Absence of reflection as a function of the coupling constant

We consider solutions of the one-dimensional equation $-u'' +(Q+ \lambda V) u = 0$ where $Q: \mathbb{R} \to \mathbb{R}$ is locally integrable, $V : \mathbb{R} \to \mathbb{R}$ is integrable with supp$(V) \subset [0,1]$, and $\lambda \in \mathbb{R}$ is a coupling constant. Given a family of solutions $\{u_{\lambda} \}_{\lambda \in \mathbb{R}}$ which satisfy $u_{\lambda}(x) = u_0(x)$ for all $x<0$, we prove that the zeros of $b(\lambda) := W[u_0, u_{\lambda}]$, the Wronskian of $u_0$ and $u_{\lambda}$, form a discrete set unless $V \equiv 0$. Setting $Q(x) := -E$, one sees that a particular consequence of this result may be stated as: if the fixed energy scattering experiment $-u'' + \lambda V u = Eu$ gives rise to a reflection coefficient which vanishes on a set of couplings with an accumulation point, then $V \equiv 0$.Comment: To appear in Journal of Mathematical Physic

ON THE DYNAMICS OF COMMERCIAL FISHING AND PARAMETER IDENTIFICATION

This paper has two main objectives. The first is to develop a dynamic model of commercial fisheries different from most existing models that assume optimizing behavior. The industry is assumed to have a well-defined index of performance. Based upon this index, the decision to invest or not is made. We do not, however, assume that the industry or firm is efficient or optimal in its operations. The second is that a new approach of fitting model dynamics to time series data is employed to simultaneously estimate the poorly known initial conditions and parameters of nonlinear fisheries dynamics. The approach is a data assimilation technique known as the variational adjoint method. Estimation of the poorly known initial conditions is one of the attractive features of the variational adjoint method.Resource /Energy Economics and Policy,

Continuous harvesting costs in sole-owner fisheries with increasing marginal returns

We develop a bioeconomic model to analyze a sole-owner fishery with fixed costs as well as a continuous cost function for the generalized Cobb-Douglas production function with increasing marginal returns to effort level. On the basis of data from the North Sea herring fishery, we analyze the consequences of the combined effects of increasing marginal returns and fixed costs. We find that regardless of the magnitude of the fixed costs, cyclical policies can be optimal instead of the optimal steady state equilibrium advocated in much of the existing literature. We also show that the risk of stock collapse increases significantly with increasing fixed costs as this implies higher period cycles which is a quite counterintuitive result as higher costs usually are considered to have a conservative effect on resources.Bioeconomic modelling; Stock collapse; Fixed costs; Pulse fishing; Cyclical dynamics; Increasing marginal returns

The Order of Phase Transitions in Barrier Crossing

A spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied. Depending on the potential, the transition can be first or second-order, but there exists no systematic theory of the relation between the order of the transition and the shape of the potential barrier. In this paper, we address that question in detail for a general class of systems whose order parameter is describable by a classical field that can vary both in space and time, and whose zero-noise dynamics are governed by a smooth polynomial potential. We show that a quartic potential barrier can only have second-order transitions, confirming an earlier conjecture [1]. We then derive, through a combination of analytical and numerical arguments, both necessary conditions and sufficient conditions to have a first-order vs. a second-order transition in noise-induced activation behavior, for a large class of systems with smooth polynomial potentials of arbitrary order. We find in particular that the order of the transition is especially sensitive to the potential behavior near the top of the barrier.Comment: 8 pages, 6 figures with extended introduction and discussion; version accepted for publication by Phys. Rev.

Cost-effectiveness of bevacizumab for diabetic macular oedema

This is the author accepted manuscript. The final version is available from Mark Allen Healthcare via the DOI in this record A Markov model was developed to predict the outcomes and cost-effectiveness of bevacizumab compared to macular laser therapy for diabetes patients with clinically significant macular oedema (CSMO). This study used outcome data from a randomised controlled trial, utility data and health states from a ranibizumab health technology assessment, and costs from the UK national tariff. A total of 37.73% of patients treated with bevacizumab in the model had a visual acuity of at least 76 Early Treatment Diabetic Retinopathy Study Research Group (ETDRS) letters after four years, compared with 4.09% of laser therapy patients. Only 0.11% of bevacizumab patients were blind after four years compared with 6.45% of laser therapy patients. However, with an incremental cost-effectiveness ratio of £51,182, we predict that bevacizumab would not be cost-effective compared to laser therapy because of the influence of the NHS national tariff costs for monitoring patients and administering bevacizumab, and the inability of the EQ-5D measure to capture the impact of sensory deprivation on quality of life sufficiently. This study recommends significant caution when interpreting the results of cost-effectiveness analyses of interventions that involve vision-related interventions.National Institute for Health Research (NIHR

