A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Au + x2u = 0, with Imx > 0. in an hrbitrary bounded or unbounded open set C c W. Assuming continuity of the solution up to the boundary and a bound on growth a infinity, that lu(x)l < Cexp (Slxl), for some C > 0 and S~< Imx, we prove that the homogeneous problem has only the trivial salution. With this resnlt we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.

Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form $\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)$ (abbreviated $\phi = g + K\phi $), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated $\phi _a = E_a g + K_a \phi _a $), obtained by replacing S by $S_a $, a closed bounded surface of class $C^2 $, the boundary of a section of the interior of S of length $2a$, is also discussed. Conditions on k are obtained (in particular, implying that K commutes with the operation of translation in the direction of the cylinder axis) which ensure that $I - K$ is invertible, that $I - K_a $ is invertible and $(I - K_a )^{ - 1} $ is uniformly bounded for all sufficiently large a, and that $\phi _a $ converges to $\phi $ in an appropriate sense as $a \to \infty $. Uniform stability and convergence results for a piecewise constant boundary element collocation method for the truncated equations are also obtained. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution (of the integral equation and the corresponding boundary value problem) and convergence of a particular collocation method.

Maximum principles for vectorial approximate minimisers on non-convex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

A high frequency $hp$ boundary element method for scattering by convex polygons

In this paper we propose and analyze a hybrid $hp$ boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods.

Teaching programming to beginners in a massive open online course

The University of Reading’s first Massive Open Online Course (MOOC) “Begin Programming: Build your first mobile game” (#FLMobiGame) was offered in Autumn 2013 on the FutureLearn platform. This course used a simple Android game framework to present basic programming concepts to complete beginners. The course attracted wide interest from all age groups. The course presented opportunities and challenges to both participants and educators. While some participants had difficulties accessing content some others had trouble grasping the concepts and applying them in a real program. Managing forums was cumbersome with the limited facilities supported by the Beta-platform. A healthy community was formed around the course with the support of social media. The case study reported here is part of an ongoing research programme exploring participants’ MOOC engagement and experience using a grounded, ethnographical approach.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Precise analysis of array usage in scientific programs

The automatic transformation of sequential programs for efficient execution on parallel computers involves a number of analyses and restructurings of the input. Some of these analyses are based on computing array sections, a compact description of a range of array elements. Array sections describe the set of array elements that are either read or written by program statements. These sections can be compactly represented using shape descriptors such as regular sections, simple sections, or generalized convex regions. However, binary operations such as Union performed on these representations do not satisfy a straightforward closure property, e.g., if the operands to Union are convex, the result may be nonconvex. Approximations are resorted to in order to satisfy this closure property. These approximations introduce imprecision in the analyses and, furthermore, the imprecisions resulting from successive operations have a cumulative effect. Delayed merging is a technique suggested and used in some of the existing analyses to minimize the effects of approximation. However, this technique does not guarantee an exact solution in a general setting. This article presents a generalized technique to precisely compute Union which can overcome these imprecisions.

Virtualization for cost-effective teaching of assembly language programming

A virtual system that emulates an ARM-based processor machine has been created to replace a traditional hardware-based system for teaching assembly language. The proposed virtual system integrates, in a single environment, all the development tools necessary to deliver introductory or advanced courses on modern assembly language programming. The virtual system runs a Linux operating system in either a graphical or console mode on a Windows or Linux host machine. No software licenses or extra hardware are required to use the virtual system, thus students are free to carry their own ARM emulator with them on a USB memory stick. Institutions adopting this, or a similar virtual system, can also benefit by reducing capital investment in hardware-based development kits and enable distance learning courses.

Rapid preconditioning of data for accelerating convex hull algorithms

Given a dataset of two-dimensional points in the plane with integer coordinates, the method proposed reduces a set of n points down to a set of s points s ≤ n, such that the convex hull on the set of s points is the same as the convex hull of the original set of n points. The method is O(n). It helps any convex hull algorithm run faster. The empirical analysis of a practical case shows a percentage reduction in points of over 98%, that is reflected as a faster computation with a speedup factor of at least 4.

