The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

A nanometre-scale non-periodic structural variation in high temperature superconducting ceramics and the implications for properties

Non-periodic structural variation has been found in the high T-c cuprates, YBa2Cu3O7-x and Hg0.67Pb0.33Ba2Ca2Cu3O8+delta, by image analysis of high resolution transmission electron microscope (HRTEM) images. We use two methods for analysis of the HRTEM images. The first method is a means for measuring the bending of lattice fringes at twin planes. The second method is a low-pass filter technique which enhances information contained by diffuse-scattered electrons and reveals what appears to be an interference effect between domains of differing lattice parameter in the top and bottom of the thin foil. We believe that these methods of image analysis could be usefully applied to the many thousands of HRTEM images that have been collected by other workers in the high temperature superconductor field. This work provides direct structural evidence for phase separation in high T-c cuprates, and gives support to recent stripes models that have been proposed to explain various angle resolved photoelectron spectroscopy and nuclear magnetic resonance data. We believe that the structural variation is a response to an opening of an electronic solubility gap where holes are not uniformly distributed in the material but are confined to metallic stripes. Optimum doping may occur as a consequence of the diffuse boundaries between stripes which arise from spinodal decomposition. Theoretical ideas about the high T-c cuprates which treat the cuprates as homogeneous may need to be modified in order to take account of this type of structural variation.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

Prediction of mortality using dobutamine echocardiography

OBJECTIVES We sought to find out whether dobutamine echocardiography (DbE) could provide independent prediction of total and cardiac mortality, incremental to clinical and angiographic variables. BACKGROUND Existing outcome studies with DbE have examined composite end points, rather than death, over a relatively short follow-up. METHODS Clinical and stress data were collected in 3,156 patients (age 63 +/- 12 years, 1,801 men) undergoing DbE. Significant stenoses (>50% diameter) were identified in 70% of 1,073 patients undergoing coronary angiography. Total and cardiac mortality were identified over nine years of follow-up (mean 3.8 +/- 1.9). Cox models were used to analyze the effect of ischemia and other variables, independent of other determinants of mortality. RESULTS The dobutamine echocardiogram was abnormal in 1,575 patients (50%). Death occurred in 716 patients (23%), 259 of whom (8%) were thought to have died from cardiac causes. Patients with normal DbE had a total mortality of 8% per year and a cardiac mortality of 1% per year over the first four years of follow-up. Ischemia and the extent of abnormal wall motion were independent predictors of cardiac death, together with age and heart failure. In sequential Cox models, the predictive power of clinical data alone (model chi-square 115) was strengthened by adding the resting left ventricular function (model chi-square 138) and the results of DbE (model chi-square 181). In the subgroup undergoing coronary angiography, the power of the model was increased to a minor degree by the addition of coronary anatomy data. CONCLUSIONS Dobutamine echocardiography is an independent predictor of death, incremental to other data. While a normal dobutamine echocardiogram predicts low risk of cardiac death ton the order of 1% per year), this risk increases with the extent of abnormal wall motion at rest and stress, (J Am Coil Cardiol 2001;37:754-60) (C) 2001 by the American College of Cardiology.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

Changing pay systems, occupational concentration and the gender pay gap: Evidence from Australia and the UK

While aggregate level pay equity comparisons between Australia and the UK confirm expectations based on their different wage distributions and regulatory systems, observation of trends and occupational level analysis reveal additional complexity. Our analysis suggests the need for a multi-faceted approach to closing the average gender pay gap.

Stenotherms at sub-zero temperatures: thermal dependence of swimming performance in Antarctic fish

