Statistics and Probability Commons^™

An Impregnable Lightweight Device Discovery (Ildd) Model For The Pervasive Computing Environment Of Enterprise Applications, Munirul H. Haque, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

The worldwide use of handheld devices (personal digital assistants, cell phones, etc.) with wireless connectivity will reach 2.6 billion units this year and 4 billion by 2010. More specifically, these handheld devices have become an integral part of industrial applications. These devices form pervasive ad hoc wireless networks that aide in industry applications. However, pervasive computing is susceptible and vulnerable to malicious active and passive snoopers. This is due to the unavoidable interdevice dependency, as well as a common shared medium, very transitory connectivity, and the absence of a fixed trust infrastructure. In order to ensure security and privacy in …

An Overview Of Conditionals And Biconditionals In Probability, Nataniel Greene

Publications and Research

Conditional and biconditional statements are a standard part of symbolic logic but they have only recently begun to be explored in probability for applications in artificial intelligence. Here we give a brief overview of the major theorems involved and illustrate them using two standard model problems from conditional probability.

Property Of Kelley For The Cartesian Products And Hyperspaces, W. J. Charatonik, J. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A continuum X having the property of Kelley is constructed such that neither X × [0, 1], nor the hyperspace C(X), nor small Whitney levels in C(X) have the property of Kelley. This answers several questions asked in the literature.

Iterated Oscillation Criteria For Delay Dynamic Equations Of First Order, B. Karpuz, O. Öcalan, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We obtain new sufficient conditions for the oscillation of all solutions of first-order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential and difference equations. Examples, some of which coincide with well-known results on particular time scales, are provided to illustrate the applicability of our results.

Maximum Likelihood Estimation Methodology Comparison For The Three-Parameter Weibull Distribution With Applications To Offshore Oil Spills In The Gulf Of Mexico, William V. Harper, Thomas R. James, Ted G. Eschenbach, Leigh Slauson

Mathematics Faculty Scholarship

Maximum Likelihood estimation of the two-parameter Weibull distribution is straightforward; however, there are multiple methods for maximum likelihood estimation of the three-parameter Weibull. This paper presents an evaluation of these methods using four data sets including oil spill data from the Gulf of Mexico. Highlighted are fairly major differences in the estimated parameters between nine statistical packages. A VBA routine has been developed allowing practitioners to implement three-parameter Weibull maximum likelihood estimate within Excel. The code and support documentation are available free at http:faculty.otterbein.edu/WHarper.

On The Asymptotic Integration Of Nonlinear Dynamic Equations, Elvan Akin, Smail Djebali, Toufik Moussaoui, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The purpose of this paper is to study the existence and asymptotic behavior of solutions to a class of second-order nonlinear dynamic equations on unbounded time scales. Four different results are obtained by using the Banach fixed point theorem, the Boyd and Wong fixed point theorem, the Leray-Schauder nonlinear alternative, and the Schauder fixed point theorem. For each theorem, an illustrative example is presented. The results provide unification and some extensions in the time scale setup of the theory of asymptotic integration of nonlinear equations both in the continuous and discrete cases

Transition To Turbulence, Small Disturbances, And Sensitivity Analysis Ii: The Navier-Stokes Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

Recent research has shown that small disturbances in the linearized Navier-Stokes equations cause large energy growth in solutions. Although many researchers believe that this interaction triggers transition to turbulence in flow systems, the role of the nonlinearity in this process has not been thoroughly investigated. This paper is the second of a two part work in which sensitivity analysis is used to study the effects of small disturbances on the transition process. In the first part, sensitivity analysis was used to predict the effects of a small disturbance on solutions of a motivating problem, a highly sensitive one dimensional Burgers' …

Transition To Turbulence, Small Disturbances, And Sensitivity Analysis I: A Motivating Problem, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new "mostly linear" theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity …

Octahedral Dice, Todd Estroff, Jeremiah Farrell

Scholarship and Professional Work - LAS

All five Platonic solids have been used as random number generators in games involving chance with the cube being the most popular. Martin Gardenr, in his article on dice (MG 1977) remarks: "Why cubical?... It is the easiest to make, its six sides accomodate a set of numbers neither too large nor too small, and it rolls easily enough but not too easily."

