Hypergraphic LP Relaxations for Steiner Trees

We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation to other linear relaxations. Our results are the following. Structural results: We extend the technique of uncrossing, usually applied to families of sets, to families of partitions. As a consequence we show that any basic feasible solution to the partition LP formulation has sparse support. Although the number of variables could be exponential, the number of positive variables is at most the number of terminals. Relations with other relaxations: We show the equivalence of the partition LP relaxation with other known hypergraphic relaxations. We also show that these hypergraphic relaxations are equivalent to the well studied bidirected cut relaxation, if the instance is quasibipartite. Integrality gap upper bounds: We show an upper bound of sqrt(3) ~ 1.729 on the integrality gap of these hypergraph relaxations in general graphs. In the special case of uniformly quasibipartite instances, we show an improved upper bound of 73/60 ~ 1.216. By our equivalence theorem, the latter result implies an improved upper bound for the bidirected cut relaxation as well.Comment: Revised full version; a shorter version will appear at IPCO 2010

At what stage in the drinking process does drinking water affect attention and memory? Effects of mouth rinsing and mouth drying in adults

Drinking water is important for health and there is agreement that drinking water facilitates certain cognitive processes. However, the mechanism underlying the effect of drinking water on cognition is unknown. While attention performance is improved by even a very small drink, memory performance seems to require larger drinks for performance enhancement. This suggests that attention could be affected earlier in the drinking process than memory. We aimed to elucidate further the mechanism involved, by investigating the stage during the drinking process influencing performance on cognitive tasks. To this end, we compared mouth rinsing and mouth drying. Mouth rinsing was expected to result in improved attention performance and would suggest that the mechanism responsible is located in the mouth and occurs early in the drinking process, before swallowing. Eighty-seven adults participated in either a treatment (mouth rinsing or mouth drying) or control (no intervention) condition. They were assessed at baseline and 20 minutes later after intervention on measures of visual attention, short-term memory, subjective thirst and mood. Our results showed that mouth rinsing improved visual attention, but not short-term memory, mood or subjective thirst. Mouth drying did not affect performance. Our results support the hypothesis that different mechanisms underlie the effect of drinking water on different cognitive processes. They suggest that merely sipping water, as opposed to having a large drink, can improve attention

Cylindrical gravitational waves in expanding universes: Models for waves from compact sources

New boundary conditions are imposed on the familiar cylindrical gravitational wave vacuum spacetimes. The new spacetime family represents cylindrical waves in a flat expanding (Kasner) universe. Space sections are flat and nonconical where the waves have not reached and wave amplitudes fall off more rapidly than they do in Einstein-Rosen solutions, permitting a more regular null inifinity.Comment: Minor corrections to references. A note added in proo

Fault-tolerant quantum computation with high threshold in two dimensions

We present a scheme of fault-tolerant quantum computation for a local architecture in two spatial dimensions. The error threshold is 0.75% for each source in an error model with preparation, gate, storage and measurement errors.Comment: 4 pages, 4 figures; v2: A single 2D layer of qubits (simple square lattice) with nearest-neighbor translation-invariant Ising interaction suffices. Slightly improved threshol

Ground state of two electrons on concentric spheres

We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79}, 062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on concentric spheres with different radii. The strengths and weaknesses of several electronic structure models are analyzed, ranging from the mean-field approximation (restricted and unrestricted Hartree-Fock solutions) to configuration interaction expansion, leading to near-exact wave functions and energies. The M{\o}ller-Plesset energy corrections (up to third-order) and the asymptotic expansion for the large-spheres regime are also considered. We also study the position intracules derived from approximate and exact wave functions. We find evidence for the existence of a long-range Coulomb hole in the large-spheres regime, and infer that unrestricted Hartree-Fock theory over-localizes the electrons.Comment: 10 pages, 10 figure

An introduction to the EULAR–OMERACT rheumatoid arthritis MRI reference image atlas

This article gives a short overview of the development and characteristics of the OMERACT rheumatoid arthritis MRI scoring system (RAMRIS), followed by an introduction to the use of the EULAR–OMERACT rheumatoid arthritis MRI reference image atlas. With this atlas, MRIs of wrist and metacarpophalangeal joints of patients with rheumatoid arthritis can be scored for synovitis, bone oedema, and bone erosion, guided by standard reference images

Semi-relativistic description of quasielastic neutrino reactions and superscaling in a continuum shell model

The so-called semi-relativistic expansion of the weak charged current in powers of the initial nucleon momentum is performed to describe charge-changing, quasielastic neutrino reactions $(\nu_\mu,\mu^-)$ at intermediate energies. The quality of the expansion is tested by comparing with the relativistic Fermi gas model using several choices of kinematics of interest for ongoing neutrino oscillation experiments. The new current is then implemented in a continuum shell model together with relativistic kinematics to investigate the scaling properties of $(e,e')$ and $(\nu_\mu,\mu^-)$ cross sections.Comment: 33 pages, 10 figures, to appear in PR