Physical Sciences and Mathematics Commons^™

Inexact Fixed-Point Proximity Algorithms For Nonsmooth Convex Optimization, Jin Ren

Mathematics & Statistics Theses & Dissertations

The aim of this dissertation is to develop efficient inexact fixed-point proximity algorithms with convergence guaranteed for nonsmooth convex optimization problems encountered in data science. Nonsmooth convex optimization is one of the core methodologies in data science to acquire knowledge from real-world data and has wide applications in various fields, including signal/image processing, machine learning and distributed computing. In particular, in the context of image reconstruction, compressed sensing and sparse machine learning, either the objective functions or the constraints of the modeling optimization problems are nondifferentiable. Hence, traditional methods such as the gradient descent method and the Newton method are …

Chen-Fliess Series For Linear Distributed Systems, Natalie T. Pham

Electrical & Computer Engineering Theses & Dissertations

Distributed systems like fluid flow and heat transfer are modeled by partial differential equations (PDEs). In control theory, distributed systems are generally reformulated in terms of a linear state space realization, where the state space is an infinite dimensional Banach space or Hilbert space. In the finite dimension case, the input-output map can always be written in terms of a Chen-Fliess functional series, that is, a weighted sum of iterated integrals of the components of the input function. The Chen-Fliess functional series has been used to describe interconnected nonlinear systems, to solve system inversion and tracking problems, and to design …

Machine Learning Classification Of Digitally Modulated Signals, James A. Latshaw

Electrical & Computer Engineering Theses & Dissertations

Automatic classification of digitally modulated signals is a challenging problem that has traditionally been approached using signal processing tools such as log-likelihood algorithms for signal classification or cyclostationary signal analysis. These approaches are computationally intensive and cumbersome in general, and in recent years alternative approaches that use machine learning have been presented in the literature for automatic classification of digitally modulated signals. This thesis studies deep learning approaches for classifying digitally modulated signals that use deep artificial neural networks in conjunction with the canonical representation of digitally modulated signals in terms of in-phase and quadrature components. Specifically, capsule networks are …

Wiener-Fliess Composition Of Formal Power Series: Additive Static Feedback And Shuffle Rational Series, Subbarao Venkatesh Guggilam

Electrical & Computer Engineering Theses & Dissertations

The problem statement for this dissertation is two-fold. The first problem considered is when does a Chen-Fliess series in an additive static feedback connection with a formal static map yield a closed-loop system with a Chen-Fliess series expansion? This work proves that such a closed-loop system always has a Chen-Fliess series representation. Furthermore, an algorithm based on the Hopf algebras for the shuffle group and the dynamic output feedback group is designed to compute the generating series of the closed-loop system. It is proved that the additive static feedback connection preserves local convergence and relative degree, but a counterexample shows …

Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis

Mathematics & Statistics Theses & Dissertations

Volterra integral equations arise in a variety of applications in modern physics and engineering, namely in interactions that contain a memory term. Classical formulations of these problems are largely inflexible when considering non-homogeneous media, which can be problematic when considering long term interactions of real-world applications. The use of fractional derivative and integral terms naturally relax these restrictions in a natural way to consider these problems in a more general setting. One major drawback to the use of fractional derivatives and integrals in modeling is the regularity requirement for functions, where we can no longer assume that functions are as …

Onboard Autonomous Controllability Assessment For Fixed Wing Suavs, Brian Edward Duvall

Mechanical & Aerospace Engineering Theses & Dissertations

Traditionally fixed-wing small Unmanned Arial Vehicles (sUAV) are flown while in direct line of sight with commands from a remote operator. However, this is changing with the increased popularity and ready availability of low-cost flight controllers. Flight controllers provide fixed-wing sUAVs with functions that either minimize or eliminate the need for a remote operator. Since the remote operator is no longer controlling the sUAV, it is impossible to determine if the fixed-wing sUAV has proper control authority. In this work, a controllability detection system was designed, built, and flight-tested using COTS hardware. The method features in-situ measurement and analysis of …

