Physical Sciences and Mathematics Commons^™

Homogenization Of Stokes Systems With Periodic Coefficients, Shu Gu

Theses and Dissertations--Mathematics

In this dissertation we study the quantitative theory in homogenization of Stokes systems. We study uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L^∞ estimates for the pressure as well as Liouville property for solutions in ℝ^d. We are able to obtain the boundary W^{1,p} estimates in a bounded C¹ domain for any 1 < p < ∞. We also study the convergence rates in L² and H¹ of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.

On Skew-Constacyclic Codes, Neville Lyons Fogarty

Theses and Dissertations--Mathematics

Cyclic codes are a well-known class of linear block codes with efficient decoding algorithms. In recent years they have been generalized to skew-constacyclic codes; such a generalization has previously been shown to be useful. We begin with a study of skew-polynomial rings so that we may examine these codes algebraically as quotient modules of non-commutative skew-polynomial rings. We introduce a skew-generalized circulant matrix to aid in examining skew-constacyclic codes, and we use it to recover a well-known result on the duals of skew-constacyclic codes from Boucher/Ulmer in 2011. We also motivate and develop a notion of idempotent elements in these …

Inverse Scattering For The Zero-Energy Novikov-Veselov Equation, Michael Music

Theses and Dissertations--Mathematics

For certain initial data, we solve the Novikov-Veselov equation by the inverse scat- tering method. This is a (2+1)-dimensional completely integrable system that gen- eralizes the (1+1)-dimensional Korteweg-de-Vries equation. The method used is the inverse scattering method. To study the direct and inverse scattering maps, we prove existence and uniqueness properties of exponentially growing solutions of the two- dimensional Schrodinger equation. For conductivity-type potentials, this was done by Nachman in his work on the inverse conductivity problem. Our work expands the set of potentials for which the analysis holds, completes the study of the inverse scattering map, and show that …

Development In Normal Mixture And Mixture Of Experts Modeling, Meng Qi

Theses and Dissertations--Statistics

In this dissertation, first we consider the problem of testing homogeneity and order in a contaminated normal model, when the data is correlated under some known covariance structure. To address this problem, we developed a moment based homogeneity and order test, and design weights for test statistics to increase power for homogeneity test. We applied our test to microarray about Down’s syndrome. This dissertation also studies a singular Bayesian information criterion (sBIC) for a bivariate hierarchical mixture model with varying weights, and develops a new data dependent information criterion (sFLIC).We apply our model and criteria to birth- weight and gestational …

Multi-State Models With Missing Covariates, Wenjie Lou

Theses and Dissertations--Statistics

Multi-state models have been widely used to analyze longitudinal event history data obtained in medical studies. The tools and methods developed recently in this area require the complete observed datasets. While, in many applications measurements on certain components of the covariate vector are missing on some study subjects. In this dissertation, several likelihood-based methodologies were proposed to deal with datasets with different types of missing covariates efficiently when applying multi-state models.

Firstly, a maximum observed data likelihood method was proposed when the data has a univariate missing pattern and the missing covariate is a categorical variable. The construction of the …

Solutions To The LP Mixed Boundary Value Problem In C1,1 Domains, Laura D. Croyle

Theses and Dissertations--Mathematics

We look at the mixed boundary value problem for elliptic operators in a bounded C^1,1(ℝⁿ) domain. The boundary is decomposed into disjoint parts, D and N, with Dirichlet and Neumann data, respectively. Expanding on work done by Ott and Brown, we find a larger range of values of p, 1 < p < n/(n-1), for which the L^p mixed problem has a unique solution with the non-tangential maximal function of the gradient in L^p(∂Ω).

