","intvolume":" 48","scopus_import":1,"file":[{"creator":"system","file_size":508379,"date_updated":"2020-07-14T12:45:03Z","file_name":"IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf","date_created":"2018-12-12T10:17:36Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"5292","checksum":"5b33719a86f7f4c8e5dc62c1b6893f49"}],"language":[{"iso":"eng"}],"publication_status":"published","related_material":{"record":[{"relation":"other","id":"1582","status":"public"}]},"issue":"5","volume":48,"_id":"1584","status":"public","pubrep_id":"475","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":["000"],"date_updated":"2023-02-23T10:05:22Z","file_date_updated":"2020-07-14T12:45:03Z","department":[{"_id":"HeEd"}],"publisher":"Elsevier","quality_controlled":"1","oa":1,"day":"01","publication":"Computational Geometry: Theory and Applications","has_accepted_license":"1","year":"2015","date_published":"2015-07-01T00:00:00Z","doi":"10.1016/j.comgeo.2015.01.004","date_created":"2018-12-11T11:52:51Z","page":"429 - 442","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier, 2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004.","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 5. Elsevier, pp. 429–442, 2015.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004.","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(5), 429–442."},"title":"Reprint of: Weighted straight skeletons in the plane","author":[{"last_name":"Biedl","full_name":"Biedl, Therese","first_name":"Therese"},{"first_name":"Martin","full_name":"Held, Martin","last_name":"Held"},{"last_name":"Huber","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kaaser, Dominik","last_name":"Kaaser","first_name":"Dominik"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"publist_id":"5587"},{"author":[{"last_name":"Biedl","full_name":"Biedl, Therese","first_name":"Therese"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","last_name":"Huber","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"last_name":"Kaaser","full_name":"Kaaser, Dominik","first_name":"Dominik"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"}],"publist_id":"5589","title":"Weighted straight skeletons in the plane","citation":{"mla":"Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33, doi:10.1016/j.comgeo.2014.08.006.","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 2. Elsevier, pp. 120–133, 2015.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133. doi:10.1016/j.comgeo.2014.08.006","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006.","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(2), 120–133."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"120 - 133","date_created":"2018-12-11T11:52:51Z","date_published":"2015-02-01T00:00:00Z","doi":"10.1016/j.comgeo.2014.08.006","year":"2015","has_accepted_license":"1","publication":"Computational Geometry: Theory and Applications","day":"01","oa":1,"publisher":"Elsevier","quality_controlled":"1","file_date_updated":"2020-07-14T12:45:02Z","department":[{"_id":"HeEd"}],"date_updated":"2023-02-23T10:05:27Z","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)"},"type":"journal_article","pubrep_id":"474","status":"public","_id":"1582","issue":"2","volume":48,"related_material":{"record":[{"relation":"other","status":"public","id":"1584"}]},"publication_status":"published","language":[{"iso":"eng"}],"file":[{"file_id":"5215","checksum":"c1ef67f6ec925e12f73a96b8fe285ab4","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2018-12-12T10:16:28Z","file_name":"IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf","date_updated":"2020-07-14T12:45:02Z","file_size":505987,"creator":"system"}],"scopus_import":1,"intvolume":" 48","month":"02","abstract":[{"lang":"eng","text":"We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights."}],"oa_version":"Published Version"},{"title":"A simple algorithm for computing positively weighted straight skeletons of monotone polygons","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"first_name":"Martin","full_name":"Held, Martin","last_name":"Held"},{"full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan"},{"last_name":"Kaaser","full_name":"Kaaser, Dominik","first_name":"Dominik"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"publist_id":"5588","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” Information Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021","mla":"Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021.","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 115(2), 243–247.","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021."