Mathematics Commons^™

G-Cimp Status Prediction Of Glioblastoma Samples Using Mrna Expression Data, Mehmet Baysan, Serdar Bozdag, Margaret C. Cam, Svetlana Kotliarova, Susie Ahn, Jennifer Walling, Jonathan K. Killian, Holly Stevenson, Paul Meltzer, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Glioblastoma Multiforme (GBM) is a tumor with high mortality and no known cure. The dramatic molecular and clinical heterogeneity seen in this tumor has led to attempts to define genetically similar subgroups of GBM with the hope of developing tumor specific therapies targeted to the unique biology within each of these subgroups. Recently, a subset of relatively favorable prognosis GBMs has been identified. These glioma CpG island methylator phenotype, or G-CIMP tumors, have distinct genomic copy number aberrations, DNA methylation patterns, and (mRNA) expression profiles compared to other GBMs. While the standard method for identifying G-CIMP tumors is based on …

On Lattices Of Varieties Of Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The left restriction semigroups have arisen in a number of contexts, one being as the abstract characterization of semigroups of partial maps, another as the ‘weakly left E-ample’ semigroups of the ‘York school’, and, more recently as a variety of unary semigroups defined by a set of simple identities. We initiate a study of the lattice of varieties of such semigroups and, in parallel, of their two-sided versions, the restriction semigroups. Although at the very bottom of the respective lattices the behaviour is akin to that of varieties of inverse semigroups, more interesting features are soon found in the …

The Sense-Isomorphism Theoretical Image Voxel Estimation (Sense-Itive) Model For Reconstruction And Observing Statistical Properties Of Reconstruction Operators, Iain P. Bruce, M. Muge Karaman, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

The acquisition of sub-sampled data from an array of receiver coils has become a common means of reducing data acquisition time in MRI. Of the various techniques used in parallel MRI, SENSitivity Encoding (SENSE) is one of the most common, making use of a complex-valued weighted least squares estimation to unfold the aliased images. It was recently shown in Bruce et al. [Magn. Reson. Imag. 29(2011):1267-1287] that when the SENSE model is represented in terms of a real-valued isomorphism,it assumes a skew-symmetric covariance between receiver coils, as well as an identity covariance structure between voxels. In this manuscript, we show …

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 …

Mathematical Problem Posing As A Measure Of Curricular Effect On Students' Learning, Jinfa Cai, John Moyer, Ning Wang, Stephen Hwang, Bikai Nie, Tammy Garber

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of …

Analyzing Multiple-Probe Microarray: Estimation And Application Of Gene Expression Indexes, Mehdi Maadooliat, Jianhua Z. Huang, Jianhua Hu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Gene expression index estimation is an essential step in analyzing multiple probe microarray data. Various modeling methods have been proposed in this area. Amidst all, a popular method proposed in Li and Wong (2001) is based on a multiplicative model, which is similar to the additive model discussed in Irizarry et al. (2003a) at the logarithm scale. Along this line, Hu et al. (2006) proposed data transformation to improve expression index estimation based on an ad hoc entropy criteria and naive grid search approach. In this work, we re-examined this problem using a new profile likelihood-based transformation estimation approach that …

On Order Statistics For Gs-Distributions, M. M. Mohie El-Din, M. M. Amein, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this article, a class of distributions is used to establish several recurrence relations satisfied by single and product moments of order statistics and progressive Type-II right censoring. The recurrence relations for moments of some specific distributions including uniform (a;b); exponential (λ); generalized exponential (α;λ;ν); beta (1;b); beta (b;1); logistic (α;β) and other distributions from order statistics and progressive Type-II right censoring can be obtained as special cases. A short explanation of GS-distribution can be found in reference [27]. As an example, means, variances and covariances for standard exponential distribution of progressive Type-II right censored order statistics are computed. Various …

H-Coloring Tori, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, an H-coloring of G is a function from the vertices of G to the vertices of H that preserves adjacency. H-colorings encode graph theory notions such as independent sets and proper colorings, and are a natural setting for the study of hard-constraint models in statistical physics. We study the set of H-colorings of the even discrete torus View the MathML source, the graph on vertex set {0,…,m−1}d (m even) with two strings adjacent if they differ by 1 (mod m) on one coordinate and agree on all others. This is a bipartite graph, with bipartition …

An Efficient Methodology For Learning Bayesian Networks, Emmanuel Owusu Asante-Asamani

Theses and Dissertations

Statistics from the National Cancer Institute indicate that 1 in 8 women will develop Breast cancer in their lifetime. Researchers have developed numerous statistical models to predict breast cancer risk however physicians are hesitant to use these models because of disparities in the predictions they produce. In an effort to reduce these disparities, we use Bayesian networks to capture the joint distribution of risk factors, and simulate artificial patient populations (clinical avatars) for interrogating the existing risk prediction models. The challenge in this effort has been to produce a Bayesian network whose dependencies agree with literature and are good estimates …

