Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Model based procedure for scale-up of wet overflow ball mills Part 1: Outline of the methodology

Bond's method for ball mill scale-up only gives the mill power draw for a given duty. This method is incompatible with computer modelling and simulation techniques. It might not be applicable for the design of fine grinding ball mills and ball mills preceded by autogenous and semi-autogenous grinding mills. Model-based ball mill scale-up methods have not been validated using a wide range of full-scale circuit data. Their accuracy is therefore questionable. Some of these methods also need expensive pilot testing. A new ball mill scale-up procedure is developed which does not have these limitations. This procedure uses data from two laboratory tests to determine the parameters of a ball mill model. A set of scale-up criteria then scales-up these parameters. The procedure uses the scaled-up parameters to simulate the steady state performance of full-scale mill circuits. At the end of the simulation, the scale-up procedure gives the size distribution, the volumetric flowrate and the mass flowrate of all the streams in the circuit, and the mill power draw.

Effect of power Doppler and digital subtraction techniques on the comparison of myocardial contrast echocardiography with SPECT

Objective-To compare the accuracy and feasibility of harmonic power Doppler and digitally subtracted colour coded grey scale imaging for the assessment of perfusion defect severity by single photon emission computed tomography (SPECT) in an unselected group of patients. Design-Cohort study. Setting-Regional cardiothoracic unit. Patients-49 patients (mean (SD) age 61 (11) years; 27 women, 22 men) with known or suspected coronary artery disease were studied with simultaneous myocardial contrast echo (MCE) and SPECT after standard dipyridamole stress. Main outcome measures-Regional myocardial perfusion by SPECT, performed with Tc-99m tetrafosmin, scored qualitatively and also quantitated as per cent maximum activity. Results-Normal perfusion was identified by SPECT in 225 of 270 segments (83%). Contrast echo images were interpretable in 92% of patients. The proportion of normal MCE by grey scale, subtracted, and power Doppler techniques were respectively 76%, 74%, and 88% (p < 0.05) at > 80% of maximum counts, compared with 65%, 69%, and 61% at < 60% of maximum counts. For each technique, specificity was lowest in the lateral wail, although power Doppler was the least affected. Grey scale and subtraction techniques were least accurate in the septal wall, but power Doppler showed particular problems in the apex. On a per patient analysis, the sensitivity was 67%, 75%, and 83% for detection of coronary artery disease using grey scale, colour coded, and power Doppler, respectively, with a significant difference between power Doppler and grey scale only (p < 0.05). Specificity was also the highest for power Doppler, at 55%, but not significantly different from subtracted colour coded images. Conclusions-Myocardial contrast echo using harmonic power Doppler has greater accuracy than with grey scale imaging and digital subtraction. However, power Doppler appears to be less sensitive for mild perfusion defects.

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.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

On surrogate methods for detecting lateral gene transfer

Surrogate methods for detecting lateral gene transfer are those that do not require inference of phylogenetic trees. Herein I apply four such methods to identify open reading frames (ORFs) in the genome of Escherichia coli K12 that may have arisen by lateral gene transfer. Only two of these methods detect the same ORFs more frequently than expected by chance, whereas several intersections contain many fewer ORFs than expected. Each of the four methods detects a different non-random set of ORFs. The methods may detect lateral ORFs of different relative ages; testing this hypothesis will require rigorous inference of trees. (C) 2001 Federation of European Microbiological Societies. Published by Elsevier Science BN. All rights reserved.

Stickiness in foods: A review of mechanisms and test methods

Problems associated with the stickiness of food in processing and storage practices along with its causative factors are outlined. Fundamental mechanisms that explain why and how food products become sticky are discussed. Methods currently in use for characterizing and overcoming stickiness problems in food processing and storage operations are described. The use of glass transition temperature-based model, which provides a rational basis for understanding and characterizing the stickiness of many food products, is highlighted.

