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.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Uptake of a free coronary heart disease risk screening programme in community pharmacy: the Healthy Heart Assessment service

Introduction Health promotion (HP) aims to enhance good health while preventing ill-health at three levels of activity; primary (preventative), secondary (diagnostic) and tertiary (management).1 It can range from simple provision of health education to ongoing support, but the effectiveness of HP is ultimately dependent on its ability to influence change. HP as part of the Community Pharmacy Contract (CPC) aims to increase public knowledge and target ‘hard-to-reach’ individuals by focusing mainly on primary and tertiary HP. The CPC does not include screening programmes (secondary HP) as a service. Coronary heart disease (CHD) is a significant cause of morbidity and mortality in the UK. While there is evidence to support the effectiveness of some community pharmacy HP strategies in CHD, there is paucity of research in relation to screening services.2 Against this background, Alliance Pharmacy introduced a free CHD risk screening programme to provide tailored HP advice as part of a participant–pharmacist consultation. The aim of this study is to report on the CHD risk levels of participants and to provide a qualitative indication of consultation outcomes. Methods Case records for 12 733 people who accessed a free CHD risk screening service between August 2004 and April 2006 offered at 217 community pharmacies were obtained. The service involved initial self-completion of the Healthy Heart Assessment (HHA) form and measurement of height, weight, body mass index, blood pressure, total cholesterol and highdensity lipoprotein levels by pharmacists to calculate CHD risk.3 Action taken by pharmacists (lifestyle advice, statin recommendation or general practitioner (GP) referral) and qualitative statements of advice were recorded, and a copy provided to the participants. The service did not include follow-up of participants. All participants consented to taking part in evaluations of the service. Ethical committee scrutiny was not required for this service development evaluation. Results Case records for 10 035 participants (3658 male) were evaluable; 5730 (57%) were at low CHD risk (<15%); 3636 (36%) at moderate-to-high CHD risk (≥15%); and 669 (7%) had existing heart disease. A significantly higher proportion of male (48% versus 30% female) participants were at moderate- to-high risk of CHD (chi-square test; P < 0.005). A range of outcomes resulted from consultations. Lifestyle advice was provided irrespective of participants’ CHD risk or existing disease. In the moderate-to-high-risk group, of which 52% received prescribed medication, lifestyle advice was recorded for 62%, 16% were referred and 34% were advised to have a re-assessment. Statin recommendations were made in 1% of all cases. There was evidence of supportive and motivational statements in the advice recorded. Discussion Pharmacists were able to identify individuals’ level of CHD risk and provide them with bespoke advice. Identification of at-risk participants did not automatically result in referrals or statin recommendation. One-third of those accessing the screening service had moderate-to-high risk of CHD, a significantly higher proportion of whom were men. It is not known whether these individuals had been previously exposed to HP but presumably by accessing this service they may have contemplated change. As effectiveness of HP advice will depend among other factors on ability to influence change, future consultations may need to explore patients’ attitude towards change in relation to the Trans Theoretical Model4 to better tailor HP advice. The high uptake of the service by those at moderate-to-high CHD risk indicates a need for this type of screening programme in community pharmacy, perhaps specifically to reach men who access medical services less.

Viscoelastic properties of high pressure and heat induced tofu gels

Tofu gels were rheologically examined to determine their storage or elastic (G′) and loss or viscous (G″) moduli as a function of frequency within their linear viscoelastic limits. The tofu gels were made using either glucono-δ-lactone (GDL) or calcium sulphate (CaSO4·2H2O), followed by either heat treatment (heated soymilk at 97 °C prior to coagulation and subsequently held at 70 °C for 60 min, HT) or high pressure treatment (400 MPa at 20 °C for 10 min, HP). The overall moduli values of the GDL gels and CaSO4·2H2O gels of both physical treatments were similar, each gave frequency profiles expected for weak viscoelastic materials. However, although both temperature and high pressure treatments could be used to produce tofu gels, the final products were not the same. Pressure formed gels, despite having a higher overall “consistency” (increasing values of their moduli), had a proportionately higher contribution from the loss modulus (increased tan δ). Differences could also be observed using confocal scanning laser microscopy. While such treatment may give rise to differing systems/structures, with new or modified organoleptic properties, the more “open” structures obtained by pressure treatment may well cause processing difficulties if subsequent reworking or moulding is required.

