A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Synthesis of novel hyperbranched polymers featuring oxazoline linear units and their application in fast-drying solvent-borne coating formulations

Novel acid-terminated hyperbranched polymers (HBPs) containing adipic acid and oxazoline monomers derived from oleic and linoleic acid have been synthesized via a bulk polymerization procedure. Branching was achieved as a consequence of an acid-catalyzed opening of the oxazoline ring to produce a trifunctional monomer in situ which delivered branching levels of >45% as determined by 1H and 13C NMR spectroscopy. The HBPs were soluble in common solvents, such as CHCl3, acetone, tetrahydrofuran, dimethylformamide, and dimethyl sulfoxide and were further functionalized by addition of citronellol to afford white-spirit soluble materials that could be used in coating formulations. During end group modification, a reduction in branching levels of the HBPs (down to 12–24%) was observed, predominantly on account of oxazoline ring reformation and trans-esterification processes under the reaction conditions used. In comparison to commercial alkyd resin paint coatings, formulations of the citronellol-functionalized hyperbranched materials blended with a commercial alkyd resin exhibited dramatic decreases of the blend viscosity when the HBP content was increased. The curing characteristics of the HBP/alkyd blend formulations were studied by dynamic mechanical analysis which revealed that the new coatings cured more quickly and produced tougher materials than otherwise identical coatings prepared from only the commercial alkyd resins.

Generation of nonvernal-obligate, faster-cycling Noccaea caerulescens lines through fast neutron mutagenesis

Noccaea caerulescens (formerly Thlaspi caerulescens) is a widely studied metal hyperaccumulator. However, molecular genetic studies are challenging in this species because of its vernal-obligate biennial life cycle of 7-9 months. Here, we describe the development of genetically stable, faster cycling lines of N. caerulescens which are nonvernal-obligate. A total of 5500 M(0) seeds from Saint Laurent Le Minier (France) were subjected to fast neutron mutagenesis. Following vernalization of young plants, 79 of plants survived to maturity. In all, 80 000 M(2) lines were screened for flowering in the absence of vernalization. Floral initials were observed in 35 lines, with nine flowering in < 12 wk. Two lines (A2 and A7) were selfed to the M(4) generation. Floral initials were observed 66 and 87 d after sowing (DAS) in A2 and A7, respectively. Silicle development occurred for all A2 and for most A7 at 92 and 123 DAS, respectively. Floral or silicle development was not observed in wild-type (WT) plants. Leaf zinc (Zn) concentration was similar in WT, A2 and A7 lines. These lines should facilitate future genetic studies of this remarkable species. Seed is publicly available through the European Arabidopsis Stock Centre (NASC).

A fast algorithm for sparse probability density function construction

A new sparse kernel density estimator is introduced. Our main contribution is to develop a recursive algorithm for the selection of significant kernels one at time using the minimum integrated square error (MISE) criterion for both kernel selection. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Fast identification algorithms for Gaussian process model

A class identification algorithms is introduced for Gaussian process(GP)models.The fundamental approach is to propose a new kernel function which leads to a covariance matrix with low rank,a property that is consequently exploited for computational efficiency for both model parameter estimation and model predictions.The objective of either maximizing the marginal likelihood or the Kullback–Leibler (K–L) divergence between the estimated output probability density function(pdf)and the true pdf has been used as respective cost functions.For each cost function,an efficient coordinate descent algorithm is proposed to estimate the kernel parameters using a one dimensional derivative free search, and noise variance using a fast gradient descent algorithm. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

Criteria for validation and selection of cognitive tests for investigating the effects of foods and nutrients.

