[{"extern":1,"abstract":[{"lang":"eng","text":"A study was conducted on the one-dimensional (1D) bosons in three-dimensional (3D) traps. A rigorous analysis was carried out on the parameter regions in which various types of 1D or 3D behavior occurred in the ground state. The four parameter regions include density, transverse, longitudinal dimensions and scattering length."}],"issue":"15","publist_id":"4571","type":"journal_article","date_updated":"2021-01-12T06:57:00Z","date_created":"2018-12-11T11:57:12Z","volume":91,"author":[{"last_name":"Lieb","first_name":"Élliott","full_name":"Lieb, Élliott H"},{"first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer"},{"full_name":"Yngvason, Jakob","first_name":"Jakob","last_name":"Yngvason"}],"publication_status":"published","title":"One-dimensional Bosons in three-dimensional traps","status":"public","publisher":"American Physical Society","intvolume":" 91","_id":"2358","year":"2003","month":"10","day":"10","doi":"10.1103/PhysRevLett.91.150401","date_published":"2003-10-10T00:00:00Z","quality_controlled":0,"page":"1504011 - 1504014","publication":"Physical Review Letters","main_file_link":[{"url":"http://arxiv.org/abs/cond-mat/0304071","open_access":"1"}],"oa":1,"citation":{"apa":"Lieb, É., Seiringer, R., & Yngvason, J. (2003). One-dimensional Bosons in three-dimensional traps. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.91.150401","ieee":"É. Lieb, R. Seiringer, and J. Yngvason, “One-dimensional Bosons in three-dimensional traps,” Physical Review Letters, vol. 91, no. 15. American Physical Society, pp. 1504011–1504014, 2003.","ista":"Lieb É, Seiringer R, Yngvason J. 2003. One-dimensional Bosons in three-dimensional traps. Physical Review Letters. 91(15), 1504011–1504014.","ama":"Lieb É, Seiringer R, Yngvason J. One-dimensional Bosons in three-dimensional traps. Physical Review Letters. 2003;91(15):1504011-1504014. doi:10.1103/PhysRevLett.91.150401","chicago":"Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “One-Dimensional Bosons in Three-Dimensional Traps.” Physical Review Letters. American Physical Society, 2003. https://doi.org/10.1103/PhysRevLett.91.150401.","short":"É. Lieb, R. Seiringer, J. Yngvason, Physical Review Letters 91 (2003) 1504011–1504014.","mla":"Lieb, Élliott, et al. “One-Dimensional Bosons in Three-Dimensional Traps.” Physical Review Letters, vol. 91, no. 15, American Physical Society, 2003, pp. 1504011–14, doi:10.1103/PhysRevLett.91.150401."}},{"extern":1,"publist_id":"4511","type":"dissertation","date_created":"2018-12-11T11:57:31Z","date_updated":"2021-01-12T06:57:20Z","author":[{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","full_name":"Uli Wagner"}],"publisher":"ETH Zurich","status":"public","publication_status":"published","title":"On k-Sets and Their Applications","year":"2003","_id":"2414","month":"01","day":"01","doi":"10.3929/ethz-a-004708408","date_published":"2003-01-01T00:00:00Z","quality_controlled":0,"citation":{"chicago":"Wagner, Uli. “On K-Sets and Their Applications.” ETH Zurich, 2003. https://doi.org/10.3929/ethz-a-004708408.","mla":"Wagner, Uli. On K-Sets and Their Applications. ETH Zurich, 2003, doi:10.3929/ethz-a-004708408.","short":"U. Wagner, On K-Sets and Their Applications, ETH Zurich, 2003.","ista":"Wagner U. 2003. On k-Sets and Their Applications. ETH Zurich.","apa":"Wagner, U. (2003). On k-Sets and Their Applications. ETH Zurich. https://doi.org/10.3929/ethz-a-004708408","ieee":"U. Wagner, “On k-Sets and Their Applications,” ETH Zurich, 2003.","ama":"Wagner U. On k-Sets and Their Applications. 