The (weighted) metric dimension of graphs : hard and easy cases

Given an input undirected graph G=(V,E), we say that a vertex l separates u from v (where u,v ¿ V) if the distance between u and l differs from the distance from v to l. A set of vertices L¿V is a feasible solution if for every pair of vertices, u,v ¿ V (u¿v), there is a vertex l ¿ L that separates u from v. Such a feasible solution is called a landmark set, and the metric dimension of a graph is the minimum cardinality of a landmark set. Here, we extend this well-studied problem to the case where each vertex v has a non-negative cost, and the goal is to find a feasible solution with a minimum total cost. This weighted version is NP-hard since the unweighted variant is known to be NP-hard. We show polynomial time algorithms for the cases where G is a path, a tree, a cycle, a cograph, a k-edge-augmented tree (that is, a tree with additional k edges) for a constant value of k, and a (not necessarily complete) wheel. The results for paths, trees, cycles, and complete wheels extend known polynomial time algorithms for the unweighted version, whereas the other results are the first known polynomial time algorithms for these classes of graphs even for the unweighted version. Next, we extend the set of graph classes for which computing the unweighted metric dimension of a graph is known to be NP-hard. We show that for split graphs, bipartite graphs, co-bipartite graphs, and line graphs of bipartite graphs, the problem of computing the unweighted metric dimension of the graph is NP-hard

Evaluation of a locally produced rapid urease test for the diagnosis of Helicobacter pylori infection

Background. The rapid urease test (RUT) is used at Groote Schuur Hospital for diagnosing Helicobacter pylori infection. This is an in-house method, which has not been validated. Objective. To validate our practice of reading the RUT immediately after endoscopy (RUT0), by comparing this with a reading at 24 hours (RUT24) and with histological analysis. Design. Ninety consecutive patients undergoing upper endoscopy over a 6-week period from October 2005 to November 2005, and in whom rapid urease testing was indicated, were included in the study. Patients with recent exposure (within 2 weeks of endoscopy) to proton pump inhibitors (PPIs), histamine receptor antagonists (H2RAs) and antibiotics (confounders) were noted and included in the cohort. Two antral and two body biopsies were taken for histological examination and a third antral biopsy was placed in the RUT bottle. Both haematoxylin and eosin and modified Giemsa staining methods were used to identify H. pylori. The RUT was read immediately (within 5 minutes of upper endoscopy) (RUT0), as per our current practice, and each specimen was re-read at 24 hours (RUT24). Sensitivity, specificity, positive and negative predictive values and the impact of confounders were calculated. Results. Of the 90 patients undergoing rapid urease testing, 39% were male and 61% were female, with a mean age of 55 years (range 22 - 79 years). Histological examination revealed H. pylori in 67.8% (N=61) of the biopsy specimens. In the 65 patients without confounders, the sensitivity and specificity of the RUT0 were 65.9% and 100% respectively, and 90.9% and 100% for RUT24. After including the 25 patients with confounders, the sensitivity and specificity were 68.8% and 100% for RUT0, and 90.1% and 100% for RUT24 respectively. Thirteen RUT0 specimens (30.9%) that were initially negative became positive at the RUT24 reading. There were 6 (9.8%) RUT0- and RUT24-negative but histology-positive specimens. Four of these 6 false-negative RUT24 results could be accounted for by a low H. pylori density on histological analysis (2 patients were taking PPIs). Confounders did not alter the sensitivity and specificity outcomes or impact on the number of false-negative RUTs. Conclusions. Our locally prepared RUT is a specific test for the detection of H. pylori infection. The sensitivity is greatly enhanced by reading the test at 24 hours. The use of PPIs, H2RAs and antibiotics preceding endoscopy did not impact significantly on the results

Evaluation of a locally produced rapid urease test for the diagnosis of Helicobacter pylori infection

Background. The rapid urease test (RUT) is used at Groote Schuur Hospital for diagnosing Helicobacter pylori infection. This is an in-house method, which has not been validated. Objective. To validate our practice of reading the RUT immediately after endoscopy (RUT0), by comparing this with a reading at 24 hours (RUT24) and with histological analysis. Design. Ninety consecutive patients undergoing upper endoscopy over a 6-week period from October 2005 to November 2005, and in whom rapid urease testing was indicated, were included in the study. Patients with recent exposure (within 2 weeks of endoscopy) to proton pump inhibitors (PPIs), histamine receptor antagonists (H2RAs) and antibiotics (confounders) were noted and included in the cohort. Two antral and two body biopsies were taken for histological examination and a third antral biopsy was placed in the RUT bottle. Both haematoxylin and eosin and modified Giemsa staining methods were used to identify H. pylori. The RUT was read immediately (within 5 minutes of upper endoscopy) (RUT0), as per our current practice, and each specimen was re-read at 24 hours (RUT24). Sensitivity, specificity, positive and negative predictive values and the impact of confounders were calculated. Results. Of the 90 patients undergoing rapid urease testing, 39% were male and 61% were female, with a mean age of 55 years (range 22 - 79 years). Histological examination revealed H. pylori in 67.8% (N=61) of the biopsy specimens. In the 65 patients without confounders, the sensitivity and specificity of the RUT0 were 65.9% and 100% respectively, and 90.9% and 100% for RUT24. After including the 25 patients with confounders, the sensitivity and specificity were 68.8% and 100% for RUT0, and 90.1% and 100% for RUT24 respectively. Thirteen RUT0 specimens (30.9%) that were initially negative became positive at the RUT24 reading. There were 6 (9.8%) RUT0- and RUT24-negative but histology-positive specimens. Four of these 6 false-negative RUT24 results could be accounted for by a low H. pylori density on histological analysis (2 patients were taking PPIs). Confounders did not alter the sensitivity and specificity outcomes or impact on the number of false-negative RUTs. Conclusions. Our locally prepared RUT is a specific test for the detection of H. pylori infection. The sensitivity is greatly enhanced by reading the test at 24 hours. The use of PPIs, H2RAs and antibiotics preceding endoscopy did not impact significantly on the results. South African Medical Journal Vol. 97 (12) 2007: pp. 1281-128

