Minimal point cubatures of precision seven for symmetric planar regions: Revisited

The key theorem concerning a lower bound for the number of points required by cubature formulas of precision seven for certain symmetric planar regions is extended to arbitrary symmetric planar regions, with a simplified proof.supported in part by the Foundation Research Program of the Naval Postgraduate School with funds provided by the Chief of Naval Researchhttp://archive.org/details/minimalpointcuba00franN

On the computation of optimal approximations in Sard corner spaces

The subject of linear optimal approximation has received considerable attention in recent years [4], [5], [6], [7], [8]. The subject of multivariate approximation for scattered data, including optimal approximations, is reviewed in [9]. The idea is appealing since the optimal approximation in a certain space of functions minimizes the norm of the error functional for approximations in that space. When the space is a Hilbert space, the computation of optimal approximations becomes rather simple, in theory [2]. A known reproducing kernel function provides the representers of linear functional s defined on the space. The optimal approximation satisfies the system of equations obtained by requiring that the approximation be exact for the representers of the functional s being used for the approximation, usually point evaluation functionals.supported by the Foundation Research Program of the Naval Postgraduate School with funds provided by the Chief of Naval Researchhttp://archive.org/details/oncomputationofo00franN0007476WR6005

Least squares surface approximation to scattered data using multiquadric functions

This report documents an investigation into some methods for fitting surfaces to scattered data. The form of the fitting function is a multiquadric function with the criteria for the fit being the least mean squared resifual for the data points. The principal problem is the selection of knot points (or base points for the multiquadric basis functions), although the selection of the multiquadric parameter also plays a nontrivial role in the process. We first describe a greedy algorithm for knot selection, and this procedure is used as an initial step in what follows. The minimization including knot locations and multiquadric parameter is explored, with some unexpected results in terms of 'near repeated' knots. This phenomenon is explored, and leads us to consider variable parameter values for the basis functions. Examples and results are given throughout.http://archive.org/details/leastsquaressurf00franApproved for public release; distribution is unlimited

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supported by the Weapon Systems Simulation Branch, Naval Missile Center, Pt. Mugu, Californiahttp://archive.org/details/somemethodsforap00fra

On the convergence of an algorithm for rational Chebyshev approximation

An algorithm for rational Chebyshev approximation based on computing the zeros of the error curve was investigated. At each iteration the proposed zeros are corrected by changing them toward the abscissa of the adjacent extreme of largest magnitude. The algorithm is formulated as a numerical solution of a certain system of ordinary differential equations. Convergence is obtained by showing the system is asymptotically stable at the zeros of the best approximation. With an adequate initial guess, the algorithm has never failed for functions which have a standard error curve. (Foundation Research Program Naval Postgraduate Schoolhttp://archive.org/details/onconvergenceofa00fra

PTGER4 expression-modulating polymorphisms in the 5p13.1 region predispose to Crohn's disease and affect NF-κB and XBP1 binding sites.

Genome-wide association studies identified a PTGER4 expression-modulating region on chromosome 5p13.1 as Crohn's disease (CD) susceptibility region. The study aim was to test this association in a large cohort of patients with inflammatory bowel disease (IBD) and to elucidate genotypic and phenotypic interactions with other IBD genes. A total of 7073 patients and controls were genotyped: 844 CD and 471 patients with ulcerative colitis and 1488 controls were analyzed for the single nucleotide polymorphisms (SNPs) rs4495224 and rs7720838 on chromosome 5p13.1. The study included two replication cohorts of North American (CD: n = 684; controls: n = 1440) and of German origin (CD: n = 1098; controls: n = 1048). Genotype-phenotype, epistasis and transcription factor binding analyses were performed. In the discovery cohort, an association of rs4495224 (p = 4.10×10⁻⁵; 0.76 [0.67-0.87]) and of rs7720838 (p = 6.91×10⁻⁴; 0.81 [0.71-0.91]) with susceptibility to CD was demonstrated. These associations were confirmed in both replication cohorts. In silico analysis predicted rs4495224 and rs7720838 as essential parts of binding sites for the transcription factors NF-κB and XBP1 with higher binding scores for carriers of the CD risk alleles, providing an explanation of how these SNPs might contribute to increased PTGER4 expression. There was no association of the PTGER4 SNPs with IBD phenotypes. Epistasis detected between 5p13.1 and ATG16L1 for CD susceptibility in the discovery cohort (p = 5.99×10⁻⁷ for rs7720838 and rs2241880) could not be replicated in both replication cohorts arguing against a major role of this gene-gene interaction in the susceptibility to CD. We confirmed 5p13.1 as a major CD susceptibility locus and demonstrate by in silico analysis rs4495224 and rs7720838 as part of binding sites for NF-κB and XBP1. Further functional studies are necessary to confirm the results of our in silico analysis and to analyze if changes in PTGER4 expression modulate CD susceptibility

Feasibility of predicting allele specific expression from DNA sequencing using machine learning

Allele specific expression (ASE) concerns divergent expression quantity of alternative alleles and is measured by RNA sequencing. Multiple studies show that ASE plays a role in hereditary diseases by modulating penetrance or phenotype severity. However, genome diagnostics is based on DNA sequencing and therefore neglects gene expression regulation such as ASE. To take advantage of ASE in absence of RNA sequencing, it must be predicted using only DNA variation. We have constructed ASE models from BIOS (n = 3432) and GTEx (n = 369) that predict ASE using DNA features. These models are highly reproducible and comprise many different feature types, highlighting the complex regulation that underlies ASE. We applied the BIOS-trained model to population variants in three genes in which ASE plays a clinically relevant role: BRCA2, RET and NF1. This resulted in predicted ASE effects for 27 variants, of which 10 were known pathogenic variants. We demonstrated that ASE can be predicted from DNA features using machine learning. Future efforts may improve sensitivity and translate these models into a new type of genome diagnostic tool that prioritizes candidate pathogenic variants or regulators thereof for follow-up validation by RNA sequencing. All used code and machine learning models are available at GitHub and Zenodo

TESLA Technical Design Report Part III: Physics at an e+e- Linear Collider

The TESLA Technical Design Report Part III: Physics at an e+e- Linear ColliderComment: 192 pages, 131 figures. Some figures have reduced quality. Full quality figures can be obtained from http://tesla.desy.de/tdr. Editors - R.-D. Heuer, D.J. Miller, F. Richard, P.M. Zerwa

Genetic association study of QT interval highlights role for calcium signaling pathways in myocardial repolarization.

The QT interval, an electrocardiographic measure reflecting myocardial repolarization, is a heritable trait. QT prolongation is a risk factor for ventricular arrhythmias and sudden cardiac death (SCD) and could indicate the presence of the potentially lethal mendelian long-QT syndrome (LQTS). Using a genome-wide association and replication study in up to 100,000 individuals, we identified 35 common variant loci associated with QT interval that collectively explain ∼8-10% of QT-interval variation and highlight the importance of calcium regulation in myocardial repolarization. Rare variant analysis of 6 new QT interval-associated loci in 298 unrelated probands with LQTS identified coding variants not found in controls but of uncertain causality and therefore requiring validation. Several newly identified loci encode proteins that physically interact with other recognized repolarization proteins. Our integration of common variant association, expression and orthogonal protein-protein interaction screens provides new insights into cardiac electrophysiology and identifies new candidate genes for ventricular arrhythmias, LQTS and SCD