The Bourgain Spaces And Recovery Of Magnetic And Electric Potentials Of Schrödinger Operators, Yaowei Zhang

Theses and Dissertations--Mathematics

We consider the inverse problem for the magnetic Schrödinger operator with the assumption that the magnetic potential is in C^λ and the electric potential is of the form p₁ + div p₂ with p₁, p₂ ∈ C^λ. We use semiclassical pseudodifferential operators on semiclassical Sobolev spaces and Bourgain type spaces. The Bourgain type spaces are defined using the symbol of the operator h²Δ + hμ ⋅ D. Our main result gives a procedure for recovering the curl of the magnetic field and the electric potential from the Dirichlet to Neumann …

Ecology Of Two Reintroduced Black Bear Populations In The Central Appalachians, Sean Mccarthy Murphy

Theses and Dissertations--Animal and Food Sciences

Reintroduced populations are vulnerable to demographic and environmental stochasticity, deleterious genetic effects, and reduced population fitness, all of which can increase extinction probability. Population viability is principle to determining the status of reintroduced populations and for guiding management decisions. To attempt to reestablish black bear (Ursus americanus) populations in the central Appalachians, two reintroductions using small founder groups occurred during the 1990s in the Big South Fork area along the Kentucky-Tennessee border (BSF) and in the Jefferson National Forest along the Kentucky-Virginia border (KVP). My objectives were to estimate demographic and genetic parameters, and to evaluate long-term viability …

Magnetic Field Non-Uniformity Challenges In Neutron Electric Dipole Moment Experiments, Nima Nouri

Theses and Dissertations--Physics and Astronomy

A new neutron Electric Dipole Moment (nEDM) experiment was proposed to be commissioned at the Fundamental Neutron Physics Beamline at the Spallation Neutron Source (SNS) of the Oak Ridge National Laboratory (ORNL). The underlying theme of this experiment (first conceived by Golub and Lamoreaux in 1994) is the search for new physics beyond the Standard Model of particle physics. The discovery of a non-zero nEDM would be of revolutionary importance to physics, with the discovery of such providing for evidence for new-beyond-the-Standard-Model physics required for a resolution to the unresolved puzzle of why the universe is dominated by matter, as …

Towards An Understanding Of The Role Of Cation Packaging On Dna Protection From Oxidative Damage, Cody E. Gay

Theses and Dissertations--Chemistry

In sperm chromatin, DNA exists in a highly condensed state reaching a final volume roughly twenty times that of a somatic nucleus. For the vast majority (>90%) of sperm DNA in mammals, somatic-like histones are first replaced by transition proteins which in turn are replaced by arginine-rich protamines. This near crystalline organization of the DNA in mature sperm is thought crucial for both the transport and protection of genetic information since all DNA repair mechanisms are shut down. Recent studies show that increased DNA damage is linked to dysfunctions in replacing histones with protamines resulting in mispackaged DNA. This …

Towards Catalytic Oxidative Depolymerization Of Lignin, Justin K. Mobley

Theses and Dissertations--Chemistry

Lignin is one of the most abundant and underutilized biopolymers on earth. Primarily composed on three monolignol units (sinapyl, coniferyl, and p-coumaryl alcohol), lignin is formed through a radical pathway resulting in an assortment of linkages, of which the β-O-4 linkage is the most prevalent (up to 60% in some hardwood species). In planta, lignin plays an important role in water transport and in protecting plants from chemical and biological attack. Traditional attempts to depolymerize lignin have focused on the cleavage of β-O-4 linkages via thermal or reductive routes. However these pathways lead to low-value, unstable product mixtures. Moreover, …

Towards An Understanding Of Pharmacologically Induced Intracellular Changes In Nicotinic Acetylcholine Receptors: A Fluorescence Microscopy Approach, Ashley M. Loe

Theses and Dissertations--Chemistry

Upregulation of nicotinic acetylcholine receptors (nAChRs) is a well-documented response to chronic nicotine exposure. Nicotinic acetylcholine receptors are pentameric ligand-gated ion channels consisting of alpha (α2-10) and beta (β2-4) subunits. Nicotine, an agonist of nAChRs, alters trafficking and assembly of some subtypes of nAChRs, leading to an increase in expression of high sensitivity receptors on the plasma membrane. These physiological changes in nAChRs are believed to contribute to nicotine addiction, although the mechanism of these processes has not been resolved. Recently, many studies have converged on the idea that nicotine induces upregulation by an intracellular mechanism. In this dissertation, expression …

Organometallic Materials: Ferroceno[C]Thiophenes And 1,2-Bisthienylmetallocenes, Surya R. Banks

