Physical Sciences and Mathematics Commons^™

Towards Theory And Applications Of Generalized Categories To Areas Of Type Theory And Categorical Logic, Lucius Traylor Schoenbaum

LSU Doctoral Dissertations

Motivated by potential applications to theoretical computer science, in particular those areas where the Curry-Howard correspondence plays an important role, as well as by the ongoing search in pure mathematics for feasible approaches to higher category theory, we undertake a detailed study of a new mathematical abstraction, the generalized category. It is a partially defined monoid equipped with endomorphism maps defining sources and targets on arbitrary elements, possibly allowing a proximal behavior with respect to composition. We first present a formal introduction to the theory of generalized categories. We describe functors, equivalences, natural transformations, adjoints, and limits in the generalized …

Exploration Of Bimetallic Nickel And Cobalt Complexes For Catalytic Oxidative Cleavage Of Alkenes And Hydroformylation, Ciera Vonn Duronslet

LSU Doctoral Dissertations

The “old” bimetallic nickel complexes, meso- and rac-Ni2Cl4(et,ph-P4) were investigated as possible “catalysts” for the oxidative cleavage of alkenes using an unsaturated fatty acid, oleic acid, as the substrate. The “new” bimetallic nickel complexes with a stronger chelating tetraphosphine ligand, meso- and rac-Ni2Cl4(et,ph-P4-Ph), were also synthesized and tested for the oxidative cleavage of oleic acid. All four dinickel complexes were found to be active for the oxidative cleavage of oleic acid, producing extremely small amounts of aldehyde product. The Stanley research group also discovered the oxidative cleavage of alkenes using only the “old” et,ph-P4 tetraphosphine ligands with no metal centers. …

Synthesis And Characterization Of Cyclic Polypeptoids By Organo-Mediated Controlled Zwitterionic Ring-Opening Polymerization And Development Of Redox-Responsive Polypeptoid Micelles As Drug Delivery Carriers, Ang Li

LSU Doctoral Dissertations

Peptoids are peptidomimetic polymers, which have attracted much attention over the past two decades. They have similar building blocks to peptides, and the similarity makes the backbone of peptoids hydrophilic and biocompatible.1 Two types of peptoid polymers are under development. One is sequence-defined peptoids, which exhibit excellent bioactivities.2 Another one is polypeptoids. The good biocompatibility and highly tunable side chain substituents allow polypeptoids to be used broadly in future biomedical applications. Varying polymer architectures, including linear polymers, cyclic polymers, comb-like polymers, and dendrimers can provide distinctive properties to the polymers. Cyclic polymers employ a cyclic architecture and lack chain ends, …

Turbulence And Overturning Gravity Wave Effects Deduced From Mesospheric Na Density Between 100-105 Km At Andes Lidar Observatory, Chile, Alan Z. Liu, Channing P. Philbrick, Gary R. Swenson, Fabio A. Vargas

Publications

Atmospheric turbulence activity in the mesosphere and lower thermosphere (MLT) region is determined from narrowband Na lidar measurements obtained over 27 nights between 85-105 km altitude at the Andes Lidar Observatory (ALO) in Cerro Pachón, Chile (30.3ºS, 70.7ºW). Photocount perturbations in the applicable spectral subrange are used as a tracer of turbulence activity. Mean altitude profiles reveal a log-scale linear increase in turbulence perturbation amplitude above 95 km. The observed trend is compared against global mean constituent transport profiles derived from SABER and SCIAMACHY satellite borne measurements.

Chemical Transport Of Neutral Atmospheric Constituents By Waves And Turbulence: Theory And Observations, Chester S. Gardner, Alan Liu

Publications

Vertical chemical transport occurs when the density fluctuations of a species, caused by perturbations of its chemistry, are strongly correlated with the vertical wind fluctuations. Chemical transport can exceed dynamical and eddy transport of chemically active species. Theoretical expressions are derived for the chemical fluxes and transport velocities and used to characterize the vertical transport of mesospheric O3 and meteoric Na and Fe between 85 and 100 km. Chemical transport is dependent on the intrinsic frequency spectrum of the temperature fluctuations and on the chemical cutoff periods of the species. For O3 only high-frequency fluctuations contribute to chemical transport because …

Southern Hemisphere Summer Mesopause Responses To El Niño–Southern Oscillation, Tao Li, Natalia Calvo, Jia Yue, James Russell Iii, Alan Liu

Publications

In the Southern Hemisphere (SH) polar region, satellite observations reveal a significant uppermesosphere cooling and a lower-thermosphere warming during warm ENSO events in December. An opposite pattern is observed in the tropical mesopause region. The observed upper-mesosphere cooling agrees with a climate model simulation. Analysis of the simulation suggests that enhanced planetary wave (PW) dissipation in the Northern Hemisphere (NH) high-latitude stratosphere during El Niño strengthens the Brewer–Dobson circulation and cools the equatorial stratosphere. This increases the magnitude of the SH stratosphere meridional temperature gradient and thus causes the anomalous stratospheric easterly zonal wind and early breakdown of the SH …

