RILU preconditioning; a computational study

AbstractWe present a computational study of the RILU preconditioning strategy applied to finite-difference discretizations of self-adjoint elliptic boundary value problems with highly discontinuous coefficients. The behaviour of the eigenvalues of the preconditioned system, the numerical stability of the factorization process and the efficiency of the preconditioning strategy are discussed

Unstable eigenmodes are possible drivers for cardiac arrhythmias

The well-organized contraction of each heartbeat is enabled by an electrical wave traversing and exciting the myocardium in a regular manner. Perturbations to this wave, referred to as arrhythmias, can lead to lethal fibrillation if not treated within minutes. One manner in which arrhythmias originate is an ill-fated interaction of the regular electrical signal controlling the heartbeat, the sinus wave, with an ectopic stimulus. It is not fully understood how and when ectopic waves are generated. Based on mathematical models, we show that ectopic beats can be characterized in terms of unstable eigenmodes of the resting state

High‐resolution monthly precipitation climatologies over Norway (1981–2010): Joining numerical model data sets and in situ observations

The 1981-2010 monthly precipitation climatologies for Norway at 1 km resolution are presented. They are computed by an interpolation procedure (HCLIM+RK) combining the output from a numerical model with the in situ observations. Specifically, the regional climate model data set HCLIM-AROME, based on the dynamical downscaling of the global ERA-Interim reanalysis onto 2.5 km resolution, is considered together with 2009 rain-gauges located within the model domain. The precipitation climatologies are defined by superimposing the grid of 1981-2010 monthly normals from the numerical model and the kriging interpolation of station residuals. The combined approach aims at improving the quality of gridded climatologies and at providing reliable precipitation gradients also over those remote Norwegian regions not covered by observations, especially over the northernmost mountainous areas. The integration of rain-gauge data greatly reduces the original HCLIM-AROME biases. The HCLIM+RK errors obtained from the leave-one-out station validation turn out to be lower than those provided by two considered interpolation schemes based on observations only: a multi-linear local regression kriging (MLRK) and a local weighted linear regression (LWLR). As average over all months, the mean absolute (percentage) error is 10.0 mm (11%) for HCLIM+RK, and 11.4 (12%) and 11.6 mm (12%) for MLRK and LWLR, respectively. In addition, by comparing the results at both station and grid cell level, the accuracy of MLRK and LWLR is more sensitive to the spatial variability of station distribution over the domain and their interpolated fields are more affected by discontinuities and outliers, especially over those areas not covered by the rain-gauge network. The obtained HCLIM+RK climatologies clearly depict the main west-to-east gradient occurring from the orographic precipitation regime of the coast to the more continental climate of the inland and it allows to point out the features of the climatic subzones of Norway

Effective interactions and large-scale diagonalization for quantum dots

The widely used large-scale diagonalization method using harmonic oscillator basis functions (an instance of the Rayleigh-Ritz method, also called a spectral method, configuration-interaction method, or ``exact diagonalization'' method) is systematically analyzed using results for the convergence of Hermite function series. We apply this theory to a Hamiltonian for a one-dimensional model of a quantum dot. The method is shown to converge slowly, and the non-smooth character of the interaction potential is identified as the main problem with the chosen basis, while on the other hand its important advantages are pointed out. An effective interaction obtained by a similarity transformation is proposed for improving the convergence of the diagonalization scheme, and numerical experiments are performed to demonstrate the improvement. Generalizations to more particles and dimensions are discussed.Comment: 7 figures, submitted to Physical Review B Single reference error fixe

Finite difference schemes for the symmetric Keyfitz-Kranzer system

We are concerned with the convergence of numerical schemes for the initial value problem associated to the Keyfitz-Kranzer system of equations. This system is a toy model for several important models such as in elasticity theory, magnetohydrodynamics, and enhanced oil recovery. In this paper we prove the convergence of three difference schemes. Two of these schemes is shown to converge to the unique entropy solution. Finally, the convergence is illustrated by several examples.Comment: 31 page

Protocol for the SEED-Trial: Supported Employment and Preventing Early Disability

Early withdrawal or exclusion from the labor market leads to significant personal and societal costs. In Norway, the increasing numbers of young adults receiving disability pension is a growing problem. While a large body of research demonstrates positive effects of Supported Employment (SE) in patients with severe mental illness, no studies have yet investigated the effectiveness of SE in young adults with a range of social and health conditions who are receiving benefits

Estimating the number needed to treat from continuous outcomes in randomised controlled trials: methodological challenges and worked example using data from the UK Back Pain Exercise and Manipulation (BEAM) trial

Background Reporting numbers needed to treat (NNT) improves interpretability of trial results. It is unusual that continuous outcomes are converted to numbers of individual responders to treatment (i.e., those who reach a particular threshold of change); and deteriorations prevented are only rarely considered. We consider how numbers needed to treat can be derived from continuous outcomes; illustrated with a worked example showing the methods and challenges. Methods We used data from the UK BEAM trial (n = 1, 334) of physical treatments for back pain; originally reported as showing, at best, small to moderate benefits. Participants were randomised to receive 'best care' in general practice, the comparator treatment, or one of three manual and/or exercise treatments: 'best care' plus manipulation, exercise, or manipulation followed by exercise. We used established consensus thresholds for improvement in Roland-Morris disability questionnaire scores at three and twelve months to derive NNTs for improvements and for benefits (improvements gained+deteriorations prevented). Results At three months, NNT estimates ranged from 5.1 (95% CI 3.4 to 10.7) to 9.0 (5.0 to 45.5) for exercise, 5.0 (3.4 to 9.8) to 5.4 (3.8 to 9.9) for manipulation, and 3.3 (2.5 to 4.9) to 4.8 (3.5 to 7.8) for manipulation followed by exercise. Corresponding between-group mean differences in the Roland-Morris disability questionnaire were 1.6 (0.8 to 2.3), 1.4 (0.6 to 2.1), and 1.9 (1.2 to 2.6) points. Conclusion In contrast to small mean differences originally reported, NNTs were small and could be attractive to clinicians, patients, and purchasers. NNTs can aid the interpretation of results of trials using continuous outcomes. Where possible, these should be reported alongside mean differences. Challenges remain in calculating NNTs for some continuous outcomes