Theses and Dissertations--Chemistry

Development of synthetic routes toward two general organometallic frameworks was undertaken. The first project involved synthetic attempts of substituted and unsubstituted ferroceno[c]thiophene while the second one was the synthesis of 1,2-dithienylmetallocenes. The long-term goal of this work is to lay the foundations for study of electronic, electrochromic, redox, and optical properties of thiophene-based materials integrated with organometallic systems such as ferrocene, ruthenocene and cymantrene. The synthetic pathway for the target molecule in the first project involved converting 1,2-bis(hydroxymethyl)ferrocene to 1,2-bis(thiouroniummethyl)ferrocene with thiourea under acidic conditions. Refluxing the salt in base followed by acidification resulted in 1,2-bis(mercaptomethyl)ferrocene, which is …

Using Conventional And In Situ Transmission Electron Microscopy Techniques To Understand Nanoscale Crystallography, Bethany M. Hudak

Theses and Dissertations--Chemistry

Transmission electron microscopy (TEM) is a powerful tool for studying solidstate crystalline systems. With the advances in aberration correction, monochromation, and in situ capabilities, these microscopes are now more useful for addressing fundamental materials chemistry problems than ever before. This dissertation will illustrate the ways in which I have been using high-resolution imaging and in situ heating in the TEM during my Ph.D. research to investigate unique solid state chemistry questions.

This dissertation will focus on four unique crystal systems: thermoelectric skutterudite crystals, vapor-liquid-solid (VLS) grown nanowires, and hafnium dioxide nanorods. Although these systems are very different from one another, …

Effects Of Epichloë Coenophiala−Tall Fescue Symbiosis On Plant-Microbe-Soil Interactions In A Temperate Pasture, Lindsey C. Slaughter

Theses and Dissertations--Plant and Soil Sciences

Plants interact in myriad ways with microorganisms to influence ecosystem processes such as nutrient cycling, which can regulate ecosystem response to global change. One important plant-microbe symbiosis occurs between cool-season grasses and asexual fungal Epichloë endophytes, such as tall fescue (Schedonorus arundinaceus) and Epichloë coenophiala. Because the common toxic strain of the endophyte (CTE) harms grazing livestock, non-livestock toxic endophyte (NTE) strains have been developed and are increasingly deployed in pastures. Little is known about how these symbioses impact other plant-microbe interactions and microbe-mediated soil processes in grassland ecosystems. I conducted three studies to determine how E. …

Statistical Methods For Handling Intentional Inaccurate Responders, Kristen J. Mcquerry

Theses and Dissertations--Statistics

In self-report data, participants who provide incorrect responses are known as intentional inaccurate responders. This dissertation provides statistical analyses for address intentional inaccurate responses in the data.

Previous work with adolescent self-report, labeled survey participants who intentionally provide inaccurate answers as mischievous responders. This phenomenon also occurs in clinical research. For example, pregnant women who smoke may report that they are nonsmokers. Our advantage is that we do not solely have self-report answers and can verify responses with lab values. Currently, there is no clear method for handling these intentional inaccurate respondents when it comes to making statistical inferences.

We …

Continuous Time Multi-State Models For Interval Censored Data, Lijie Wan

Theses and Dissertations--Statistics

Continuous-time multi-state models are widely used in modeling longitudinal data of disease processes with multiple transient states, yet the analysis is complex when subjects are observed periodically, resulting in interval censored data. Recently, most studies focused on modeling the true disease progression as a discrete time stationary Markov chain, and only a few studies have been carried out regarding non-homogenous multi-state models in the presence of interval-censored data. In this dissertation, several likelihood-based methodologies were proposed to deal with interval censored data in multi-state models.