Modifiable predictors of ventricular ectopy in the community

Background Premature ventricular contractions (PVCs) predict heart failure and death. Data regarding modifiable risk factors for PVCs are scarce. Methods and Results We studied 1424 Cardiovascular Health Study participants randomly assigned to 24-hour Holter monitoring. Demographics, comorbidities, habits, and echocardiographic measurements were examined as predictors of PVC frequency and, among 845 participants, change in PVC frequency 5 years later. Participants exhibited a median of 0.6 (interquartile range, 0.1-7.1) PVCs per hour. Of the more directly modifiable characteristics and after multivariable adjustment, every SD increase in systolic blood pressure was associated with 9% more PVCs (95% confidence interval [CI], 2%-17%; P=0.01), regularly performing no or low-intensity exercise compared with more physical activity was associated with ≈15% more PVCs (95% CI, 3-25%; P=0.02), and those with a history of smoking exhibited an average of 18% more PVCs (95% CI, 3-36%; P=0.02) than did never smokers. After 5 years, PVC frequency increased from a median of 0.5 (IQR, 0.1-4.7) to 1.2 (IQR, 0.1-13.8) per hour ( P&lt;0.0001). Directly modifiable predictors of 5-year increase in PVCs, described as the odds per each quintile increase in PVCs, included increased diastolic blood pressure (odds ratio per SD increase, 1.16; 95% CI, 1.02-1.31; P=0.02) and a history of smoking (OR, 1.31; 95% CI, 1.02-1.68; P=0.04). Conclusions Enhancing physical activity, smoking cessation, and aggressive control of blood pressure may represent fruitful strategies to mitigate PVC frequency and PVC-associated adverse outcomes

New Limits on Local Lorentz Invariance in Mercury and Cesium

We report new bounds on Local Lorentz Invariance (LLI) violation in Cs and Hg. The limits are obtained through the observation of the the spin- precession frequencies of 199Hg and 133Cs atoms in their ground states as a function of the orientation of an applied magnetic field with respect to the fixed stars. We measure the amplitudes of the dipole couplings to a preferred direction in the equatorial plane to be 19(11) nHz for Hg and 9(5) microHz for Cs. The upper bounds established here improve upon previous bounds by about a factor of four. The improvement is primarily due to mounting the apparatus on a rotating table. New bounds are established on several terms in the standard model extension including the first bounds on the spin-couplings of the neutron and proton to the z direction, <7e-30 GeV and <7e-29 GeV, respectively.Comment: 17 pages, 6 figure

Research review: young people leaving care

This paper reviews the international research on young people leaving care. Set in the context of a social exclusion framework, it explores young people's accelerated and compressed transitions to adulthood, and discusses the development and classification of leaving care services in responding to their needs. It then considers the evidence from outcome studies and argues that adopting a resilience framework suggests that young people leaving care may fall into three groups: young people 'moving on', 'survivors' and 'victims'. In concluding, it argues that these three pathways are associated with the quality of care young people receive, their transitions from care and the support they receive after care

Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments

With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already too vast to be summarized here, in scalable methodologies for analyzing large spatial datasets. Scalable spatial process models have been found especially attractive due to their richness and flexibility and, particularly so in the Bayesian paradigm, due to their presence in hierarchical model settings. However, the vast majority of research articles present in this domain have been geared toward innovative theory or more complex model development. Very limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article is submitted to the Practice section of the journal with the aim of developing massively scalable Bayesian approaches that can rapidly deliver Bayesian inference on spatial process that are practically indistinguishable from inference obtained using more expensive alternatives. A key emphasis is on implementation within very standard (modest) computing environments (e.g., a standard desktop or laptop) using easily available statistical software packages without requiring message-parsing interfaces or parallel programming paradigms. Key insights are offered regarding assumptions and approximations concerning practical efficiency.Comment: 20 pages, 4 figures, 2 table