Physical Sciences and Mathematics Commons^™

Numerical Solutions Of Stochastic Differential Equations, Liguo Wang

Doctoral Dissertations

In this dissertation, we consider the problem of simulation of stochastic differential equations driven by Brownian motions or the general Levy processes. There are two types of convergence for a numerical solution of a stochastic differential equation, the strong convergence and the weak convergence. We first introduce the strong convergence of the tamed Euler-Maruyama scheme under non-globally Lipschitz conditions, which allow the polynomial growth for the drift and diffusion coefficients. Then we prove a new weak convergence theorem given that the drift and diffusion coefficients of the stochastic differential equation are only twice continuously differentiable with bounded derivatives up to …

Effects Of Bullying And Victimization On Friendship Selection, Reciprocation, And Maintenance In Elementary School Children, Marisa Lynn Whitley

Masters Theses

This study examined the effects of elementary school children’s bullying and victimization experiences on their friendships over time. The majority of children experience acts of aggression or bullying before the end of elementary school, and bullying and peer victimization is associated with academic, social, behavioral, and psychological difficulties. This study used social networks analysis (R SIENA 4.0) to examine whether peer reports of forms of bullying and victimization (i.e., overt and relational) affect the likelihood of friendship selection, reciprocation, and maintenance in 2^nd-4^th grade children. Children (N = 143) from the Midwestern region of the United …

Walking To Recovery - The Effects Of Postsurgical Ambulation On Patient Recovery Times, Trent William Stethen

Chancellor’s Honors Program Projects

No abstract provided.

Developing An Optimal Model For Infant Home Visitation, Isaac Atuahene

Doctoral Dissertations

The United States, Great Britain, Denmark, Canada and many other countries have accepted home visitation (HV) as a promising strategy for interventions for infants after births and for their mothers. Prior HV studies have focused on theoretical foundations, evaluations of programs, cost/benefit analysis and cost estimation by using hospital/payer/insurance data to prove its effectiveness and high cost. As governments and private organizations continue to fund HVs, it is an opportune time to develop and formulate operations research (OR) models of HV coverage, quality and cost so they might be used in program implementation as done for adult home healthcare (HHC) …

Evaluating The Effects Of Standardized Patient Care Pathways On Clinical Outcomes, Anna V. Romanova

Doctoral Dissertations

The main focus of this study is to create a standardized approach to evaluating the impact of the patient care pathways across all major disease categories and key outcome measures in a hospital setting when randomized clinical trials are not feasible. Toward this goal I identify statistical methods, control factors, and adjustments that can correct for potential confounding in observational studies. I investigate the efficiency of existing bias correction methods under varying conditions of imbalanced samples through a Monte Carlo simulation. The simulation results are then utilized in a case study for one of the largest primary diagnosis areas, chronic …

Nanoscaled Cellulose And Its Carbonaceous Material: Application And Local Structure Investigation, Yujie Meng

Doctoral Dissertations

In this dissertation, cellulose nanocrystals three-dimensional morphology, size distribution, and the crystal structure were statistically and quantitatively investigated. Lognormal distribution was identified as the most likely for cellulose nanocrystals’ size distribution. Height and width dimensions were shown to decrease toward the ends from the midpoint of individual CNCs, implying a spindle-like shape. XRD analysis of crystallite size accompanied with TEM and AFM measurements revealed that the cross-sectional dimensions of individual switchgrass CNC were either rectangular or elliptical shape, with an approximately 3~5 nm [nanometer] lateral element length range. A sponge-like carbon aerogel from microfibril cellulose with high porosity, ultra-low density, …

Modelling Supercomputer Maintenance Interrupts: Maintenance Policy Recommendations, Jagadish Cherukuri

Masters Theses

A supercomputer is a repairable system with large number of compute nodes interconnected to work in harmony to achieve superior computational performance. Reliability of such a complex system depends on an effective maintenance strategy that involves both emergency and preventive maintenance. This thesis analyzes the maintenance records of four supercomputers operational at The National Institute of Computational Science located at Oak Ridge National Laboratory. We propose to use the generalized proportional intensities model (GPIM) to model the maintenance interrupts as it can capture both the reliability parameters and maintenance parameters and allows the inclusion of both emergency and preventive maintenance. …

Numerical Methods For Deterministic And Stochastic Phase Field Models Of Phase Transition And Related Geometric Flows, Yukun Li

Doctoral Dissertations

This dissertation consists of three integral parts with each part focusing on numerical approximations of several partial differential equations (PDEs). The goals of each part are to design, to analyze and to implement continuous or discontinuous Galerkin finite element methods for the underlying PDE problem.