2003. doi:10.3929/ethz-a-004708408"}},{"status":"public","title":"Shape dimension and intrinsic metric from samples of manifolds with high co-dimension","publication_status":"published","publisher":"ACM","_id":"2424","year":"2003","date_updated":"2021-01-12T06:57:24Z","date_created":"2018-12-11T11:57:35Z","author":[{"full_name":"Giesen, Joachim","last_name":"Giesen","first_name":"Joachim"},{"last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Uli Wagner"}],"type":"conference","extern":1,"abstract":[{"lang":"eng","text":"We introduce the adaptive neighborhood graph as a data structure for modeling a smooth manifold M embedded in some (potentially very high-dimensional) Euclidean space ℝd. We assume that M is known to us only through a finite sample P ⊂ M, as it is often the case in applications. The adaptive neighborhood graph is a geometric graph on P. Its complexity is at most min{2O(k)(n, n2}, where n = |P| and k = dim M, as opposed to the n⌈d/2⌉ complexity of the Delaunay triangulation, which is often used to model manifolds. We show that we can provably correctly infer the connectivity of M and the dimension of M from the adaptive neighborhood graph provided a certain standard sampling condition is fulfilled. The running time of the dimension detection algorithm is d2O(k7 log k) for each connected component of M. If the dimension is considered constant, this is a constant-time operation, and the adaptive neighborhood graph is of linear size. Moreover, the exponential dependence of the constants is only on the intrinsic dimension k, not on the ambient dimension d. This is of particular interest if the co-dimension is high, i.e., if k is much smaller than d, as is the case in many applications. The adaptive neighborhood graph also allows us to approximate the geodesic distances between the points in P."}],"publist_id":"4501","quality_controlled":0,"page":"329 - 337","citation":{"ama":"Giesen J, Wagner U. Shape dimension and intrinsic metric from samples of manifolds with high co-dimension. In: ACM; 2003:329-337. doi:10.1145/777792.777841","apa":"Giesen, J., & Wagner, U. (2003). Shape dimension and intrinsic metric from samples of manifolds with high co-dimension (pp. 329–337). Presented at the SoCG: Symposium on Computational Geometry, ACM. https://doi.org/10.1145/777792.777841","ieee":"J. Giesen and U. Wagner, “Shape dimension and intrinsic metric from samples of manifolds with high co-dimension,” presented at the SoCG: Symposium on Computational Geometry, 2003, pp. 329–337.","ista":"Giesen J, Wagner U. 2003. Shape dimension and intrinsic metric from samples of manifolds with high co-dimension. SoCG: Symposium on Computational Geometry, 329–337.","short":"J. Giesen, U. Wagner, in:, ACM, 2003, pp. 329–337.","mla":"Giesen, Joachim, and Uli Wagner. Shape Dimension and Intrinsic Metric from Samples of Manifolds with High Co-Dimension. ACM, 2003, pp. 329–37, doi:10.1145/777792.777841.","chicago":"Giesen, Joachim, and Uli Wagner. “Shape Dimension and Intrinsic Metric from Samples of Manifolds with High Co-Dimension,” 329–37. ACM, 2003. https://doi.org/10.1145/777792.777841."},"conference":{"name":"SoCG: Symposium on Computational Geometry"},"date_published":"2003-06-01T00:00:00Z","doi":"10.1145/777792.777841","day":"01","month":"06"},{"quality_controlled":0,"page":"129 - 135","citation":{"apa":"Matoušek, J., & Wagner, U. (2003). New constructions of weak epsilon-nets (pp. 129–135). Presented at the SoCG: Symposium on Computational Geometry, ACM. https://doi.org/10.1145/777792.777813","ieee":"J. Matoušek and U. Wagner, “New constructions of weak epsilon-nets,” presented at the SoCG: Symposium on Computational Geometry, 2003, pp. 129–135.","ista":"Matoušek J, Wagner U. 2003. New constructions of weak epsilon-nets. SoCG: Symposium on Computational Geometry, 129–135.","ama":"Matoušek J, Wagner U. New constructions of weak epsilon-nets. In: ACM; 2003:129-135. doi:10.1145/777792.777813","chicago":"Matoušek, Jiří, and Uli Wagner. “New Constructions of Weak Epsilon-Nets,” 129–35. ACM, 2003. https://doi.org/10.1145/777792.777813.","short":"J. Matoušek, U. Wagner, in:, ACM, 2003, pp. 129–135.","mla":"Matoušek, Jiří, and Uli Wagner. New Constructions of Weak Epsilon-Nets. ACM, 2003, pp. 129–35, doi:10.1145/777792.777813."