Firstly, a continuous time version of a homogenous Markov multi-state model with backward transitions was …

Statistical Methods For Environmental Exposure Data Subject To Detection Limits, Yuchen Yang

Theses and Dissertations--Statistics

In this dissertation, we develop unified and efficient nonparametric statistical methods for estimating and comparing environmental exposure distributions in presence of detection limits. In the first part, we propose a kernel-smoothed nonparametric estimator for the exposure distribution without imposing any independence assumption between the exposure level and detection limit. We show that the proposed estimator is consistent and asymptotically normal. Simulation studies demonstrate that the proposed estimator performs well in practical situations. A colon cancer study is provided for illustration. In the second part, we develop a class of test statistics to compare exposure distributions between two groups by using …

Aggregated Quantitative Multifactor Dimensionality Reduction, Rebecca E. Crouch

Theses and Dissertations--Statistics

We consider the problem of making predictions for quantitative phenotypes based on gene-to-gene interactions among selected Single Nucleotide Polymorphisms (SNPs). Previously, Quantitative Multifactor Dimensionality Reduction (QMDR) has been applied to detect gene-to-gene interactions associated with elevated quantitative phenotypes, by creating a dichotomous predictor from one interaction which has been deemed optimal. We propose an Aggregated Quantitative Multifactor Dimensionality Reduction (AQMDR), which exhaustively considers all k-way interactions among a set of SNPs and replaces the dichotomous predictor from QMDR with a continuous aggregated score. We evaluate this new AQMDR method in a series of simulations for two-way and three-way interactions, …

Improved Models For Differential Analysis For Genomic Data, Hong Wang

Theses and Dissertations--Statistics

This paper intend to develop novel statistical methods to improve genomic data analysis, especially for differential analysis. We considered two different data type: NanoString nCounter data and somatic mutation data. For NanoString nCounter data, we develop a novel differential expression detection method. The method considers a generalized linear model of the negative binomial family to characterize count data and allows for multi-factor design. Data normalization is incorporated in the model framework through data normalization parameters, which are estimated from control genes embedded in the nCounter system. For somatic mutation data, we develop beta-binomial model-based approaches to identify highly or lowly …

Understanding Electrical Conduction In Lithium Ion Batteries Through Multi-Scale Modeling, Jie Pan

Theses and Dissertations--Chemical and Materials Engineering

Silicon (Si) has been considered as a promising negative electrode material for lithium ion batteries (LIBs) because of its high theoretical capacity, low discharge voltage, and low cost. However, the utilization of Si electrode has been hampered by problems such as slow ionic transport, large stress/strain generation, and unstable solid electrolyte interphase (SEI). These problems severely influence the performance and cycle life of Si electrodes. In general, ionic conduction determines the rate performance of the electrode, while electron leakage through the SEI causes electrolyte decomposition and, thus, causes capacity loss. The goal of this thesis research is to design Si …

Empirical Likelihood And Differentiable Functionals, Zhiyuan Shen

Theses and Dissertations--Statistics

Empirical likelihood (EL) is a recently developed nonparametric method of statistical inference. It has been shown by Owen (1988,1990) and many others that empirical likelihood ratio (ELR) method can be used to produce nice confidence intervals or regions. Owen (1988) shows that -2logELR converges to a chi-square distribution with one degree of freedom subject to a linear statistical functional in terms of distribution functions. However, a generalization of Owen's result to the right censored data setting is difficult since no explicit maximization can be obtained under constraint in terms of distribution functions. Pan and Zhou (2002), instead, study the …

Topics In Logistic Regression Analysis, Zhiheng Xie

Theses and Dissertations--Statistics

Discrete-time Markov chains have been used to analyze the transition of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient states, and death as competing risk. A multinomial logistic regression model is used to estimate the probability distribution in each row of the one-step transition matrix that correspond to the transient states. We investigate some goodness of fit tests for a multinomial distribution with covariates to assess the fit of this model to the data. We propose a modified chi-square test statistic and a score test statistic for the multinomial assumption in each …

Developing An Alternative Way To Analyze Nanostring Data, Shu Shen

Theses and Dissertations--Statistics

Nanostring technology provides a new method to measure gene expressions. It's more sensitive than microarrays and able to do more gene measurements than RT-PCR with similar sensitivity. This system produces counts for each target gene and tabulates them. Counts can be normalized by using an Excel macro or nSolver before analysis. Both methods rely on data normalization prior to statistical analysis to identify differentially expressed genes. Alternatively, we propose to model gene expressions as a function of positive controls and reference gene measurements. Simulations and examples are used to compare this model with Nanostring normalization methods. The results show that …

Statistical Inference On Trimmed Means, Lorenz Curves, And Partial Area Under Roc Curves By Empirical Likelihood Method, Yumin Zhao