'Neighbourhood' size, dispersal and density estimates in the prickly forest skink (Gnypetoscincus queenslandiae) using individual genetic and demographic methods

Dispersal, or the amount of dispersion between an individual's birthplace and that of its offspring, is of great importance in population biology, behavioural ecology and conservation, however, obtaining direct estimates from field data on natural populations can be problematic. The prickly forest skink, Gnypetoscincus queenslandiae, is a rainforest endemic skink from the wet tropics of Australia. Because of its log-dwelling habits and lack of definite nesting sites, a demographic estimate of dispersal distance is difficult to obtain. Neighbourhood size, defined as 4 piD sigma (2) (where D is the population density and sigma (2) the mean axial squared parent-offspring dispersal rate), dispersal and density were estimated directly and indirectly for this species using mark-recapture and microsatellite data, respectively, on lizards captured at a local geographical scale of 3 ha. Mark-recapture data gave a dispersal rate of 843 m(2)/generation (assuming a generation time of 6.5 years), a time-scaled density of 13 635 individuals * generation/km(2) and, hence, a neighbourhood size of 144 individuals. A genetic method based on the multilocus (10 loci) microsatellite genotypes of individuals and their geographical location indicated that there is a significant isolation by distance pattern, and gave a neighbourhood size of 69 individuals, with a 95% confidence interval between 48 and 184. This translates into a dispersal rate of 404 m(2)/generation when using the mark-recapture density estimation, or an estimate of time-scaled population density of 6520 individuals * generation/km(2) when using the mark-recapture dispersal rate estimate. The relationship between the two categories of neighbourhood size, dispersal and density estimates and reasons for any disparities are discussed.

Surface diffusion of hydrocarbons in activated carbon: Comparison between constant molar flow, differential permeation and differential adsorption bed methods

This paper presents the comparison of surface diffusivities of hydrocarbons in activated carbon. The surface diffusivities are obtained from the analysis of kinetic data collected using three different kinetics methods- the constant molar flow, the differential adsorption bed and the differential permeation methods. In general the values of surface diffusivity obtained by these methods agree with each other, and it is found that the surface diffusivity increases very fast with loading. Such a fast increase can not be accounted for by a thermodynamic Darken factor, and the surface heterogeneity only partially accounts for the fast rise of surface diffusivity versus loading. Surface diffusivities of methane, ethane, propane, n-butane, n-hexane, benzene and ethanol on activated carbon are reported in this paper.

Power of the joint segregation analysis method for testing mixed major-gene and polygene inheritance models of quantitative traits

Understanding the genetic architecture of quantitative traits can greatly assist the design of strategies for their manipulation in plant-breeding programs. For a number of traits, genetic variation can be the result of segregation of a few major genes and many polygenes (minor genes). The joint segregation analysis (JSA) is a maximum-likelihood approach for fitting segregation models through the simultaneous use of phenotypic information from multiple generations. Our objective in this paper was to use computer simulation to quantify the power of the JSA method for testing the mixed-inheritance model for quantitative traits when it was applied to the six basic generations: both parents (P-1 and P-2), F-1, F-2, and both backcross generations (B-1 and B-2) derived from crossing the F-1 to each parent. A total of 1968 genetic model-experiment scenarios were considered in the simulation study to quantify the power of the method. Factors that interacted to influence the power of the JSA method to correctly detect genetic models were: (1) whether there were one or two major genes in combination with polygenes, (2) the heritability of the major genes and polygenes, (3) the level of dispersion of the major genes and polygenes between the two parents, and (4) the number of individuals examined in each generation (population size). The greatest levels of power were observed for the genetic models defined with simple inheritance; e.g., the power was greater than 90% for the one major gene model, regardless of the population size and major-gene heritability. Lower levels of power were observed for the genetic models with complex inheritance (major genes and polygenes), low heritability, small population sizes and a large dispersion of favourable genes among the two parents; e.g., the power was less than 5% for the two major-gene model with a heritability value of 0.3 and population sizes of 100 individuals. The JSA methodology was then applied to a previously studied sorghum data-set to investigate the genetic control of the putative drought resistance-trait osmotic adjustment in three crosses. The previous study concluded that there were two major genes segregating for osmotic adjustment in the three crosses. Application of the JSA method resulted in a change in the proposed genetic model. The presence of the two major genes was confirmed with the addition of an unspecified number of polygenes.