This review is an output of the International Life Sciences Institute (ILSI) Europe Marker Initiative, which aims to identify evidence-based criteria for selecting adequate measures of nutrient effects on health through comprehensive literature review. Experts in cognitive and nutrition sciences examined the applicability of these proposed criteria to the field of cognition with respect to the various cognitive domains usually assessed to reflect brain or neurological function. This review covers cognitive domains important in the assessment of neuronal integrity and function, commonly used tests and their state of validation, and the application of the measures to studies of nutrition and nutritional intervention trials. The aim is to identify domain-specific cognitive tests that are sensitive to nutrient interventions and from which guidance can be provided to aid the application of selection criteria for choosing the most suitable tests for proposed nutritional intervention studies using cognitive outcomes. The material in this review serves as a background and guidance document for nutritionists, neuropsychologists, psychiatrists, and neurologists interested in assessing mental health in terms of cognitive test performance and for scientists intending to test the effects of food or food components on cognitive function.

Evidence for a second meal cognitive effect: glycaemic responses to high and low glycaemic index evening meals are associated with cognition the following morning

Low glycaemic index (GI) foods consumed at breakfast can enhance memory in comparison to high-GI foods; however, the impact of evening meal GI manipulations on cognition the following morning remains unexplored. Fourteen healthy males consumed a high-GI evening meal or a low-GI evening meal in a counterbalanced order on two separate evenings. Memory and attention were assessed before and after a high-GI breakfast the following morning. The high-GI evening meal elicited significantly higher evening glycaemic responses than the low-GI evening meal. Verbal recall was better the morning following the high-GI evening meal compared to after the low-GI evening meal. In summary, the GI of the evening meal was associated with memory performance the next day, suggesting a second meal cognitive effect. The present findings imply that an overnight fast may not be sufficient to control for previous nutritional consumption.

A phosphoramidite-based [FeFe]H2ase functional mimic displaying fast electrocatalytic proton reduction

A phosphoramidite modified [FeFe]H2ase mimic is studied as a model for photodriven production of H2. On cathodic activation, the pyridyl–phosphoramidite complex exhibits a strongly enhanced rate of proton reduction over the previously reported pyridylphosphine model at the same overpotential. Analysis of the cyclic voltammograms shows an apparent H2 evolution rate strongly influenced by the presence of both side-bound pyridyl and phosphorous-bound dimethylamino moieties at the phosphoramidite ligands. This difference is ascribed to the basic amines acting as proton relays.

Impacts of plant-based foods in ancestral hominin diets on the metabolism and function of gut microbiota in vitro

Ancestral human populations had diets containing more indigestible plant material than present-day diets in industrialized countries. One hypothesis for the rise in prevalence of obesity is that physiological mechanisms for controlling appetite evolved to match a diet with plant fiber content higher than that of present-day diets. We investigated how diet affects gut microbiota and colon cells by comparing human microbial communities with those from a primate that has an extreme plant-based diet, namely, the gelada baboon, which is a grazer. The effects of potato (high starch) versus grass (high lignin and cellulose) diets on human-derived versus gelada-derived fecal communities were compared in vitro. We especially focused on the production of short-chain fatty acids, which are hypothesized to be key metabolites influencing appetite regulation pathways. The results confirmed that diet has a major effect on bacterial numbers, short-chain fatty acid production, and the release of hormones involved in appetite suppression. The potato diet yielded greater production of short-chain fatty acids and hormone release than the grass diet, even in the gelada cultures, which we had expected should be better adapted to the grass diet. The strong effects of diet on hormone release could not be explained, however, solely by short-chain fatty acid concentrations. Nuclear magnetic resonance spectroscopy found changes in additional metabolites, including betaine and isoleucine, that might play key roles in inhibiting and stimulating appetite suppression pathways. Our study results indicate that a broader array of metabolites might be involved in triggering gut hormone release in humans than previously thought. IMPORTANCE: One theory for rising levels of obesity in western populations is that the body's mechanisms for controlling appetite evolved to match ancestral diets with more low-energy plant foods. We investigated this idea by comparing the effects of diet on appetite suppression pathways via the use of gut bacterial communities from humans and gelada baboons, which are modern-day primates with an extreme diet of low-energy plant food, namely, grass. We found that diet does play a major role in affecting gut bacteria and the production of a hormone that suppresses appetite but not in the direction predicted by the ancestral diet hypothesis. Also, bacterial products were correlated with hormone release that were different from those normally thought to play this role. By comparing microbiota and diets outside the natural range for modern humans, we found a relationship between diet and appetite pathways that was more complex than previously hypothesized on the basis of more-controlled studies of the effects of single compounds.