Tick Control Methods For Amblyomma Americanum In Virginia: Applications And Modeling, Alexis Lynn White

Biological Sciences Theses & Dissertations

Tick-borne diseases continue to increase in the United States, and yet no comprehensive method of tick control currently exists. The lone star tick, Amblyomma americanum, is an aggressive human-biting tick and vector of several pathogens which effect both humans and other animals. Standard control methods do not work as well for A. americanum as they do for the more commonly studied blacklegged tick, Ixodes scapularis. TickBot, a tick-killing robot, is a potential method to control A. americanum that lures ticks to its path with carbon dioxide and the ticks die from contact with a permethrin-treated cloth that is …

Copula-Based Zero-Inflated Count Time Series Models, Mohammed Sulaiman Alqawba

Mathematics & Statistics Theses & Dissertations

Count time series data are observed in several applied disciplines such as in environmental science, biostatistics, economics, public health, and finance. In some cases, a specific count, say zero, may occur more often than usual. Additionally, serial dependence might be found among these counts if they are recorded over time. Overlooking the frequent occurrence of zeros and the serial dependence could lead to false inference. In this dissertation, we propose two classes of copula-based time series models for zero-inflated counts with the presence of covariates. Zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and zero-inflated Conway-Maxwell-Poisson (ZICMP) distributed marginals of the …

On Analytic Nonlinear Input-Output Systems: Expanded Global Convergence And System Interconnections, Irina M. Winter Arboleda

Electrical & Computer Engineering Theses & Dissertations

Functional series representations of nonlinear systems first appeared in engineering in the early 1950’s. One common representation of a nonlinear input-output system are Chen-Fliess series or Fliess operators. Such operators are described by functional series indexed by words over a noncommutative alphabet. They can be viewed as a noncommutative generalization of a Taylor series. A Fliess operator is said to be globally convergent when its radius of convergence is infinite, in other words, when there is no a priori upper bound on both the L1-norm of an admissible input and the length of time over which the corresponding output is …

The Effects Of Metacognitive Training On Algebra Students’ Calibration Accuracy, Achievement, And Mathematical Literacy, Deana J. Ford

Teaching & Learning Theses & Dissertations

This dissertation describes an empirical study that investigated how metacognitive training influenced lower achieving Algebra students’ calibration accuracy, achievement, and development of mathematics literacy. Multiple methods were used to collect and analyze the data. Close analysis of students’ work and classroom observations revealed that students that were exposed to the metacognitive training had significantly higher prediction accuracy and made gains in their understanding of the mathematics word problems than did students who did not receive the metacognitive training. Overall, however, both the intervention and comparison groups improved in their academic performance and became more mathematically literate and accurate in their …

Computational Methods For Nonlinear Systems Analysis With Applications In Mathematics And Engineering, Geoffrey Kenneth Rose

Mechanical & Aerospace Engineering Theses & Dissertations

An investigation into current methods and new approaches for solving systems of nonlinear equations was performed. Nontraditional methods for implementing arc-length type solvers were developed in search of a more robust capability for solving general systems of nonlinear algebraic equations. Processes for construction of parameterized curves representing the many possible solutions to systems of equations versus finding single or point solutions were established. A procedure based on these methods was then developed to identify static equilibrium states for solutions to multi-body-dynamic systems. This methodology provided for a pictorial of the overall solution to a given system, which demonstrated the possibility …

Ray- And Wave-Theoretic Approach To Electromagnetic Scattering From Radially Inhomogeneous Spheres And Cylinders, Michael A. Pohrivchak

Mathematics & Statistics Theses & Dissertations

With applications in the areas of chemistry, physics, microbiology, meteorology, radar, astronomy, and many other fields, electromagnetic scattering is an important area of research. Many everyday phenomena that we experience are a result of the scattering of electromagnetic and acoustic waves. In this dissertation, the scattering of plane electromagnetic waves from radially inhomogeneous spheres and cylinders using both ray- and wave-theoretic principles is considered. Chapters 2 and 3 examine the use of the ray approach. The deviation undergone by an incident ray from its original direction is related to the angle through which the radius vector turns from the point …