R-Modes in Superfluid Neutron Stars

The analogs of r-modes in superfluid neutron stars are studied here. These modes, which are governed primarily by the Coriolis force, are identical to their ordinary-fluid counterparts at the lowest order in the small angular-velocity expansion used here. The equations that determine the next order terms are derived and solved numerically for fairly realistic superfluid neutron-star models. The damping of these modes by superfluid ``mutual friction'' (which vanishes at the lowest order in this expansion) is found to have a characteristic time-scale of about 10^4 s for the m=2 r-mode in a ``typical'' superfluid neutron-star model. This time-scale is far too long to allow mutual friction to suppress the recently discovered gravitational radiation driven instability in the r-modes. However, the strength of the mutual friction damping depends very sensitively on the details of the neutron-star core superfluid. A small fraction of the presently acceptable range of superfluid models have characteristic mutual friction damping times that are short enough (i.e. shorter than about 5 s) to suppress the gravitational radiation driven instability completely.Comment: 15 pages, 8 figure

The r-modes in accreting neutron stars with magneto-viscous boundary layers

We explore the dynamics of the r-modes in accreting neutron stars in two ways. First, we explore how dissipation in the magneto-viscous boundary layer (MVBL) at the crust-core interface governs the damping of r-mode perturbations in the fluid interior. Two models are considered: one assuming an ordinary-fluid interior, the other taking the core to consist of superfluid neutrons, type II superconducting protons, and normal electrons. We show, within our approximations, that no solution to the magnetohydrodynamic equations exists in the superfluid model when both the neutron and proton vortices are pinned. However, if just one species of vortex is pinned, we can find solutions. When the neutron vortices are pinned and the proton vortices are unpinned there is much more dissipation than in the ordinary-fluid model, unless the pinning is weak. When the proton vortices are pinned and the neutron vortices are unpinned the dissipation is comparable or slightly less than that for the ordinary-fluid model, even when the pinning is strong. We also find in the superfluid model that relatively weak radial magnetic fields ~ 10^9 G (10^8 K / T)^2 greatly affect the MVBL, though the effects of mutual friction tend to counteract the magnetic effects. Second, we evolve our two models in time, accounting for accretion, and explore how the magnetic field strength, the r-mode saturation amplitude, and the accretion rate affect the cyclic evolution of these stars. If the r-modes control the spin cycles of accreting neutron stars we find that magnetic fields can affect the clustering of the spin frequencies of low mass x-ray binaries (LMXBs) and the fraction of these that are currently emitting gravitational waves.Comment: 19 pages, 8 eps figures, RevTeX; corrected minor typos and added a referenc

Lyapunov exponents, bifurcation currents and laminations in bifurcation loci

Bifurcation loci in the moduli space of degree $d$ rational maps are shaped by the hypersurfaces defined by the existence of a cycle of period $n$ and multiplier 0 or $e^{i\theta}$. Using potential-theoretic arguments, we establish two equidistribution properties for these hypersurfaces with respect to the bifurcation current. To this purpose we first establish approximation formulas for the Lyapunov function. In degree $d=2$, this allows us to build holomorphic motions and show that the bifurcation locus has a lamination structure in the regions where an attracting basin of fixed period exists

Quantum gauge models without classical Higgs mechanism

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRS formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is explained without recourse to a Higgs(-Englert-Brout-Guralnik-Hagen-Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.Comment: 20 pages in two-column EPJC format, shortened version accepted for publication. For more details, consult version

Cost-effectiveness analysis of 3-D computerized tomography colonography versus optical colonoscopy for imaging symptomatic gastroenterology patients.

BACKGROUND: When symptomatic gastroenterology patients have an indication for colonic imaging, clinicians have a choice between optical colonoscopy (OC) and computerized tomography colonography with three-dimensional reconstruction (3-D CTC). 3-D CTC provides a minimally invasive and rapid evaluation of the entire colon, and it can be an efficient modality for diagnosing symptoms. It allows for a more targeted use of OC, which is associated with a higher risk of major adverse events and higher procedural costs. A case can be made for 3-D CTC as a primary test for colonic imaging followed if necessary by targeted therapeutic OC; however, the relative long-term costs and benefits of introducing 3-D CTC as a first-line investigation are unknown. AIM: The aim of this study was to assess the cost effectiveness of 3-D CTC versus OC for colonic imaging of symptomatic gastroenterology patients in the UK NHS. METHODS: We used a Markov model to follow a cohort of 100,000 symptomatic gastroenterology patients, aged 50 years or older, and estimate the expected lifetime outcomes, life years (LYs) and quality-adjusted life years (QALYs), and costs (£, 2010-2011) associated with 3-D CTC and OC. Sensitivity analyses were performed to assess the robustness of the base-case cost-effectiveness results to variation in input parameters and methodological assumptions. RESULTS: 3D-CTC provided a similar number of LYs (7.737 vs 7.739) and QALYs (7.013 vs 7.018) per individual compared with OC, and it was associated with substantially lower mean costs per patient (£467 vs £583), leading to a positive incremental net benefit. After accounting for the overall uncertainty, the probability of 3-D CTC being cost effective was around 60 %, at typical willingness-to-pay values of £20,000-£30,000 per QALY gained. CONCLUSION: 3-D CTC is a cost-saving and cost-effective option for colonic imaging of symptomatic gastroenterology patients compared with OC