Evidence Of The Excitation Of A Ring-Like Gravity Wave In The Mesosphere Over The Andes Lidar Observatory, Fabio Vargas, Gary Swenson,, Alan Liu, Dominique Pautet

Publications

On 23 March 2012, our all-sky imager recorded a concentric, ring-like gravity wave pattern. The wave arose within the area covered by images of both OH and O(1S) nightglow emissions taken at the Andes Lidar Observatory (ALO), Chile (30.3°S, 70.7°W). We have estimated the observed and intrinsic parameters of the event and located the wave source within the lower mesosphere altitude range using a reverse ray tracing method. By the analysis of GOES and LIS satellite images, we have not found evidence of neither convective nor lightning activity nearby ALO, indicating that the source of the ring-like wave …

From Enrollment To Employment: A Dacum Approach To Information Systems And Information Security And Assurance Curriculum Design, Leila Halawi, Wendi M. Kappers, Aaron Glassman

Publications

Issues associated with information security are numerous and diverse. Since the majority of organizational actions rely greatly on information and communication technologies, Information Systems (IS) security is now a main concern for firms, governments, institutes, and society as a whole. As a result, a plethora of graduate programs have been created, covering nearly every aspect of IS security. The authors review the current state of the IS industry presented in the literature, and identify a panel of IS experts in which to explore current job skill needs using a “Developing a Curriculum,” DACUM, process to support curriculum design for two …

Plasma Density Analysis Of Cubesat Wakes In The Earth’S Ionosphere, Robert M. Albarran Ii, Aroh Barjatya

Publications

Spinning or tumbling CubeSats with Langmuir probes deployed on booms will render spin-modulated plasma densities as the probes move in and out of the spacecraft wake. It is traditionally assumed that the lower-density measurements from the spin cycle are made in the spacecraft wake, and the higher-density measurements are outside the wake. Although this assumption is valid for larger spacecraft in the Earth’s ionosphere, this paper scrutinizes its validity for CubeSats in similar conditions. Spacecraft–plasma interactions (surface charging, plasma sheaths, and wakes) are less understood for CubeSats, and the small CubeSat dimensions must be considered with respect to characteristic length …

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 …

Beyond Just Sea-Level Rise: Considering Macroclimatic Drivers Within Coastal Wetland Vulnerability Assessments To Climate Change, Michael J. Osland, Nicholas M. Enwright, Richard H. Day, Christopher A. Gabler, Camille L. Stagg, James B. Grace

School of Earth, Environmental, and Marine Sciences Faculty Publications and Presentations

Due to their position at the land-sea interface, coastal wetlands are vulnerable to many aspects of climate change. However, climate change vulnerability assessments for coastal wetlands generally focus solely on sea-level rise without considering the effects of other facets of climate change. Across the globe and in all ecosystems, macroclimatic drivers (e.g., temperature and rainfall regimes) greatly influence ecosystem structure and function. Macroclimatic drivers have been the focus of climate change-related threat evaluations for terrestrial ecosystems, but largely ignored for coastal wetlands. In some coastal wetlands, changing macroclimatic conditions are expected to result in foundation plant species replacement, which would …

Chemical Flocculation For Removing Bentonite Spills In Water, James Jihoon Kang, Jacob D. Wiseman, Mckhenzy A. Welch, Richard A. Mclaughlin

School of Earth, Environmental, and Marine Sciences Faculty Publications and Presentations

A potential environmental impact associated with horizontal directional drilling is the inadvertent return of bentonite-based drilling fluid to the surface via naturally occurring fractures or fissures. This study investigated a range of flocculants consisting of water-soluble linear polyacrylamides (PAMs) differing in charge (anionic, neutral, and cationic), biopolymer (chitosan) and gypsum for treating the bentonite suspension that might release with runoff or into stream water. Laboratory jar test were conducted with a 0.4 % (w/v) bentonite suspension having an average initial turbidity of 1,217 nephelometric turbidity units (NTU). None of the PAMs by themselves were effective in flocculating bentonite suspension ( …

Tridiagonal Matrices And Boundary Conditions, J. J. P. Veerman, David K. Hammond

Mathematics and Statistics Faculty Publications and Presentations

We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end of a one-dimensional flock. We apply our results to demonstrate how asymptotic stability for consensus and flocking systems depends on the imposed boundary condition.

Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, J. J. P. Veerman, Jovan Petrovic

Mathematics and Statistics Faculty Publications and Presentations

Coherent state transfer is an important requirement in the construction of quantum computer hardware. The state transfer can be realized by linear next-neighbour-coupled finite chains. Starting from the commensurability of chain eigenvalues as the general condition of periodic dynamics, we find chains that support full periodic state revivals. For short chains, exact solutions are found analytically by solving the inverse eigenvalue problem to obtain the coupling coefficients between chain elements. We apply the solutions to design optical waveguide arrays and perform numerical simulations of light propagation thorough realistic waveguide structures. Applications of the presented method to the realization of a …

A Multivariate Nonlinear Mixed Effects Model For Longitudinal Image Analysis: Application To Amyloid Imaging, Murat Bilgel, Jerry L. Prince, Dean F. Wong, Susan M. Resnick, Bruno M. Jedynak

Mathematics and Statistics Faculty Publications and Presentations

It is important to characterize the temporal trajectories of disease-related biomarkers in order to monitor progression and identify potential points of intervention. These are especially important for neurodegenerative diseases, as therapeutic intervention is most likely to be effective in the preclinical disease stages prior to significant neuronal damage. Neuroimaging allows for the measurement of structural, functional, and metabolic integrity of the brain at the level of voxels, whose volumes are on the order of mm³. These voxelwise measurements provide a rich collection of disease indicators. Longitudinal neuroimaging studies enable the analysis of changes in these voxelwise measures. However, …

Voxel Based Morphometry In Optical Coherence Tomography: Validation & Core Findings, Bhavna J. Antony, Min Chen, Aaron Carass, Bruno M. Jedynak, Omar Al-Louzi, Sharon D. Solomon, Shiv Saidha, Peter Calabresi, Jerry L. Prince

Mathematics and Statistics Faculty Publications and Presentations

Optical coherence tomography (OCT) of the human retina is now becoming established as an important modality for the detection and tracking of various ocular diseases. Voxel based morphometry (VBM) is a long standing neuroimaging analysis technique that allows for the exploration of the regional differences in the brain. There has been limited work done in developing registration based methods for OCT, which has hampered the advancement of VBM analyses in OCT based population studies. Following on from our recent development of an OCT registration method, we explore the potential benefits of VBM analysis in cohorts of healthy controls (HCs) and …

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 …

Visual Properties Of Generalized Kloosterman Sums, Paula Burkhardt '16, Alice Zhuo-Yu Chan '14, Gabriel Currier '16, Stephan Ramon Garcia, Florian Luca, Hong Suh '16

Pomona Faculty Publications and Research

For a positive integer m and a subgroup A of the unit group (Z/mZ)^x, the corresponding generalized Kloosterman sum is the function K(a, b, m, A) = Σ_uEA e(au+bu^-1/m). Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when their values are plotted in the complex plane. In a variety of instances, we identify the precise number-theoretic conditions that give rise to particular phenomena.

Lattices From Hermitian Function Fields, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj

Pomona Faculty Publications and Research

We consider the well-known Rosenbloom-Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the total number of minimal vectors, and derive properties of the automorphism groups of these lattices. Our study continues previous investigations of lattices coming from elliptic curves and finite Abelian groups. The lattices we are faced with here are more subtle than those considered previously, and the proofs of the main results require the replacement of the existing linear algebra approaches by deep results of …

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, …

Dimension Reduction And Variable Selection, Hossein Moradi Rekabdarkolaee

Theses and Dissertations

High-dimensional data are becoming increasingly available as data collection technology advances. Over the last decade, significant developments have been taking place in high-dimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics, signal processing, and environmental studies. Statistical techniques such as dimension reduction and variable selection play important roles in high dimensional data analysis. Sufficient dimension reduction provides a way to find the reduced space of the original space without a parametric model. This method has been widely applied in many scientific fields such as genetics, brain imaging analysis, econometrics, environmental sciences, etc. …

Enhancing Silicon Solar Cell Efficiency With Double Layer Antireflection Coating, Mohamed Medhat, El-Sayed El-Zaiat, Samy Farag, Gamal Youssef, Reda Alkhadry

Turkish Journal of Physics

Antireflection coating on silicon, a high refractive index substrate, was theoretically investigated. The effects of antireflection coating on electrical parameters such as the short circuit current, open circuit voltage, maximum current density, maximum voltage, maximum power, power density, and conversion efficiency of the solar cell were simulated. Various previous works in which solar cell efficiencies were investigated after applying double layer antireflection coating (DLARC) were reviewed. Ti$_{2}$O$_{3}$ and MgF$_{2}$ were then applied in a DLARC design, taking into consideration the refractive index dispersion of the two materials. The results were compared with other works in the solar spectral range (400-1200 …

Neutron Stars: Compact Objects With Relativistic Gravity, Kazim Yavuz Ekşi̇

Turkish Journal of Physics

General properties of neutron stars are briefly reviewed with an emphasis on the indispensability of general relativity in our understanding of these fascinating objects. In Newtonian gravity the pressure within a star merely plays the role of opposing self-gravity. In general relativity all sources of energy and momentum contribute to the gravity. As a result, the pressure not only opposes gravity but also enhances it. The latter role of pressure becomes more pronounced with increasing compactness, $M/R$, where $M$ and $R$ are the mass and radius of the star, and sets a critical mass beyond which collapse is inevitable. This …