Digital Commons Network^™

A Statistical Comparison Of Covid-19 In The United States Across Political Affiliations And Census Regions, Margarito Torres

Theses and Dissertations

In mid-January 2020, the United States reported their first cases of the coronavirus disease (COVID-19) from a passenger returning from Wuhan, China. Initially, the situation wasn’t very alarming as in China and European countries, but the situation began to worsen in March 2020 when the number of cases began to multiply. Then, in a matter of a few months, the United States became the number one country in terms of total cases and total deaths from COVID-19. We have been closely observing the United States and the world since July 2020. Our study aims to compare the political affiliations and …

Theoretical And Computational Modeling Of Contaminant Removal In Porous Water Filters, Aman Raizada

Theses and Dissertations

Contaminant transport in porous media is a well-researched problem across many scientific and engineering disciplines, including soil sciences, groundwater hydrology, chemical engineering, and environmental engineering. In this thesis, we attempt to tackle this multiscale transport problem using the upscaling approach, which leads to the development of macroscale models while considering a porous medium as an averaged continuum system.

First, we describe a volume averaging-based method for estimating flow permeability in porous media. This numerical method overcomes several challenges faced during the application of traditional permeability estimation techniques, and is able to accurately provide the complete permeability tensor of a porous …

Empirical Bayes Estimates For The Reproduction Number Of Epidemics, Elijah Lee Hight

Theses and Dissertations

Epidemic outbreaks can be modelled as a branching process in which the total progeny or outbreak size, follows a Borel-Tanner (BT) distribution. Following a procedure described by Liang (2009), we construct empirical Bayes estimates for when the initial number of infected is a specified value r. Following the construction, we then simulate data and perform a numerical study, assuming BT distribution for the parameter θ, the reproduction number, with an initial outbreak size of three. Simulation results indicate that the empirical estimator suffers from “jumpiness.” We then proceed to monotonize the empirical estimate via a method outlined by Houwelingen (1979). …

Integrable Equation With No Solitary Traveling Waves, Miguel Rodriguez

Theses and Dissertations

We consider the negative order KdV (NKdV) hierarchy which generates nonlinear integrable equations. Selecting different seed functions produces different evolution equations. We apply the traveling wave setting to study one of these equations. Assuming a particular type of solution leads us to solve a cubic equation. New solutions are found, but none of these are classical solitary traveling wave solutions.

Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

Theses and Dissertations

Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.

Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown

Theses and Dissertations

This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.

Simulation Of Pituitary Organogenesis In Two Dimensions, Chace E. Covington

Theses and Dissertations

The pituitary gland is a vital part of the endocrine system found in all vertebrates and is responsible for the production of hormones that influence many physiological processes in the organism’s body. Although much has been learned of pituitary organogenesis, studying the dynamics of the cells in the developing pituitary gland is difficult. Pituitary organogenesis has been studied through “snapshots” of a developing pituitary gland by removing and viewing the pituitary glands of different specimens. Thus, how the individual cells in the developing pituitary gland behave and interact with one another is not fully understood. To aid in understanding pituitary …

Trimming Complexes, Keller Vandebogert

Theses and Dissertations

We produce a family of complexes called trimming complexes and explore applications. We first study ideals defining type 2 compressed rings with socle minimally generated in degrees s and 2s − 1 for s > 2. We prove that all such ideals arise as trimmings of grade 3 Gorenstein ideals and show that trimming complexes yield an explicit free resolution. In particular, we give bounds on parameters arising in the Tor-algebra classification and construct explicit ideals attaining all intermediate values for every s. This partially answers a question of realizability of Tor-algebra structures posed by Avramov. Next, we study how …

Polynomials, Primes And The Pte Problem, Joseph C. Foster

Theses and Dissertations

This dissertation considers three different topics. In the first part of the dissertation, we use Newton Polygons to show that for the arithmetic functions g(n) = n t , where t ≥ 1 is an integer, the polynomials defined with initial condition P g 0 (X) = 1 and recursion P g n (X) = X n Xn k=1 g(k)P g n−k (X) are X/ (n!) times an irreducible polynomial. In the second part of the dissertation, we show that, for 3 ≤ n ≤ 8, there are infinitely many 2-adic integer solutions to the Prouhet-Tarry-Escott (PTE) problem, that are …

Regime-Switching Jump Diffusion Processes With Countable Regimes: Feller, Strong Feller, Irreducibility And Exponential Ergodicity, Khwanchai Kunwai

Theses and Dissertations

This work is devoted to the study of regime-switching jump diffusion processes in which the switching component has countably infinite regimes. Such processes can be used to model complex hybrid systems in which both structural changes, small fluctuations as well as big spikes coexist and are intertwined. Weak sufficient conditions for Feller and strong Feller properties and irreducibility for such processes are derived; which further lead to Foster-Lyapunov drift conditions for exponential ergodicity. Our results can be applied to stochastic differential equations with non-Lipschitz coefficients. Finally, an application to feedback control problems is presented.

