Digital Commons Network^™

Constructing Associative Rings From Certain Hypergroups, Oscar Gonzalez

Theses and Dissertations

Tight hypergroups give rise to associative rings if the so-called general normality condition holds\cite{ARTICLE:1}. We consider four examples of tight hypergroups which do not satisfy the general normality condition and show that they still give rise to associative rings. Our examples are HM332(24),HM10353(32), HM10933(32) and HM10941(32)[1].

Moving Off Collections And Their Applications, In Particular To Function Spaces, Aaron Fowlkes

Theses and Dissertations

The main focus of this paper is the concept of a moving off collection of sets. We will be looking at how this relatively lesser known idea connects and interacts with other more widely used topological properties. In particular we will examine how moving off collections act with the function spaces Cp(X), C0(X), and CK (X). We conclude with a chapter on the Cantor tree and its moving off connections.

Many of the discussions of important theorems in the literature are expressed in terms that do not suggest the concept …

Numerical Methods For A Class Of Reaction-Diffusion Equations With Free Boundaries, Shuang Liu

Theses and Dissertations

The spreading behavior of new or invasive species is a central topic in ecology. The modelings of free boundary problems are widely studied to better understand the nature of spreading behavior of new species. From mathematical modeling point of view, it is a challenge to perform numerical simulations of free boundary problems, due to the moving boundary, the stiffness of the system and topological changes.

In this work, we design numerical methods to investigate the spreading behavior of new species for a diffusive logistic model with a free boundary and a diffusive competition system with free boundaries. We develop a …

The Application Of Synthetic Signals For Ecg Beat Classification, Elliot Morgan Brown

Theses and Dissertations

A brief overview of electrocardiogram (ECG) properties and the characteristics of various cardiac conditions is given. Two different models are used to generate synthetic ECG signals. Domain knowledge is used to create synthetic examples of 16 different heart beat types with these models. Other techniques for synthesizing ECG signals are explored. Various machine learning models with different combinations of real and synthetic data are used to classify individual heart beats. The performance of the different methods and models are compared, and synthetic data is shown to be useful in beat classification.

Light Scattering In Diffraction Limit Infrared Imaging, Ghazal Azarfar

Theses and Dissertations

Fourier Transform Infrared (FTIR) microspectroscopy is a noninvasive technique for chemical imaging of micrometer size samples. Employing an infrared microscope, an infrared source and FTIR spectrometer coupled to a microscope with an array of detectors (128 x 128 detectors), enables collecting combined spectral and spatial information simultaneously. Wavelength dependent images are collected, that reveal biochemical signatures of disease pathology and cell cycle. Single cell biochemistry can be evaluated with this technique, since the wavelength of light is comparable to the size of the objects of interest, which leads to additional spectral and spatial effects disturb biological signatures and can confound …

Multi-Tap Extended Kalman Filter For A Periodic Waveform With Uncertain Frequency And Waveform Shape, And Data Dropouts, Justin Saboury

Theses and Dissertations

Gait analysis presents the challenge of detecting a periodic waveform in the presence of time varying frequency, amplitude, DC offset, and waveform shape, with acquisition gaps from partial occlusions. The combination of all of these components presents a formidable challenge. The Extended Kalman Filter for this system model has six states, which makes it weakly identifiable within the standard Extended Kalman Filter network. In this work, a novel robust Extended Kalman Filter-based approach is presented and evaluated for clinical use in gait analysis. The novel aspect of the proposed method is that at each sample, the present and several past …

2-Hyponormality On Unilateral Weighted Shifts, Juan G. Benitez

Theses and Dissertations

Given the concept of a normal operator, several weaker notions have been proposed in order to extend the properties of normal operators to a wider range of operators. One such notion is that of k-hyponormal operators. In this document, we focus our attention on the 2-hyponormality of weighted shift operators over a discrete Hilbert space. It will be shown that if a certain relation between the weights α = ( α0, α1,...) of a weighted shift Wα is satisfied, then the 2-hyponormality of Wα implies the hyponormality of Wαm for any m = 2, 3,....