Viscoelastic properties of high pressure and heat induced tofu gels

Tofu gels were rheologically examined to determine their storage or elastic (G') and loss or viscous (G '') moduli as a function of frequency within their linear viscoelastic limits. The tofu gels were made using either glucono-delta-lactone (GDL) or calcium sulphate (CaSO4 center dot 2H(2)O), followed by either heat treatment (heated soymilk at >= 97 degrees C prior to coagulation and subsequently held at 70 degrees C for 60 min, HT) or high pressure treatment (400 MPa at 20 degrees C for 10 min, HP). The overall moduli values of the GDL gels and CaSO4 center dot 2H(2)O gels of both physical treatments were similar, each gave frequency profiles expected for weak viscoelastic materials. However, although both temperature and high pressure treatments could be used to produce tofu gels, the final products were not the same. Pressure formed gels, despite having a higher overall "consistency" (increasing values of their moduli), had a proportionately higher contribution from the loss modulus (increased tan delta). Differences could also be observed using confocal scanning laser microscopy. While such treatment may give rise to differing systems/structures, with new or modified organoleptic properties, the more "open" structures obtained by pressure treatment may well cause processing difficulties if subsequent reworking or moulding is required. (c) 2007 Elsevier Ltd. All rights reserved.

The cyclical behaviour of sector and regional diversification benefits: 1987-2002

This paper investigates the time series behaviour of the relative benefits of sector and regional diversification strategies, using the notion of cross-sectional dispersion introduced by Solnik and Roulet (2000). Using monthly data over the period 1987:1 to 2002:12, four sector and four regional classifications are examined in the UK. The results indicate that sector and regional dispersion indices are highly time varying and so dwarf any lower frequency cyclical components that may be present. Nonetheless, periods of high dispersion are closely followed by periods of low dispersion, suggestive of cyclical behaviour of sector and regional diversification benefits. Then, using the HP-filter we isolated the cyclical component of the various dispersion indices and found that the sector dispersion indices are generally above the regional dispersion indices. This implies that a sector diversification strategy is likely to offer greater risk reduction benefits than a regional diversification approach. Nonetheless, we find that in some periods, certain regional diversification strategies are of equal or greater benefit than certain sector approaches. The results also appear to be quite sensitive to the classifications of sectors and regions. Hence, the appropriate definition of sectors and regions can have important implications for sector and regional diversification strategies.

The impact of blanching and high-pressure pretreatments on oil uptake of fried potato slices

The effect of high-pressure (HP) pretreatment on oil uptake of potato slices is examined in this paper. Potato slices were treated either by HP or thermal blanching, or a combination of thermal blanching followed by HP prior to frying. The effect of HP on starch gelatinization and potato microstructure was assessed by differential scanning calorimeter and environmental scanning electron microscope (ESEM), respectively. After treatments, the slices were fried in sunflower oil at 185 °C for a predetermined time. Frying time was either kept constant (4 min) or varied according to the time needed to reach a desired moisture content of ≈2%. The high pressure applied in this study was found not to be sufficient to cause a significant degree of starch gelatinization. Analysis of the ESEM images showed that blanching had a limited effect on cell wall integrity. HP pretreatment was found to increase the oil uptake marginally. When frying for a fixed time, the highest total oil content was found in slices treated at 200 MPa for 5 min. The oil content was found to increase significantly (p<0.05) to 41.23±1.82 compared to 29.03±0.21 in the control slices. The same effect of pressure on oil content was found when the time of frying varied. On the other hand, HP pretreatment was found to decrease the frying time required to achieve a given moisture content. Thus, high-pressure pretreatment may be used to reduce the frying time, but not oil uptake.

The development of a ligase mediated PCR with potential for the differentiation of serovars within Leptospira interrogans

