A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces

We propose a Nystr¨om/product integration method for a class of second kind integral equations on the real line which arise in problems of two-dimensional scalar and elastic wave scattering by unbounded surfaces. Stability and convergence of the method is established with convergence rates dependent on the smoothness of components of the kernel. The method is applied to the problem of acoustic scattering by a sound soft one-dimensional surface which is the graph of a function f, and superalgebraic convergence is established in the case when f is infinitely smooth. Numerical results are presented illustrating this behavior for the case when f is periodic (the diffraction grating case). The Nystr¨om method for this problem is stable and convergent uniformly with respect to the period of the grating, in contrast to standard integral equation methods for diffraction gratings which fail at a countable set of grating periods.

On the solvability of a class of second kind integral equations on unbounded domains

We consider integral equations of the form ψ(x) = φ(x) + ∫Ωk(x, y)z(y)ψ(y) dy(in operator form ψ = φ + Kzψ), where Ω is some subset ofRn(n ≥ 1). The functionsk,z, and φ are assumed known, withz ∈ L∞(Ω) and φ ∈ Y, the space of bounded continuous functions on Ω. The function ψ ∈ Yis to be determined. The class of domains Ω and kernelskconsidered includes the case Ω = Rnandk(x, y) = κ(x − y) with κ ∈ L1(Rn), in which case, ifzis the characteristic function of some setG, the integral equation is one of Wiener–Hopf type. The main theorems, proved using arguments derived from collectively compact operator theory, are conditions on a setW ⊂ L∞(Ω) which ensure that ifI − Kzis injective for allz ∈ WthenI − Kzis also surjective and, moreover, the inverse operators (I − Kz)−1onYare bounded uniformly inz. These general theorems are used to recover classical results on Wiener–Hopf integral operators of21and19, and generalisations of these results, and are applied to analyse the Lippmann–Schwinger integral equation.

Optimising the FAMOUS climate model: inclusion of global carbon cycling

FAMOUS fills an important role in the hierarchy of climate models, both explicitly resolving atmospheric and oceanic dynamics yet being sufficiently computationally efficient that either very long simulations or large ensembles are possible. An improved set of carbon cycle parameters for this model has been found using a perturbed physics ensemble technique. This is an important step towards building the "Earth System" modelling capability of FAMOUS, which is a reduced resolution, and hence faster running, version of the Hadley Centre Climate model, HadCM3. Two separate 100 member perturbed parameter ensembles were performed; one for the land surface and one for the ocean. The land surface scheme was tested against present-day and past representations of vegetation and the ocean ensemble was tested against observations of nitrate. An advantage of using a relatively fast climate model is that a large number of simulations can be run and hence the model parameter space (a large source of climate model uncertainty) can be more thoroughly sampled. This has the associated benefit of being able to assess the sensitivity of model results to changes in each parameter. The climatologies of surface and tropospheric air temperature and precipitation are improved relative to previous versions of FAMOUS. The improved representation of upper atmosphere temperatures is driven by improved ozone concentrations near the tropopause and better upper level winds.

Oi! Oi! Oi! : class locality and British punk

This article looks at the controversial music genre Oi! in relation to youth cultural identity in late 1970s’ and early 1980s’ Britain. As a form of British punk associated with skinheads, Oi! has oft-been dismissed as racist and bound up in the politics of the far right. It is argued here, however, that such a reading is too simplistic and ignores the more complex politics contained both within Oi! and the various youth cultural currents that revolved around the term ‘punk’ at this time. Taking as its starting point the Centre for Contemporary Cultural Studies’ conception of youth culture as a site of potential ‘resistance’, the article explores the substance and motifs of Oi!’s protest to locate its actual and perceived meaning within a far wider political and socio-economic context. More broadly, it seeks to demonstrate the value of historians examining youth culture as a formative and contested socio-cultural space within which young people discover, comprehend, and express their desires, opinions, and disaffections.

Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.