Computational Solutions Of The Forward And Adjoint Euler Equations With Application To Duct Aeroacoustics, Ibrahim Kocaogul

Mathematics & Statistics Theses & Dissertations

Traditionally, the acoustic source terms are modeled by single frequency sinusoidal functions. In the present study, the acoustic sources are modeled by a broadband wave packet. Radiation of acoustic waves at all frequencies can be obtained by Time Domain Wave Packet (TDWP) method in a single time domain computation. The TDWP method is also particularly useful for computations in the ducted or waveguide environments where incident wave modes can be imposed cleanly without a potentially long transient period. Theoretical analysis as well as numerical validation are performed in this study. In addition, the adjoint equations for the linearized Euler equations …

Optimal Control Modeling And Simulation, With Application To Cholera Dynamics, Chairat Modnak

Mathematics & Statistics Theses & Dissertations

The theory of optimal control, a modern extension of the calculus of variations. has found many applications in a wide range of scientific fields, particularly in epidemiology with respect to disease prevention and intervention. In this dissertation. we conduct optimal control modeling, simulation and analysis to cholera dynamics. Cholera is a severe intestinal infectious disease that remains a serious public health threat in developing countries. Transmission of cholera involves complex interactions between the human host, the pathogen, and the environment. The worldwide cholera outbreaks and their increasing severity, frequency and duration in recent years underscore the gap between the complex …

Topics In Electromagnetic, Acoustic, And Potential Scattering Theory, Umaporn Nuntaplook

Mathematics & Statistics Theses & Dissertations

With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves — is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering …

Novel Algorithms And Instrumentation For Vibrational Spectroscopic Methods Of Analysis, Mohamed F. Abdelkader

Chemistry & Biochemistry Theses & Dissertations

Raman spectroscopy is a form of vibrational spectroscopy that has been increasingly applied to qualitative analysis of chemicals, explosives, pharmaceuticals, and fuels due to its non-invasive and non-destructive nature; its ease of sampling; and its high molecular specificity. These characteristics of Raman spectroscopy also facilitate its use for both in-line and at-line analysis. The principle limitation of Raman spectroscopy is optical interference arising from both analyte and non-analyte fluorescence. In this dissertation, a solution to this problem is presented in the form of a novel spectrometer design which operates in a sequentially shifted excitation mode to eliminate fluorescence backgrounds, fixed …

Analysis And Simulation Of Kinetic Model For Active Suspensions, Panon Phuworawong

Mathematics & Statistics Theses & Dissertations

In this research, we study the recently proposed kinetic model for active suspensions, where the active particles are assumed to be rigid rod and are driven in the suspension either by their own biological/chemical forces or external electric/magnetic fields. We first study the stability of the isotropic suspension in quiescent flow. Then we investigate the weak shear perturbation of the isotropic state and study some rheological properties of the suspension by explicit analytic formulas derived directly from the model. For imposed shear, we give some bifurcation diagrams of the stable states in some parametric spaces through numerical simulations. Some rheological …

Response Surface Optimization Of Electron Beam Freeform Fabrication Depositions Using Design Of Experiments, Patricia A. Quigley

Engineering Management & Systems Engineering Theses & Dissertations

The Electron Beam Freeform Fabrication (EBF³ ) System is a material depositing, layer additive technique that produces three dimensional (3D) parts out of a wide range of metals in high vacuum, using an electron beam and wire feedstock. Screening deposition trials on a titanium alloy, Ti-6Al-4V, at the National Aeronautics Space Administration (NASA) revealed selective vaporization of the aluminum content of linear prototypes when subjected to chemical analysis. In this study, the aluminum content, bead height and bead width output responses were analyzed from a systematic study of the effects that the interactions of the EBF³ processing parameters …

Examination Timetabling With Mathematical Programming An Application In Turkish Air Force Academy, Emrah Koksalmis

Engineering Management & Systems Engineering Theses & Dissertations

The focus of this thesis is the educational timetabling problem, which is a very challenging problem to solve especially with a high number of the departments, branches, classes, and students. Due to the large scale of educational timetabling problems and preferences of the stakeholders, it is almost impossible to form a general model that solves all of the timetabling problems in the literature. This resulted in the need to develop and employ specific models for specific institutions.