An Efficient Second Order In Time Scheme For Approximating Long Time Statistical Properties Of The Two Dimensional Navier-Stokes Equations, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We investigate the long-time behavior of the following efficient second order in time scheme for the 2D Navier-Stokes equations in a periodic box: The scheme is a combination of a 2nd-order in time backward-differentiation and a particular explicit Adams-Bashforth treatment of the advection term. Therefore, only a linear constant coefficient Poisson solver is needed at each time step. We prove uniform in time bounds on this scheme in L 2, H per1 and H per2 provided that the time-step is sufficiently small. These time uniform estimates further lead to the convergence of long-time statistics (stationary statistical properties) of the scheme …

Modeling Daily Power Demand In Southern Kentucky: A Single Household Approach, Craig M. Dickson

Masters Theses & Specialist Projects

In this study, we use a nonparametric technique, locally weighted robust least squares regression (LOESS), to forecast a 24 hour demand profile at the household level and compare it to existing aggregate demand models discussed in literature. Of these aggregate demand models, a quadratic autoregressive model was selected to be used as a basis for comparison with the LOESS forecasts. It was our goal to automate the forecasting process by using the goodness of fit metric, AICCI, for smoothing parameter selection. The statistical workflow was executed using SAS and data was provided by the Glasgow Electric Plant Board of Barren …

From Unbiased Numerical Estimates To Unbiased Interval Estimates, Baokun Li, Gang Xiang, Vladik Kreinovich, Panagios Moscopoulos

Departmental Technical Reports (CS)

One of the main objectives of statistics is to estimate the parameters of a probability distribution based on a sample taken from this distribution. Of course, since the sample is finite, the estimate X is, in general, different from the actual value x of the corresponding parameter. What we can require is that the corresponding estimate is unbiased, i.e., that the mean value of the difference X - x is equal to 0: E[X] = x. In some problems, unbiased estimates are not possible. We show that in some such problems, it is possible to have interval unbiased estimates, i.e., …

Analysis Of Bank Failure And Size Of Assets, Guancun Zhong

UNLV Theses, Dissertations, Professional Papers, and Capstones

The financial health of the banking industry is an important prerequisite for economic stability and growth. Bank failures in the United States have run in cycles largely associated with the collapse of economic bubbles. The number of bank failures has increased dramatically over the last thirty years (Halling and Hayden, 2007). In this thesis, we try to address the following two questions: 1) What is the relationship, if any, between a bank's asset size and its likelihood of failures? 2) How can we use statistical tools to predict the numbers of bank failures in the future? Various modeling techniques are …

Mathematics And The Hunger Games, Michael A. Lewis

Journal of Humanistic Mathematics

The Hunger Games plot features a dystopian future in which twelve outer districts are oppressed by a centralized capital. The story focuses on the heroism of a sixteen-year-old girl named Katniss and how she tries to rise above the oppression that she experiences. It also features a special lottery and other twists that are sources of mathematical interest. This essay focuses on some of the mathematical issues raised by The Hunger Games in an effort to show that this story can be used to teach students (as well as other interested parties) some important concepts from mathematics.

Interval And Point Estimators For The Location Parameter Of The Three-Parameter Lognormal Distribution, Zhenmin Chen, Feng Miao

Department of Mathematics and Statistics

The three-parameter lognormal distribution is the extension of the two-parameter lognormal distribution to meet the need of the biological, sociological, and other fields. Numerous research papers have been published for the parameter estimation problems for the lognormal distributions. The inclusion of the location parameter brings in some technical difficulties for the parameter estimation problems, especially for the interval estimation. This paper proposes a method for constructing exact confidence intervals and exact upper confidence limits for the location parameter of the three-parameter lognormal distribution. The point estimation problem is discussed as well. The performance of the point estimator is compared with …

Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative, Naveen K. Bansal, Gholamhossein Hamedani, Ru Sheng

Mathematics, Statistics and Computer Science Faculty Research and Publications

We consider a hypothesis problem with directional alternatives. We approach the problem from a Bayesian decision theoretic point of view and consider a situation when one side of the alternatives is more important or more probable than the other. We develop a general Bayesian framework by specifying a mixture prior structure and a loss function related to the Kullback–Leibler divergence. This Bayesian decision method is applied to Normal and Poisson populations. Simulations are performed to compare the performance of the proposed method with that of a method based on a classical z-test and a Bayesian method based on the …

Response Surface Optimization Of Electron Beam Freeform Fabrication Depositions Using Design Of Experiments, Patricia A. Quigley

