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.

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.

Gene expression changes in phosphorus deficient potato (Solanum tuberosum L.) leaves and the potential for diagnostic gene expression markers

Background: There are compelling economic and environmental reasons to reduce our reliance on inorganic phosphate (Pi) fertilisers. Better management of Pi fertiliser applications is one option to improve the efficiency of Pi fertiliser use, whilst maintaining crop yields. Application rates of Pi fertilisers are traditionally determined from analyses of soil or plant tissues. Alternatively, diagnostic genes with altered expression under Pi limiting conditions that suggest a physiological requirement for Pi fertilisation, could be used to manage Pifertiliser applications, and might be more precise than indirect measurements of soil or tissue samples. Results: We grew potato (Solanum tuberosum L.) plants hydroponically, under glasshouse conditions, to control their nutrient status accurately. Samples of total leaf RNA taken periodically after Pi was removed from the nutrient solution were labelled and hybridised to potato oligonucleotide arrays. A total of 1,659 genes were significantly differentially expressed following Pi withdrawal. These included genes that encode proteins involved in lipid, protein, and carbohydrate metabolism, characteristic of Pi deficient leaves and included potential novel roles for genes encoding patatin like proteins in potatoes. The array data were analysed using a support vector machine algorithm to identify groups of genes that could predict the Pi status of the crop. These groups of diagnostic genes were tested using field grown potatoes that had either been fertilised or unfertilised. A group of 200 genes could correctly predict the Pi status of field grown potatoes. Conclusions: This paper provides a proof-of-concept demonstration for using microarrays and class prediction tools to predict the Pi status of a field grown potato crop. There is potential to develop this technology for other biotic and abiotic stresses in field grown crops. Ultimately, a better understanding of crop stresses may improve our management of the crop, improving the sustainability of agriculture.

A novel transport mechanism for MOMP in Chlamydophila pneumoniae and its putative role in immune-therapy

Major outer membrane proteins (MOMPs) of Gram negative bacteria are one of the most intensively studied membrane proteins. MOMPs are essential for maintaining the structural integrity of bacterial outer membranes and in adaptation of parasites to their hosts. There is evidence to suggest a role for purified MOMP from Chlamydophila pneumoniae and corresponding MOMP-derived peptides in immune-modulation, leading to a reduced atherosclerotic phenotype in apoE−/− mice via a characteristic dampening of MHC class II activity. The work reported herein tests this hypothesis by employing a combination of homology modelling and docking to examine the detailed molecular interactions that may be responsible. A three-dimensional homology model of the C. pneumoniae MOMP was constructed based on the 14 transmembrane β-barrel crystal structure of the fatty acid transporter from Escherichia coli, which provides a plausible transport mechanism for MOMP. Ligand docking experiments were used to provide details of the possible molecular interactions driving the binding of MOMP-derived peptides to MHC class II alleles known to be strongly associated with inflammation. The docking experiments were corroborated by predictions from conventional immuno-informatic algorithms. This work supports further the use of MOMP in C. pneumoniae as a possible vaccine target and the role of MOMP-derived peptides as vaccine candidates for immune-therapy in chronic inflammation that can result in cardiovascular events.

Death has a touch of class: society and space in Brookwood Cemetery, 1853-1903

Changes in the cultures and spaces of death during the Victorian era reveal the shifting conceptualisations and mobilisations of class in this period. Using the example of Brookwood Necropolis, established 1852 in response to the contemporary burial reform debate, the paper explores tensions within the sanitary reform movement, 1853–1903. Whilst reformist ideology grounded the cemetery's practices in a discourse of inclusion, one of the consequences of reform was to reinforce class distinctions. Combined with commercial imperatives and the modern impulse towards separation of living and dead, this aspect of reform enacted a counter-discourse of alienation. The presence of these conflicting strands in the spaces and practices of the Necropolis and their changes during the time period reflect wider urban trends.

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.

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.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

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’.

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.