Digital Commons Network^™

Statistical Analysis And Comparison Of Optical Classification Of Atmospheric Aerosol Lidar Data, Mohammed Alqawba, Norou Diawara, Kwasi G. Afrifa, Mohamed I. Elbakary, Mecit Cetin, Khan Iftekharuddin

Mathematics & Statistics Faculty Publications

In this article, we present a new study for the analysis and classification of atmospheric aerosols in remote sensing LIDAR data. Information on particle size and associated properties are extracted from these remote sensing atmospheric data which are collected by a ground-based LIDAR system. This study first considers optical LIDAR parameter-based classification methods for clustering and classification of different types of harmful aerosol particles in the atmosphere. Since accurate methods for aerosol prediction behaviors are based upon observed data, computational approaches must overcome design limitations, and consider appropriate calibration and estimation accuracy. Consequently, two statistical methods based on generalized linear …

Multivariate Distributions Of Correlated Binary Variables Generated By Pair-Copulas, Huihui Lin, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Correlated binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. The generalized estimating equations (GEEs) and the multivariate probit (MP) model are two of the popular methods for analyzing such data. However, both methods have some significant drawbacks. The GEEs may not have an underlying likelihood and the MP model may fail to generate a multivariate binary distribution with specified marginals and bivariate correlations. In this paper, we study multivariate binary distributions that are based on D-vine pair-copula models as a superior alternative to these methods. We elucidate the construction of these binary distributions …

Em Estimation For Zero- And K-Inflated Poisson Regression Model, Monika Arora, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we …

A Class Of Copula-Based Bivariate Poisson Time Series Models With Applications, Mohammed Alqawba, Dimuthu Fernando, Norou Diawara

Mathematics & Statistics Faculty Publications

A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was …

Numerical Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Method, Charles Armstrong, Yan Peng

Mathematics & Statistics Faculty Publications

In this work a quasisteady, dual time-stepping lattice Boltzmann method is proposed for simulation of capsule deformation. At each time step the steady-state lattice Boltzmann equation is solved using the full approximation storage multigrid scheme for nonlinear equations. The capsule membrane is modeled as an infinitely thin shell suspended in an ambient fluid domain with the fluid structure interaction computed using the immersed boundary method. A finite element method is used to compute the elastic forces exerted by the capsule membrane. Results for a wide range of parameters and initial configurations are presented. The proposed method is found to reduce …

Interaction Between Genetic Risk Scores For Reduced Pulmonary Function And Smoking, Asthma And Endotoxin, Sinjini Sikdar, Annah B. Wyss, Mi Kyeong Lee, Thanh T. Hoang, Marie Richards, Laura E. Beane Freeman, Christine Parks, Peter S. Thorne, John L. Hankinson, David M. Umbach, Alison Motsinger-Reif, Stephanie J. London

Mathematics & Statistics Faculty Publications

Rationale Genome-wide association studies (GWASs) have identified numerous loci associated with lower pulmonary function. Pulmonary function is strongly related to smoking and has also been associated with asthma and dust endotoxin. At the individual SNP level, genome-wide analyses of pulmonary function have not identified appreciable evidence for gene by environment interactions. Genetic Risk Scores (GRSs) may enhance power to identify gene–environment interactions, but studies are few.

Methods We analysed 2844 individuals of European ancestry with 1000 Genomes imputed GWAS data from a case–control study of adult asthma nested within a US agricultural cohort. Pulmonary function traits were FEV₁, …

Time Domain Boundary Element Method Prediction Of Noise Shielding By A Naca 0012 Airfoil, Douglas M. Nark, Fang Q. Hu

Mathematics & Statistics Faculty Publications

As aircraft noise constraints become more stringent and the number/mixture of aircraft configurations grows, it becomes more important to understand the interaction of individual aircraft noise sources with nearby aircraft structures. Understanding these interactions and exploring possible approaches to mitigate or exploit their acoustic impact is essential for overcoming key noise barriers. This paper describes the further validation of a time domain boundary element approach for the prediction of the interactions between incident noise sources and nearby aircraft structures. Predictions were completed for multiple source locations and comparisons of these results with measured data are presented. Overall, very good agreement …