Two Counting Problems In Geometric Triangulations And Pseudoline Arrangements, Ritankar Mandal

Theses and Dissertations

The purpose of this dissertation is to study two problems in combinatorial geometry in regard to obtaining better bounds on the number of geometric objects of interest: (i) monotone paths in geometric triangulations and (ii) pseudoline arrangements.

\medskip(i) A directed path in a graph is monotone in direction of $\mathbf{u}$ if every edge in the path has a positive inner product with $\mathbf{u}$. A path is monotone if it is monotone in some direction. Monotone paths are studied in optimization problems, specially in classical simplex algorithm in linear programming. We prove that the (maximum) number of monotone paths in a …

The Gini Index In Algebraic Combinatorics And Representation Theory, Grant Joseph Kopitzke

Theses and Dissertations

The Gini index is a number that attempts to measure how equitably a resource is distributed throughout a population, and is commonly used in economics as a measurement of inequality of wealth or income. The Gini index is often defined as the area between the "Lorenz curve" of a distribution and the line of equality, normalized to be between zero and one. In this fashion, we will define a Gini index on the set of integer partitions and prove some combinatorial results related to it; culminating in the proof of an identity for the expected value of the Gini index. …

Machine Learning Approach To Predict Mortality Rates Based On Hospital Clinical Data, Rebecca Smith

Theses and Dissertations

This thesis integrates fundamental concepts from conventional statistics with the more explanatory, algorithmic, and computational techniques offered by machine learning to predict early mortality risk of surgical patients. Well-known classification methods, including Random Forest, Decision Trees, Nearest Neighbor, Stochastic Gradient Descent, Logistic Regression, Na¨ıve Bayes, Bayes Network, Neural Networks, and Support Vector Machines, are utilized to predict mortality risk of elective general surgical patients treated between January 2005 and September 2010 at the Cleveland Clinic [33]. Clinical factors include surgery type, age, gender, race, BMI, underlying chronic conditions, surgical risk indices, surgical timing predictors, the 30-day mortality, and in-hospital complication …

Factors That Influence Teachers' Utilization Of Siop Learning Strategies When Teaching English Language Learners, Courtney R. Stuart

Theses and Dissertations

Despite standardized certification tests and popular English Language Learner trainings, the strategies and methods used in two educators’ classes would not be identical. In this case-study we look to see what variables cause teachers to utilize certain strategies and how these variables affect the number of strategies used consistently when teaching ELLs. We study the effect of teachers’ language experiences, certifications, participation in SIOP trainings, education levels, perceived preparedness, and years spent in the classroom.

Using quantitative and qualitative data we conclude that dual-language fluency and professional advancements can lead to teachers using more ELL learning strategies in their classrooms, …

Applications Of A U-Net Variant Neural Network: Image Classification For Vegetation Component Identification In Outdoors Images And Image To Image Translation Of Ultrasound Images, Adam Honts

Theses and Dissertations

Convolutional Neural Networks have been applied in many image applications, for both supervised and unsupervised learning. They have shown their ability to be used in an array of diverse use cases which include but are not limited to image classification, segmentation, and image enhancement tasks. We make use of Convolutional Neural Networks' ability to perform well in these situations and propose an architecture for a Convolutional Neural Network based on a network known as U-Net. We then apply our proposed network to two different tasks, a vegetation classification task for images of outdoors environment, and an image to image translation …

Exploring The Division Algorithm In Euclidean Domains With Exploding Dots, Nicholas Johnson

Theses and Dissertations

We will give an overview of the representation of place value and arithmetic known as Exploding Dots and use this idea to explore the division algorithm. It is well-known that the ring of integers, the ring of polynomials, and the ring of Gaussian integers are all examples of Euclidean domains and therefore possess a division algorithm. Exploding Dots beautifully illustrates how one can perform division in any base and how this naturally leads us to division of polynomials. We will show how this same idea of having a “base machine” can be used to perform division in the Gaussian integers. …