Part One studies discontinuous Galerkin (DG) approximations of two phase field models, namely, the Allen-Cahn and Cahn-Hilliard equations, and their related curvature-driven geometric problems, namely, the mean curvature flow and the Hele-Shaw flow. We derive two discrete spectrum estimates, which play an important role in proving the sharper error estimates which only depend on a …

Numerical Approximation Of Stochastic Differential Equations Driven By Levy Motion With Infinitely Many Jumps, Ernest Jum

Doctoral Dissertations

In this dissertation, we consider the problem of simulation of stochastic differential equations driven by pure jump Levy processes with infinite jump activity. Examples include, the class of stochastic differential equations driven by stable and tempered stable Levy processes, which are suited for modeling of a wide range of heavy tail phenomena. We replace the small jump part of the driving Levy process by a suitable Brownian motion, as proposed by Asmussen and Rosinski, which results in a jump-diffusion equation. We obtain L^p [the space of measurable functions with a finite p-norm], for p greater than or equal to …

Monte Carlo Methods In Finance, Je Guk Kim

Doctoral Dissertations

Monte Carlo method has received significant consideration from the context of quantitative finance mainly due to its ease of implementation for complex problems in the field. Among topics of its application to finance, we address two topics: (1) optimal importance sampling for the Laplace transform of exponential Brownian functionals and (2) analysis on the convergence of quasi-regression method for pricing American option. In the first part of this dissertation, we present an asymptotically optimal importance sampling method for Monte Carlo simulation of the Laplace transform of exponential Brownian functionals via Large deviations principle and calculus of variations the closed form …

The Phenomenon Of Outbound Medical Tourism In The United States, Tanner Douglas Cabbage

Chancellor’s Honors Program Projects

No abstract provided.

Predicting High-Stakes Tests Of Math Achievement Using A Group-Administered Rti Instrument: Validating Skills Measured By The Monitoring Instructional Responsiveness: Math, Jeremy Thomas Coles

Doctoral Dissertations

Three universal screeners and nine progress monitoring probes from the Monitoring Instructional Responsiveness: Math (MIR:M), a silent, group-administered math assessment designed for implementation with an RTI Model, were administered to 223 fifth-grade students. The growth parameters of the overall MIR:M composite and two global composites (math calculation and math reasoning) identified significant variation in student growth, within significant linear and quadratic trajectories. However, there were significant differences in the nature of the growth trajectories that have applied educational implications. In addition, growth parameters across the three composites provided significant predictive potential when using the Tennessee Comprehensive Assessment Program (TCAP) Achievement …

Impacts Of Climate Change On The Evolution Of The Electrical Grid, Melissa Ree Allen

Doctoral Dissertations

Maintaining interdependent infrastructures exposed to a changing climate requires understanding 1) the local impact on power assets; 2) how the infrastructure will evolve as the demand for infrastructure changes location and volume and; 3) what vulnerabilities are introduced by these changing infrastructure topologies. This dissertation attempts to develop a methodology that will a) downscale the climate direct effect on the infrastructure; b) allow population to redistribute in response to increasing extreme events that will increase under climate impacts; and c) project new distributions of electricity demand in the mid-21^st century.

The research was structured in three parts. The first …

Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic

Masters Theses

Schramm-Loewner Evolution (SLE) has both mathematical and physical roots that extend as far back as the early 20th century. We present the progression of these humble roots from the Ideal Gas Law, all the way to the renormalization group and conformal field theory, to better understand the impact SLE has had on modern statistical mechanics. We then explore the potential application of the percolation exploration process to crack propagation processes, illustrating the interplay between mathematics and physics.