Gardner adds that the octahedron has been the next most popular as a randomizer. We offer here several problems and games using octahedral dice. The first two are extensions from Gardner's article. All answers will be given …

A Comparison Of Different Methods For Predicting Cancer Mortality Counts At The State Level, Corinne Wilson

Virginia Journal of Science

Cancer is a major health issue in the United States. Reliable estimates of yearly cancer mortality counts are essential for resourcing and planning. The American Cancer Society has used several methods of forecasting to estimate the future cancer burden and researchers are continually working to develop new methods with improved performance. There have been studies comparing different models for predicting the US cancer mortality counts. This study explores and compares several different models for cancer mortality count predictions at the state level, principally for the state of Virginia. Results of the comparisons appear to show the final improved model to …

An Order Model For Infinite Classical States, Joe Mashburn

Mathematics Faculty Publications

In 2002 Coecke and Martin (Research Report PRG-RR-02-07, Oxford University Computing Laboratory,2002) created a model for the finite classical and quantum states in physics. This model is based on a type of ordered set which is standard in the study of information systems. It allows the information content of its elements to be compared and measured. Their work is extended to a model for the infinite classical states. These are the states which result when an observable is applied to a quantum system. When this extended order is restricted to a finite number of coordinates, the model of Coecke and …

Qualitative Properties Of Nonlinear Volterra Integral Equations, Muhammad Islam, Jeffrey T. Neugebauer

Mathematics Faculty Publications

In this article, the contraction mapping principle and Liapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form x(t)=a(t)−∫^t₀C(t,s)g(s,x(s))ds,t≥0. In particular, the existence of bounded solutions and solutions with various L^p properties are studied under suitable conditions on the functions involved with this equation.

Origin Of Conductive Surface Layer In Annealed Zno, David C. Look, B. Claflin, Helen Smith

Mathematics and Statistics Faculty Publications

The highly conductive surface layers found in nearly all as-grown or annealed bulk ZnO wafers are studied by temperature-dependent Hall-effect and secondary-ion mass spectroscopy (SIMS) measurements. In this work, we have used annealing in N₂ at 900 degrees C, and forming gas (5% H₂ in N₂) at 600 degrees C, to cause a large enough surface conduction that SIMS measurements can be reliably employed. The increased near-surface donor density, as determined from two-layer Hall-effect modeling, is consistent with an increased near-surface concentration of Al, Ga, and In atoms, resulting from diffusion. There is no evidence for …

Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam

Department of Math & Statistics Faculty Publications

To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and, as a result, the sample is length-biased. The selection bias model can be demonstrated through Buffon’s needle problem, extended to general curves that more realistically represent the shape of nanotubes observed on a grid. In this article, the nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of the length bias are examined. Probability plots reveal that the corrected length …

Degradation Models, Suk Joo Bae, Paul H. Kvam

Department of Math & Statistics Faculty Publications

Reliability testing typically generates product lifetime data, but for some tests, covariate information about the wear and tear on the product during the life test can provide additional insight into the product’s lifetime distribution. This usage, or degradation, can be the physical parameters of the product (e.g., corrosion thickness on a metal plate) or merely indicated through product performance (e.g., the luminosity of a light emitting diode). The measurements made across the product’s lifetime are degradation data, and degradation analysis is the statistical tool for providing inference about the lifetime distribution from the degradation data.

Load Sharing Models, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

Consider a system of components whose lifetimes are governed by a probability distribution. Load sharing refers to a model of stochastic interdependency between components that operate within a system. If components are set up in a parallel system (see Parallel, Series, and Series–Parallel Systems) for example, the system survives as long as at least one component is operating. In a typical load-sharing system, once a component fails, the remaining components suffer an increase in failure rate due to the extra “load” they must encumber due to the failed component.

