Statistics and Probability Commons^™

A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman

Mathematics Faculty Publications

In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.

Bounded Solutions Of Almost Linear Volterra Equations, Muhammad Islam, Youssef Raffoul

Mathematics Faculty Publications

Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold.

Generalizing Amdahl’S Law For Power And Energy, Rong Ge, Kirk W. Cameron

Mathematics, Statistics and Computer Science Faculty Research and Publications

Extending Amdahl's law to identify optimal power-performance configurations requires considering the interactive effects of power, performance, and parallel overhead.

Categoricity And Topological Graphs, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let X be a topological graph, with arcs joined only at end points. If Y is any locally connected metrizable compactum that is co-elementarily equivalent to X, then Y is homeomorphic to X. In particular, X and Y are homeomorphic if some lattice base for one is elementarily equivalent to some lattice base for the other.

Abel Dynamic Equations Of The First And Second Kind, Sabrina Heike Streipert

Masters Theses

"In this work, we study Abel dynamic equations of the first and the second kind. After a brief introduction to time scales, we introduce the Abel differential equations of the first and the second kind, as well as the canonical Abel form in the continuous case. Using the existing information, we derive novel results for time scales. We provide formulas for the Abel dynamic equations of the second kind and present a solution method. We furthermore achieve a special class of Abel equations of the first kind and discuss the canonical Abel equation. We get relations between common dynamic equations …

Mathematical Analysis Of The Problems Faced By The People With Disabilities (Pwds), Florentin Smarandache, W.B. Vasantha Kandasamy, A. Praveen Prakash

Branch Mathematics and Statistics Faculty and Staff Publications

The authors in this book have analyzed the socio-economic and psychological problems faced by People with Disabilities (PWDs) and their families. The study was made by collecting data using both fuzzy linguistic questionnaire / by interviews in case they are not literates from 2,15,811 lakhs people. This data was collected using the five Non Government Organizations (NGOs) from northern Tamil Nadu. Now any reader would be interested to know whether the Tamils (natives of Tamil Nadu) had ever spoken about people with disability. Even before 2000 years tamils had heroic poetry Purananuru (28th poem) about the war fare methods. In …

Protection By 20-5,14-Hedge Against Surgically-Induced Ischemia Reperfusion Lung Injury In Rats, Irshad Ali, Stephanie Gruenloh, Ying Gao, Anne V. Clough, John R. Falck, Meetha Medhora, Elizabeth R. Jacobs

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

We previously reported that the cytochrome P450 product 20-hydroxyeicosatetraenoic acid has prosurvival effects in pulmonary artery endothelial cells and ex vivo pulmonary arteries. We tested the potential of a 20-hydroxyeicosatetraenoic acid analog N-[20-hydroxyeicosa-5(Z),14(Z)-dienoyl]glycine (20-5,14-HEDGE) to protect against lung ischemic reperfusion injury in rats. Furthermore, we examined activation of innate immune system components, high mobility group box 1 (HMGB1) and toll-like receptor 4 (TLR4), in this model as well as the effect of 20-5,14-HEDGE on this signaling pathway.

Methods

Sprague-Dawley rats treated with 20-5,14-HEDGE or vehicle were subjected to surgically induced, unilateral lung ischemia for 60 minutes followed by reperfusion …

A Direct D-Bar Reconstruction Algorithm For Recovering A Complex Conductivity In 2d, Sarah J. Hamilton, C. N. L. Herrera, J. L. Mueller, A. Von Herrmann

Mathematics, Statistics and Computer Science Faculty Research and Publications

A direct reconstruction algorithm for complex conductivities in W^{2, ∞}(Ω), where Ω is a bounded, simply connected Lipschitz domain in R² , is presented. The framework is based on the uniqueness proof by Francini (2000 Inverse Problems 6 107–19), but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.

Modeling Temporal Pattern And Event Detection Using Hidden Markov Model With Application To A Sludge Bulking Data, Naveen K. Bansal, Xin Feng, Wenjing Zhang, Wutao Wi, Yuanhao Zhao

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper discusses a method of modeling temporal pattern and event detection based on Hidden Markov Model (HMM) for a continuous time series data. We also provide methods for checking model adequacy and predicting future events. These methods are applied to a real example of sludge bulking data for detecting sludge bulking for a water plant in Chicago.

Characterizations Of Certain Continuous Univariate Distributions Based On The Conditional Distribution Of Generalized Order Statistics, M. Ahsanullah, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

The problem of characterizing probability distributions is an interesting problem which has recently attracted the attention of many researchers. Various characterization results have been established in different directions as reported in the literature. We present here, various characterizations of certain univariate continuous distributions based on the conditional distribution of generalized order statistics.