Effect of inclusion of lactulose and Lactobacillus plantarum on the intestinal environment and performance of piglets at weaning

The prebiotic lactulose, a probiotic strain of Lactobacillus plantarum (L. plantarum) and a synbiotic combination of these two agents were evaluated as growth promoters in 25–39-day old commercial weaning pigs. Ninety-six weaning pigs were allocated into 32 pens, taking initial weight into account, and distributed into four groups as follows: a control diet (CTR), the same diet supplemented daily with L. plantarum (109 CFU/mL sprayed on top; 20 mL/pig) (LPN); 10 g/kg lactulose (LAC) or a combination of both treatments (SYN). At day 14, eight piglets from each group were euthanized and proximal colon digesta was sampled for luminal pH, short-chain fatty acids (SCFA) and lactic acid concentrations. Deoxyribonucleic acid was extracted from colonic digesta and the microbial community was profiled by terminal restriction fragment length polymorphism analysis (T-RFLP) and qPCR. Blood urea nitrogen (BUN) and acute-phase proteins (Pig-MAP) were measured. Lactulose treatment (LAC) improved feed intake (P<0.05), average daily gain (P<0.01), feed:gain ratio (P<0.05) and reduced BUN (P<0.01). Both, LAC and LPN treatment, decreased the Enterobacteriaceae:Lactobacillus spp. ratio in the colonic luminal contents (P<0.05). Moreover LPN treatment promoted a decrease in the percentage of branched fatty acids (P<0.01) suggesting a reduction in proteolytic microbial activity. Microbial profiling of colonic luminal contents by T-RFLP revealed changes in some microbial species. Terminal restriction fragments (TRFs) compatible with Bifidobacterium thermoacidophilum were more frequently detected in experimental diets compared to CTR (P<0.05). Pigs receiving SYN diet demonstrated the combined positive effects of individual LAC and LPN treatment although we were not able to show a specific increase in the probiotic strain with the inclusion of lactulose. Collectively, these data suggest the combination of lactulose and L. plantarum acts as a complementary synbiotic, but not as a synergistic combination.

PDFOS: PDF estimation based over-sampling for imbalanced two-class problems

This contribution proposes a novel probability density function (PDF) estimation based over-sampling (PDFOS) approach for two-class imbalanced classification problems. The classical Parzen-window kernel function is adopted to estimate the PDF of the positive class. Then according to the estimated PDF, synthetic instances are generated as the additional training data. The essential concept is to re-balance the class distribution of the original imbalanced data set under the principle that synthetic data sample follows the same statistical properties. Based on the over-sampled training data, the radial basis function (RBF) classifier is constructed by applying the orthogonal forward selection procedure, in which the classifier’s structure and the parameters of RBF kernels are determined using a particle swarm optimisation algorithm based on the criterion of minimising the leave-one-out misclassification rate. The effectiveness of the proposed PDFOS approach is demonstrated by the empirical study on several imbalanced data sets.

The effects of flavonoid and other polyphenol consumption on cognitive performance: A systematic research review of human experimental and epidemiological studies

Literature reviews suggest flavonoids, a sub-class of polyphenols, are beneficial for cognition. This is the first review examining the effect of consumption of all polyphenol groups on cognitive function. Inclusion criteria were polyphenol vs. control interventions and epidemiological studies with an objective measure of cognitive function. Participants were healthy or mildly cognitively impaired adults. Studies were excluded if clinical assessment or diagnosis of Alzheimer’s disease, dementia, or cognitive impairment was the sole measure of cognitive function, or if the polyphenol was present with potentially confounding compounds such as caffeine (e.g. tea studies) or Ginkgo Biloba. 28 studies were identified; 4 berry juice studies, 4 cocoa studies, 13 isoflavone supplement studies, 3 other supplement studies, and 4 epidemiological surveys. Overall, 16 studies reported cognitive benefits following polyphenol consumption. Evidence suggests that consuming additional polyphenols in the diet can lead to cognitive benefits, however, the observed effects were small. Declarative memory and particularly spatial memory appear most sensitive to polyphenol consumption and effects may differ depending on polyphenol source. Polyphenol berry fruit juice consumption was most beneficial for immediate verbal memory, whereas isoflavone based interventions were associated with significant improvements for delayed spatial memory and executive function. Comparison between studies was hampered by methodological inconsistencies. Hence, there was no clear evidence for an association between cognitive outcomes and polyphenol dose response, duration of intervention, or population studied. In conclusion, however, the findings do imply that polyphenol consumption has potential to benefit cognition both acutely and chronically.

A high frequency boundary element method for scattering by a class of nonconvex obstacles

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

'Hey little rich boy, take a good look at me': punk, class and British oi!

This article looks at the controversial music genre Oi! in relation to youth cultural identity in late 1970s and early 1980s Britain. By examining the six compilation albums released to promote Oi! as a distinct strand of punk, it seeks to challenge prevailing dismissals of the genre as inherently racist or bound to the politics of the far right. Rather, Oi! – like punk more generally – was a contested cultural form. It was, moreover, centred primarily on questions of class and locality. To this end, Oi! sought to realize the working-class rebellion of punk’s early aesthetic; to give substance to its street-level pretentions and offer a genuine ‘song from the streets’.