Comparison Of Triangle And Tetrad Discrimination Methodology In Applied, Industrial Manner, Sara Lyn Carlisle

Masters Theses

The triangle method has been widely used in the food industry for many years when conducting sensory discrimination testing. Recently, however, another discrimination testing method, the tetrad, has begun to gain popularity. Based on currently published research, the tetrad method possesses statistical advantages over the triangle and would require fewer panelists, reduce testing time, and use less sample material. More testing is needed to confirm these advantages in an applied, industrial approach on a wider range of products. Over thirty triangles and thirty tetrads with untrained panelists have been completed in order to compare the two methods. Products tested ranged …

Associations Of Total Activity Counts And Physical Activity Intensity Levels With The Metabolic Syndrome: A Structural Equation Modeling Approach, Dana Lizbeth Wolff

Doctoral Dissertations

To clarify the protective benefits of physical activity (PA), epidemiologists and public health researchers continue to seek improved methods of assessing PA. In particular, accelerometers have gained acceptance with researchers as they provide reliable estimates of PA and can record both the amount and intensity of ambulatory movement. However, there is concern that accelerometer data reduction techniques may not provide quantitatively accurate measurements of time spent in various PA intensity categories. One way to circumvent these inaccuracies is to use the accelerometer-derived total activity counts (TAC), which is a more direct expression of what the monitor records.

In order to …

Asymptotic Behavior Of A Class Of Spdes, Parisa Fatheddin

Doctoral Dissertations

We establish the large and moderate deviation principles for a class of stochastic partial differential equations with a non-Lipschitz continuous coefficient. As an application we derive these principles for an important population model, Fleming-Viot Process. In addition, we establish the moderate deviation principle for another classical population model, super-Brownian motion.

Sensitivity Analysis Of A Leaf Photosynthesis-Stomatal Resistance Model, Gabriel A. Garcia

Chancellor’s Honors Program Projects

No abstract provided.

Sensitivity Analysis Of A Photosynthesis-Stomatal Resistance Model, Gabriel A. Garcia

EURēCA: Exhibition of Undergraduate Research and Creative Achievement

Abstract/Poster

Experimental And Statistical Techniques To Probe Extraordinary Electronic Properties Of Molecules, Byron Hager Smith

Doctoral Dissertations

The existence of an additional electron or hole in the presence of an electric monopole is a well understood physical system, but this ideality is far from the true physical properties of many molecules. Examples of such irregular electronic states include the attachment of an excess charge to a molecule's dipole moment, electronic correlation spanning a molecule, or attachment of multiple excess charges. Current theoretical and experimental interpretations widely vary for these states and further elucidation of the nature of irregular electronic structure may provide solutions to unexplained observations and the impetus for industrial application. For example, in the case …

Mapping Spatial Thematic Accuracy Using Indicator Kriging, Maria I. Martinez

Masters Theses

Thematic maps derived from remote sensing imagery is increasingly being used in environmental and ecological modeling. Spatial information in these maps however is not free of error. Different methodologies such as error matrices are used to assess the accuracy of the spatial information. However, most of the methods commonly used for describing the accuracy assessment of thematic data fail to describe spatial differences of the accuracy across an area of interest. This thesis describes the use of indicator kriging as a geostatistical method for mapping the spatial accuracy of thematic maps. The method is illustrated by constructing accuracy maps for …

Online Multi-Stage Deep Architectures For Feature Extraction And Object Recognition, Derek Christopher Rose

Doctoral Dissertations

Multi-stage visual architectures have recently found success in achieving high classification accuracies over image datasets with large variations in pose, lighting, and scale. Inspired by techniques currently at the forefront of deep learning, such architectures are typically composed of one or more layers of preprocessing, feature encoding, and pooling to extract features from raw images. Training these components traditionally relies on large sets of patches that are extracted from a potentially large image dataset. In this context, high-dimensional feature space representations are often helpful for obtaining the best classification performances and providing a higher degree of invariance to object transformations. …

Long Time Asymptotics Of Ornstein-Uhlenbeck Processes In Poisson Random Media, Fei Xing