Empirical Bayes Estimators And Borel-Tanner Distribution, Celestina Ruby Soltero

Theses and Dissertations

The motivation for this paper stems from the role Borel-Tanner (BT) distribution has as the distribution of the total outbreak number in epidemics modeled by branching processes. We briefly review Borel-Tanner distribution and its applications. In Chapter II we outline the Bayes decision problem, a construction for an Empirical Bayes (EB) estimator proposed by Liang [9] and discuss risk analysis. In Chapter III, the importance of randomization addressed and a classical construction of a monotonized EB estimator proposed by Houwalingen [14] is outlined. Lastly in Chapter IV we use R software to perform a Monte Carlo simulation and conduct a …

Analysis Of The Cnn Algorithm In Target Recognition By Using The Mstar Database, Ligang Zou

Theses and Dissertations

With the rapid development of artificial intelligence technology and the emergence of a large number of innovative theories, the concept of deep learning is widely used in object detection, speech recognition, language translation and other fields. One of the important practices is target recognition in SAR images. Although it shows certain effectiveness in some researches, when using deep learning algorithm, there are still many problems that have not yet been solved. For example, people do not have a good understanding of how convolution works and the impact of convolution on the algorithm, although convolution works well in the CNN algorithm. …

A Few Problems On The Steiner Distance And Crossing Number Of Graphs, Josiah Reiswig

Theses and Dissertations

We provide a brief overview of the Steiner ratio problem in its original Euclidean context and briefly discuss the problem in other metric spaces. We then review literature in Steiner distance problems in general graphs as well as in trees.

Given a connected graph G we examine the relationship between the Steiner k-diameter, sdiam_k(G), and the Steiner k-radius, srad_k(G). In 1990, Henning, Oellermann and Swart [Ars Combinatoria 12 13-19, (1990)] showed that for any connected graph G, sdiam₃(G) ≤(8/5)srad₃(G) and …

Finding Resolutions Of Mononomial Ideals, Hannah Melissa Kimbrell

Theses and Dissertations

In this paper we present two different combinatorial approaches to finding resolutions of polynomial ideals. Their goal is to get resolutions that are as small as possible while still preserving the structure of the zeroth syzygy module. Then we present the idea of a differential graded algebra and discuss when the minimal resolutions of a polynomial ideals admits such a structure.

Developing Understanding Of The Chain Rule, Implicit Differentiation, And Related Rates: Towards A Hypothetical Learning Trajectory Rooted In Nested Multivariation, Haley Paige Jeppson

Theses and Dissertations

There is an overemphasis on procedures and manipulation of symbols in calculus and not enough emphasis on conceptual understanding of the subject. Specifically, students struggle to understand and correctly apply concepts in calculus such as the chain rule, implicit differentiation, and related rates. Students can learn mathematics more deeply when they make connections between different mathematical ideas. I have hypothesized that students can make powerful connections between the chain rule, implicit differentiation, and related rates through the mathematical concept of nested multivariation. Based on this hypothesis, I created a hypothetical learning trajectory (HLT) rooted in nested multivariation for students to …

Extensions Of The Power Group Enumeration Theorem, Shawn Jeffrey Green

Theses and Dissertations

The goal of this paper is to develop extensions of Polya enumeration methods which count orbits of functions. De Bruijn, Harary, and Palmer all worked on this problem and created generalizations which involve permuting the codomain and domain of functions simultaneously. We cover their results and specifically extend them to the case where the group of permutations need not be a direct product of groups. In this situation, we develop a way of breaking the orbits into subclasses based on a characteristic of the functions involved. Additionally, we develop a formula for the number of orbits made up of bijective …

Sequential Survival Analysis With Deep Learning, Seth William Glazier

Theses and Dissertations

Survival Analysis is the collection of statistical techniques used to model the time of occurrence, i.e. survival time, of an event of interest such as death, marriage, the lifespan of a consumer product or the onset of a disease. Traditional survival analysis methods rely on assumptions that make it difficult, if not impossible to learn complex non-linear relationships between the covariates and survival time that is inherent in many real world applications. We first demonstrate that a recurrent neural network (RNN) is better suited to model problems with non-linear dependencies in synthetic time-dependent and non-time-dependent experiments.

Hyperparameters For Dense Neural Networks, Christopher James Hettinger

Theses and Dissertations

Neural networks can perform an incredible array of complex tasks, but successfully training a network is difficult because it requires us to minimize a function about which we know very little. In practice, developing a good model requires both intuition and a lot of guess-and-check. In this dissertation, we study a type of fully-connected neural network that improves on standard rectifier networks while retaining their useful properties. We then examine this type of network and its loss function from a probabilistic perspective. This analysis leads to a new rule for parameter initialization and a new method for predicting effective learning …

Unconditionally Energy Stable Linear Schemes For A Two-Phase Diffuse Interface Model With Peng-Robinson Equation Of State, Chenfei Zhang

Theses and Dissertations

Many problems in the fields of science and engineering, particularly in materials science and fluid dynamic, involve flows with multiple phases and components. From mathematical modeling point of view, it is a challenge to perform numerical simulations of multiphase flows and study interfaces between phases, due to the topological changes, inherent nonlinearities and complexities of dealing with moving interfaces.

