Language processing with dynamic fields

We construct a mapping from complex recursive linguistic data structures to spherical wave functions using Smolensky's filler/role bindings and tensor product representations. Syntactic language processing is then described by the transient evolution of these spherical patterns whose amplitudes are governed by nonlinear order parameter equations. Implications of the model in terms of brain wave dynamics are indicated.

The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.

The Klein-Gordon equation in a domain with time-dependent boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time-dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.

Boundary value problems for the N-wave interaction equations

We consider boundary value problems for the N-wave interaction equations in one and two space dimensions, posed for x [greater-or-equal, slanted] 0 and x,y [greater-or-equal, slanted] 0, respectively. Following the recent work of Fokas, we develop an inverse scattering formalism to solve these problems by considering the simultaneous spectral analysis of the two ordinary differential equations in the associated Lax pair. The solution of the boundary value problems is obtained through the solution of a local Riemann–Hilbert problem in the one-dimensional case, and a nonlocal Riemann–Hilbert problem in the two-dimensional case.

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Effect of growth time on the surface and adhesion properties of Lactobacillus rhamnosus GG

Aims: To investigate the changes in the surface properties of Lactobacillus rhamnosus GG during growth, and relate them with the ability of the Lactobacillus cells to adhere to Caco-2 cells. Methods and Results: Lactobacillus rhamnosus GG was grown in complex medium, and cell samples taken at four time points and freeze dried. Untreated and trypsin treated freeze dried samples were analysed for their composition using SDS-PAGE analysis and Fourier transform infrared spectroscopy (FTIR), hydrophobicity and zeta potential, and for their ability to adhere to Caco-2 cells. The results suggested that in the case of early exponential phase samples (4 and 8 h), the net surface properties, i.e. hydrophobicity and charge, were determined to a large extent by anionic hydrophilic components, whereas in the case of stationary phase samples (13 and 26 h), hydrophobic proteins seemed to play the biggest role. Considerable differences were also observed between the ability of the different samples to adhere to Caco-2 cells; maximum adhesion was observed for the early stationary phase sample (13 h). The results suggested that the adhesion to Caco-2 cells was influenced by both proteins and non-proteinaceous compounds present on the surface of the Lactobacillus cells. Conclusion: The surface properties of Lact. rhamnosus GG changed during growth, which in return affected the ability of the Lactobacillus cells to adhere to Caco-2 cells. Significance and Impact of the Study: The levels of adhesion of Lactobacillus cells to Caco-2 cells were influenced by the growth time and reflected changes on the bacterial surface. This study provides critical information on the physicochemical factors that influence bacterial adhesion to intestinal cells.

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.

Free amino acids and sugars in rye grain: implications for acrylamide formation

Acrylamide forms from free asparagine and sugars during cooking, and products derived from the grain of cereals, including rye, contribute a large proportion of total dietary intake. In this study, free amino acid and sugar concentrations were measured in the grain of a range of rye varieties grown at locations in Hungary, France, Poland, and the United Kingdom and harvested in 2005, 2006, and 2007. Genetic and environmental (location and harvest year) effects on the levels of acrylamide precursors were assessed. The data showed free asparagine concentration to be the main determinant of acrylamide formation in heated rye flour, as it is in wheat. However, in contrast to wheat, sugar, particularly sucrose, concentration also correlated both with asparagine concentration and with acrylamide formed. Free asparagine concentration was shown to be under genetic (G), environmental (E), and integrated (G × E) control. The same was true for glucose, whereas maltose and fructose were affected mainly by environmental factors and sucrose was largely under genetic control. The ratio of variation due to varieties (genotype) to the total variation (a measure of heritability) for free asparagine concentration in the grain was 23%. Free asparagine concentration was closely associated with bran yield, whereas sugar concentration was associated with low Hagberg falling number. Rye grain was found to contain much higher concentrations of free proline than wheat grain, and less acrylamide formed per unit of asparagine in rye than in wheat flour.

Kinetic model for the formation of acrylamide during the finish-frying of commercial French fries

Acrylamide is formed from reducing sugars and asparagine during the preparation of French fries. The commercial preparation of French fries is a multistage process involving the preparation of frozen, par-fried potato strips for distribution to catering outlets, where they are finish-fried. The initial blanching, treatment in glucose solution, and par-frying steps are crucial because they determine the levels of precursors present at the beginning of the finish-frying process. To minimize the quantities of acrylamide in cooked fries, it is important to understand the impact of each stage on the formation of acrylamide. Acrylamide, amino acids, sugars, moisture, fat, and color were monitored at time intervals during the frying of potato strips that had been dipped in various concentrations of glucose and fructose during a typical pretreatment. A mathematical model based on the fundamental chemical reaction pathways of the finish-frying was developed, incorporating moisture and temperature gradients in the fries. This showed the contribution of both glucose and fructose to the generation of acrylamide and accurately predicted the acrylamide content of the final fries.

A comparative analysis of the accuracy and uncertainty in real estate and macroeconomic forecasts

We compare and contrast the accuracy and uncertainty in forecasts of rents with those for a variety of macroeconomic series. The results show that in general forecasters tend to be marginally more accurate in the case of macro-economic series than with rents. In common across all of the series, forecasts tend to be smoothed with forecasters under-estimating performance during economic booms, and vice-versa in recessions We find that property forecasts are affected by economic uncertainty, as measured by disagreement across the macro-forecasters. Increased uncertainty leads to increased dispersion in the rental forecasts and a reduction in forecast accuracy.

Rationality and momentum in real estate investment forecasts

This study examines the rationality and momentum in forecasts for rental, capital value and total returns for the real estate investment market in the United Kingdom. In order to investigate if forecasters are affected by the general economic conditions present at the time of forecast we incorporate into the analysis Gross Domestic Product(GDP) and the Default Spread (DS). The empirical findings show high levels of momentum in the forecasts, with highly persistent forecast errors. The results also indicate that forecasters are affected by adverse conditions. This is consistent with the finding that they tend to exhibit greater forecast error when the property market is underperforming and vice-versa.

Whatever works: proportionality as a constitutional doctrine

In The Global Model of Constitutional Rights Kai Möller claims that the proportionality test is underlain by an expansive moral right to autonomy. This putative right protects everything that advances one’s self-conception. It may of course be limited when balanced against other considerations such as the rights of others. But it always creates a duty on the state to justify the limitation. Möller further contends that the practice of proportionality can best be understood as protecting the right to autonomy. This review article summarizes the main tenets of Möller’s theory and criticizes them on two counts. First, it disputes the existence of a general right to autonomy; such a right places an unacceptably heavy burden on others. Second, it argues that we do not need to invoke a right to autonomy to explain and justify the main features of the practice of proportionality. Like other constitutional doctrines, proportionality is defensible, if it is grounded in pragmatic –mainly epistemic and institutional- considerations about how to increase overall rights compliance. These considerations are independent of any substantive theory of rights.