The purpose of this study is to develop a mathematical programming model that solves the examination timetabling problem in Turkish Air Force Academy …

Epistemic Strategies For Solving Two-Dimensional Physics Problems, Mary Elyse Hing-Hickman

Physics Theses & Dissertations

An epistemic strategy is one in which a person takes a piece of knowledge and uses it to create new knowledge. Students in algebra and calculus based physics courses use epistemic strategies to solve physics problems. It is important to map how students use these epistemic strategies to solve physics problems in order to provide insight into the problem solving process.

In this thesis three questions were addressed: (1) What epistemic strategies do students use when solving two-dimensional physics problems that require vector algebra? (2) Do vector preconceptions in kinematics and Newtonian mechanics hinder a student's ability to apply the …

A Three Dimensional Green's Function Solution Technique For The Transport Of Heavy Ions In Laboratory And Space, Candice Rockell Gerstner

Mathematics & Statistics Theses & Dissertations

In the future, astronauts will be sent into space for longer durations of time compared to previous missions. The increased risk of exposure to ionizing radiation, such as Galactic Cosmic Rays and Solar Particle Events, is of great concern. Consequently, steps must be taken to ensure astronaut safety by providing adequate shielding. The shielding and exposure of space travelers is controlled by the transport properties of the radiation through the spacecraft, its onboard systems and the bodies of the individuals themselves. Meeting the challenge of future space programs will therefore require accurate and efficient methods for performing radiation transport calculations …

Post-Processing Techniques And Wavelet Applications For Hammerstein Integral Equations, Khomsan Neamprem

Mathematics & Statistics Theses & Dissertations

This dissertation is focused on the varieties of numerical solutions of nonlinear Hammerstein integral equations. In the first part of this dissertation, several acceleration techniques for post-processed solutions of the Hammerstein equation are discussed. The post-processing techniques are implemented based on interpolation and extrapolation. In this connection, we generalize the results in [29] and [28] to nonlinear integral equations of the Hammerstein type. Post-processed collocation solutions are shown to exhibit better accuracy. Moreover, an extrapolation technique for the Galerkin solution of Hammerstein equation is also obtained. This result appears new even in the setting of the linear Fredholm equation.

In …

Semi-Parametric Likelihood Functions For Bivariate Survival Data, S. H. Sathish Indika

Mathematics & Statistics Theses & Dissertations

Because of the numerous applications, characterization of multivariate survival distributions is still a growing area of research. The aim of this thesis is to investigate a joint probability distribution that can be derived for modeling nonnegative related random variables. We restrict the marginals to a specified lifetime distribution, while proposing a linear relationship between them with an unknown (error) random variable that we completely characterize. The distributions are all of positive supports, but one class has a positive probability of simultaneous occurrence. In that sense, we capture the absolutely continuous case, and the Marshall-Olkin type with a positive probability of …

Rao's Quadratic Entropy And Some New Applications, Yueqin Zhao

Mathematics & Statistics Theses & Dissertations

Many problems in statistical inference are formulated as testing the diversity of populations. The entropy functions measure the similarity of a distribution function to the uniform distribution and hence can be used as a measure of diversity. Rao (1982a) proposed the concept of quadratic entropy. Its concavity property makes the decomposition similar to ANOVA for categorical data feasible. In this thesis, after reviewing the properties and providing a modification to quadratic entropy, various applications of quadratic entropy are explored. First, analysis of quadratic entropy with the suggested modification to analyze the contingency table data is explored. Then its application to …

