On the numerical integration of a class of singular perturbation problems

A three-point difference scheme recently proposed in Ref. 1 for the numerical solution of a class of linear, singularly perturbed, two-point boundary-value problems is investigated. The scheme is derived from a first-order approximation to the original problem with a small deviating argument. It is shown here that, in the limit, as the deviating argument tends to zero, the difference scheme converges to a one-sided approximation to the original singularly perturbed equation in conservation form. The limiting scheme is shown to be stable on any uniform grid. Therefore, no advantage arises from using the deviating argument, and the most accurate and efficient results are obtained with the deviation at its zero limit.

Attention, visual consciousness and indeterminacy

I propose a new argument showing that conscious vision sometimes depends constitutively on conscious attention. I criticise traditional arguments for this constitutive connection, on the basis that they fail adequately to dissociate evidence about visual consciousness from evidence about attention. On the same basis, I criticise Ned Block's recent counterargument that conscious vision is independent of one sort of attention (‘cognitive access'). Block appears to achieve the dissociation only because he underestimates the indeterminacy of visual consciousness. I then appeal to empirical work on the interaction between visual indeterminacy and attention, to argue for the constitutive connection.

Transnational urbanism in Port of Spain: returning middle-class urban elites

Port of Spain, Trinidad offers an ideal context in which to analyze pre-retirement return migration to a Global South urban realm, expanding transnational urban research beyond the conventional focus on Global North metropolitan destinations. In this article, we draw on the transnational narratives of a selected sample of relatively youthful Trinidadians, who have spent many years abroad acquiring education and professional experience, but who have then decided to return in mid-career to the capital region of the island nation of their birth, or of their parent(s). Theoretically, we position these returning professionals as members of a "middling" transnational urban class whose return is at least partly motivated by a desire to "make a difference." Our results contribute to a growing literature that documents the role of transnational middle-class urban elites returning elsewhere in the Carribbean: "middling" transnational urbanism is reshaping key facets of urbanization in the Global South.

A neurofuzzy classifier for two class problems

A neurofuzzy classifier identification algorithm is introduced for two class problems. The initial fuzzy base construction is based on fuzzy clustering utilizing a Gaussian mixture model (GMM) and the analysis of covariance (ANOVA) decomposition. The expectation maximization (EM) algorithm is applied to determine the parameters of the fuzzy membership functions. Then neurofuzzy model is identified via the supervised subspace orthogonal least square (OLS) algorithm. Finally a logistic regression model is applied to produce the class probability. The effectiveness of the proposed neurofuzzy classifier has been demonstrated using a real data set.

Elastic-net prefiltering for two-class classification

A two-stage linear-in-the-parameter model construction algorithm is proposed aimed at noisy two-class classification problems. The purpose of the first stage is to produce a prefiltered signal that is used as the desired output for the second stage which constructs a sparse linear-in-the-parameter classifier. The prefiltering stage is a two-level process aimed at maximizing a model's generalization capability, in which a new elastic-net model identification algorithm using singular value decomposition is employed at the lower level, and then, two regularization parameters are optimized using a particle-swarm-optimization algorithm at the upper level by minimizing the leave-one-out (LOO) misclassification rate. It is shown that the LOO misclassification rate based on the resultant prefiltered signal can be analytically computed without splitting the data set, and the associated computational cost is minimal due to orthogonality. The second stage of sparse classifier construction is based on orthogonal forward regression with the D-optimality algorithm. Extensive simulations of this approach for noisy data sets illustrate the competitiveness of this approach to classification of noisy data problems.

The effect of class size on student achievement: evidence from Bangladesh

This study examines the effect of class size on student achievement in Bangladesh using national secondary school survey data. A Ministry of Education rule regarding allocation of teachers to secondary grades is exploited to construct an instrument for class size. This rule causes a discontinuity between grade enrolment and class size thereby generating exogenous variation in the latter. It is found that OLS and IV estimates of class size effects have perverse signs: both yield a positive coefficient on the class size variable. The results suggest that reduction in class size in secondary grades is not efficient in a developing country like Bangladesh. Last, as by-product, some evidence is found suggesting that greater competition among schools improve student achievement.

Spectral gap for Glauber type dynamics for a special class of potentials

We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on Rd. These Glauber type dynamics are Markov processes constructed for pre-given reversible measures. A representation for the ``carré du champ'' and ``second carré du champ'' for the associate infinitesimal generators L are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of L are given. These techniques are applied to Glauber dynamics associated to Gibbs measure and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with non-trivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.

Creating a world class business through a merger of two equals: an interview with Paul Walsh, Chief Executive Officer of Diageo Plc

Purpose – The purpose of this paper is to explore, from a practical point-of-view, a number of key strategic issues that critically influence organisations' competitiveness. Design/methodology/approach – The paper is based on a semi-structured interview with Mr Paul Walsh, CEO of Diageo. Diageo is a highly successful company and Mr Walsh has played a central role in making Diageo the number one branded drink company in the world. Findings – The paper discusses the key attributes of successful merger, lessons from a complex cross boarder acquisition, rationale for strategic alliance with competitors, distinctive resources, and the role of corporate social responsibility. Research limitations/implications – It is not too often that management scholars have the opportunity to discuss with the CEOs of large multinationals the rational of key strategic decisions. In this paper these issues are explored from the perspective of a CEO of a large and successful company. The lessons, while not generalisable, offer unique insights to students of management and management researchers. Originality/value – The paper offers a bridge between theory and practice. It demonstrates that from Diageo's perspective the distinctive capabilities are intangible. It also offers insight into how to successfully execute strategic decision. In terms of originality it offers a view from the top, which is often missing from strategy research.

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.

On the solvability of a class of second kind integral equations on unbounded domains

We consider integral equations of the form ψ(x) = φ(x) + ∫Ωk(x, y)z(y)ψ(y) dy(in operator form ψ = φ + Kzψ), where Ω is some subset ofRn(n ≥ 1). The functionsk,z, and φ are assumed known, withz ∈ L∞(Ω) and φ ∈ Y, the space of bounded continuous functions on Ω. The function ψ ∈ Yis to be determined. The class of domains Ω and kernelskconsidered includes the case Ω = Rnandk(x, y) = κ(x − y) with κ ∈ L1(Rn), in which case, ifzis the characteristic function of some setG, the integral equation is one of Wiener–Hopf type. The main theorems, proved using arguments derived from collectively compact operator theory, are conditions on a setW ⊂ L∞(Ω) which ensure that ifI − Kzis injective for allz ∈ WthenI − Kzis also surjective and, moreover, the inverse operators (I − Kz)−1onYare bounded uniformly inz. These general theorems are used to recover classical results on Wiener–Hopf integral operators of21and19, and generalisations of these results, and are applied to analyse the Lippmann–Schwinger integral equation.

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.