Statistics and Probability Commons^™

Logistic Models With Missing Categorical Covariates, Jeremiah Rounds

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We present an EM based solution to missing categorical covariates in Binomial models with logit links using an assumption that experimental units are drawn from a Multinomial population of infinite size. We further address the problem of separation of points inducing large variances on parameter estimates by the use of a novel score-modification based on Firth's bias-reduction score-modification. We simulate to address questions about estimate bias, distribution, and appropriate parameter coverage by Wald intervals.

A Compartmentalized Approach To The Assembly Of Physical Maps, Serdar Bozdag, Timothy J. Close, Stefano Lonardi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Physical maps have been historically one of the cornerstones of genome sequencing and map-based cloning strategies. They also support marker assisted breeding and EST mapping. The problem of building a high quality physical map is computationally challenging due to unavoidable noise in the input fingerprint data. Results: We propose a novel compartmentalized method for the assembly of high quality physical maps from fingerprinted clones. The knowledge of genetic markers enables us to group clones into clusters so that clones in the same cluster are more likely to overlap. For each cluster of clones, a local physical map is first …

Extending The Skill Test For Disease Diagnosis, Shu-Chuan Lin, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

For diagnostic tests, we present an extension to the skill plot introduced by Briggs and Zaretski (Biometrics 2008; 64:250–261). The method is motivated by diagnostic measures for osteopetrosis in a study summarized by Hans et al. (The Lancet 1996; 348:511–514). Diagnostic test accuracy is typically defined using the area (or partial area) under the receiver operator characteristic (ROC) curve. If partial area is used, the resulting statistic can be highly subjective because the focus region of the ROC curve corresponds to a set of low false‐positive rates that are chosen by the experimenter. This paper introduces a more …

An Investigation Of The Ends Of Finitely Generated Groups, Daniel T. Murphree

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Geometric group theory is a relatively new branch of mathematics, studied as a distinct area since the 1990's. It explores invariant properties of groups based on group actions defined on topological or geometrical spaces. One of the pioneering works in geometric group theory is the article "Topological Methods in Group Theory" by Peter Scott and Terry Wall, written in 1977. This article was an overview of revised notes from an advanced course give in Liverpool in the same year. This report is an attempt to make these notes more accessible to lower level graduate students in the fields of topology …

Compartmentalized Approach To The Assembly Of Physical Maps, Serdar Bozdag, Timothy J. Close, Stefano Lonardi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

Physical maps have been historically one of the cornerstones of genome sequencing and map-based cloning strategies. They also support marker assisted breeding and EST mapping. The problem of building a high quality physical map is computationally challenging due to unavoidable noise in the input fingerprint data.

Results

We propose a novel compartmentalized method for the assembly of high quality physical maps from fingerprinted clones. The knowledge of genetic markers enables us to group clones into clusters so that clones in the same cluster are more likely to overlap. For each cluster of clones, a local physical map is first …

Development And Implementation Of High-Throughput Snp Genotyping In Barley, Timothy J. Close, Prasanna R. Bhat, Stefano Lonardi, Yonghui Wu, Nils Rostoks, Luke Ramsay, Arnis Druka, Nils Stein, Jan T. Svensson, Steve Wanamaker, Serdar Bozdag, Mikeal L. Roose, Matthew J. Moscou, Shiaoman Chao, Rajeev K. Varshney, Peter Szucs, Kazuhiro Sato, Patrick M. Hayes, David E. Matthews, Andris Kleinhofs, Gary J. Muehlbauer, Joseph Deyoung, David F. Marshall, Kavitha Madishetty, Raymond D. Fenton, Pascal Condamine, Andreas Graner, Robbie Waugh

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

High density genetic maps of plants have, nearly without exception, made use of marker datasets containing missing or questionable genotype calls derived from a variety of genic and non-genic or anonymous markers, and been presented as a single linear order of genetic loci for each linkage group. The consequences of missing or erroneous data include falsely separated markers, expansion of cM distances and incorrect marker order. These imperfections are amplified in consensus maps and problematic when fine resolution is critical including comparative genome analyses and map-based cloning. Here we provide a new paradigm, a high-density consensus genetic map of …

Preferential Utilization Of Nadph As The Endogenous Electron Donor For Nad(P)H:Quinone Oxidoreductase 1 (Nqo1) In Intact Pulmonary Arterial Endothelial Cells, Robert D. Bongard, Brian J. Lindemer, Gary S. Krenz, Marilyn P. Merker

