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

Polarized entangled Bose-Einstein condensation

We consider a mixture of two distinct species of atoms of pseudospin-1/2 with both intraspecies and Interspecies spin-exchange interactions, and find all the ground stats in a general case of the parameters in the effective Hamiltonian. In general, corresponding to the two species and two pseudo-spin states, there are four orbital wave functions into which the atoms condense. We find that in certain parameter regimes, the ground state is the so-called polarized entangled Bose-Einstein condensation, i.e. in addition to condensation of interspecies singlet pairs, there are unpaired atoms with spins polarized in the same direction. The interspecies entanglement and polarization significantly affect the generalized Gross-Pitaevskii equations governing the four orbital wave functions into which the atoms condense, as an interesting interplay between spin and orbital degrees of freedom.Comment: 14 pages, received by PRA on 27 October 201

X-ray Studies of Two Neutron Stars in 47 Tucanae: Toward Constraints on the Equation of State

We report spectral and variability analysis of two quiescent low mass X-ray binaries (X5 and X7, previously detected with the ROSAT HRI) in a Chandra ACIS-I observation of the globular cluster 47 Tuc. X5 demonstrates sharp eclipses with an 8.666+-0.01 hr period, as well as dips showing an increased N_H column. The thermal spectra of X5 and X7 are well-modeled by unmagnetized hydrogen atmospheres of hot neutron stars. No hard power law component is required. A possible edge or absorption feature is identified near 0.64 keV, perhaps an OV edge from a hot wind. Spectral fits imply that X7 is significantly more massive than the canonical 1.4 \Msun neutron star mass, with M>1.8 \Msun for a radius range of 9-14 km, while X5's spectrum is consistent with a neutron star of mass 1.4 \Msun for the same radius range. Alternatively, if much of the X-ray luminosity is due to continuing accretion onto the neutron star surface, the feature may be the 0.87 keV rest-frame absorption complex (O VIII & other metal lines) intrinsic to the neutron star atmosphere, and a mass of 1.4 \Msun for X7 may be allowed.Comment: 16 pages, 7 figures, accepted by Ap

Children with neonatal Hypoxic Ischemic Encephalopathy (HIE) treated with therapeutic hypothermia are not as school ready as their peers

Aim: We aimed to determine whether children with neonatal hypoxic-ischaemic encephalopathy (HIE) treated with therapeutic hypothermia (TH) differ from their peers on measures of fine motor skills, executive function, language and general cognitive abilities; factors that are important for school readiness. Methods: We compared school readiness in 31children with HIE treated with TH (without Cerebral Palsy; mean age 5 years 4 months) with 20 typically developing children without HIE (mean age 5 years 6 months). Results: Children with HIE scored significantly lower than typically developing children on fine motor skills, executive functions, memory and language. Conclusion: While general cognitive abilities and attainment were in the normal range, our findings suggest those scores mask specific underlying difficulties identified by more focussed assessments. Children with HIE treated with TH may not be as “school ready” as their typically developing classmates and may benefit from long-term follow-up until starting school

Node-balancing by edge-increments

Suppose you are given a graph $G=(V,E)$ with a weight assignment $w:V\rightarrow\mathbb{Z}$ and that your objective is to modify $w$ using legal steps such that all vertices will have the same weight, where in each legal step you are allowed to choose an edge and increment the weights of its end points by $1$. In this paper we study several variants of this problem for graphs and hypergraphs. On the combinatorial side we show connections with fundamental results from matching theory such as Hall's Theorem and Tutte's Theorem. On the algorithmic side we study the computational complexity of associated decision problems. Our main results are a characterization of the graphs for which any initial assignment can be balanced by edge-increments and a strongly polynomial-time algorithm that computes a balancing sequence of increments if one exists.Comment: 10 page

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