Predicting The Winning Percentage Of Limited-Overs Cricket Using The Pythagorean Formula, Hasika K. W. Senevirathne, Ananda B.W. Manage

Mathematics & Statistics Faculty Publications

The Pythagorean Win-Loss formula can be effectively used to estimate winning percentages for sporting events. This formula was initially developed by baseball statistician Bill James and later was extended by other researchers to sports such as football, basketball, and ice hockey. Although one can calculate actual winning percentages based on the outcomes of played games, that approach does not take into account the margin of victory. The key benefit of the Pythagorean formula is its utilization of actual average runs scored and actual average runs allowed. This article presents the application of the Pythagorean Win-Loss formula to two different types …

Novel Statistical Analysis In The Context Of A Comprehensive Needs Assessment For Secondary Stem Recruitment, Norou Diawara, Sarah Ferguson, Melva Grant, Kumer Das

Mathematics & Statistics Faculty Publications

There is a myriad of career opportunities stemming from science, technology, engineering, and mathematics (STEM) disciplines. In addition to careers in corporate settings, teaching is a viable career option for individuals pursuing degrees in STEM disciplines. With national shortages of secondary STEM teachers, efforts to recruit, train, and retain quality STEM teachers is greatly important. Prior to exploring ways to attract potential STEM teacher candidates to pursue teacher training programs, it is important to understand the perceived value that potential recruits place on STEM careers, disciplines, and the teaching profession. The purpose of this study was to explore students’ perceptions …

Morphology-Dependent Resonances In Two Concentric Spheres With Variable Refractive Index In The Outer Layer: Analytic Solutions, Umaporn Nuntaplook, John A. Adam

Mathematics & Statistics Faculty Publications

In many applications constant or piecewise constant refractive index profiles are used to study the scattering of plane electromagnetic waves by a spherical object. When the structured media has variable refractive indices, this is more of a challenge. In this paper, we investigate the morphology dependent resonances for the scattering of electromagnetic waves from two concentric spheres when the outer shell has a variable refractive index. The resonance analysis is applied to the general solutions of the radial Debye potential for both transverse magnetic and transverse electric modes. Finally, the analytic conditions to determine the resonance locations for this system …

Representer Theorems In Banach Spaces: Minimum Norm Interpolation, Regularized Learning And Semi-Discrete Inverse Problems, Rui Wang, Yusheng Xu

Mathematics & Statistics Faculty Publications

Learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation (MNI) problem, a regularized learning problem or, in general, a semi discrete inverse problem (SDIP), in either Hilbert spaces or Banach spaces. The goal of this paper is to systematically study solutions of these problems in Banach spaces. We aim at obtaining explicit representer theorems for their solutions, on which convenient solution methods can then be developed. For the MNI problem, the explicit representer theorems enable us to express the infimum …

A Semiparametric Modeling Approach For Analyzing Clinical Biomarkers Restricted To Limits Of Detection, Sandipan Dutta, Susan Halabi

Mathematics & Statistics Faculty Publications

Before biomarkers can be used in clinical trials or patients' management, the laboratory assays that measure their levels have to go through development and analytical validation. One of the most critical performance metrics for validation of any assay is related to the minimum amount of values that can be detected and any value below this limit is referred to as below the limit of detection (LOD). Most of the existing approaches that model such biomarkers, restricted by LOD, are parametric in nature. These parametric models, however, heavily depend on the distributional assumptions, and can result in loss of precision under …

Stable And Convergent Difference Schemes For Weakly Singular Convolution Integrals, Wesley Davis, Richard D. Noren

Mathematics & Statistics Faculty Publications

We obtain new numerical schemes for weakly singular integrals of convolution type called Caputo fractional order integrals using Taylor and fractional Taylor series expansions and grouping terms in a novel manner. A fractional Taylor series expansion argument is utilized to provide fractional-order approximations for functions with minimal regularity. The resulting schemes allow for the approximation of functions in C^γ [0, T], where 0 < γ <= 5. A mild invertibility criterion is provided for the implicit schemes. Consistency and stability are proven separately for the whole-number-order approximations and the fractional-order approximations. The rate of convergence in the time variable is shown …