We examined the burst swimming performance of two Antarctic fishes, Trematomus bernacchii and T. centronotus, at five temperatures between -1 degreesC and 10 degreesC. As Antarctic fishes are considered one of the most cold specialised and stenothermal of all ectotherms, we predicted they would possess a narrow thermal performance breadth for burst swimming and a correlative decrease in performance at high temperatures. Burst swimming was assessed by videotaping swimming sequences with a 50-Hz video camera and analysing the sequences frame-by-frame to determine maximum velocity, the distance moved throughout the initial 200 ms, and the time taken to reach maximum velocity. In contrast to our prediction, we found both species possessed a wide thermal performance breadth for burst swimming. Although maximum swimming velocity for both T. bernacchii and T. centronotus was significantly highest at 6 degreesC, maximum velocity at ah other test temperatures was less than 20% lower. Thus, it appears that specialisation to a highly stable and cold environment is not necessarily associated with a narrow thermal performance breadth for burst swimming in Antarctic fish. We also examined the ability of the Antarctic fish Pagothenia borchgrevinki to acclimate their burst-swimming performance to different temperatures. We exposed P, borchgrevinki to either -1 degreesC or 4 degreesC for 4 weeks and tested their burst-swimming performance at four temperatures between -1 degreesC and 10 degreesC. Burst-swimming performance of Pagothenia borchgrevinki was unaffected by exposure to either -1 degreesC or 4 degreesC for 4 weeks. Maximum swimming velocity of both acclimation groups was thermally independent over the total temperature range of -1 degreesC to 10 degreesC. Therefore, the loss of any capacity to restructure the phenotype and an inability to thermally acclimate swimming performance appears to be associated with inhabiting a highly stable thermal environment.

Apoptotic deletion of Th cells specific for the 19-kDa carboxyl-terminal fragment of merozoite surface protein 1 during malaria infection

Immunity induced by the 19-kDa fragment of merozoite surface protein 1 is dependent on CD4(+) Th cells. However, we found that adoptively transferred CFSE-labeled Th cells specific for an epitope on Plasmodium yoelii 19-kDa fragment of merozoite surface protein 1 (peptide (p)24), but not OVA-specific T cells, were deleted as a result of P. yoelii infection. As a result of infection, spleen cells recovered from infected p24-specific T cell-transfused mice demonstrated reduced response to specific Ag. A higher percentage of CFSE-labeled p24-specific T cells stained positive with annexin and anti-active caspase-3 in infected compared with uninfected mice, suggesting that apoptosis contributed to deletion of p24-specific T cells during infection. Apoptosis correlated with increased percentages of p24-specific T cells that stained positive for Fas from infected mice, suggesting that P. yoelii-induced apoptosis is, at least in part, mediated by Fas. However, bystander cells of other specificities also showed increased Fas expression during infection, suggesting that Fas expression alone is not sufficient for apoptosis. These data have implications for the development of immunity in the face of endemic parasite exposure.

Modern scientific methods and their potential in wastewater science and technology

Application of novel analytical and investigative methods such as fluorescence in situ hybridization, confocal laser scanning microscopy (CLSM), microelectrodes and advanced numerical simulation has led to new insights into micro-and macroscopic processes in bioreactors. However, the question is still open whether or not these new findings and the subsequent gain of knowledge are of significant practical relevance and if so, where and how. To find suitable answers it is necessary for engineers to know what can be expected by applying these modern analytical tools. Similarly, scientists could benefit significantly from an intensive dialogue with engineers in order to find out about practical problems and conditions existing in wastewater treatment systems. In this paper, an attempt is made to help bridge the gap between science and engineering in biological wastewater treatment. We provide an overview of recently developed methods in microbiology and in mathematical modeling and numerical simulation. A questionnaire is presented which may help generate a platform from which further technical and scientific developments can be accomplished. Both the paper and the questionnaire are aimed at encouraging scientists and engineers to enter into an intensive, mutually beneficial dialogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

A zero-augmented gamma mixed model for longitudinal data with many zeros

In many occupational safety interventions, the objective is to reduce the injury incidence as well as the mean claims cost once injury has occurred. The claims cost data within a period typically contain a large proportion of zero observations (no claim). The distribution thus comprises a point mass at 0 mixed with a non-degenerate parametric component. Essentially, the likelihood function can be factorized into two orthogonal components. These two components relate respectively to the effect of covariates on the incidence of claims and the magnitude of claims, given that claims are made. Furthermore, the longitudinal nature of the intervention inherently imposes some correlation among the observations. This paper introduces a zero-augmented gamma random effects model for analysing longitudinal data with many zeros. Adopting the generalized linear mixed model (GLMM) approach reduces the original problem to the fitting of two independent GLMMs. The method is applied to evaluate the effectiveness of a workplace risk assessment teams program, trialled within the cleaning services of a Western Australian public hospital.