In this work, we investigate numerical solutions of a diffuse interface model with Peng-Robinson equation of state. Based on the invariant energy quadratization approach, we develop first and second order time stepping schemes to solve the liquid-gas diffuse interface problems for …

Reduction Of The Kp Hierarchy, Adrian Eugenio Torres

Theses and Dissertations

This thesis will delve into the Kadomtsev-Petviashvili equation or KP equation and it's hierarchy. More specifically, the solition theory around it. To do so, we first explore the soliton theory for the Korteweg de-Vries equation or KdV equation by analysing it through the inverse scattering transform method and presenting it's soliton solutions. Second, we will introduce, Hirota's bilinear form, and understand its main idea. Third, introduce Sato Theory, and use it to formulate the KP hierarchy, via using pseudo-differential operators, presenting the lax operator, the dressing operator, Sato’s equation, and the zero curvature equation (Zakharov-Shabat Equation). Fourth, find the general …

A Nonlinear Parallel Model For Reversible Polymer Solutions In Steady And Oscillating Shear Flow, Erik Tracey Palmer

Theses and Dissertations

A mathematical model for reversible polymers in steady and oscillating shear flows is presented. Using a mean-field approach, the behavior of the polymer network is characterized by a finitely extensible nonlinear elastic bead-spring model that stochastically transitions between dumbbell states to represent attachments, detachments and loops. An efficient parallel scheme for computation on GPUs utilizes populations of over a million dumbbells to characterize steady, large and small amplitude oscillatory shear (SAOS) flows in Brownian dynamics simulations. In steady-shear a novel attachment species transition function enables shear thickening and shear thinning by the adjustment of either attachment or detachment parameters. Three …

An Implementation Of The Kapustin-Li Formula, Jessica Otis

Theses and Dissertations

Let R be a regular local ring and take ! to be an isolated singularity on R. Taking Z/2-graded R-modules, X and Y , a matrix factorization of ω is a pair of morphisms (ϕ, ψ) such that ϕ⃝◦ψ = ω and ψ⃝◦ϕ = ω are satisfied in the diagram X ϕ → Y ψ→ X. We will discuss the category of matrix factorizations of ! in R and lead into the homotopy category of matrix factorizations as well as its historical development. Finally, we will conclude with the statement …

Cocyclic Hadamard Matrices: An Efficient Search Based Algorithm, Jonathan S. Turner

Theses and Dissertations

This dissertation serves as the culmination of three papers. “Counting the decimation classes of binary vectors with relatively prime fixed-density" presents the first non-exhaustive decimation class counting algorithm. “A Novel Approach to Relatively Prime Fixed Density Bracelet Generation in Constant Amortized Time" presents a novel lexicon for binary vectors based upon the Discrete Fourier Transform, and develops a bracelet generation method based upon the same. “A Novel Legendre Pair Generation Algorithm" expands upon the bracelet generation algorithm and includes additional constraints imposed by Legendre Pairs. It further presents an efficient sorting and comparison algorithm based upon symmetric functions, as well …

Mirror Symmetry For Non-Abelian Landau-Ginzburg Models, Matthew Michael Williams

Theses and Dissertations

We consider Landau-Ginzburg models stemming from non-abelian groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group G*, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors in general.

Secondary Preservice Mathematics Teachers' Curricular Reasoning, Kimber Anne Mathis

Theses and Dissertations

Researchers have found that teachers' decisions affect students' opportunity to learn. Prior researchers have investigated teachers' decisions while planning, implementing, or reflecting on lessons, but few researchers have studied teachers' decisions and their reasoning throughout the teaching process. It is important to study teachers' reasoning for why they make the decisions they do throughout the teaching process. Furthermore, because inservice and preservice teachers differ in experience and available resources that they draw on while making decisions, it is helpful to consider the resources PSTs' draw on while reasoning. Curricular reasoning is a framework that describes teachers' thinking processes when making …

An Analysis Of Momentum Flux Budgets And Profiles In A Large-Eddy Model, Steffen Domke

Theses and Dissertations

Momentum fluxes and variances play an important role in the characterization and forecast of weather phenomena, but cannot be measured easily.

A subdivision of the flux changes into budget terms by the underlying physical processes, such as buoyancy transport, can assist in understanding their sources and influences.

Momentum flux and variance budgets for SAM, the System for Atmospheric Modeling, have been implemented and are compared to existing budgets from other simulations.