},"oa":1,"quality_controlled":"1","publisher":"Elsevier","date_created":"2018-12-11T11:52:51Z","date_published":"2015-02-01T00:00:00Z","doi":"10.1016/j.ipl.2014.09.021","page":"243 - 247","publication":"Information Processing Letters","day":"01","year":"2015","has_accepted_license":"1","pubrep_id":"473","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":"1583","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:03Z","ddc":["000"],"date_updated":"2021-01-12T06:51:45Z","intvolume":" 115","month":"02","scopus_import":1,"oa_version":"Published Version","abstract":[{"text":"We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon.","lang":"eng"}],"volume":115,"issue":"2","language":[{"iso":"eng"}],"file":[{"date_created":"2018-12-12T10:18:45Z","file_name":"IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf","creator":"system","date_updated":"2020-07-14T12:45:03Z","file_size":270137,"checksum":"2779a648610c9b5c86d0b51a62816d23","file_id":"5367","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publication_status":"published"},{"citation":{"mla":"Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:10.1007/978-3-319-27261-0_28.","ama":"Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28","apa":"Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., & Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28","short":"O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347.","ieee":"O. Aichholzer et al., “Representing directed trees as straight skeletons,” in Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–347.","chicago":"Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28.","ista":"Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 335–347."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publist_id":"5581","author":[{"last_name":"Aichholzer","full_name":"Aichholzer, Oswin","first_name":"Oswin"},{"last_name":"Biedl","full_name":"Biedl, Therese","first_name":"Therese"},{"first_name":"Thomas","last_name":"Hackl","full_name":"Hackl, Thomas"},{"first_name":"Martin","full_name":"Held, Martin","last_name":"Held"},{"first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"last_name":"Palfrader","full_name":"Palfrader, Peter","first_name":"Peter"},{"first_name":"Birgit","last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit"}],"article_processing_charge":"No","title":"Representing directed trees as straight skeletons","quality_controlled":"1","publisher":"Springer Nature","oa":1,"year":"2015","day":"27","publication":"Graph Drawing and Network Visualization","page":"335 - 347","date_published":"2015-11-27T00:00:00Z","doi":"10.1007/978-3-319-27261-0_28","date_created":"2018-12-11T11:52:54Z","_id":"1590","type":"book_chapter","conference":{"name":"GD: International Symposium on Graph Drawing","start_date":"2015-09-24","location":"Los Angeles, CA, United States","end_date":"2015-09-26"},"status":"public","date_updated":"2022-01-28T09:10:37Z","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed."}],"oa_version":"Preprint","alternative_title":["LNCS"],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1508.01076"}],"month":"11","intvolume":" 9411","publication_identifier":{"eisbn":["978-3-319-27261-0"],"isbn":["978-3-319-27260-3"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":9411},{"abstract":[{"lang":"eng","text":"We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K→ ℝn on a finite simplicial complex K and α > 0, it holds that each function g: K → ℝn such that ||g - f || ∞ < α, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K > 2n - 2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in other possible settings."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1402.0858"}],"oa":1,"quality_controlled":"1","publisher":"ACM","scopus_import":1,"intvolume":" 62","month":"08","year":"2015","publication_status":"published","publication":"Journal of the ACM","language":[{"iso":"eng"}],"day":"01","date_created":"2018-12-11T11:53:27Z","volume":62,"doi":"10.1145/2751524","date_published":"2015-08-01T00:00:00Z","issue":"4","_id":"1682","article_number":"26","type":"journal_article","status":"public","citation":{"chicago":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM. ACM, 2015. https://doi.org/10.1145/2751524.","ista":"Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal of the ACM. 62(4), 26.","mla":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM, vol. 62, no. 4, 26, ACM, 2015, doi:10.1145/2751524.","short":"P. Franek, M. Krcál, Journal of the ACM 62 (2015).","ieee":"P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” Journal of the ACM, vol. 62, no. 4. ACM, 2015.","apa":"Franek, P., & Krcál, M. (2015). Robust satisfiability of systems of equations. Journal of the ACM. ACM. https://doi.org/10.1145/2751524","ama":"Franek P, Krcál M. Robust satisfiability of systems of equations. Journal of the ACM. 