---
_id: '2358'
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.
author:
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
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
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
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.
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.
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.
short: É. Lieb, R. Seiringer, J. Yngvason, Physical Review Letters 91 (2003) 1504011–1504014.
date_created: 2018-12-11T11:57:12Z
date_published: 2003-10-10T00:00:00Z
date_updated: 2021-01-12T06:57:00Z
day: '10'
doi: 10.1103/PhysRevLett.91.150401
extern: 1
intvolume: ' 91'
issue: '15'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/cond-mat/0304071
month: '10'
oa: 1
page: 1504011 - 1504014
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '4571'
quality_controlled: 0
status: public
title: One-dimensional Bosons in three-dimensional traps
type: journal_article
volume: 91
year: '2003'
...
---
_id: '2414'
author:
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Wagner U. On k-Sets and Their Applications. 2003. doi:10.3929/ethz-a-004708408
apa: Wagner, U. (2003). On k-Sets and Their Applications. ETH Zurich. https://doi.org/10.3929/ethz-a-004708408
chicago: Wagner, Uli. “On K-Sets and Their Applications.” ETH Zurich, 2003. https://doi.org/10.3929/ethz-a-004708408.
ieee: U. Wagner, “On k-Sets and Their Applications,” ETH Zurich, 2003.
ista: Wagner U. 2003. On k-Sets and Their Applications. ETH Zurich.
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.
date_created: 2018-12-11T11:57:31Z
date_published: 2003-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:20Z
day: '01'
doi: 10.3929/ethz-a-004708408
extern: 1
month: '01'
publication_status: published
publisher: ETH Zurich
publist_id: '4511'
quality_controlled: 0
status: public
title: On k-Sets and Their Applications
type: dissertation
year: '2003'
...
---
_id: '2424'
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.
author:
- first_name: Joachim
full_name: Giesen, Joachim
last_name: Giesen
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
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'
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.
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.'
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.
short: J. Giesen, U. Wagner, in:, ACM, 2003, pp. 329–337.
conference:
name: 'SoCG: Symposium on Computational Geometry'
date_created: 2018-12-11T11:57:35Z
date_published: 2003-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:24Z
day: '01'
doi: 10.1145/777792.777841
extern: 1
month: '06'
page: 329 - 337
publication_status: published
publisher: ACM
publist_id: '4501'
quality_controlled: 0
status: public
title: Shape dimension and intrinsic metric from samples of manifolds with high co-dimension
type: conference
year: '2003'
...
---
_id: '2423'
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.
author:
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Matoušek J, Wagner U. New constructions of weak epsilon-nets. In: ACM; 2003:129-135.
doi:10.1145/777792.777813'
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'
chicago: Matoušek, Jiří, and Uli Wagner. “New Constructions of Weak Epsilon-Nets,”
129–35. ACM, 2003. 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.'
mla: Matoušek, Jiří, and Uli Wagner. New Constructions of Weak Epsilon-Nets.
ACM, 2003, pp. 129–35, doi:10.1145/777792.777813.
short: J. Matoušek, U. Wagner, in:, ACM, 2003, pp. 129–135.
conference:
name: 'SoCG: Symposium on Computational Geometry'
date_created: 2018-12-11T11:57:34Z
date_published: 2003-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:24Z
day: '01'
doi: 10.1145/777792.777813
extern: 1
month: '06'
page: 129 - 135
publication_status: published
publisher: ACM
publist_id: '4502'
quality_controlled: 0
status: public
title: New constructions of weak epsilon-nets
type: conference
year: '2003'
...
---
_id: '2422'
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.
author:
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Wagner U. On the rectilinear crossing number of complete graphs. In: SIAM;
2003:583-588.'
apa: 'Wagner, U. (2003). On the rectilinear crossing number of complete graphs (pp.
583–588). Presented at the SODA: Symposium on Discrete Algorithms, SIAM.'
chicago: Wagner, Uli. “On the Rectilinear Crossing Number of Complete Graphs,” 583–88.
SIAM, 2003.
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.'
mla: Wagner, Uli. On the Rectilinear Crossing Number of Complete Graphs.
SIAM, 2003, pp. 583–88.
short: U. Wagner, in:, SIAM, 2003, pp. 583–588.
conference:
name: 'SODA: Symposium on Discrete Algorithms'
date_created: 2018-12-11T11:57:34Z
date_published: 2003-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:24Z
day: '01'
extern: 1
main_file_link:
- open_access: '0'
url: http://dl.acm.org/citation.cfm?id=644206
month: '01'
page: 583 - 588
publication_status: published
publisher: SIAM
publist_id: '4503'
quality_controlled: 0
status: public
title: On the rectilinear crossing number of complete graphs
type: conference
year: '2003'
...