A tool for the visualization of these quantities from three-dimensional grid data has been developed to show and explain their distribution in conjunction with shallow cumulus and stratocumulus clouds. …

A Stochastic Control Model For Electricity Producers, Charles William Beer

Theses and Dissertations

Modern electricity pricing models include a strong reversion to a long run mean and a

number of non-local operators to encapsulate the discontinuous price behavior observed in

such markets. However, incorporating non-local processes into a stochastic control problem

presents significant analytical challenges. The motivation for this work is to solve the problem

of optimal control of the burn rate for a coal-powered electricity plant. We first construct a

pricing model that is a good general representative of the class of models currently used for

electricity pricing as well as a model for the supply of fuel to the plant. Under …

Graded Multiplicity In Harmonic Polynomials From The Vinberg Setting, Alexander Heaton

Theses and Dissertations

We consider a family of examples falling into the following context (first considered by

Vinberg): Let G be a connected reductive algebraic group over the complex numbers. A

subgroup, K, of fixed points of a finite-order automorphism acts on the Lie algebra of G.

Each eigenspace of the automorphism is a representation of K. Let g1 be one of the

eigenspaces. We consider the harmonic polynomials on g1 as a representation of K, which

is graded by homogeneous degree. Given any irreducible representation of K, we will see

how its multiplicity in the harmonic polynomials is distributed among the various …

Mathematical Modeling And Analysis Of A Phytoplankton Competition Model Incorporating Preferential Nutrient Uptake, Thomas George Stojsavljevic Jr

Theses and Dissertations

Phytoplankton live in a complex environment with two essential resources forming various gradients. Light supplied from above is never homogeneously distributed in a body of water due to refraction and absorption from biomass present in the

ecosystem and from other sources. Nutrients in turn are typically supplied from below. In poorly mixed water columns, phytoplankton can be heterogeneously distributed forming various layering patterns. We present a new reaction-diffusion-taxis model describing the vertical distribution of two phytoplankton species competing for two nutrients, one of which is assumed to be preferred. The parameter space of the model is analyzed for parameter identifiability …

Identification Of Parameters In Systems Biology, Roby Poteau

Theses and Dissertations

Systems Biology is an actively emerging interdisciplinary area between biology and applied mathematics, based on the idea of treating biological systems as a whole entity which is more than the sum of its interrelated components. One of the major goals of systems biology is to reveal, understand, and predict such properties through the development of mathematical models based on experimental data. In many cases, predictive models of systems biology are described by large systems of nonlinear differential equations. Quantitative identification of such systems requires the solution of inverse problems on the identification of parameters of the system. This dissertation explores …

Ensemble Correlation Coefficient For Variable Association Detection, Wejdan Deebani

Theses and Dissertations

Subjects in a population are represented by their characteristics, and the characteristics are represented by variables. Identifying the relationship between these variables is essential for prediction, hypothesis testing, and decision making. The relation between two variables is often quantified using a correlation factor. Once correlations between response and independent variables are known, they can be used to make predictions regarding response variables. That is, if two variables are correlated, by observing one, we can make predictions about the other one. A more accurate prediction can be made where there is a strong relationship between variables. Several correlation factors have been …

Model-Independent Estimation Of Optimal Hedging Strategies With Deep Neural Networks, Tobias Michael Furtwaengler

Theses and Dissertations

Inspired by the recent paper Buehler et al. (2018), this thesis aims to investigate the optimal hedging and pricing of financial derivatives with neural networks. We utilize the concept of convex risk measures to define optimal hedging strategies without strong assumptions on the underlying market dynamics. Furthermore, the setting allows the incorporation of market frictions and thus the determination of optimal hedging strategies and prices even in incomplete markets. We then use the approximation capabilities of neural networks to find close-to optimal estimates for these strategies.

We will elaborate on the theoretical foundations of this approach and carry out implementations …

Large Scale Geometry Of Surfaces In 3-Manifolds, Hoang Thanh Nguyen

Theses and Dissertations

A compact, orientable, irreducible 3-manifold M with empty or toroidal boundary is

called geometric if its interior admits a geometric structure in the sense of Thurston. The

manifold M is called non-geometric if it is not geometric. Coarse geometry of an immersed

surface in a geometric 3-manifold is relatively well-understood by previous work of Hass,

Bonahon-Thurston. In this dissertation, we study the coarse geometry of an immersed

surface in a non-geometric 3- manifold.

The first chapter of this dissertation is a joint work with my advisor, Chris Hruska. We

answer a question of Daniel Wise about distortion of a horizontal …