Mathematics, Statistics and Computer Science Faculty Research and Publications

The goal was to determine whether endogenous cytosolic NAD(P)H:quinone oxidoreductase 1 (NQO1) preferentially uses NADPH or NADH in intact pulmonary arterial endothelial cells in culture. The approach was to manipulate the redox status of the NADH/NAD⁺ and NADPH/NADP⁺ redox pairs in the cytosolic compartment using treatment conditions targeting glycolysis and the pentose phosphate pathway alone or with lactate, and to evaluate the impact on the intact cell NQO1 activity. Cells were treated with 2-deoxyglucose, iodoacetate, or epiandrosterone in the absence or presence of lactate, NQO1 activity was measured in intact cells using duroquinone as the electron acceptor, and …

Dendrites, Topological Graphs, And 2-Dominance, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

For each positive ordinal α, the reflexive and transitive binary relation of α-dominance between compacta was first defined in our paper [Mapping properties of co-existentially closed continua, Houston J. Math., 31 (2005), 1047-1063] using the ultracopower construction. Here we consider the important special case α =2, and show that any Peano compactum 2-dominated by a dendrite is itself a dendrite (with the same being true for topological graphs and trees). We also characterize the topological graphs that 2-dominate arcs (resp., simple closed curves) as those that have cut points of order 2 (resp., those that are not trees).

Survey Research On Communication And Language For English Language Learners And Native English Speakers Enrolled In A College Course On Statistical Literacy, Maria Guadalupe Valenzuela

Open Access Theses & Dissertations

The purpose of this study was to examine in what ways language is a factor that affects the learning process of students in an introductory statistics class. This research used a questionnaire survey instrument called: CLASS, Communication, Language And Statistics Survey that was applied to a total of 137 college students from a large southwestern public university, 83 of these students were self-identified as native English speakers (NOELL) and 53 were self-identified as English learner speakers (ELL) and one was dropped. This research found that in statistical instruction, there are some particular differences in behavior and learning process in the …

On The Estimation Of Averages Over Infinite Intervals With An Application To Average Persistence In Population Models, Sean F. Ellermeyer

Faculty Articles

We establish a general result for estimating the upper average of a continuous and bounded function over an infinite interval. As an application, we show that a previously studied model of microbial growth in a chemostat with time–varying nutrient input admits solutions (populations) that exhibit weak persistence but not weak average persistence.

A Comparison Of Methods For Generating Bivariate Non-Normally Distributed Random Variables, Jaimee E. Stewart

UNF Graduate Theses and Dissertations

Many distributions of multivariate data in the real world follow a non-normal model with distributions being skewed and/or heavy tailed. In studies in which multivariate non-normal distributions are needed, it is important for simulations of those variables to provide data that is close to the desired parameters while also being fast and easy to perform. Three algorithms for generating multivariate non-normal distributions are reviewed for accuracy, speed and simplicity. They are the Fleishman Power Method, the Fifth-Order Polynomial Transformation Method, and the Generalized Lambda Distribution Method. Simulations were run in order to compare the three methods by how well they …

A Trust-Based Secure Service Discovery (Tssd) Model For Pervasive Computing, Sheikh Iqbal Ahamed, Moushumi Sharmin

Mathematics, Statistics and Computer Science Faculty Research and Publications

To cope with the challenges posed by device capacity and capability, and also the nature of ad hoc networks, a Service discovery model is needed that can resolve security and privacy issues with simple solutions. The use of complex algorithms and powerful fixed infrastructure is infeasible due to the volatile nature of pervasive environment and tiny pervasive devices. In this paper, we present a trust-based secure Service discovery model, TSSD (trust-based secure service discovery) for a truly pervasive environment. Our model is a hybrid one that allows both secure and non-secure discovery of services. This model allows Service discovery and …

A Uniformly Dissipative Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang (Wendy) Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The purpose of this short communication is to announce that a class of numerical schemes, uniformly dissipative approximations, which uniformly preserve the dissipativity of the continuous infinite dimensional dissipative complex (chaotic) systems possess desirable properties in terms of approximating stationary statistics properties. in particular, the stationary statistical properties of these uniformly dissipative schemes converge to those of the continuous system at vanishing mesh size. the idea is illustrated on the infinite Prandtl number model for convection and semi-discretization in time, although the general strategy works for a broad class of dissipative complex systems and fully discretized approximations. as far as …

A Semi-Implicit Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We propose a semisecret in time semi-implicit numerical scheme for the infinite Prandtl model for convection. Besides the usual finite time convergence, this scheme enjoys the additional highly desirable feature that the stationary statistical properties of the scheme converge to those of the infinite Prandtl number model at vanishing time stop. One of the key characteristics of the scheme is that it preserves the dissipativity of the infinite Prandtl number model uniformly in terms of the time stop. So far as wo know, this is the first rigorous result on convergence of stationary statistical properties of numerical schemes for infinite …

Asymptotic Behavior Of Linearized Viscoelastic Flow Problem, Yinnian He, Yi Li

Mathematics and Statistics Faculty Publications

In this article, we provide some asymptotic behaviors of linearized viscoelastic flows in a general two-dimensional domain with certain parameters small and the time variable large.