2015;62(4). doi:10.1145/2751524"},"date_updated":"2021-01-12T06:52:30Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"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"}],"publist_id":"5466","title":"Robust satisfiability of systems of equations","department":[{"_id":"UlWa"},{"_id":"HeEd"}]},{"quality_controlled":"1","publisher":"SIAM","oa":1,"page":"2754 - 2769","date_published":"2015-07-14T00:00:00Z","doi":"10.1137/140993843","date_created":"2018-12-11T11:53:36Z","year":"2015","day":"14","publication":"Society for Industrial and Applied Mathematics","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"publist_id":"5423","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alexander","last_name":"Plakhov","full_name":"Plakhov, Alexander"}],"title":"Minimal resistance of curves under the single impact assumption","citation":{"ista":"Akopyan A, Plakhov A. 2015. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 47(4), 2754–2769.","chicago":"Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” Society for Industrial and Applied Mathematics. SIAM, 2015. https://doi.org/10.1137/140993843.","ama":"Akopyan A, Plakhov A. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 2015;47(4):2754-2769. doi:10.1137/140993843","apa":"Akopyan, A., & Plakhov, A. (2015). Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. SIAM. https://doi.org/10.1137/140993843","short":"A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47 (2015) 2754–2769.","ieee":"A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single impact assumption,” Society for Industrial and Applied Mathematics, vol. 47, no. 4. SIAM, pp. 2754–2769, 2015.","mla":"Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” Society for Industrial and Applied Mathematics, vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:10.1137/140993843."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1410.3736","open_access":"1"}],"month":"07","intvolume":" 47","abstract":[{"lang":"eng","text":"We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles incident on the hollow. It is assumed that u satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph(u) and goes away without hitting the graph of u anymore. We solve the problem: find the function u minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals 1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730-2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1 is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x = (x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as d → ∞."}],"oa_version":"Preprint","issue":"4","volume":47,"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"1710","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T06:52:41Z"},{"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"first_name":"Sergey","full_name":"Pirogov, Sergey","last_name":"Pirogov"},{"last_name":"Rybko","full_name":"Rybko, Aleksandr","first_name":"Aleksandr"}],"publist_id":"5276","article_processing_charge":"No","title":"Invariant measures of genetic recombination process","citation":{"mla":"Akopyan, Arseniy, et al. “Invariant Measures of Genetic Recombination Process.” Journal of Statistical Physics, vol. 160, no. 1, Springer, 2015, pp. 163–67, doi:10.1007/s10955-015-1238-5.","short":"A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015) 163–167.","ieee":"A. Akopyan, S. Pirogov, and A. Rybko, “Invariant measures of genetic recombination process,” Journal of Statistical Physics, vol. 160, no. 1. Springer, pp. 163–167, 2015.","apa":"Akopyan, A., Pirogov, S., & Rybko, A. (2015). Invariant measures of genetic recombination process. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-015-1238-5","ama":"Akopyan A, Pirogov S, Rybko A. Invariant measures of genetic recombination process. Journal of Statistical Physics. 2015;160(1):163-167. doi:10.1007/s10955-015-1238-5","chicago":"Akopyan, Arseniy, Sergey Pirogov, and Aleksandr Rybko. “Invariant Measures of Genetic Recombination Process.” Journal of Statistical Physics. Springer, 2015. https://doi.org/10.1007/s10955-015-1238-5.","ista":"Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination process. Journal of Statistical Physics. 160(1), 163–167."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publisher":"Springer","oa":1,"page":"163 - 167","doi":"10.1007/s10955-015-1238-5","date_published":"2015-07-01T00:00:00Z","date_created":"2018-12-11T11:54:14Z","year":"2015","day":"01","publication":"Journal of Statistical Physics","type":"journal_article","status":"public","_id":"1828","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T06:53:28Z","scopus_import":1,"main_file_link":[{"url":"arxiv.org/abs/1406.5313","open_access":"1"}],"month":"07","intvolume":" 160","abstract":[{"lang":"eng","text":"We construct a non-linear Markov process connected with a biological model of a bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory."