Physical Sciences and Mathematics Commons^™

Reconstructability Of Epistatic Functions, Martin Zwick, Joe Fusion, Beth Wilmot

Systems Science Faculty Publications and Presentations

Background: Reconstructability Analysis (RA) has been used to detect epistasis in genomic data; in that work, even the simplest RA models (variable-based models without loops) gave performance superior to two other methods. A follow-on theoretical study showed that RA also offers higher-resolution models, namely variable-based models with loops and state-based models, likely to be even more effective in modeling epistasis, and also described several mathematical approaches to classifying types of epistasis.

Methods: The present paper extends this second study by discussing a non-standard use of RA: the analysis of epistasis in quantitative as opposed to nominal variables; such quantitative variables …

Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc

Mathematics and Statistics Faculty Publications and Presentations

We present several well-posed, well-conditioned direct and indirect integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We focus mainly on Direct Regularized Combined Field Integral Equation (DCFIE-R) formulations whose name reflects that (1) they consist of combinations of direct boundary integral equations of the second-kind and first-kind integral equations which are preconditioned on the left by coercive boundary single-layer operators, and (2) their unknowns are physical quantities, i.e., the total field on the boundary of the scatterer. The DCFIE-R equations are shown to be uniquely solvable in appropriate function …

Bayesian And Related Methods: Techniques Based On Bayes' Theorem, Mehmet Vurkaç

Systems Science Friday Noon Seminar Series

Bayes' theorem is a simple algebraic consequence of conditional probability. Yet, its consequences are critical to philosophy, society, and technology. Starting from its simple derivation, we will show how its interpretation in terms of base rates (priors) and class-conditional likelihoods illuminates everyday problems in medicine and law, and provides signal processing, communications, machine learning, model selection, and other applications of statistics with powerful classification and estimation tools. Next, we will briefly examine some of the ways in which this theorem can be adopted to include multiple attributes, contexts, hypotheses, and levels of risk. Methods derived from or related to Bayes’ …

Application Of Inter-Die Rank Statistics In Defect Detection, Vivek Bakshi

Dissertations and Theses

This thesis presents a statistical method to identify the test escapes. Test often acquires parametric measurements as a function of logical state of a chip. The usual method of classifying chips as pass or fail is to compare each state measurement to a test limit. Subtle manufacturing defects are escaping the test limits due to process variations in deep sub-micron technologies which results in mixing of healthy and faulty parametric test measurements. This thesis identifies the chips with subtle defects by using rank order of the parametric measurements. A hypothesis is developed that a defect is likely to disturb the …

Benchmark Results For Testing Adaptive Finite Element Eigenvalue Procedures Ii (Cluster Robust Eigenvector And Eigenvalue Estimates), Stefano Giani, Luka Grubisic, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

As a model benchmark problem for this study we consider a highly singular transmission type eigenvalue problem which we study in detail both analytically as well as numerically. In order to justify our claim of cluster robust and highly accurate approximation of a selected groups of eigenvalues and associated eigenfunctions, we give a new analysis of a class of direct residual eigenspace/vector approximation estimates. Unlike in the first part of the paper, we now use conforming higher order finite elements, since the canonical choice of an appropriate norm to measure eigenvector approximation by discontinuous Galerkin methods is an open problem.

On The Skewness Of Order Statistics With Applications, Subhash C. Kochar, Maochao Xu

Mathematics and Statistics Faculty Publications and Presentations

Order statistics from heterogenous samples have been extensively studied in the literature. However, most of the work focused on the effect of heterogeneity on the magnitude and dispersion of order statistics. In this paper, we study the skewness of order statistics from heterogeneous samples in the sense of star order. The main results extended the results in Kochar and Xu (2009, 2011). Examples and applications in statistical inference are highlighted.