Phospholipid-based microemulsions suitable for use in foods

The preparation of nonaqueous microemulsions using food-acceptable components is reported. The effect of oil on the formation of microemulsions stabilized by lecithin (Epikuron 200) and containing propylene glycol as immiscible solvent was investigated. When the triglycerides were used as oil, three types of phase behavior were noted, namely, a two-phase cloudy region (occurring at low lecithin concentrations), a liquid crystalline (LC) phase (occurring at high surfactant and low oil concentrations), and a clear monophasic microemulsion region. The extent of this clear one-phase region was found to be dependent upon the molecular volume of the oil being solubilized. Large molecular volume oils, such as soybean and sunflower oils, produced a small microemulsion region, whereas the smallest molecular volume triglyceride, tributyrin, produced a large, clear monophasic region. Use of the ethyl ester, ethyl oleate, as oil produced a clear, monophasic region of a size comparable to that seen with tributyrin. Substitution of some of the propylene glycol with water greatly reduced the extent of the clear one-phase region and increased the extent of the liquid crystalline region. In contrast, ethanol enhanced the clear, monophasic region by decreasing the LC phase. Replacement of some of the lecithin with the micelle-forming nonionic surfactant Tween 80 to produce mixed lecithin/Tween 80 mixtures of weight ratios (Km) 1:2 and 1:3 did not significantly alter the phase behavior, although there was a marginal increase in the area of the two-phase, cloudy region of the phase diagram. The use of the lower phosphatidylcholine content lecithin, Epikuron 170, in place of Epikuron 200 resulted in a reduction in the LC region for all of the systems investigated. In conclusion, these studies show that it is possible to prepare one-phase, clear lecithin-based microemulsions over a wide range of compositions using components that are food-acceptable.

Development of personalised functional foods needs metabolic profiling

Purpose of review There is growing interest in applying metabolic profiling technologies to food science as this approach is now embedded into the foodomics toolbox. This review aims at exploring how metabolic profiling can be applied to the development of functional foods. Recent findings One of the biggest challenges of modern nutrition is to propose a healthy diet to populations worldwide that must suit high inter-individual variability driven by complex gene-nutrient-environment interactions. Although a number of functional foods are now proposed in support of a healthy diet, a one-size-fits-all approach to nutrition is inappropriate and new personalised functional foods are necessary. Metabolic profiling technologies can assist at various levels of the development of functional foods, from screening for food composition to identification of new biomarkers of food intake to support diet intervention and epidemiological studies. Summary Modern ‘omics’ technologies, including metabolic profiling, will support the development of new personalised functional foods of high relevance to twenty-first-century medical challenges such as controlling the worldwide spread of metabolic disorders and ensuring healthy ageing.

Hyperbranched polymers containing oxazoline monomers andsuccinic anhydride: applications in fast drying, low solvent coating formulations

tMelt-polycondensation of succinic acid anhydride with oxazoline-based diol monomers gave hyper-branched polymers with carboxylicacids terminal groups.1H NMR and quantitative13C NMRspectroscopy coupled with DEPT-13513C NMR experiment showed high degrees of branching (over 60%).Esterification of the acid end groups by addition of citronellol at 160◦C produced novel white spirit solubleresins which were characterized by Fourier transform-infrared (FTIR) spectroscopy, gel permeation chro-matography (GPC), differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Blendsof the new hyperbranched materials with commercial alkyd resins resulted in a dramatic, concentrationdependent drop in viscosity. Solvent-borne coatings were formulated containing the hyperbranchedpolymers. Dynamic mechanical analysis studies revealed that the air drying rates of the new coatingsystems were enhanced compared with identical formulations containing only commercial alkyd resins.