Sieve Bootstrap Based Prediction Intervals And Unit Root Tests For Time Series, Maduka Rupasinghe

Doctoral Dissertations

"The application of the sieve bootstrap procedure, which resamples residuals obtained by fitting a finite autoregressvie (AR) approximation to empirical time series, to obtaining prediction intervals for integrated, long-memory, and seasonal time series as well as constructing a test for seasonal unit roots, is considered. The advantage of this resampling method is that it does not require knowledge about the underlying process generating a given time series and has been shown to work well for ARMA processes. We extend the application of the sieve bootstrap to ARIMA and FARIMA processes. The asymptotic properties of the sieve bootstrap prediction intervals for …

Multi-Time Scales Stochastic Dynamic Processes: Modeling, Methods, Algorithms, Analysis, And Applications, Jean-Claude Pedjeu

USF Tampa Graduate Theses and Dissertations

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model is formulated and it leads to a system of multi-time scale stochastic differential equations. The classical Picard-Lindel\"{o}f successive approximations scheme is expended to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this generates to a problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations. To illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are exhibited. Without loss in generality, …

Stochastic Hybrid Dynamic Systems: Modeling, Estimation And Simulation, Daniel Siu

USF Tampa Graduate Theses and Dissertations

Stochastic hybrid dynamic systems that incorporate both continuous and discrete dynamics have been an area of great interest over the recent years. In view of applications, stochastic hybrid dynamic systems have been employed to diverse fields of studies, such as communication networks, air traffic management, and insurance risk models. The aim of the present study is to investigate properties of some classes of stochastic hybrid dynamic systems.

The class of stochastic hybrid dynamic systems investigated has random jumps driven by a non-homogeneous Poisson process and deterministic jumps triggered by hitting the boundary. Its real-valued continuous dynamic between jumps is described …

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.

A General Family Of Dual To Ratio-Cum-Product Estimator In Sample Surveys, Florentin Smarandache, Rajesh Singh, Mukesh Kumar, Pankaj Chauhan, Nirmala Sawan

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a family of dual to ratio-cum-product estimators for the finite population mean. Under simple random sampling without replacement (SRSWOR) scheme, expressions of the bias and mean-squared error (MSE) up to the first order of approximation are derived. We show that the proposed family is more efficient than usual unbiased estimator, ratio estimator, product estimator, Singh estimator (1967), Srivenkataramana (1980) and Bandyopadhyaya estimator (1980) and Singh et al. (2005) estimator. An empirical study is carried out to illustrate the performance of the constructed estimator over others.

Design And Implementation Of An Open Framework For Ubiquitous Carbon Footprint Calculator Applications, Farzana Rahman, Casey O'Brien, Sheikh Iqbal Ahamed, He Zhang, Lin Liu

Mathematics, Statistics and Computer Science Faculty Research and Publications

As climate change is becoming an important global issue, more and more people are beginning to pay attention to reducing greenhouse gas emissions. To measure personal or household carbon dioxide emission, there are already plenty of carbon footprint calculators available on the web. Most of these calculators use quantitative models to estimate carbon emission caused by a user's activities. Although these calculators can promote public awareness regarding carbon emission due to an individual's behavior, there are concerns about the consistency and transparency of these existing CO₂ calculators. Apart from a small group of smart phone based carbon footprint calculator …

Reliable A-Posteriori Error Estimators For Hp-Adaptive Finite Element Approximations Of Eigenvalue/Leigenvector Problems, Stefano Giani, Luka Grubisic, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

We present reliable a-posteriori error estimates for hp-adaptive finite element approxima- tions of eigenvalue/eigenvector problems. Starting from our earlier work on h adaptive finite element approximations we show a way to obtain reliable and efficient a-posteriori estimates in the hp-setting. At the core of our analysis is the reduction of the problem on the analysis of the associated boundary value problem. We start from the analysis of Wohlmuth and Melenk and combine this with our a-posteriori estimation framework to obtain eigenvalue/eigenvector approximation bounds.

Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics, Funda Ekiz

Masters Theses & Specialist Projects

Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational expectations was given approximately fifty years ago by John F. Muth. Many models in economics have been studied using the rational expectations idea. The most familiar one among them is the rational expectations version of the Cagans hyperination model where the expectation for tomorrow is formed using all the information available today. This model was reinterpreted by Thomas J. Sargent and Neil Wallace in 1973. After that time, many solution techniques were suggested to solve the …

Interactive Real-Time Embedded Systems Education Infused With Applied Internet Telephony, Kyle Persohn, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

The transition from traditional circuit-switched phone systems to modern packet-based Internet telephony networks demands tools to support Voice over Internet Protocol (VoIP) development. In this paper, we introduce the XinuPhone, an integrated hardware/software approach for educating users about VoIP technology on a real-time embedded platform. We propose modular course topics for design-oriented, hands-on laboratory exercises: filter design, timing, serial communications, interrupts and resource budgeting, network transmission, and system benchmarking. Our open-source software platform encourages development and testing of new CODECs alongside existing standards, unlike similar commercial solutions. Furthermore, the supporting hardware features inexpensive, readily available components designed specifically for educational …

An Experimental Nexos Laboratory Using Virtual Xinu, Paul Ruth, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

The Nexos Project is a joint effort between Marquette University, the University of Buffalo, and the University of Mississippi to build curriculum materials and a supporting experimental laboratory for hands-on projects in computer systems courses. The approach focuses on inexpensive, flexible, commodity embedded hardware, freely available development and debugging tools, and a fresh implementation of a classic operating system, Embedded Xinu, that is ideal for student exploration. This paper describes an extension to the Nexos laboratory that includes a new target platform composed of Qemu virtual machines. Virtual Xinu addresses two challenges that limit the effectiveness of Nexos. First, potential …

Integral Inequalities On Time Scales Via The Theory Of Isotonic Linear Functionals, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić

Mathematics and Statistics Faculty Research & Creative Works

We apply the theory of isotonic linear functionals to derive a series of known inequalities, extensions of known inequalities, and new inequalities in the theory of dynamic equations on time scales. © 2011 Matloob Anwar et al.