Towards A Formal Theory Of Interoperability, Saikou Y. Diallo

Computational Modeling & Simulation Engineering Theses & Dissertations

This dissertation proposes a formal theory of interoperability that explains 1) what interoperability is as opposed to how it works, 2) how to tell whether two or more systems can interoperate and 3) how to identify whether systems are interoperating or merely exchanging bits and bytes. The research provides a formal model of data in M&S that captures all possible representations of a real or imagined thing and distinguishes between existential dependencies and transformational dependencies. Existential dependencies capture the relationships within a model while transformational dependencies capture the relationships between interactions with a model. These definitions are used to formally …

Analysis Of Models For Longitudinal And Clustered Binary Data, Weiming Yang

Mathematics & Statistics Theses & Dissertations

This dissertation deals with modeling and statistical analysis of longitudinal and clustered binary data. Such data consists of observations on a dichotomous response variable generated from multiple time or cluster points, that exhibit either decaying correlation or equi-correlated dependence. The current literature addresses modeling the dependence using an appropriate correlation structure, but ignores the feasible bounds on the correlation parameter imposed by the marginal means.

The first part of this dissertation deals with two multivariate probability models, the first order Markov chain model and the multivariate probit model, that adhere to the feasible bounds on the correlation. For both the …

An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron

Mathematics & Statistics Theses & Dissertations

Reactive-diffusive systems modeling physical phenomena in certain situations develop a singularity at a finite value of the independent variable referred to as "blow-up." The attempt to find the blow-up time analytically is most often impossible, thus requiring a numerical determination of the value. The numerical methods often use a priori knowledge of the blow-up solution such as monotonicity or self-similarity. For equations where such a priori knowledge is unavailable, ad hoc methods were constructed. The object of this research is to develop a simple and consistent approach to find numerically the blow-up solution without having a priori knowledge or resorting …

A Study Of Decision Analysis Methods In Aerospace Technology Assessments, Sharon Monica Jones

Engineering Management & Systems Engineering Theses & Dissertations

Managers of aerospace technology programs and projects are faced with the challenge of making technology portfolio decisions under conditions of limited data, rapidly changing macro level factors and organizational uncertainties. To help make these technology investment decisions, some aerospace managers and analysts have used techniques from the field of decision analysis. In addition, there have been a limited number of research studies of real decision problems.

This dissertation presents the results of a non-experimental examination of the use of decision analysis methods for the assessment of aerospace technology portfolios. A web-based survey instrument was developed based on the results of …

Analysis And Application Of Perfectly Matched Layer Absorbing Boundary Conditions For Computational Aeroacoustics, Sarah Anne Parrish

Mathematics & Statistics Theses & Dissertations

The Perfectly Matched Layer (PML) was originally proposed by Berenger as an absorbing boundary condition for Maxwell's equations in 1994 and is still used extensively in the field of electromagnetics. The idea was extended to Computational Aeroacoustics in 1996, when Hu applied the method to Euler's equations. Since that time much of the work done on PML in the field of acoustics has been specific to the case where mean flow is perpendicular to a boundary, with an emphasis on Cartesian coordinates. The goal of this work is to further extend the PML methodology in a two-fold manner: First, to …

Dgm-Fd: A Finite Difference Scheme Based On The Discontinuous Galerkin Method, Anne Marguerite Fernando

Mathematics & Statistics Theses & Dissertations

Accurate and efficient numerical wave propagation is important in many areas of study such as computational aero-acoustics (CAA). While dissipation and dispersion errors influence the accuracy of a method, efficiency can be assessed by convergence rates and effective adaptability to different mesh structures. Finite difference and finite element methods are commonly used numerical schemes in CAA. Finite difference methods have the advantages of ease of use as well as high order convergence, but often require a uniform grid, and stable boundary closure can be non-trivial. Finite element methods adapt well to different mesh structures but can become difficult to implement …