A sparse parallel hybrid Monte Carlo algorithm for matrix computations

In this paper we introduce a new algorithm, based on the successful work of Fathi and Alexandrov, on hybrid Monte Carlo algorithms for matrix inversion and solving systems of linear algebraic equations. This algorithm consists of two parts, approximate inversion by Monte Carlo and iterative refinement using a deterministic method. Here we present a parallel hybrid Monte Carlo algorithm, which uses Monte Carlo to generate an approximate inverse and that improves the accuracy of the inverse with an iterative refinement. The new algorithm is applied efficiently to sparse non-singular matrices. When we are solving a system of linear algebraic equations, Bx = b, the inverse matrix is used to compute the solution vector x = B(-1)b. We present results that show the efficiency of the parallel hybrid Monte Carlo algorithm in the case of sparse matrices.

Computational complexity of weighted splitting schemes on parallel computers

In models of complicated physical-chemical processes operator splitting is very often applied in order to achieve sufficient accuracy as well as efficiency of the numerical solution. The recently rediscovered weighted splitting schemes have the great advantage of being parallelizable on operator level, which allows us to reduce the computational time if parallel computers are used. In this paper, the computational times needed for the weighted splitting methods are studied in comparison with the sequential (S) splitting and the Marchuk-Strang (MSt) splitting and are illustrated by numerical experiments performed by use of simplified versions of the Danish Eulerian model (DEM).

Parallel implementation and one year experiments with the Danish Eulerian Model

Large scale air pollution models are powerful tools, designed to meet the increasing demand in different environmental studies. The atmosphere is the most dynamic component of the environment, where the pollutants can be moved quickly on far distnce. Therefore the air pollution modeling must be done in a large computational domain. Moreover, all relevant physical, chemical and photochemical processes must be taken into account. In such complex models operator splitting is very often applied in order to achieve sufficient accuracy as well as efficiency of the numerical solution. The Danish Eulerian Model (DEM) is one of the most advanced such models. Its space domain (4800 × 4800 km) covers Europe, most of the Mediterian and neighboring parts of Asia and the Atlantic Ocean. Efficient parallelization is crucial for the performance and practical capabilities of this huge computational model. Different splitting schemes, based on the main processes mentioned above, have been implemented and tested with respect to accuracy and performance in the new version of DEM. Some numerical results of these experiments are presented in this paper.

On improvement of classification accuracy for stochastic discrimination

Stochastic discrimination (SD) depends on a discriminant function for classification. In this paper, an improved SD is introduced to reduce the error rate of the standard SD in the context of a two-class classification problem. The learning procedure of the improved SD consists of two stages. Initially a standard SD, but with shorter learning period is carried out to identify an important space where all the misclassified samples are located. Then the standard SD is modified by 1) restricting sampling in the important space, and 2) introducing a new discriminant function for samples in the important space. It is shown by mathematical derivation that the new discriminant function has the same mean, but with a smaller variance than that of the standard SD for samples in the important space. It is also analyzed that the smaller the variance of the discriminant function, the lower the error rate of the classifier. Consequently, the proposed improved SD improves standard SD by its capability of achieving higher classification accuracy. Illustrative examples are provided to demonstrate the effectiveness of the proposed improved SD.

A similarity solution for a shock reflection problem in isentropic gas dynamics

A one-dimensional shock-reflection test problem in the case of slab, cylindrical, or spherical symmetry is discussed. The differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankie-Hugoniot shock relations.

Numerical solution of some nonlocal, nonlinear dispersive wave equations

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

Assessing the accuracy of a computerized decision support system for digoxin dosing in primary care: an observational study

