The Euro Diffusion Project

From 1st January 2002 we have the unique possibility to follow the spread of national euro coins over the different European countries. We model and analyse this movement and estimate the time it will take before on average half the coins in our wallet will be foreign

Multidirectional Subspace Expansion for One-Parameter and Multiparameter Tikhonov Regularization

Tikhonov regularization is a popular method to approximate solutions of linear discrete ill-posed problems when the observed or measured data is contaminated by noise. Multiparameter Tikhonov regularization may improve the quality of the computed approximate solutions. We propose a new iterative method for large-scale multiparameter Tikhonov regularization with general regularization operators based on a multidirectional subspace expansion. The multidirectional subspace expansion may be combined with subspace truncation to avoid excessive growth of the search space. Furthermore, we introduce a simple and effective parameter selection strategy based on the discrepancy principle and related to perturbation results

On the Convergence of Ritz Pairs and Refined Ritz Vectors for Quadratic Eigenvalue Problems

For a given subspace, the Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the Rayleigh-Ritz method defines the Ritz values and the Ritz vectors of the QEP with respect to the projection subspace. We analyze the convergence of the method when the angle between the subspace and the desired eigenvector converges to zero. We prove that there is a Ritz value that converges to the desired eigenvalue unconditionally but the Ritz vector converges conditionally and may fail to converge. To remedy the drawback of possible non-convergence of the Ritz vector, we propose a refined Ritz vector that is mathematically different from the Ritz vector and is proved to converge unconditionally. We construct examples to illustrate our theory.Comment: 20 page

Fast Approximated POD for a Flat Plate Benchmark with a Time Varying Angle of Attack

An approximate POD algorithm provides an empirical Galerkin approximation with guaranteed a priori lower bound on the required resolution. The snapshot ensemble is partitioned into several sub-ensembles. Cross correlations between these sub-ensembles are approximated in terms of a far smaller correlation matrix. Computational speedup is nearly linear in the number of partitions, up to a saturation that can be estimated a priori. The algorithm is particularly suitable for analyzing long transient trajectories of high dimensional simulations, but can be applied also for spatial partitioning and parallel processing of very high spatial dimension data. The algorithm is demonstrated using transient data from two simulations. First, a two dimensional simulation of the flow over a flat plate, as it transitions from AOA = 30° to a horizontal position and back. Second, a three dimensional simulation of a flat plate with aspect ratio two as it transitions from a horizontal position to AOA = 30°

Prenatal maternal plasma DNA screening for cystic fibrosis: A computer modelling study of screening performance.

Background: Prenatal cystic fibrosis (CF) screening is currently based on determining the carrier status of both parents. We propose a new method based only on the analysis of DNA in maternal plasma. Methods: The method relies on the quantitative amplification of the CF gene to determine the percentage of DNA fragments in maternal plasma at targeted CF mutation sites that carry a CF mutation. Computer modelling was carried out to estimate the distributions of these percentages in pregnancies with and without a fetus affected with CF. This was done according to the number of DNA fragments counted and fetal fraction, using the 23 CF mutations recommended by the American College of Medical Genetics for parental carrier testing. Results: The estimated detection rate (sensitivity) is 70% (100% of those detected using the 23 mutations), the false-positive rate 0.002%, and the odds of being affected given a positive screening result 14:1, compared with 70%, 0.12%, and 1:3, respectively, with current prenatal screening based on parental carrier testing. Conclusions: Compared with current screening practice based on parental carrier testing, the proposed method would substantially reduce the number of invasive diagnostic procedures (amniocentesis or chorionic villus sampling) without reducing the CF detection rate. The expected advantages of the proposed method justify carrying out the necessary test development for use in a clinical validation study.The author(s) declared that no grants were involved in supporting this work

Rapid screening for chromosomal aneuploidies using array-MLPA

<p>Abstract</p> <p>Background</p> <p>Chromosome abnormalities, especially trisomy of chromosome 21, 13, or 18 as well as sex chromosome aneuploidy, are a well-established cause of pregnancy loss. Cultured cell karyotype analysis and FISH have been considered reliable detectors of fetal abnormality. However, results are usually not available for 3-4 days or more. Multiplex ligation-dependent probe amplification (MLPA) has emerged as an alternative rapid technique for detection of chromosome aneuploidies. However, conventional MLPA does not allow for relative quantification of more than 50 different target sequences in one reaction and does not detect mosaic trisomy. A multiplexed MLPA with more sensitive detection would be useful for fetal genetic screening.</p> <p>Methods</p> <p>We developed a method of array-based MLPA to rapidly screen for common aneuploidies. We designed 116 universal tag-probes covering chromosomes 13, 18, 21, X, and Y, and 8 control autosomal genes. We performed MLPA and hybridized the products on a 4-well flow-through microarray system. We determined chromosome copy numbers by analyzing the relative signals of the chromosome-specific probes.</p> <p>Results</p> <p>In a blind study of 161 peripheral blood and 12 amniotic fluid samples previously karyotyped, 169 of 173 (97.7%) including all the amniotic fluid samples were correctly identified by array-MLPA. Furthermore, we detected two chromosome X monosomy mosaic cases in which the mosaism rates estimated by array-MLPA were basically consistent with the results from karyotyping. Additionally, we identified five Y chromosome abnormalities in which G-banding could not distinguish their origins for four of the five cases.</p> <p>Conclusions</p> <p>Our study demonstrates the successful application and strong potential of array-MLPA in clinical diagnosis and prenatal testing for rapid and sensitive chromosomal aneuploidy screening. Furthermore, we have developed a simple and rapid procedure for screening copy numbers on chromosomes 13, 18, 21, X, and Y using array-MLPA.</p