A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

On the spectra of certain integro-differential-delay problems with applications in neurodynamics

We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a= 0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs.

Pausing patterns: differences between L2 learners and native speakers

This paper reports on a comparative study of pauses made by L2 learners and native speakers of English while narrating picture stories. The comparison is based on the number of pauses and total amount of silence in themiddle and at the end of clauses in the performance of 40 native speakers and 40 L2 learners of English. The results of the quantitative analyses suggest that, although the L2 learners generally pausemore repeatedly and have longer periods of silence than the native speakers, the distinctive feature of their pausing pattern is that they pause frequently in the middle of clauses rather than at the end. The qualitative analysis of the data suggests that some of the L2 learners’mid-clause pauses are associated with processes such as replacement, reformulation, and online planning. Formulaic sequences, however, contain very few pauses and therefore appear to facilitate the learners’ fluency.

Sensory profiles and consumer acceptability of a range of sugar-reduced products on the UK market

Current UK intake of non-milk extrinsic sugars (NMES) is above recommendations. Reducing the sugar content of processed high sugar foods through reformulation is one option for reducing consumption of NMES at a population level. However, reformulation can alter the sensory attributes of food products and influence consumer liking. This study evaluated consumer acceptance of a selection of products that are commercially-available in the UK; these included regular and sugar-reduced baked beans, strawberry jam, milk chocolate, cola and cranberry & raspberry juice. Sweeteners were present in the reformulated chocolate (maltitol), cola (aspartame and acesulfame-K) and juice (sucralose) samples. Healthy, non-smoking consumers (n = 116; 55 men, 61 women, age: 33 ± 9 years; BMI: 25.7 ± 4.6 kg/m2) rated the products for overall liking and on liking of appearance, flavor and texture using a nine-point hedonic scale. There were significant differences between standard and reduced sugar products in consumers’ overall liking and on liking of each modality (appearance, flavor and texture; all P < 0.0001). For overall liking, only the regular beans and cola were significantly more liked than their reformulated counterparts (P < 0.0001). Cluster analysis identified three consumer clusters that were representative of different patterns of consumer liking. For the largest cluster (cluster 3: 45%), there was a significant difference in mean liking scores across all products, except jam. Differences in liking were predominantly driven by sweet taste in 2 out of 3 clusters. The current research has demonstrated that a high proportion of consumers prefer conventional products over sugar-reduced products across a wide range of product types (45%) or across selected products (27%), when tasted unbranded, and so there is room for further optimization of commercial reduced sugar products that were evaluated in the current study. Future work should evaluate strategies to facilitate compliance to dietary recommendations on NMES and free sugars, such as the impact of sugar-reduced food exposure on their acceptance.

Optimization of a sponge cake formulation with inulin as fat replacer: structure, physicochemical, and sensory properties

The effects of several fat replacement levels (0%, 35%, 50%, 70%, and 100%) by inulin in sponge cake microstructure and physicochemical properties were studied. Oil substitution for inulin decreased significantly (P < 0.05) batter viscosity, giving heterogeneous bubbles size distributions as it was observed by light microscopy. Using confocal laser scanning microscopy the fat was observed to be located at the bubbles’ interface, enabling an optimum crumb cake structure development during baking. Cryo-SEM micrographs of cake crumbs showed a continuous matrix with embedded starch granules and coated with oil; when fat replacement levels increased, starch granules appeared as detached structures. Cakes with fat replacement up to 70% had a high crumb air cell values; they were softer and rated as acceptable by an untrained sensory panel (n = 51). So, the reformulation of a standard sponge cake recipe to obtain a new product with additional health benefits and accepted by consumers is achieved.

Energy compensation following consumption of sugar-reduced products: a randomized controlled trial

PURPOSE: Consumption of sugar-reformulated products (commercially available foods and beverages that have been reduced in sugar content through reformulation) is a potential strategy for lowering sugar intake at a population level. The impact of sugar-reformulated products on body weight, energy balance (EB) dynamics and cardiovascular disease risk indicators has yet to be established. The REFORMulated foods (REFORM) study examined the impact of an 8-week sugar-reformulated product exchange on body weight, EB dynamics, blood pressure, arterial stiffness, glycemia and lipemia. METHODS: A randomized, controlled, double-blind, crossover dietary intervention study was performed with fifty healthy normal to overweight men and women (age 32.0 ± 9.8 year, BMI 23.5 ± 3.0 kg/m2) who were randomly assigned to consume either regular sugar or sugar-reduced foods and beverages for 8 weeks, separated by 4-week washout period. Body weight, energy intake (EI), energy expenditure and vascular markers were assessed at baseline and after both interventions. RESULTS: We found that carbohydrate (P < 0.001), total sugars (P < 0.001) and non-milk extrinsic sugars (P < 0.001) (% EI) were lower, whereas fat (P = 0.001) and protein (P = 0.038) intakes (% EI) were higher on the sugar-reduced than the regular diet. No effects on body weight, blood pressure, arterial stiffness, fasting glycemia or lipemia were observed. CONCLUSIONS: Consumption of sugar-reduced products, as part of a blinded dietary exchange for an 8-week period, resulted in a significant reduction in sugar intake. Body weight did not change significantly, which we propose was due to energy compensation.