Molecular Targets Of 2,3,7,8-Tetrachlorodibenzo-P-Dioxin (Tcdd) Within The Zebrafish Ovary: Insights Into Tcdd-Induced Endocrine Disruption And Reproductive Toxicity, Tisha C. King Heiden, Craig Struble, Matthew L. Rise, Martin J. Hessner, Reinhold J. Hutz, Michael J. Carvan Iii

Mathematics, Statistics and Computer Science Faculty Research and Publications

TCDD is a reproductive toxicant and endocrine disruptor, yet the mechanisms by which it causes these reproductive alterations are not fully understood. In order to provide additional insight into the molecular mechanisms that underlie TCDD's reproductive toxicity, we assessed TCDD-induced transcriptional changes in the ovary as they relate to previously described impacts on serum estradiol concentrations and altered follicular development in zebrafish. In silico computational approaches were used to correlate candidate regulatory motifs with observed changes in gene expression. Our data suggest that TCDD inhibits follicle maturation via attenuated gonadotropin responsiveness and/or depressed estradiol biosynthesis, and that interference of estrogen-regulated …

Pathos: Pervasive At Home Sleep Monitoring, Ian Obermiller, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Sleeping disorders affect a large percentage of the population, and many of them go undiagnosed each year because the method of diagnosis is to stay overnight at a sleep center. Because pervasive technologies have become so prevalent and affordable, sleep monitoring is no longer confined to a permanent installation, and can therefore be brought directly into the user home. We present a unique solution to the problem of home sleep monitoring that has the possibility to take the place of and expand on the data from a sleep center. PATHOS focuses not only on analyzing patterns during the night, but …

Characterization Of Digraphs With Equal Domination Graphs And Underlying Graphs, Kim A. S. Factor, Larry J. Langley

Mathematics, Statistics and Computer Science Faculty Research and Publications

A domination graph of a digraph D , dom(D)dom(D), is created using the vertex set of D and edge {u,v}∈E[dom(D)]{u,v}∈E[dom(D)] whenever (u,z)∈A(D)(u,z)∈A(D) or (v,z)∈A(D)(v,z)∈A(D) for every other vertex z∈V(D)z∈V(D). The underlying graph of a digraph DD, UG(D)UG(D), is the graph for which D is a biorientation. We completely characterize digraphs whose underlying graphs are identical to their domination graphs, UG(D)=dom(D)UG(D)=dom(D). The maximum and minimum number of single arcs in these digraphs, and their characteristics, is given.

Empirical Bayes And Hierarchical Bayes Estimation Of Skew Normal Populations, Naveen K. Bansal, Mehdi Maadooliat, Xiaowei Wang

Mathematics, Statistics and Computer Science Faculty Research and Publications

We develop empirical and hierarchical Bayesian methodologies for the skew normal populations through the EM algorithm and the Gibbs sampler. A general concept of skewness to the normal distribution is considered throughout. Motivations are given for considering the skew normal population in applications, and an example is presented to demonstrate why the skew normal distribution is more applicable than the normal distribution for certain applications.

Statistical Issues In The Normalization Of Multi-Species Microarray Data, John R. Stevens, Balasubramanian Ganesan, Prerak Desai, Sweta Rajan, Bart C. Weimer

Mathematics and Statistics Faculty Publications

Several species of bacteria are involved in the production of cheese, including Lactobacillus brevis and Lactococcus lactis. A custom-designed Affymetrix microarray was recently developed to study gene expression in three organisms on a single chip. This array contains only perfect match features for the coding and non-coding regions in the genomes of all three sequences. The multi-species nature of this array version raises interesting questions regarding the preprocessing or normalization strategies for the analysis of gene expression data. We present and evaluate several possible strategies using both cDNA dilution data and experimental expression data from a repeated measures design. …

Tests For Correlation On Bivariate Nonnormal Distributions, Louanne Margaret Beversdorf

UNF Graduate Theses and Dissertations

Many samples in the real world are very small in size and often do not follow a normal distribution. Existing tests for correlation have restrictions on the distribution of data and sample sizes, therefore the current tests cannot be used in some real world situations.

