Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.

Sampling uncertainty properties of cloud fraction estimates from random transect observations

[1] Cloud cover is conventionally estimated from satellite images as the observed fraction of cloudy pixels. Active instruments such as radar and Lidar observe in narrow transects that sample only a small percentage of the area over which the cloud fraction is estimated. As a consequence, the fraction estimate has an associated sampling uncertainty, which usually remains unspecified. This paper extends a Bayesian method of cloud fraction estimation, which also provides an analytical estimate of the sampling error. This method is applied to test the sensitivity of this error to sampling characteristics, such as the number of observed transects and the variability of the underlying cloud field. The dependence of the uncertainty on these characteristics is investigated using synthetic data simulated to have properties closely resembling observations of the spaceborne Lidar NASA-LITE mission. Results suggest that the variance of the cloud fraction is greatest for medium cloud cover and least when conditions are mostly cloudy or clear. However, there is a bias in the estimation, which is greatest around 25% and 75% cloud cover. The sampling uncertainty is also affected by the mean lengths of clouds and of clear intervals; shorter lengths decrease uncertainty, primarily because there are more cloud observations in a transect of a given length. Uncertainty also falls with increasing number of transects. Therefore a sampling strategy aimed at minimizing the uncertainty in transect derived cloud fraction will have to take into account both the cloud and clear sky length distributions as well as the cloud fraction of the observed field. These conclusions have implications for the design of future satellite missions. This paper describes the first integrated methodology for the analytical assessment of sampling uncertainty in cloud fraction observations from forthcoming spaceborne radar and Lidar missions such as NASA's Calipso and CloudSat.

Systolic random number generation for genetic algorithms

A parallel hardware random number generator for use with a VLSI genetic algorithm processing device is proposed. The design uses an systolic array of mixed congruential random number generators. The generators are constantly reseeded with the outputs of the proceeding generators to avoid significant biasing of the randomness of the array which would result in longer times for the algorithm to converge to a solution. 1 Introduction In recent years there has been a growing interest in developing hardware genetic algorithm devices [1, 2, 3]. A genetic algorithm (GA) is a stochastic search and optimization technique which attempts to capture the power of natural selection by evolving a population of candidate solutions by a process of selection and reproduction [4]. In keeping with the evolutionary analogy, the solutions are called chromosomes with each chromosome containing a number of genes. Chromosomes are commonly simple binary strings, the bits being the genes.

Hydrolyzable tannin structures influence relative globular and random coil protein binding strengths

Binding parameters for the interactions of pentagalloyl glucose (PGG) and four hydrolyzable tannins (representing gallotannins and ellagitannins) with gelatin and bovine serum albumin (BSA) have been determined from isothermal titration calorimetry data. Equilibrium binding constants determined for the interaction of PGG and isolated mixtures of tara gallotannins and of sumac gallotannins with gelatin and BSA were of the same order of magnitude for each tannin (in the range of 10(4)-10(5) M-1 for stronger binding sites when using a binding model consisting of two sets of multiple binding sites). In contrast, isolated mixtures of chestnut ellagitannins and of myrabolan ellagitannins exhibited 3-4 orders of magnitude greater equilibrium binding constants for the interaction with gelatin (similar to 2 x 10(6) M-1) than for that with BSA (similar to 8 x 10(2) M-1). Binding stoichiometries revealed that the stronger binding sites on gelatin outnumbered those on BSA by a ratio of at least similar to 2:1 for all of the hydrolyzable tannins studied. Overall, the data revealed that relative binding constants for the interactions with gelatin and BSA are dependent on the structural flexibility of the tannin molecule.

Genetic diversity and structure of natural and managed populations of Cedrus atlantica (Pinaceae) assessed using random amplified polymorphic DNA

Cedrus atlantica (Pinaceae) is a large and exceptionally long-lived conifer native to the Rif and Atlas Mountains of North Africa. To assess levels and patterns of genetic diversity of this species. samples were obtained throughout the natural range in Morocco and from a forest plantation in Arbucies, Girona (Spain) and analyzed using RAPD markers. Within-population genetic diversity was high and comparable to that revealed by isozymes. Managed populations harbored levels of genetic variation similar to those found in their natural counterparts. Genotypic analyses Of Molecular variance (AMOVA) found that most variation was within populations. but significant differentiation was also found between populations. particularly in Morocco. Bayesian estimates of F,, corroborated the AMOVA partitioning and provided evidence for Population differentiation in C. atlantica. Both distance- and Bayesian-based Clustering methods revealed that Moroccan populations comprise two genetically distinct groups. Within each group, estimates of population differentiation were close to those previously reported in other gymnosperms. These results are interpreted in the context of the postglacial history of the species and human impact. The high degree of among-group differentiation recorded here highlights the need for additional conservation measures for some Moroccan Populations of C. atlantica.

Parametric accelerated failure time models with random effects and an application to kidney transplant survival

Accelerated failure time models with a shared random component are described, and are used to evaluate the effect of explanatory factors and different transplant centres on survival times following kidney transplantation. Different combinations of the distribution of the random effects and baseline hazard function are considered and the fit of such models to the transplant data is critically assessed. A mixture model that combines short- and long-term components of a hazard function is then developed, which provides a more flexible model for the hazard function. The model can incorporate different explanatory variables and random effects in each component. The model is straightforward to fit using standard statistical software, and is shown to be a good fit to the transplant data. Copyright (C) 2004 John Wiley Sons, Ltd.

Preventive maintenance models with random maintenance quality

In real-world environments it is usually difficult to specify the quality of a preventive maintenance (PM) action precisely. This uncertainty makes it problematic to optimise maintenance policy.-This problem is tackled in this paper by assuming that the-quality of a PM action is a random variable following a probability distribution. Two frequently studied PM models, a failure rate PM model and an age reduction PM model, are investigated. The optimal PM policies are presented and optimised. Numerical examples are also given.

Random number generation as an index of controlled processing

Random number generation (RNG) is a functionally complex process that is highly controlled and therefore dependent on Baddeley's central executive. This study addresses this issue by investigating whether key predictions from this framework are compatible with empirical data. In Experiment 1, the effect of increasing task demands by increasing the rate of the paced generation was comprehensively examined. As expected, faster rates affected performance negatively because central resources were increasingly depleted. Next, the effects of participants' exposure were manipulated in Experiment 2 by providing increasing amounts of practice on the task. There was no improvement over 10 practice trials, suggesting that the high level of strategic control required by the task was constant and not amenable to any automatization gain with repeated exposure. Together, the results demonstrate that RNG performance is a highly controlled and demanding process sensitive to additional demands on central resources (Experiment 1) and is unaffected by repeated performance or practice (Experiment 2). These features render the easily administered RNG task an ideal and robust index of executive function that is highly suitable for repeated clinical use.