Background: This study was carried out as part of a European Union funded project (PharmDIS-e+), to develop and evaluate software aimed at assisting physicians with drug dosing. A drug that causes particular problems with drug dosing in primary care is digoxin because of its narrow therapeutic range and low therapeutic index. Objectives: To determine (i) accuracy of the PharmDIS-e+ software for predicting serum digoxin levels in patients who are taking this drug regularly; (ii) whether there are statistically significant differences between predicted digoxin levels and those measured by a laboratory and (iii) whether there are differences between doses prescribed by general practitioners and those suggested by the program. Methods: We needed 45 patients to have 95% Power to reject the null hypothesis that the mean serum digoxin concentration was within 10% of the mean predicted digoxin concentration. Patients were recruited from two general practices and had been taking digoxin for at least 4 months. Exclusion criteria were dementia, low adherence to digoxin and use of other medications known to interact to a clinically important extent with digoxin. Results: Forty-five patients were recruited. There was a correlation of 0·65 between measured and predicted digoxin concentrations (P < 0·001). The mean difference was 0·12 μg/L (SD 0·26; 95% CI 0·04, 0·19, P = 0·005). Forty-seven per cent of the patients were prescribed the same dose as recommended by the software, 44% were prescribed a higher dose and 9% a lower dose than recommended. Conclusion: PharmDIS-e+ software was able to predict serum digoxin levels with acceptable accuracy in most patients.

Evidence that indirect inhibition of saccade initiation improves saccade accuracy

Saccadic eye-movements to a visual target are less accurate if there are distracters close to its location (local distracters). The addition of more distracters, remote from the target location (remote distracters), invokes an involuntary increase in the response latency of the saccade and attenuates the effect of local distracters on accuracy. This may be due to the target and distracters directly competing (direct route) or to the remote distracters acting to impair the ability to disengage from fixation (indirect route). To distinguish between these we examined the development of saccade competition by recording saccade latency and accuracy responses made to a target and local distracter compared with those made with an addition of a remote distracter. The direct route would predict that the remote distracter impacts on the developing competition between target and local distracter, while the indirect route would predict no change as the accuracy benefit here derives from accessing the same competitive process but at a later stage. We found that the presence of the remote distracter did not change the pattern of accuracy improvement. This suggests that the remote distracter was acting along an indirect route that inhibits disengagement from fixation, slows saccade initiation, and enables more accurate saccades to be made.

Overseas trained teachers: part of a problem or part of a solution?

Overseas trained teachers (OTTs) have grown in numbers during the past decade, particularly in London and the South East of England. In this recruitment explosion many OTTs have experienced difficulties. In professional literature as well as press coverage OTTs often become part of a deficit discourse. A small-scale pilot investigation of OTT experience has begun to suggest why OTTs have been successful as well as the principal challenges they have faced. An important factor in their success was felt to be the quality of support in school from others on the staff. Major challenges included the complexity of the primary curriculum. The argument that globalisation leads to brain-drain may be exaggerated. Suggestions for further research are made, which might indicate the positive benefits OTTs can bring to a school.

SARS coronavirus unique domain: three-domain molecular architecture in solution and RNA binding

Nonstructural protein 3 of the severe acute respiratory syndrome (SARS) coronavirus includes a "SARS-unique domain" (SUD) consisting of three globular domains separated by short linker peptide segments. This work reports NMR structure determinations of the C-terminal domain (SUD-C) and a two-domain construct (SUD-MC) containing the middle domain (SUD-M) and the C-terminal domain, and NMR data on the conformational states of the N-terminal domain (SUD-N) and the SUD-NM two-domain construct. Both SUD-N and SUD-NM are monomeric and globular in solution; in SUD-NM, there is high mobility in the two-residue interdomain linking sequence, with no preferred relative orientation of the two domains. SUD-C adopts a frataxin like fold and has structural similarity to DNA-binding domains of DNA-modifying enzymes. The structures of both SUD-M (previously determined) and SUD-C (from the present study) are maintained in SUD-MC, where the two domains are flexibly linked. Gel-shift experiments showed that both SUD-C and SUD-MC bind to single-stranded RNA and recognize purine bases more strongly than pyrimidine bases, whereby SUD-MC binds to a more restricted set of purine-containing RNA sequences than SUD-M. NMR chemical shift perturbation experiments with observations of (15)N-labeled proteins further resulted in delineation of RNA binding sites (i.e., in SUD-M, a positively charged surface area with a pronounced cavity, and in SUD-C, several residues of an anti-parallel beta-sheet). Overall, the present data provide evidence for molecular mechanisms involving the concerted actions of SUD-M and SUD-C, which result in specific RNA binding that might be unique to the SUD and, thus, to the SARS coronavirus.