The inclusion of forage mixtures in the diet of growing dairy heifers: impacts on digestion, energy utilisation, and methane emissions

Intensive farming focusing on monoculture grass species to maximise forage production has led to a reduction in the extent and diversity of species-rich grasslands. However, plant communities with higher species number (richness) are a potential strategy for more sustainable production and mitigation of greenhouse gas (GHG) emissions. Research has indicated the need to understand opportunities that forage mixtures can offer sustainable ruminant production systems. The objective of the two experiments reported here were to evaluate multiple species forage mixtures in comparison to ryegrass-dominant pasture, when conserved or grazed, on digestion, energy utilisation, N excretion, and methane emissions by growing 10–15 month old heifers. Experiment 1 was a 4 × 4 Latin square design with five week periods. Four forage treatments of: (1) ryegrass (control); permanent pasture with perennial ryegrass (Lolium perenne); (2) clover; a ryegrass:red clover (Trifolium pratense) mixture; (3) trefoil; a ryegrass:birdsfoot trefoil (Lotus corniculatus) mixture; and (4) flowers; a ryegrass:wild flower mixture of predominately sorrel (Rumex acetosa), ox-eye daisy (Leucanthemum vulgare), yarrow (Achillea millefolium), knapweed (Centaurea nigra) and ribwort plantain (Plantago lanceolata), were fed as haylages to four dairy heifers. Measurements included digestibility, N excretion, and energy utilisation (including methane emissions measured in respiration chambers). Experiment 2 used 12 different dairy heifers grazing three of the same forage treatments used to make haylage in experiment 1 (ryegrass, clover and flowers) and methane emissions were estimated using the sulphur hexafluoride (SF6) tracer technique. Distribution of ryegrass to other species (dry matter (DM) basis) was approximately 70:30 (clover), 80:20 (trefoil), and 40:60 (flowers) for experiment 1. During the first and second grazing rotations (respectively) in experiment 2, perennial ryegrass accounted for 95 and 98% of DM in ryegrass, and 84 and 52% of DM in clover, with red clover accounting for almost all of the remainder. In the flowers mixture, perennial ryegrass was 52% of the DM in the first grazing rotation and only 30% in the second, with a variety of other flower species occupying the remainder. Across both experiments, compared to the forage mixtures (clover, trefoil and flowers), ryegrass had a higher crude protein (CP) content (P < 0.001, 187 vs. 115 g kg −1 DM) and DM intake (P < 0.05, 9.0 vs. 8.1 kg day −1). Heifers in experiment 1 fed ryegrass, compared to the forage mixtures, had greater total tract digestibility (g kg −1) of DM (DMD; P < 0.008, 713 vs. 641) and CP (CPD, P < 0.001, 699 vs. 475), and used more intake energy (%) for body tissue deposition (P < 0.05, 2.6 vs. −4.9). For both experiments, heifers fed flowers differed the most compared to the ryegrass control for a number of measurements. Compared to ryegrass, flowers had 40% lower CP content (P < 0.001, 113 vs. 187 g kg −1), 18% lower DMD (P < 0.01, 585 vs. 713 g kg −1), 42% lower CPD (P < 0.001, 407 vs. 699 g kg −1), and 10% lower methane yield (P < 0.05, 22.6 vs. 25.1 g kg −1 DM intake). This study has shown inclusion of flowers in forage mixtures resulted in a lower CP concentration, digestibility and intake. These differences were due in part to sward management and maturity at harvest. Further research is needed to determine how best to exploit the potential environmental benefits of forage mixtures in sustainable ruminant production systems.

British working-class household composition, labour supply, and commercial leisure participation during the 1930s

The early twentieth century constituted the heyday of the ‘breadwinner–homemaker’ household, characterized by a high degree of intra-household functional specialization between paid and domestic work according to age, gender, and marital status. This article examines the links between formal workforce participation and access to resources for individualized discretionary spending in British working-class households during the late 1930s, via an analysis of household leisure expenditures. Leisure spending is particularly salient to intra-household resource allocation, as it constitutes one of the most highly prioritized areas of individualized expenditure, especially for young, single people. Using a database compiled from surviving returns to the Ministry of Labour's national 1937/8 working-class expenditure survey, we examine leisure participation rates for over 600 households, using a detailed set of commercial leisure activities together with other relevant variables. We find that the employment status of family members other than the male breadwinner was a key factor influencing their access to commercial leisure. Our analysis thus supports the view that the breadwinner–homemaker household was characterized by strong power imbalances that concentrated resources—especially for individualized expenditures—in the hands of those family members who engaged in paid labour.