Theses and Dissertations--Statistics

Traditionally the inference on trimmed means, Lorenz Curves, and partial AUC (pAUC) under ROC curves have been done based on the asymptotic normality of the statistics. Based on the theory of empirical likelihood, in this dissertation we developed novel methods to do statistical inferences on trimmed means, Lorenz curves, and pAUC. A common characteristic among trimmed means, Lorenz curves, and pAUC is that their inferences are not based on the whole set of samples. Qin and Tsao (2002), Qin et al. (2013), and Qin et al. (2011) recently published their re- searches on the inferences of trimmed means, Lorenz curves, …

Purin-6-One Derivatives As Phosphodiesterase-2 Inhibitors, Wei Yuan, Xin-Yun Zhao, Xi Chen, Chang-Guo Zhan

Pharmaceutical Sciences Faculty Publications

A series of purin-6-one derivatives were synthesized, and their in vitro inhibitory activity against phosphodiesterase-2 (PDE2) was evaluated by using a fluorescence polarization assay. Three compounds, that are, 2j, 2p, and 2q, showed significant inhibitory activity against PDE2 with IC₅₀ values of 1.73, 0.18, and 3.43 μM, respectively. Structure-activity relationship (SAR) analysis was performed to explore the relationship between the chemical structures of these compounds and their inhibitory activity. Compounds 2j, 2p, and 2q were further selected for molecular docking study. The docking results suggested that these ligands bind with hydrophobic pockets of …

Cp-Nets: From Theory To Practice, Thomas E. Allen

Theses and Dissertations--Computer Science

Conditional preference networks (CP-nets) exploit the power of ceteris paribus rules to represent preferences over combinatorial decision domains compactly. CP-nets have much appeal. However, their study has not yet advanced sufficiently for their widespread use in real-world applications. Known algorithms for deciding dominance---whether one outcome is better than another with respect to a CP-net---require exponential time. Data for CP-nets are difficult to obtain: human subjects data over combinatorial domains are not readily available, and earlier work on random generation is also problematic. Also, much of the research on CP-nets makes strong, often unrealistic assumptions, such as that decision variables must …

Modeling, Learning And Reasoning About Preference Trees Over Combinatorial Domains, Xudong Liu

Theses and Dissertations--Computer Science

In my Ph.D. dissertation, I have studied problems arising in various aspects of preferences: preference modeling, preference learning, and preference reasoning, when preferences concern outcomes ranging over combinatorial domains. Preferences is a major research component in artificial intelligence (AI) and decision theory, and is closely related to the social choice theory considered by economists and political scientists. In my dissertation, I have exploited emerging connections between preferences in AI and social choice theory. Most of my research is on qualitative preference representations that extend and combine existing formalisms such as conditional preference nets, lexicographic preference trees, answer-set optimization programs, possibilistic …

Topics On Register Synthesis Problems, Weihua Liu

Theses and Dissertations--Computer Science

Pseudo-random sequences are ubiquitous in modern electronics and information technology. High speed generators of such sequences play essential roles in various engineering applications, such as stream ciphers, radar systems, multiple access systems, and quasi-Monte-Carlo simulation. Given a short prefix of a sequence, it is undesirable to have an efficient algorithm that can synthesize a generator which can predict the whole sequence. Otherwise, a cryptanalytic attack can be launched against the system based on that given sequence.

Linear feedback shift registers (LFSRs) are the most widely studied pseudorandom sequence generators. The LFSR synthesis problem can be solved by the Berlekamp-Massey algorithm, …

Preferences: Optimization, Importance Learning And Strategic Behaviors, Ying Zhu

Theses and Dissertations--Computer Science

Preferences are fundamental to decision making and play an important role in artificial intelligence. Our research focuses on three group of problems based on the preference formalism Answer Set Optimization (ASO): preference aggregation problems such as computing optimal (near optimal) solutions, strategic behaviors in preference representation, and learning ranks (weights) for preferences.

In the first group of problems, of interest are optimal outcomes, that is, outcomes that are optimal with respect to the preorder defined by the preference rules. In this work, we consider computational problems concerning optimal outcomes. We propose, implement and study methods to compute an optimal outcome; …