Ubi-App: A Ubiquitous Application For Universal Access From Handheld Devices, Shameem Ahmed, Moushumi Sharmin, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Universal access from a handheld device (such as a PDA, cell phone) at any time or anywhere is now a reality. Ubicomp Assistant (UA) (Sharmin et al. in Proceedings of the 21st annual ACM symposium on applied computing (ACM SAC 2006), Dijon, France, pp 1013–1017, 2006) is an integral service of MARKS (Sharmin et al. in Proceedings of the third international conference on information technology: new generations (ITNG 2006), Las Vegas, Nevada, USA, pp 306–313, 2006). It is a middleware developed for handheld devices, and has been designed to accommodate different types of users (e.g., education, healthcare, marketing, or business). …

Coenzyme Q1 Redox Metabolism During Passage Through The Rat Pulmonary Circulation And The Effect Of Hyperoxia, Said H. Audi, Marilyn P. Merker, Gary S. Krenz, Taniya Ahuja, David L. Roerig, Robert D. Bongard

Mathematics, Statistics and Computer Science Faculty Research and Publications

The objective was to evaluate the pulmonary disposition of the ubiquinone homolog coenzyme Q₁ (CoQ₁) on passage through lungs of normoxic (exposed to room air) and hyperoxic (exposed to 85% O₂ for 48 h) rats. CoQ₁ or its hydroquinone (CoQ₁H₂) was infused into the arterial inflow of isolated, perfused lungs, and the venous efflux rates of CoQ₁H₂ and CoQ₁ were measured. CoQ₁H₂ appeared in the venous effluent when CoQ₁ was infused, and CoQ₁ appeared when CoQ1H2 was infused. In normoxic lungs, CoQ …

A Poisson-Like Model Of Sub-Clinical Signs From The Examination Of Healthy Aging Subjects, Stephen Merrill, Barbara Myklebust, Joel B. Myklebust, Norman Reynolds, Edmund Duthie

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background and aims: Our studies of the standard neurological examination on 66 middle-aged (50–64 yrs) and elderly subjects (65–84 yrs) demonstrate that healthy elders have neurological deficits (or “signs”) that are not associated with specific known neurological disease. The purpose of the current study is to describe this loss of neurological function in healthy aging subjects as seen through accumulated subclinical neurological signs present.

Methods: Logistic regression is applied to the data on each of six signs. Parameters determined are used to describe the distribution of first occurrence times for each sign. The results are then used to construct a …

Confluent Mappings And Arc Kelley Continua, W. J. Charatonik, Janusz R. Prajs, J. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A Kelley continuum X, also called a continuum with the property of Kelley, such that, for each p X, each subcontinuum K containing p is approximated by arc-wise connected continua containing p, is called an arc Kelley continuum. A continuum homeomorphic to the inverse limit of locally connected continua with confluent bonding maps is said to be confluently LC-representable. The main subject of the paper is a study of deep connections between the arc Kelley continua and confluent mappings. It is shown that if a continuum X admits, for each ε > 0, a confluent ε-mapping onto a(n) (arc) Kelley continuum, …

Generically There Is But One Self Homeomorphism Of The Cantor Set, Ethan Akin, Eli Glasner, Benjamin Weiss

Mathematics and Statistics Faculty Research & Creative Works

We describe a self-homeomorphism R of the Cantor set X and then show that its conjugacy class in the Polish group H(X) of all homeomorphisms of X forms a dense Gδ subset of H(X). We also provide an example of a locally compact, second countable topological group which has a dense conjugacy class. © 2008 American Mathematical Society.

The Detection Of Unsteady Flow Separation With Bioinspired Hair-Cell Sensors, Benjamin T. Dickinson, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

Biologists hypothesize that thousands of micro-scale hairs found on bat wings function as a network of air-flow sensors as part of a biological feedback flow control loop. In this work, we investigate hair-cell sensors as a means of detecting flow features in an unsteady separating flow over a cylinder. Individual hair-cell sensors were modeled using an Euler-Bernoulli beam equation forced by the fluid flow. When multiple sensor simulations are combined into an array of hair-cells, the response is shown to detect the onset and span of flow reversal, the upstream movement of the point of zero wall shear-stress, and the …

Approximate Low Rank Solutions Of Lyapunov Equations Via Proper Orthogonal Decomposition, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We present an algorithm to approximate the solution Z of a stable Lyapunov equation AZ + ZA* + BB* = 0 using proper orthogonal decomposition (POD). This algorithm is applicable to large-scale problems and certain infinite dimensional problems as long as the rank of B is relatively small. In the infinite dimensional case, the algorithm does not require matrix approximations of the operators A and B. POD is used in a systematic way to provide convergence theory and simple a priori error bounds.