A ligase mediated polymerase chain reaction (LMPCR) was developed to amplify between the repetitive element, IS1533, of Leptospira and adjacent chromosomally located BglII restriction endonuclease enzyme sites. To do this, complimentary oligonucleotide linkers designed to anneal together with an overhanging BglII end were ligated to BglII digested DNA from 35 leptospiral reference strains and field isolates, This ligated DNA was used as template for PCR with oligonucleotide primers specific for the linker and for the repetitive element IS1533. The resultant amplicon profile hybridised a 102 hp region derived from the terminus of IS1533 thus confirming that amplicons generated by LMPCR contained part of IS1533. The number of fragments generated containing IS1533 was significantly fewer than that generated by RFLP but the LMPCR method has the potential to use far less template DNA and be quicker than standard RFLP. Obvious and reproducible interserovar differences were demonstrated by LMPCR whereas for 20 of 21 L. hardjo-bovis isolates tested no intraserovar differences were observed. Of those serovars known to possess IS1533 homologues and tested here by LMPCR, each produced a unique amplicon profile which hybridised the IS1533 terminus probe. The limited heterogeneity amongst hardjo-bovis isolates is discussed as is the potential contribution of this method to diagnosis, differentiation and the phylogenetics of the Leptospires.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

High-throughput root phenotyping screens identify genetic loci associated with root architectural traits in Brassica napus under contrasting phosphate availabilities

Background and Aims: Phosphate (Pi) deficiency in soils is a major limiting factor for crop growth worldwide. Plant growth under low Pi conditions correlates with root architectural traits and it may therefore be possible to select these traits for crop improvement. The aim of this study was to characterize root architectural traits, and to test quantitative trait loci (QTL) associated with these traits, under low Pi (LP) and high Pi (HP) availability in Brassica napus. Methods: Root architectural traits were characterized in seedlings of a double haploid (DH) mapping population (n = 190) of B. napus 'Tapidor' x 'Ningyou 7' (TNDH) using high-throughput phenotyping methods. Primary root length (PRL), lateral root length (LRL), lateral root number (LRN), lateral root density (LRD) and biomass traits were measured 12 d post-germination in agar at LP and HP. Key Results: In general, root and biomass traits were highly correlated under LP and HP conditions. 'Ningyou 7' had greater LRL, LRN and LRD than 'Tapidor', at both LP and HP availability, but smaller PRL. A cluster of highly significant QTL for LRN, LRD and biomass traits at LP availability were identified on chromosome A03; QTL for PRL were identified on chromosomes A07 and C06. Conclusions: High-throughput phenotyping of Brassica can be used to identify root architectural traits which correlate with shoot biomass. It is feasible that these traits could be used in crop improvement strategies. The identification of QTL linked to root traits under LP and HP conditions provides further insights on the genetic basis of plant tolerance to P deficiency, and these QTL warrant further dissection.

Meta-analysis of the INSIG2 association with obesity including 74,345 individuals: does heterogeneity of estimates relate to study design?

The INSIG2 rs7566605 polymorphism was identified for obesity (BMI> or =30 kg/m(2)) in one of the first genome-wide association studies, but replications were inconsistent. We collected statistics from 34 studies (n = 74,345), including general population (GP) studies, population-based studies with subjects selected for conditions related to a better health status ('healthy population', HP), and obesity studies (OB). We tested five hypotheses to explore potential sources of heterogeneity. The meta-analysis of 27 studies on Caucasian adults (n = 66,213) combining the different study designs did not support overall association of the CC-genotype with obesity, yielding an odds ratio (OR) of 1.05 (p-value = 0.27). The I(2) measure of 41% (p-value = 0.015) indicated between-study heterogeneity. Restricting to GP studies resulted in a declined I(2) measure of 11% (p-value = 0.33) and an OR of 1.10 (p-value = 0.015). Regarding the five hypotheses, our data showed (a) some difference between GP and HP studies (p-value = 0.012) and (b) an association in extreme comparisons (BMI> or =32.5, 35.0, 37.5, 40.0 kg/m(2) versus BMI<25 kg/m(2)) yielding ORs of 1.16, 1.18, 1.22, or 1.27 (p-values 0.001 to 0.003), which was also underscored by significantly increased CC-genotype frequencies across BMI categories (10.4% to 12.5%, p-value for trend = 0.0002). We did not find evidence for differential ORs (c) among studies with higher than average obesity prevalence compared to lower, (d) among studies with BMI assessment after the year 2000 compared to those before, or (e) among studies from older populations compared to younger. Analysis of non-Caucasian adults (n = 4889) or children (n = 3243) yielded ORs of 1.01 (p-value = 0.94) or 1.15 (p-value = 0.22), respectively. There was no evidence for overall association of the rs7566605 polymorphism with obesity. Our data suggested an association with extreme degrees of obesity, and consequently heterogeneous effects from different study designs may mask an underlying association when unaccounted for. The importance of study design might be under-recognized in gene discovery and association replication so far.