Engineering Management & Systems Engineering Theses & Dissertations

The Electron Beam Freeform Fabrication (EBF³ ) System is a material depositing, layer additive technique that produces three dimensional (3D) parts out of a wide range of metals in high vacuum, using an electron beam and wire feedstock. Screening deposition trials on a titanium alloy, Ti-6Al-4V, at the National Aeronautics Space Administration (NASA) revealed selective vaporization of the aluminum content of linear prototypes when subjected to chemical analysis. In this study, the aluminum content, bead height and bead width output responses were analyzed from a systematic study of the effects that the interactions of the EBF³ processing parameters …

Experimental And Computational Validation And Verification Of The Stokes-Darcy And Continuum Pipe Flow Models For Karst Aquifers With Dual Porosity Structure, Xiaolong Hu, Xiaoming Wang, Max Gunzburger, Fei Hua, Yanzhao Cao

Mathematics and Statistics Faculty Research & Creative Works

In our previous study, we developed the Stokes-Darcy (SD) model was developed for flow in a karst aquifer with a conduit bedded in matrix, and the Beavers-Joseph (BJ) condition was used to describe the matrix-conduit interface. We also studied the mathematical well-posedness of a coupled continuum pipe flow (CCPF) model as well as convergence rates of its finite element approximation. in this study, to compare the SD model with the CCPF model, we used numerical analyses to validate finite element discretisation methods for the two models. using computational experiments, simulation codes implementing the finite element discretisations are then verified. Further …

Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager

Department of Mathematics: Dissertations, Theses, and Student Research

Population dynamics tries to explain in a simple mechanistic way the variations of the size and structure of biological populations. In this dissertation we use mathematical modeling and analysis to study the various aspects of the dynamics of plant populations and their seed banks.

In Chapter 2 we investigate the impact of structural model uncertainty by considering different nonlinear recruitment functions in an integral projection model for Cirsium canescens. We show that, while having identical equilibrium populations, these two models can elicit drastically different transient dynamics. We then derive a formula for the sensitivity of the equilibrium population to …

Adaptive Randomization Designs, Jenna Colavincenzo

Statistics

Adaptive design methodologies use prior information to develop a clinical trial design. The goal of an adaptive design is to maintain the integrity and validity of the study while giving the researcher flexibility in identifying the optimal treatment. An example of an adaptive design can be seen in a basic pharmaceutical trial. There are three phases of the overall trial to compare treatments and experimenters use the information from the previous phase to make changes to the subsequent phase before it begins.

Adaptive design methods have been in practice since the 1970s, but have become increasingly complex ever since. One …

Involvement Of Microrna Families In Cancer, Stefan Wuchty, Dolores Arjona, Serdar Bozdag, Peter O. Bauer

Mathematics, Statistics and Computer Science Faculty Research and Publications

Collecting representative sets of cancer microRNAs (miRs) from the literature we show that their corresponding families are enriched in sets of highly interacting miR families. Targeting cancer genes on a statistically significant level, such cancer miR families strongly intervene with signaling pathways that harbor numerous cancer genes. Clustering miR family-specific profiles of pathway intervention, we found that different miR families share similar interaction patterns. Resembling corresponding patterns of cancer miRs families, such interaction patterns may indicate a miR family’s potential role in cancer. As we find that the number of targeted cancer genes is a naı¨ve proxy for a cancer …

Rank-Based Estimation And Prediction For Mixed Effects Models In Nested Designs, Yusuf K. Bilgic

Dissertations

Hierarchical designs frequently occur in many research areas. The experimental design of interest is expressed in terms of fixed effects but, for these designs, nested factors are a natural part of the experiment. These nested effects are generally considered random and must be taken into account in the statistical analysis. Traditional analyses are quite sensitive to outliers and lose considerable power to detect the fixed effects of interest.

This work proposes three rank-based fitting methods for handling random, fixed and scale effects in k-level nested designs for estimation and inference. An algorithm, which iteratively obtains robust prediction for both scale …

Simplified Models Of Vector Control Impact Upon Malaria Transmission By Zoophagic Mosquitoes, Samson S. Kiware, Nakul Chitnis, Sarah J. Moore, Gregor J. Devine, Silas Majambere, Stephen Merrill, Gerry F. Killeen

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

High coverage of personal protection measures that kill mosquitoes dramatically reduce malaria transmission where vector populations depend upon human blood. However, most primary malaria vectors outside of sub-Saharan Africa can be classified as “very zoophagic,” meaning they feed occasionally (