Analysis And Finite Element Approximation Of A Coupled, Continuum Pipe-Flow/Darcy Model For Flow In Porous Media With Embedded Conduits, Yanzhao Cao, Max Gunzburger, Fei Hua, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We consider the continuum Darcy/pipe flow model for flows in a porous matrix containing embedded conduits; such coupled flows are present in, e.g., karst aquifers. the mathematical well-posedness of the coupled problem as well as convergence rates of finite element approximation are established in the two-dimensional case. Computational results are also provided. © 2010 Wiley Periodicals, Inc.

A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh

Mathematics Faculty Publications

The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry, mathematics rather than interdisciplinary courses. This fragmented teaching of sciences in majority of universities leave biology outside the quantitative and mathematical approaches. The landscape of biomedical science has transformed dramatically with advances in high throughput experimental approaches, which led to the huge amount of data. The best possible approach to generate …

The Constructions Of Almost Binary Sequence Pairs And Binary Sequence Pairs With Three-Level Autocorrelation, Xiuping Peng, Chengqian Xu, Guang Li, Krishnasamy T. Arasu

Mathematics and Statistics Faculty Publications

In this letter, a new class of almost binary sequence pairs with a single zero element and three autocorrelation values is presented. The new almost binary sequence pairs are based on cyclic difference sets and difference set pairs. By applying the method to the binary sequence pairs, new binary sequence pairs with three-level autocorrelation are constructed. It is shown that new sequence pairs from our constructions are balanced or almost balanced and have optimal three-level autocorrelation when the characteristic sequences or sequence pairs of difference sets or difference set pairs are balanced or almost balanced and have optimal autocorrelations.

Utilizing Induced Voxel Correlation In Fmri Analysis, Daniel B. Rowe, Andrew S. Nencka

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

A Parallel Robin-Robin Domain Decomposition Method For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Fei Hua, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We propose a new parallel Robin-Robin domain decomposition method for the coupled Stokes-Darcy system with Beavers-Joseph-Saffman-Jones interface boundary condition. in particular, we prove that, with an appropriate choice of parameters, the scheme converges geometrically independent of the mesh size. © 2011 Society for Industrial and Applied Mathematics.

Stability And Change In Self-Reported Sexual Orientation Identity In Young People: Application Of Mobility Metrics, Miles Q. Ott, Heather L. Corliss, David Wypij, Margaret Rosario, S. Bryn Austin

Statistical and Data Sciences: Faculty Publications

This study investigated stability and change in self-reported sexual orientation identity over time in youth. We describe gender- and age-related changes in sexual orientation identity from early adolescence through emerging adulthood in 13,840 youth ages 12–25 employing mobility measure M, a measure we modified from its original application for econometrics. Using prospective data from a large, ongoing cohort of U.S. adolescents, we examined mobility in sexual orientation identity in youth with up to four waves of data. Ten percent of males and 20% of females at some point described themselves as a sexual minority, while 2% of both males and …

The Utility Of Transient Sensitivity For Wildlife Management And Conservation: Bison As A Case Study, Michael Buhnerkempe, Nathanial Burch, Sarah J. Hamilton, Kerry M. Byrne, Eddie Childers, Kirstin A. Holfelder, Lindsay Mcmanus, Matthew I. Pyne, Greg Schroeder, Paul F. Doherty

Mathematics, Statistics and Computer Science Faculty Research and Publications

Developing effective management strategies is essential to conservation biology. Population models and sensitivity analyses on model parameters have provided a means to quantitatively compare different management strategies, allowing managers to objectively assess the resulting impacts. Inference from traditional sensitivity analyses (i.e., eigenvalue sensitivity methods) is only valid for a population at its stable age distribution, while more recent methods have relaxed this assumption and instead focused on transient population dynamics. However, very few case studies, especially in long-lived vertebrates where transient dynamics are potentially most relevant, have applied these transient sensitivity methods and compared them to eigenvalue sensitivity methods. We …

The Quantum Dialectic, Logan Kelley

Pitzer Senior Theses

A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part …

A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we prove a range and existence theorem for multivalued pseudomonotone perturbations of maximal monotone operators. We assume a general coercivity condition on the sum of a maximal monotone and a pseudomonotone operator instead of a condition on the pseudomonotone operator only. An illustrative example of a variational inequality in a Sobolev space with variable exponent is given.