}],"oa_version":"Preprint","issue":"1","volume":160,"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}]},{"date_published":"2015-03-06T00:00:00Z","issue":"6","volume":379,"doi":"10.1016/j.physleta.2014.12.010","date_created":"2018-12-11T11:54:49Z","page":"535 - 541","day":"06","publication":"Physics Letters, Section A","language":[{"iso":"eng"}],"year":"2015","publication_status":"published","month":"03","intvolume":" 379","scopus_import":1,"quality_controlled":"1","publisher":"Elsevier","oa_version":"None","acknowledgement":"F.P. was supported by the Graduate School of IST Austria. S.S. was partially supported by CRC1060 of the DFG\r\nThe authors thank Olga Symonova and Michael Kerber for sharing their implementation of the persistence algorithm. ","abstract":[{"text":"We numerically investigate the distribution of extrema of 'chaotic' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy, which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2.","lang":"eng"}],"title":"On the distribution of local extrema in quantum chaos","department":[{"_id":"HeEd"}],"author":[{"first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","last_name":"Pausinger"},{"first_name":"Stefan","full_name":"Steinerberger, Stefan","last_name":"Steinerberger"}],"publist_id":"5152","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:54:12Z","citation":{"ista":"Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 379(6), 535–541.","chicago":"Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A. Elsevier, 2015. https://doi.org/10.1016/j.physleta.2014.12.010.","ieee":"F. Pausinger and S. Steinerberger, “On the distribution of local extrema in quantum chaos,” Physics Letters, Section A, vol. 379, no. 6. Elsevier, pp. 535–541, 2015.","short":"F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.","ama":"Pausinger F, Steinerberger S. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 2015;379(6):535-541. doi:10.1016/j.physleta.2014.12.010","apa":"Pausinger, F., & Steinerberger, S. (2015). On the distribution of local extrema in quantum chaos. Physics Letters, Section A. Elsevier. https://doi.org/10.1016/j.physleta.2014.12.010","mla":"Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A, vol. 379, no. 6, Elsevier, 2015, pp. 535–41, doi:10.1016/j.physleta.2014.12.010."},"status":"public","type":"journal_article","_id":"1938"},{"intvolume":" 15","month":"10","scopus_import":1,"oa_version":"Published Version","abstract":[{"text":"Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.\r\n","lang":"eng"}],"ec_funded":1,"issue":"5","volume":15,"language":[{"iso":"eng"}],"file":[{"date_created":"2018-12-12T10:08:10Z","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","date_updated":"2020-07-14T12:45:26Z","file_size":1317546,"creator":"system","checksum":"3566f3a8b0c1bc550e62914a88c584ff","file_id":"4670","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","pubrep_id":"486","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":"2035","file_date_updated":"2020-07-14T12:45:26Z","department":[{"_id":"HeEd"}],"ddc":["000"],"date_updated":"2021-01-12T06:54:53Z","oa":1,"publisher":"Springer","quality_controlled":"1","acknowledgement":"This research is partially supported by the Toposys project 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 Polish National Science Center under Grant No. N201 419639.","date_created":"2018-12-11T11:55:20Z","date_published":"2015-10-01T00:00:00Z","doi":"10.1007/s10208-014-9223-y","page":"1213 - 1244","publication":"Foundations of Computational Mathematics","day":"01","year":"2015","has_accepted_license":"1","project":[{"name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"title":"The persistent homology of a self-map","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","last_name":"Jablonski","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866"},{"full_name":"Mrozek, Marian","last_name":"Mrozek","first_name":"Marian"}],"publist_id":"5022","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:10.1007/s10208-014-9223-y.","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244.","ieee":"H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” Foundations of Computational Mathematics, vol. 15, no. 5. Springer, pp. 1213–1244, 2015.","ama":"Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. Foundations of Computational Mathematics. 2015;15(5):1213-1244. doi:10.1007/s10208-014-9223-y","apa":"Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2015). The persistent homology of a self-map. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9223-y","chicago":"Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics. Springer, 2015. https://doi.org/10.1007/s10208-014-9223-y.","ista":"Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244."}}]