Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

Kinetic energy conserving integrators for Gaussian thermostatted SLLOD

A new integration scheme is developed for nonequilibrium molecular dynamics simulations where the temperature is constrained by a Gaussian thermostat. The utility of the scheme is demonstrated by its application to the SLLOD algorithm which is the standard nonequilibrium molecular dynamics algorithm for studying shear flow. Unlike conventional integrators, the new integrators are constructed using operator-splitting techniques to ensure stability and that little or no drift in the kinetic energy occurs. Moreover, they require minimum computer memory and are straightforward to program. Numerical experiments show that the efficiency and stability of the new integrators compare favorably with conventional integrators such as the Runge-Kutta and Gear predictor-corrector methods. (C) 1999 American Institute of Physics. [S0021-9606(99)50125-6].

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.

The use of a change in gentamicin clearance as an early predictor of gentamicin-induced nephrotoxicity

A retrospective review was undertaken in 744 patients who were dose-individualized with gentamicin once daily to evaluate a change in gentamicin clearance as a potential predictor of nephrotoxicity. The definition of nephrotoxicity was chosen to be a change in creatinine clearance greater than 20%. Similarly, a change in gentamicin clearance of greater than 20% was also considered a possible index of nephrotoxicity. Four criteria were developed to assess the usefulness of gentamicin clearance as a predictor of nephrotoxicity. Following the application of the inclusion/exclusion criteria, 132 patients were available for the analysis. The sensitivity, specificity, positive predictive value, and negative predictive value were assessed for each of the criteria. Receiver operating characteristic (ROC) curves were produced to determine if an optimum value in the change of gentamicin clearance could be found to maximize sensitivity and specificity. The overall incidence of nephrotoxicity based on a decrease in creatinine clearance by 20% or more was 3.8%. Women were overrepresented in the nephrotoxic group [71.4% versus 40.1% (P = 0.0025)]. Patients with nephrotoxicity had statistically longer treatment periods, increased cumulative dose, and more dosing predictions (P < 0.05 in each case). The sensitivity of the criteria ranged from 43 to 46%, and specificity ranged from 93 to 99%. The positive and negative predictive values ranged from 63 to 94% and 86 to 89%, respectively. In those patients in whom nephrotoxicity was predicted from a change in gentamicin clearance, this change occurred on average 3 days before the change in creatinine clearance (P < 0.05). A change in gentamicin clearance to predict nephrotoxicity may be a useful addition to current monitoring methods, although it is not the complete answer.

Adolescents' intentions to smoke as a predictor of smoking

Background. Adolescents' intentions to smoke are generally regarded as a valid and reliable predictor of subsequent smoking. This association is largely based on research with adults and needs a more detailed analysis for adolescents. Methods. Data on intentions and smoking status were collected as part of a longitudinal, birth-cohort study when the study members were 9, 11, 13, 15, 18, and 21 years of age. Results. The results showed that intention to smoke only had an important predictive power in the subgroup of previous nonsmokers. Among those already smoking (on a monthly basis or greater), previous level of smoking was a more important predictor of future behavior than intention to smoke. In addition, the effect of positive intention to smoke was nonlinear over age and had the greatest effect at age 15. Conclusion. The results indicated that in adolescence, measurement of intentions to smoke or not smoke cannot be assumed to be a general predictor of behavior at a later age for all groups of adolescents. (C) 2004 The Institute For Cancer Prevention and Elsevier Inc. All rights reserved.

Assessing the competitiveness of loss allocation methods in a deregulated electricity market

This paper critically assesses several loss allocation methods based on the type of competition each method promotes. This understanding assists in determining which method will promote more efficient network operations when implemented in deregulated electricity industries. The methods addressed in this paper include the pro rata [1], proportional sharing [2], loss formula [3], incremental [4], and a new method proposed by the authors of this paper, which is loop-based [5]. These methods are tested on a modified Nordic 32-bus network, where different case studies of different operating points are investigated. The varying results obtained for each allocation method at different operating points make it possible to distinguish methods that promote unhealthy competition from those that encourage better system operation.

Calculation of line integrals in boundary integral methods

We propose quadrature rules for the approximation of line integrals possessing logarithmic singularities and show their convergence. In some instances a superconvergence rate is demonstrated.

A framework for electricity price spike analysis with advanced data mining methods

There are many techniques for electricity market price forecasting. However, most of them are designed for expected price analysis rather than price spike forecasting. An effective method of predicting the occurrence of spikes has not yet been observed in the literature so far. In this paper, a data mining based approach is presented to give a reliable forecast of the occurrence of price spikes. Combined with the spike value prediction techniques developed by the same authors, the proposed approach aims at providing a comprehensive tool for price spike forecasting. In this paper, feature selection techniques are firstly described to identify the attributes relevant to the occurrence of spikes. A simple introduction to the classification techniques is given for completeness. Two algorithms: support vector machine and probability classifier are chosen to be the spike occurrence predictors and are discussed in details. Realistic market data are used to test the proposed model with promising results.

A demonstration of artificial dissipation effects in some finite volume solution methods for the Navier-Stokes equations

The artificial dissipation effects in some solutions obtained with a Navier-Stokes flow solver are demonstrated. The solvers were used to calculate the flow of an artificially dissipative fluid, which is a fluid having dissipative properties which arise entirely from the solution method itself. This was done by setting the viscosity and heat conduction coefficients in the Navier-Stokes solvers to zero everywhere inside the flow, while at the same time applying the usual no-slip and thermal conducting boundary conditions at solid boundaries. An artificially dissipative flow solution is found where the dissipation depends entirely on the solver itself. If the difference between the solutions obtained with the viscosity and thermal conductivity set to zero and their correct values is small, it is clear that the artificial dissipation is dominating and the solutions are unreliable.

A shift from passive teaching at medical conferences to more interactive methods improves physician learning

Conferences that deliver interactive sessions designed to enhance physician participation, such as role play, small discussion groups, workshops, hands-on training, problem- or case-based learning and individualised training sessions, are effective for physician education.