Stationary Statistical Properties Of Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

This is the third in a series of our study of Rayleigh-Bénard convection at large Prandtl number. Here we investigate whether stationary statistical properties of the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number are related to those of the infinite Prandtl number model for convection that is formally derived from the Boussinesq system via setting the Prandtl number to infinity. We study asymptotic behavior of stationary statistical solutions, or in-variant measures, to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. in particular, we show that the invariant measures of the Boussinesq system for Rayleigh-Bénard convection converge …

Evaluating Statistical Methods Using Plasmode Data Sets In The Age Of Massive Public Databases: An Illustration Using False Discovery Rates, Gary L. Gadbury, Qinfang Xiang, Lin Yang, Stephen Barnes, Grier P. Page, David B. Allison

Mathematics and Statistics Faculty Research & Creative Works

Plasmode is a term coined several years ago to describe data sets that are derived from real data but for which some truth is known. Omic techniques, most especially microarray and genome wide association studies, have catalyzed a new zeitgeist of data sharing that is making data and data sets publicly available on an unprecedented scale. Coupling such data resources with a science of plasmode use would allow statistical methodologists to vet proposed techniques empirically (as opposed to only theoretically) and with data that are by definition realistic and representative. We illustrate the technique of empirical statistics by consideration of …

Architecture And Implementation Of A Trust Model For Pervasive Applications, Sheikh Iqbal Ahamed, Mohammad Zulkernine, Sailaja Bulusu, Mehrab Monjur

Mathematics, Statistics and Computer Science Faculty Research and Publications

Collaborative effort to share resources is a significant feature of pervasive computing environments. To achieve secure service discovery and sharing, and to distinguish between malevolent and benevolent entities, trust models must be defined. It is critical to estimate a device's initial trust value because of the transient nature of pervasive smart space; however, most of the prior research work on trust models for pervasive applications used the notion of constant initial trust assignment. In this paper, we design and implement a trust model called DIRT. We categorize services in different security levels and depending on the service requester's context information, …

The Weak Euler Scheme For Stochastic Delay Equations, Evelyn Buckwar, Rachel Kuske, Salah-Eldin A. Mohammed, Tony Shardlow

Articles and Preprints

We study weak convergence of an Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.

Methods Of Assessing And Ranking Probable Sources Of Error, Nataniel Greene

Publications and Research

A classical method for ranking n potential events as sources of error is Bayes' theorem. However, a ranking based on Bayes' theorem lacks a fundamental symmetry: the ranking in terms of blame for error will not be the reverse of the ranking in terms of credit for lack of error. While this is not a flaw in Bayes' theorem, it does lead one to inquire whether there are related methods which have such symmetry. Related methods explored here include the logical version of Bayes' theorem based on probabilities of conditionals, probabilities of biconditionals, and ratios or differences of credit to …

Connectivity In Frame Matroids, Dan Slilaty, Hongxun Qin

Mathematics and Statistics Faculty Publications

We discuss the relationship between the vertical connectivity of a biased graph Ω and the Tutte connectivity of the frame matroid of Ω (also known as the bias matroid of Ω).

The Signed-Graphic Representations Of Wheels And Whirls, Dan Slilaty, Hongxun Qin

Mathematics and Statistics Faculty Publications

We characterize all of the ways to represent the wheel matroids and whirl matroids using frame matroids of signed graphs. The characterization of wheels is in terms of topological duality in the projective plane and the characterization of whirls is in terms of topological duality in the annulus.

Quasigeometric Distributions And Extra Inning Baseball Games, Darren B. Glass, Philip J. Lowry

Math Faculty Publications

Each July, the eyes of baseball fans across the country turn to Major League Baseball’s All-Star Game, gathering the best and most popular players from baseball’s two leagues to play against each other in a single game. In most sports, the All-Star Game is an exhibition played purely for entertainment. Since 2003, the baseball All-Star Game has actually ‘counted’, because the winning league gets home field advantage in the World Series. Just one year before this rule went into effect, there was no winner in the All-Star Game, as both teams ran out of pitchers in the 11th inning and …