Doctoral Dissertations

The Models of Random Motions in Random Media (RMRM) have been shown to have fruitful applications in various scientific areas such as polymer physics, statistical mechanics, oceanography, etc. In this dissertation, we consider a special model of RMRM: the Ornstein-Uhlenbeck process in a Poisson random medium and investigate the long time evolution of its random energy. We give complete answers to the long time asymptotics of the exponential moments of the random energy with both positive and negative coefficients, under both quenched and annealed regimes. Through these results, we find out a dramatic difference between the long time behavior of …

Geographic And Temporal Epidemiology Of Campylobacteriosis, Jennifer Weisent

Doctoral Dissertations

Campylobacteriosis is a leading cause of gastroenteritis in the United States. The focus of this research was to (i) analyze and predict spatial and temporal patterns and associations for campylobacteriosis risk and (ii) compare the utility of advanced modeling methods. Laboratory-confirmed Campylobacter case data, obtained from the Foodborne Diseases Active Surveillance Network were used in all investigations.

We compared the accuracy of forecasting techniques for campylobacteriosis risk in Minnesota, Oregon and Georgia and found that time series regression, decomposition, and Box-Jenkins Autoregressive Integrated Moving Averages reliably predict monthly risk of infection for campylobacteriosis. Decomposition provided the fastest, most accurate, user-friendly …

Automating Large-Scale Simulation Calibration To Real-World Sensor Data, Richard Everett Edwards

Doctoral Dissertations

Many key decisions and design policies are made using sophisticated computer simulations. However, these sophisticated computer simulations have several major problems. The two main issues are 1) gaps between the simulation model and the actual structure, and 2) limitations of the modeling engine's capabilities. This dissertation's goal is to address these simulation deficiencies by presenting a general automated process for tuning simulation inputs such that simulation output matches real world measured data. The automated process involves the following key components -- 1) Identify a model that accurately estimates the real world simulation calibration target from measured sensor data; 2) Identify …

A Study Of Poisson And Related Processes With Applications, Phillip Mingola

Chancellor’s Honors Program Projects

No abstract provided.

Modeling The Relationship Between Coal Mining And Respiratory Health In West Virginia, Jessica Welch

Chancellor’s Honors Program Projects

No abstract provided.

Mussel Survivorship, Growth Rate And Shell Decay Rate In The New River Basin Of Tennessee: An Experimental Approach Using Corbicula Fluminea, Grant Andrew Mincy

Masters Theses

The New River Basin (NRB) of Tennessee is home to a number of rare endemic aquatic communities. One such community of particular importance to the area, experiencing a precipitous population decline due to the fouling and pollution of their freshwater systems, is that of freshwater mussels (Bogan 2006). This study in the NRB involves measuring the mortality rates of live Asian clams (Corbicula fluminea) assemblages and the shell decay rates of their death assemblages. This study also examines the decay rates of the native Villosa iris to gather information on molluscan health and the ability of their shells …

Stability Of Nonlinear Filters And Branching Particle Approximations To The Filtering Problems, Zhiqiang Li

Doctoral Dissertations

Various particle filters have been proposed and their convergence to the optimal filter are obtained for finite time intervals. However, uniform convergence results have been established only for discrete time filters. We prove the uniform convergence of a branching particle filter for continuous time setup when the optimal filter itself is exponentially stable.

The short interest rate process is modeled by an asymptotically stationary diffusion process. With the counting process observations, a filtering problem is formulated and its exponential stability is derived. Base on the stability result, the uniform convergence of a branching particle filter is proved.

Identifying The Spatial Distribution Of Three Plethodontid Salamanders In Great Smoky Mountains National Park Using Two Habitat Modeling Methods, Matthew Stephen Kookogey

Masters Theses

The main objective was to create habitat models of three plethodontid salamander species (Desmognathus conanti, D. ocoee, and Plethodon jordani) in GSMNP. To investigate the relationships between salamanders and their habitats, I used three models—logistic regression with use-availability sampling, logistic regression with case-control sampling, and Mahalanobis distance (D²)—for each species to gain a robust view of the relationships. The secondary objective was to compare the different modeling methods within and across the three species. Elevation was the dominant variable for all three species.

D² for D. conanti predicted low elevations, close proximity …