},"conference":{"name":"SoCG: Symposium on Computational Geometry"},"date_published":"2003-06-01T00:00:00Z","doi":"10.1145/777792.777813","day":"01","month":"06","status":"public","publication_status":"published","title":"New constructions of weak epsilon-nets","publisher":"ACM","_id":"2423","year":"2003","date_updated":"2021-01-12T06:57:24Z","date_created":"2018-12-11T11:57:34Z","author":[{"first_name":"Jiří","last_name":"Matoušek","full_name":"Matoušek, Jiří"},{"full_name":"Uli Wagner","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"type":"conference","extern":1,"abstract":[{"lang":"eng","text":"A finite set N ⊃ Rd is a weak ε-net for an n-point set X ⊃ Rd (with respect to convex sets) if N intersects every convex set K with |K ∩ X| ≥ εn. We give an alternative, and arguably simpler, proof of the fact, first shown by Chazelle et al. [7], that every point set X in Rd admits a weak ε-net of cardinality O(ε-d polylog(1/ε)). Moreover, for a number of special point sets (e.g., for points on the moment curve), our method gives substantially better bounds. The construction yields an algorithm to construct such weak ε-nets in time O(n ln(1/ε)). We also prove, by a different method, a near-linear upper bound for points uniformly distributed on the (d - 1)-dimensional sphere."}],"publist_id":"4502"},{"abstract":[{"lang":"eng","text":"We prove a lower bound of 0.3288(4 n) for the rectilinear crossing number cr̄(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadrilaterals in any set of n points in general position in the Euclidean plane. As we see it, the main contribution of this paper is not so much the concrete numerical improvement over earlier bounds, as the novel method of proof, which is not based on bounding cr̄(Kn) for some small n."}],"publist_id":"4503","extern":1,"type":"conference","author":[{"full_name":"Uli Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner"}],"date_created":"2018-12-11T11:57:34Z","date_updated":"2021-01-12T06:57:24Z","year":"2003","_id":"2422","title":"On the rectilinear crossing number of complete graphs","status":"public","publication_status":"published","publisher":"SIAM","day":"01","month":"01","conference":{"name":"SODA: Symposium on Discrete Algorithms"},"date_published":"2003-01-01T00:00:00Z","citation":{"chicago":"Wagner, Uli. “On the Rectilinear Crossing Number of Complete Graphs,” 583–88. SIAM, 2003.","short":"U. Wagner, in:, SIAM, 2003, pp. 583–588.","mla":"Wagner, Uli. On the Rectilinear Crossing Number of Complete Graphs. SIAM, 2003, pp. 583–88.","apa":"Wagner, U. (2003). On the rectilinear crossing number of complete graphs (pp. 583–588). Presented at the SODA: Symposium on Discrete Algorithms, SIAM.","ieee":"U. Wagner, “On the rectilinear crossing number of complete graphs,” presented at the SODA: Symposium on Discrete Algorithms, 2003, pp. 583–588.","ista":"Wagner U. 2003. On the rectilinear crossing number of complete graphs. SODA: Symposium on Discrete Algorithms, 583–588.","ama":"Wagner U. On the rectilinear crossing number of complete graphs. In: SIAM; 2003:583-588."},"main_file_link":[{"url":"http://dl.acm.org/citation.cfm?id=644206","open_access":"0"}],"quality_controlled":0,"page":"583 - 588"}]