In this thesis, two tests are considered to test hypotheses about the population correlation coefficient. The tests are based on statistics transformed by a saddlepoint approximation and by Fisher's Z-transformation. The tests are conducted on small samples of bivariate nonnormal data and found to perfom well.

Simulations were run in order to compare the type …

Unit Rectangle Visibility Graphs, Alice M. Dean, Joanna A. Ellis-Monaghan, Sarah J. Hamilton, Greta Pangborn

Mathematics, Statistics and Computer Science Faculty Research and Publications

Over the past twenty years, rectangle visibility graphs have generated consider- able interest, in part due to their applicability to VLSI chip design. Here we study unit rectangle visibility graphs, with fixed dimension restrictions more closely modeling the constrained dimensions of gates and other circuit components in computer chip applications. A graph G is a unit rectangle visibility graph (URVG) if its vertices can be represented by closed unit squares in the plane with sides parallel to the axes and pairwise disjoint interiors, in such a way that two vertices are adjacent if and only if there is a non-degenerate …

The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang

Articles and Preprints

In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating …

Image Reconstruction In Multi-Channel Model Under Gaussian Noise, Veera Holdai, Alexander Korostelev

Mathematics Research Reports

The image reconstruction from noisy data is studied. A nonparametric boundary function is estimated from observations in N independent channels in Gaussian white noise. In each channel the image and the background intensities are unknown. They define a non-identifiable nuisance "parameter" that slows down the typical minimax rate of convergence. The large sample asymptotics of the minimax risk is found and an asymptotically optimal estimator for boundary function is suggested.

A Software-Based Trust Framework For Distributed Industrial Management Systems, Sheikh Iqbal Ahamed, Mohammad Zulkernine, Steve Wolfe

Mathematics, Statistics and Computer Science Faculty Research and Publications

One of the major problems in industrial security management is that most organizations or enterprises do not provide adequate guidelines or well-defined policy with respect to trust management, and trust is still an afterthought in most security engineering projects. With the increase of handheld devices, managers of business organizations tend to use handheld devices to access the information systems. However, the connection or access to an information system requires appropriate level of trust. In this paper, we present a flexible, manageable, and configurable software-based trust framework for the handheld devices of mangers to access distributed information systems. The presented framework …

Asymptotic Behavior Of The Global Attractors To The Boussinesq System For Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We study asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. in particular, we show that the global attractors to the Boussinesq system for Rayleigh-Bénard convection converge to that of the infinite-Prandtl- number model for convection as the Prandtl number approaches infinity. This offers partial justification of the infinite-Prandtl-number model for convection as a valid simplified model for convection at large Prandtl number even in the long-time regime. © 2006 Wiley Periodicals, Inc.

Decompositions Of Signed-Graphic Matroids, Dan Slilaty, Hongxun Qin

Mathematics and Statistics Faculty Publications

We give a decomposition theorem for signed graphs whose frame matroids are binary and a decomposition theorem for signed graphs whose frame matroids are quaternary.

Transmission Dynamics Of Avian Influenza Among Poultry With And Without Vaccination, Qiao Liang

Mathematics & Statistics ETDs

The continuing avian influenza (AI) out break that began in late 2003 and early 2004 has been disastrous for the poultry industry worldwide. It has resulted in severe socio-economic damage, and it has raised serious concerns for general public health. In this research, we use mathematics to analyze transmission dynamics of AI among poultry. We use a status-based approach to construct systems of differential equations to describe virus transmission dynamics. We develop theoretical means to eradicate the spread of the disease, and we calculate the size of healthy and infected populations during an AI outbreak, and the final population size …

Double Integral Calculus Of Variations On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among them an analogue of the Euler-Lagrange equation.