Methods and Findings

We extended a published malaria transmission model to examine the relationship between transmission, control, and the baseline proportion of bloodmeals obtained from humans (human blood index). The lower limit of the human blood index enables derivation of simplified models for zoophagic vectors that (1) Rely on only three field-measurable parameters. (2) Predict immediate and delayed (with …

Second-Order Convex Splitting Schemes For Gradient Flows With Ehrlich-Schwoebel Type Energy: Application To Thin Film Epitaxy, Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

We construct unconditionally stable, unconditionally uniquely solvable, and second order accurate (in time) schemes for gradient flows with energy of the form {equation presented} dx. the construction of the schemes involves the appropriate combination and extension of two classical ideas: (i) appropriate convex-concave decomposition of the energy functional and (ii) the secant method. as an application, we derive schemes for epitaxial growth models with slope selection (F(y) = 1/4 (|y| 2 - 1) 2) or without slope selection (F(y) = -1/2 ln(1 + |y| 2)). Two types of unconditionally stable uniquely solvable second-order schemes are presented. the first type inherits …

Long Time Stability Of A Classical Efficient Scheme For Two-Dimensional Navier-Stokes Equations, S. Gottlieb, F. Tone, C. Wang, X. Wang, D. Wirosoetisno

Mathematics and Statistics Faculty Research & Creative Works

This paper considers the long-time stability property of a popular semi-implicit scheme for the two-dimensional incompressible Navier-Stokes equations in a periodic box that treats the viscous term implicitly and the nonlinear advection term explicitly. We consider both the semi discrete (discrete in time but continuous in space) and fully discrete schemes with either Fourier Galerkin spectral or Fourier pseudo spectral (collocation) methods. We prove that in all cases, the scheme is long time stable provided that the timestep is sufficiently small. the long-time stability in the L 2 and H 1 norms further leads to the convergence of the global …

Local Torsion On Abelian Surfaces, Adam Gamzon

Open Access Dissertations

Fix an integer d > 0. In 2008, Chantal David and Tom Weston showed that, on average, an elliptic curve over Q picks up a nontrivial p-torsion point defined over a finite extension K of the p-adics of degree at most d for only finitely many primes p. This dissertation is an extension of that work, investigating the frequency with which a principally polarized abelian surface A over Q with real multiplication by Q adjoin a squared-root of 5 has a nontrivial p-torsion point defined over K. Averaging by height, the main result shows that A …

A Study Of Women Working In The Actuarial Field, Jillian Emberg

Honors Projects in Mathematics

The goal of this project is to examine how women fit into the actuarial career path and how cultural expectations, biological factors, and personal aspirations affect their experiences in the field. Dramatic changes in the profession have occurred since its emergence in the nineteenth century to become more welcoming to women who choose to enter the profession. However, despite the equalizing demographic shifts of the field, it is still a male-dominated profession. This paper attempts to analyze why some of the changes in the demographics of the field have occurred as well as explain what factors contribute to women’s underrepresentation …

H-Colouring Bipartite Graphs, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, an H-colouring of G (or homomorphism from G to H) is a function from the vertices of G to the vertices of H that preserves adjacency. H-colourings generalize such graph theory notions as proper colourings and independent sets. For a given H, k∈V(H) and G we consider the proportion of vertices of G that get mapped to k in a uniformly chosen H-colouring of G. Our main result concerns this quantity when G is regular and bipartite. We find numbers 0⩽a−(k)⩽a+(k)⩽1 with the property that for all such G, with high probability the proportion is …

Human Gene Copy Number Spectra Analysis In Congenital Heart Malformations, Aoy Tomita-Mitchell, Donna K. Mahnke, Craig Struble, Maureen E. Tuffnell, Karl D. Stamm, Mats Hidestrand, Susan Harris, Mary A. Goetsch, Pippa Simpson, David P. Bick, Ulrich Broeckel, Andrew N. Pelech, James S. Tweddell, Michael Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

The clinical significance of copy number variants (CNVs) in congenital heart disease (CHD) continues to be a challenge. Although CNVs including genes can confer disease risk, relationships between gene dosage and phenotype are still being defined. Our goal was to perform a quantitative analysis of CNVs involving 100 well-defined CHD risk genes identified through previously published human association studies in subjects with anatomically defined cardiac malformations. A novel analytical approach permitting CNV gene frequency “spectra” to be computed over prespecified regions to determine phenotype-gene dosage relationships was employed. CNVs in subjects with CHD (n = 945), subphenotyped into 40 …

Translation Representations And Scattering By Two Intervals, Palle Jorgensen, Steen Pedersen, Feng Tian

Mathematics and Statistics Faculty Publications

Studying unitary one-parameter groups in Hilbert space (U(t), H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L²-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U(t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator and scattering matrix. We illustrate our results in the Lax-Phillips model where (U(t), H) represents an acoustic wave equation …