{"_id":"2418","doi":"10.1145/336154.336176","author":[{"orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"},{"full_name":"Welzl, Emo","first_name":"Emo","last_name":"Welzl"}],"conference":{"name":"SCG: Symposium on Computational Geometry","location":"Clear Water Bay Kowloon, Hong Kong","end_date":"2000-04-14","start_date":"2000-06-12"},"quality_controlled":"1","scopus_import":"1","title":"Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem","publication_status":"published","publication":"Proceedings of the 16th annual symposium on Computational geometry","oa_version":"None","abstract":[{"text":"For an absolutely continuous probability measure μ on Rd and a nonnegative integer k, let sk(μ, 0) denote the probability that the convex hull of k+d+1 random points which are i.i.d. according to μ contains the origin 0. For d and k given, we determine a tight upper bound on sk(μ, 0), and we characterize the measures in Rd which attain this bound. This result can be considered a continuous analogue of the Upper Bound Theorem for the maximal number of faces of convex polytopes with a given number of vertices. For our proof we introduce so-called h-functions, continuous counterparts of h-vectors for simplicial convex polytopes.","lang":"eng"}],"date_updated":"2023-05-03T12:41:02Z","publist_id":"4507","extern":"1","type":"conference","publication_identifier":{"isbn":["9781581132243"]},"language":[{"iso":"eng"}],"year":"2000","status":"public","publisher":"ACM","page":"50 - 56","day":"01","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_published":"2000-05-01T00:00:00Z","article_processing_charge":"No","citation":{"apa":"Wagner, U., &#38; Welzl, E. (2000). Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem. In <i>Proceedings of the 16th annual symposium on Computational geometry</i> (pp. 50–56). Clear Water Bay Kowloon, Hong Kong: ACM. <a href=\"https://doi.org/10.1145/336154.336176\">https://doi.org/10.1145/336154.336176</a>","chicago":"Wagner, Uli, and Emo Welzl. “Origin-Embracing Distributions or a Continuous Analogue of the Upper Bound Theorem.” In <i>Proceedings of the 16th Annual Symposium on Computational Geometry</i>, 50–56. ACM, 2000. <a href=\"https://doi.org/10.1145/336154.336176\">https://doi.org/10.1145/336154.336176</a>.","ista":"Wagner U, Welzl E. 2000. Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem. Proceedings of the 16th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 50–56.","ieee":"U. Wagner and E. Welzl, “Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem,” in <i>Proceedings of the 16th annual symposium on Computational geometry</i>, Clear Water Bay Kowloon, Hong Kong, 2000, pp. 50–56.","short":"U. Wagner, E. Welzl, in:, Proceedings of the 16th Annual Symposium on Computational Geometry, ACM, 2000, pp. 50–56.","mla":"Wagner, Uli, and Emo Welzl. “Origin-Embracing Distributions or a Continuous Analogue of the Upper Bound Theorem.” <i>Proceedings of the 16th Annual Symposium on Computational Geometry</i>, ACM, 2000, pp. 50–56, doi:<a href=\"https://doi.org/10.1145/336154.336176\">10.1145/336154.336176</a>.","ama":"Wagner U, Welzl E. Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem. In: <i>Proceedings of the 16th Annual Symposium on Computational Geometry</i>. ACM; 2000:50-56. doi:<a href=\"https://doi.org/10.1145/336154.336176\">10.1145/336154.336176</a>"},"month":"05","date_created":"2018-12-11T11:57:33Z"}