Sex differences in the programming effects of prenatal stress on psychopathology and stress responses: an evolutionary perspective

There is strong evidence from animal studies that prenatal stress has different effects on male and female offspring. In general, although not always, prenatal stress increases anxiety, depression and stress responses, both hypothalamic–pituitary–adrenal and cardiovascular, in female offspring rather than in male. Males are more likely to show learning and memory deficits. There have been few studies so far in humans which differentiate effects of prenatal stress on male and female psychopathology. Some studies support the animal models, but the evidence is inconsistent. The mediating mechanisms for any sex specific effects are little understood, but there is evidence that placental function can differ depending on the sex of the fetus. We suggest that there may be an evolutionary reason for any sex differences in the long term effects of prenatal stress. In a stressful environment it may be adaptive for females, who are more likely to stay in one place and look after children, to be more vigilant, alert to danger and thus show more stress responsiveness. This can give rise to a more anxious or depressed phenotype. With males it may be more adaptive to go out and explore new environments, compete with other males, and be more aggressive. For this it may help to be less responsive to external stressors. More research is needed into sex differences in the effects of prenatal stress in humans, to test these ideas.

Evidence for sex differences in fetal programming of physiological stress reactivity in infancy

Associations between low birth weight and prenatal anxiety and later psychopathology may arise from programming effects likely to be adaptive under some, but not other, environmental exposures and modified by sex differences. If physiological reactivity, which also confers vulnerability or resilience in an environment-dependent manner, is associated with birth weight and prenatal anxiety, it will be a candidate to mediate the links with psychopathology. From a general population sample of 1,233 first-time mothers recruited at 20 weeks gestation, a sample of 316 stratified by adversity was assessed at 32 weeks and when their infants were aged 29 weeks (N = 271). Prenatal anxiety was assessed by self-report, birth weight from medical records, and vagal reactivity from respiratory sinus arrhythmia during four nonstressful and one stressful (still-face) procedure. Lower birth weight for gestational age predicted higher vagal reactivity only in girls (interaction term, p = .016), and prenatal maternal anxiety predicted lower vagal reactivity only in boys (interaction term, p = .014). These findings are consistent with sex differences in fetal programming, whereby prenatal risks are associated with increased stress reactivity in females but decreased reactivity in males, with distinctive advantages and penalties for each sex.

Maternal antenatal anxiety, postnatal stroking and emotional problems in children: outcomes predicted from pre and postnatal programming hypotheses

Background Mothers' self-reported stroking of their infants over the first weeks of life modifies the association between prenatal depression and physiological and emotional reactivity at 7 months, consistent with animal studies of the effects of tactile stimulation. We now investigate whether the effects of maternal stroking persist to 2.5 years. Given animal and human evidence for sex differences in the effects of prenatal stress we compare associations in boys and girls. Method From a general population sample of 1233 first-time mothers recruited at 20 weeks gestation we drew a random sample of 316 for assessment at 32 weeks, stratified by reported inter-partner psychological abuse, a risk indicator for child development. Of these mothers, 243 reported at 5 and 9 weeks how often they stroked their infants, and completed the Child Behavior Checklist (CBCL) at 2.5 years post-delivery. Results There was a significant interaction between prenatal anxiety and maternal stroking in the prediction of CBCL internalizing (p = 0.001) and anxious/depressed scores (p < 0.001). The effects were stronger in females than males, and the three-way interaction prenatal anxiety × maternal stroking × sex of infant was significant for internalizing symptoms (p = 0.003). The interactions arose from an association between prenatal anxiety and internalizing symptoms only in the presence of low maternal stroking. Conclusions The findings are consistent with stable epigenetic effects, many sex specific, reported in animal studies. While epigenetic mechanisms may be underlying the associations, it remains to be established whether stroking affects gene expression in humans.

Fetal programming of adipose tissue function: an evolutionary perspective

Obesity is an escalating threat of pandemic proportions and has risen to such unrivaled prominence in such a short period of time that it has come to define a whole generation in many countries around the globe. The burden of obesity, however, is not equally shared among the population, with certain ethnicities being more prone to obesity than others, while some appear to be resistant to obesity altogether. The reasons behind this ethnic basis for obesity resistance and susceptibility, however, have remained largely elusive. In recent years, much evidence has shown that the level of brown adipose tissue thermogenesis, which augments energy expenditure and is negatively associated with obesity in both rodents and humans, varies greatly between ethnicities. Interestingly, the incidence of low birth weight, which is associated with an increased propensity for obesity and cardiovascular disease in later life, has also been shown to vary by ethnic background. This review serves to reconcile ethnic variations in BAT development and function with ethnic differences in birth weight outcomes to argue that the variation in obesity susceptibility between ethnic groups may have its origins in the in utero programming of BAT development and function as a result of evolutionary adaptation to cold environments.