Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

The connection between the method of comparison equations (generalized WKB method) and the Ermakov-Pinney equation is established. A perturbative scheme of solution of the generalized Ermakov-Pinney equation is developed and is applied to the construction of perturbative series for second-order differential equations with and without turning points.Comment: The collective of the authors is enlarged and the calculations in Sec. 3 are correcte

An extension of Laplace's method

Asymptotic expansions are obtained for contour integrals of the form $$\int_a^b \exp \left( - zp(t) + z^{\nu /\mu } r(t) \right)q(t)dt,$$ in which $z$ is a large real or complex parameter, $p(t)$, $q(t)$ and $r(t)$ are analytic functions of $t$, and the positive constants $\mu$ and $\nu$ are related to the local behaviour of the functions $p(t)$ and $r(t)$ near the endpoint $a$. Our main theorem includes as special cases several important asymptotic methods for integrals such as those of Laplace, Watson, Erd\'elyi and Olver. Asymptotic expansions similar to ours were derived earlier by Dingle using formal, non-rigorous methods. The results of the paper also serve to place Dingle's investigations on a rigorous mathematical foundation. The new results have potential applications in the asymptotic theory of special functions in transition regions, and we illustrate this by two examples.Comment: 19 pages, 2 figures, revised version, accepted for publication in Constructive Approximatio

The Coulomb phase shift revisited

We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling approximation, and show that they are important at small values of the angular momentum $l$ and other regimes. We employ the uniform approximation. The use of our expressions in low energy scattering of charged particles is discussed and some comparisons are made with other approximation methods.Comment: 13 pages, 5 figures, 1 tabl

What two models may teach us about duality violations in QCD

Though the operator product expansion is applicable in the calculation of current correlation functions in the Euclidean region, when approaching the Minkowskian domain, violations of quark-hadron duality are expected to occur, due to the presence of bound-state or resonance poles. In QCD finite-energy sum rules, contour integrals in the complex energy plane down to the Minkowskian axis have to be performed, and thus the question arises what the impact of duality violations may be. The structure and possible relevance of duality violations is investigated on the basis of two models: the Coulomb system and a model for light-quark correlators which has already been studied previously. As might yet be naively expected, duality violations are in some sense "maximal" for zero-width bound states and they become weaker for broader resonances whose poles lie further away from the physical axis. Furthermore, to a certain extent, they can be suppressed by choosing appropriate weight functions in the finite-energy sum rules. A simplified Ansatz for including effects of duality violations in phenomenological QCD sum rule analyses is discussed as well.Comment: 17 pages, 6 figures; version to appear in JHE

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of supersymmetric models added at the end of section 8.1, reference adde

Investigation of the Enteric Pathogenic Potential of Oral Campylobacter concisus Strains Isolated from Patients with Inflammatory Bowel Disease

BACKGROUND: Campylobacter concisus, a bacterium colonizing the human oral cavity, has been shown to be associated with inflammatory bowel disease (IBD). This study investigated if patients with IBD are colonized with specific oral C. concisus strains that have potential to cause enteric diseases. METHODOLOGY: Seventy oral and enteric C. concisus isolates obtained from eight patients with IBD and six controls were examined for housekeeping genes by multilocus sequence typing (MLST), Caco2 cell invasion by gentamicin-protection-assay, protein analysis by mass spectrometry and SDS-PAGE, and morphology by scanning electron microscopy. The whole genome sequenced C. concisus strain 13826 which was isolated from an individual with bloody diarrhea was included in MLST analysis. PRINCIPAL FINDINGS: MLST analysis showed that 87.5% of individuals whose C. concisus belonged to Cluster I had inflammatory enteric diseases (six IBD and one with bloody diarrhea), which was significantly higher than that in the remaining individuals (28.6%) (P<0.05). Enteric invasive C. concisus (EICC) oral strain was detected in 50% of patients with IBD and none of the controls. All EICC strains were in Cluster 1. The C. concisus strain colonizing intestinal tissues of patient No. 1 was closely related to the oral C. concisus strain from patient No. 6 and had gene recombination with the patient's own oral C. concisus. The oral and intestinal C. concisus strains of patient No. 3 were the same strain. Some individuals were colonized with multiple oral C. concisus strains that have undergone natural recombination. CONCLUSIONS: This study provides the first evidence that patients with IBD are colonized with specific oral C. concisus strains, with some being EICC strains. C. concisus colonizing intestinal tissues of patients with IBD at least in some instances results from an endogenous colonization of the patient's oral C. concisus and that C. concisus strains undergo natural recombination

Optimal Swimming Speed in Head Currents and Effects on Distance Movement of Winter-Migrating Fish

Migration is a commonly described phenomenon in nature that is often caused by spatial and temporal differences in habitat quality. However, as migration requires energy, the timing of migration may depend not only on differences in habitat quality, but also on temporal variation in migration costs. Such variation can, for instance, arise from changes in wind or current velocity for migrating birds and fish, respectively. Whereas behavioural responses of birds to such changing environmental conditions have been relatively well described, this is not the case for fish, although fish migrations are both ecologically and economically important. We here use passive and active telemetry to study how winter migrating roach regulate swimming speed and distance travelled per day in response to variations in head current velocity. Furthermore, we provide theoretical predictions on optimal swimming speeds in head currents and relate these to our empirical results. We show that fish migrate farther on days with low current velocity, but travel at a greater ground speed on days with high current velocity. The latter result agrees with our predictions on optimal swimming speed in head currents, but disagrees with previously reported predictions suggesting that fish ground speed should not change with head current velocity. We suggest that this difference is due to different assumptions on fish swimming energetics. We conclude that fish are able to adjust both swimming speed and timing of swimming activity during migration to changes in head current velocity in order to minimize energy use

Characterisation of Clostridium difficile Hospital Ward–Based Transmission Using Extensive Epidemiological Data and Molecular Typing

A population-based study in Oxfordshire (UK) hospitals by Sarah Walker and colleagues finds that in an endemic setting with good infection control, ward-based contact cannot account for most new cases of Clostridium difficile infection

Home on the Range: Factors Explaining Partial Migration of African Buffalo in a Tropical Environment

Partial migration (when only some individuals in a population undertake seasonal migrations) is common in many species and geographical contexts. Despite the development of modern statistical methods for analyzing partial migration, there have been no studies on what influences partial migration in tropical environments. We present research on factors affecting partial migration in African buffalo (Syncerus caffer) in northeastern Namibia. Our dataset is derived from 32 satellite tracking collars, spans 4 years and contains over 35,000 locations. We used remotely sensed data to quantify various factors that buffalo experience in the dry season when making decisions on whether and how far to migrate, including potential man-made and natural barriers, as well as spatial and temporal heterogeneity in environmental conditions. Using an information-theoretic, non-linear regression approach, our analyses showed that buffalo in this area can be divided into 4 migratory classes: migrants, non-migrants, dispersers, and a new class that we call “expanders”. Multimodel inference from least-squares regressions of wet season movements showed that environmental conditions (rainfall, fires, woodland cover, vegetation biomass), distance to the nearest barrier (river, fence, cultivated area) and social factors (age, size of herd at capture) were all important in explaining variation in migratory behaviour. The relative contributions of these variables to partial migration have not previously been assessed for ungulates in the tropics. Understanding the factors driving migratory decisions of wildlife will lead to better-informed conservation and land-use decisions in this area