[{"department":[{"_id":"HeEd"}],"title":"Multiple covers with balls II: Weighted averages","publist_id":"5976","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","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.","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.","ista":"Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 54, 169–174."},"date_updated":"2021-01-12T06:49:41Z","status":"public","project":[{"name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"type":"journal_article","_id":"1295","ec_funded":1,"date_created":"2018-12-11T11:51:12Z","date_published":"2016-10-01T00:00:00Z","volume":54,"doi":"10.1016/j.endm.2016.09.030","page":"169 - 174","publication":"Electronic Notes in Discrete Mathematics","language":[{"iso":"eng"}],"day":"01","year":"2016","publication_status":"published","intvolume":" 54","month":"10","scopus_import":1,"publisher":"Elsevier","quality_controlled":"1","acknowledgement":"This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.","oa_version":"None","abstract":[{"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.","lang":"eng"}]},{"issue":"2","volume":150,"language":[{"iso":"eng"}],"publication_status":"published","month":"12","intvolume":" 150","scopus_import":1,"main_file_link":[{"url":"https://arxiv.org/abs/1605.00794","open_access":"1"}],"oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T06:49:40Z","status":"public","type":"journal_article","_id":"1292","doi":"10.1007/s10474-016-0648-4","date_published":"2016-12-01T00:00:00Z","date_created":"2018-12-11T11:51:11Z","page":"441 - 455","day":"01","publication":"Acta Mathematica Hungarica","year":"2016","quality_controlled":"1","publisher":"Springer","oa":1,"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.","title":"Computing the Thurston–Bennequin invariant in open books","author":[{"last_name":"Durst","full_name":"Durst, Sebastian","first_name":"Sebastian"},{"full_name":"Kegel, Marc","last_name":"Kegel","first_name":"Marc"},{"id":"34927512-F248-11E8-B48F-1D18A9856A87","first_name":"Mirko D","full_name":"Klukas, Mirko D","last_name":"Klukas"}],"publist_id":"6023","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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."}},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"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","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","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.","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.","ista":"Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845.","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."},"title":"Billiards in convex bodies with acute angles","publist_id":"5938","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"last_name":"Balitskiy","full_name":"Balitskiy, Alexey","first_name":"Alexey"}],"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","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":[{"lang":"eng","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."}],"month":"10","intvolume":" 216","scopus_import":1,"main_file_link":[{"url":"https://arxiv.org/abs/1506.06014","open_access":"1"}]},{"scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1401.0442"}],"month":"10","intvolume":" 144","abstract":[{"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. ","lang":"eng"}],"oa_version":"Preprint","volume":144,"issue":"10","ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"1360","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T06:50:09Z","quality_controlled":"1","publisher":"American Mathematical Society","oa":1,"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).","page":"4501 - 4513","date_published":"2016-10-01T00:00:00Z","doi":"10.1090/proc/13062","date_created":"2018-12-11T11:51:34Z","year":"2016","day":"01","publication":"Proceedings of the American Mathematical Society","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"publist_id":"5885","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"first_name":"Alexey","last_name":"Balitskiy","full_name":"Balitskiy, Alexey"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"},{"first_name":"Anastasia","full_name":"Sharipova, Anastasia","last_name":"Sharipova"}],"article_processing_charge":"No","title":"Elementary approach to closed billiard trajectories in asymmetric normed spaces","citation":{"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.","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.","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.","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.","short":"A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513.","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","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"},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"oa":1,"publisher":"Springer","quality_controlled":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","page":"126 - 164","date_created":"2018-12-11T11:51:51Z","doi":"10.1007/s00454-016-9794-2","date_published":"2016-07-01T00:00:00Z","year":"2016","has_accepted_license":"1","publication":"Discrete & Computational Geometry","day":"01","project":[{"name":"Robust invariants of Nonlinear Systems","grant_number":"M01980","call_identifier":"FWF","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"article_processing_charge":"Yes (via OA deal)","author":[{"id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Franek","full_name":"Franek, Peter"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","full_name":"Krcál, Marek","last_name":"Krcál"}],"publist_id":"5799","title":"On computability and triviality of well groups","citation":{"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","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","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.","short":"P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164.","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.","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."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"intvolume":" 56","month":"07","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."}],"oa_version":"Published Version","license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"issue":"1","volume":56,"related_material":{"record":[{"status":"public","id":"1510","relation":"earlier_version"}]},"publication_status":"published","language":[{"iso":"eng"}],"file":[{"date_updated":"2020-07-14T12:44:53Z","file_size":905303,"creator":"system","date_created":"2018-12-12T10:10:55Z","file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"e0da023abf6b72abd8c6a8c76740d53c","file_id":"4846"}],"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":"614","status":"public","_id":"1408","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:44:53Z","date_updated":"2023-02-23T10:02:11Z","ddc":["510"]}]