Distributed Approximation of Minimum Routing Cost Trees

We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes that minimizes the sum of distances between all pairs of nodes. In the considered model every node can transmit a different (but short) message to each of its neighbors in each synchronous round. We provide a randomized $(2+\epsilon)$-approximation with runtime $O(D+\frac{\log n}{\epsilon})$ for unweighted graphs. Here, $D$ is the diameter of $G$. This improves over both, the (expected) approximation factor $O(\log n)$ and the runtime $O(D\log^2 n)$ of the best previously known algorithm. Due to stating our results in a very general way, we also derive an (optimal) runtime of $O(D)$ when considering $O(\log n)$-approximations as done by the best previously known algorithm. In addition we derive a deterministic $2$-approximation

Gastrostomies Preserve but do not Increase Quality of Life for Patients and Caregivers

BACKGROUND & AIMS: Gastrostomies are widely used to provide long-term enteral nutrition to patients with neurological conditions that affect swallowing (such as following a cerebrovascular accident or for patients with motor neuron disease) or with oropharyngeal malignancies. The benefits derived from this intervention are uncertain for patients and caregivers. We conducted a prospective, multicenter cohort study to determine how gastrostomies affect health-related quality of life (HRQoL) in recipients and caregivers. METHODS: We performed a study of 100 patients who received gastrostomies (55% percutaneous endoscopic gastrostomy, 45% radiologically inserted) at 5 centers in the United Kingdom, 100 caregivers, and 200 population controls. We used the EuroQol-5D (EQ-5D, comprising a questionnaire, index, visual analogue scale) to assess HRQoL for patients and caregivers before the gastrostomy insertion and then 3 months afterward; findings were compared with those from controls. Ten patients and 10 caregivers were also interviewed after the procedure to explore quantitative findings. Findings from the EQ-5D and semi-structured interviews were integrated using a mixed methods matrix. RESULTS: Six patients died before the 3-month HRQoL reassessments. We observed no significant longitudinal changes in mean EQ-5D index scores for patients (0.70 before vs 0.710 after; P=.83) or caregivers (0.95 before vs 0.95 after; P=.32) following gastrostomy insertion. The semi-structured interviews revealed problems in managing gastrostomy tubes, social isolation, and psychological and emotional consequences that reduced HRQoL. CONCLUSIONS: We performed a mixed methods prospective study of the effects of gastrostomy feeding on HRQoL. HRQoL did not significantly improve after gastrostomy insertion for patients or caregivers. The lack of significant decrease in HRQoL after the procedure indicates that gastrostomies may help maintain HRQoL. Findings have relevance to those involved in gastrostomy insertion decisions and indicate the importance of carefully selecting patients for this intervention, despite the relative ease of insertion

Effects of Pore Walls and Randomness on Phase Transitions in Porous Media

We study spin models within the mean field approximation to elucidate the topology of the phase diagrams of systems modeling the liquid-vapor transition and the separation of He$^3$--He$^4$ mixtures in periodic porous media. These topologies are found to be identical to those of the corresponding random field and random anisotropy spin systems with a bimodal distribution of the randomness. Our results suggest that the presence of walls (periodic or otherwise) are a key factor determining the nature of the phase diagram in porous media.Comment: REVTeX, 11 eps figures, to appear in Phys. Rev.

Testing Broken U(1) Symmetry in a Two-Component Atomic Bose-Einstein Condensate

We present a scheme for determining if the quantum state of a small trapped Bose-Einstein condensate is a state with well defined number of atoms, a Fock state, or a state with a broken U(1) gauge symmetry, a coherent state. The proposal is based on the observation of Ramsey fringes. The population difference observed in a Ramsey fringe experiment will exhibit collapse and revivals due to the mean-field interactions. The collapse and revival times depend on the relative strength of the mean-field interactions for the two components and the initial quantum state of the condensate.Comment: 20 Pages RevTex, 3 Figure

Interference between the halves of a double-well trap containing a Bose-Einstein condensate

Interference between the halves of a double-well trap containing a Bose-Einstein condensate is studied. It is found that when the atoms in the two wells are initially in the coherent state, the intensity exhibits collapses and revivals, but it does not for the initial Fock states. Whether the initial states are in the coherent states or in a Fock states, the fidelity time has nothing to do with collision. We point out that interference and its fidelity can be adjusted experimentally by properly preparing the number and initial states of the system.Comment: 10 pages, 3 figures, accepted by Phy. rev.

Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes

We consider the problem of `discrete-time persistence', which deals with the zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no crossing) probability decays as exp(-\theta_D T) = [\rho(a)]^n for large n, where a = \exp[-(\Delta T)/2], and the discrete persistence exponent, \theta_D, is given by \theta_D = \ln(\rho)/2\ln(a). Using the `Independent Interval Approximation', we show how \theta_D varies with (\Delta T) for small (\Delta T) and conclude that experimental measurements of persistence for smooth processes, such as diffusion, are less sensitive to the effects of discrete sampling than measurements of a randomly accelerated particle or random walker. We extend the matrix method developed by us previously [Phys. Rev. E 64, 015151(R) (2001)] to determine \rho(a) for a two-dimensional random walk and the one-dimensional random acceleration problem. We also consider `alternating persistence', which corresponds to a < 0, and calculate \rho(a) for this case.Comment: 14 pages plus 8 figure

OC-040 A pre-endoscopy point of care test (iga/igg-deamidated gliadin peptide) as a case finding tool for coeliac diseasein secondary care

Coeliac disease (CD) is common yet underdiagnosed. 12.4% CD patients had a gastroscopy within 5 years without duodenal biopsies taken, and coeliac serology was performed in only 30% of patients with anaemia or suspected CD. A pre-endoscopy point of care test (POCT) could potentially fill this gap. We aimed to evaluate the diagnostic accuracy and acceptability of the POCT, Simtomax (IgA/IgG-deamidated gliadin peptide, Tillotts Pharma, Rheinfelden, Switzerland), in detecting CD