Examining Virtual Mathematics Instruction: A Comparative Case Study Of In-Service Elementary Teachers With Mathematics Anxiety And Mathematics Teaching Self-Efficacy, Telashay Swope-Farr

Theses and Dissertations

Mathematics Anxiety (MA) and Mathematics Teaching Self-Efficacy (MTSE) have been reported as factors related to teachers’ mathematics instruction. This study investigated MA and MTSE in in-service elementary teachers’ virtual mathematics instruction. A comparative case study design was used to understand the relationship between MA, MTSE, and their virtual mathematics instructional practices. Two in-service elementary teachers from an urban public charter school district in a large metropolitan city in the Midwest participated. I employed qualitative methods to examine the results from the Abbreviated Mathematics Anxiety Rating Scale (AMAS), an adapted version of a researcher-developed instrument called the Mathematics Teaching and Mathematics …

Development Of Novel Compound Controllers To Reduce Chattering Of Sliding Mode Control, Mehran Rahmani

Theses and Dissertations

The robotics and dynamic systems constantly encountered with disturbances such as micro electro mechanical systems (MEMS) gyroscope under disturbances result in mechanical coupling terms between two axes, friction forces in exoskeleton robot joints, and unmodelled dynamics of robot manipulator. Sliding mode control (SMC) is a robust controller. The main drawback of the sliding mode controller is that it produces high-frequency control signals, which leads to chattering. The research objective is to reduce chattering, improve robustness, and increase trajectory tracking of SMC. In this research, we developed controllers for three different dynamic systems: (i) MEMS, (ii) an Exoskeleton type robot, and …

Pattern Based Classification Of Chronic Kidney Disease Patients, Melissa Megan Moreno Cole

Theses and Dissertations

We apply a pattern-based classification method to identify clinical and genomic features associated with the progression of Chronic Kidney Disease (CKD). We analyze the African-American Study of Chronic Kidney Disease with Hypertension (AASK) dataset and construct a decision-tree classification model, consisting 15 combinatorial patterns of clinical features and single nucleotide polymorphisms (SNPs), seven of which are associated with slow progression and eight with rapid progression of renal disease among AASK patients. We identify four clinical features and two SNPs that can accurately predict CKD progression. These features are validated with using sophisticated machine learning techniques including Random Forest, Nearest Neighbor, …

Blood Flow Through An Artery In The Presence Of A Stenosis, Martin Carrillo

Theses and Dissertations

We consider blood flow through an artery in the form of a cylindrical pipe in the presence of a stenosis. Here blood is treated as an incompressible, viscous and non-Newtonian Bingham plastic fluid. We derive the equation of continuity and the momentum equation which are obtained using mass conservation law and momentum conservation law, respectively. Assuming that the flow is due to the pressure drop and wall shear stress, we derive the expressions for the velocity component in the axial direction and the volumetric flow rate in an artery. Computational results for the axial velocity and flow rate are obtained …

Gupta, Ramanujan, Dyson And Ehrhart: Formulas For Partition Functions, Congruences, Cranks, And Polyhedral Geometry, Joselyne Rodriguez

Theses and Dissertations

We will revisit Gupta's result regarding properties of a formula for restricted partitions and generalize this. We will then use this result to prove an infinite family of congruences for a certain restricted partition function. We find and prove combinatorial witnesses, also known as cranks, for the congruences using polyhedral geometry.

Optimal Quantization For Mixtures Of Two Uniform Distributions, Eduardo Orozco

Theses and Dissertations

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixtures of probability distributions, also known as mixed distributions, are an exciting new area for optimal quantization. In this thesis, for a mixed distribution we determine the optimal sets of n-means and the nth quantization errors for all positive integers n.

A Numerical Investigation Of Fractional Models For Viscoelastic Materials With Applications On Concrete Subjected To Extreme Temperatures, Murray Macnamara

Theses and Dissertations

Materials exhibiting both elastic and viscous properties have been termed the name viscoelastic materials and have been modeled using a combination of integer order derivatives affixed in varying ways called viscoelastic models. This results in highly complicated numerical procedures necessitating highly expensive computational time which we will show. To that end the use of fractional derivatives were researched and determined to be the ideal solution for modeling these materials, of which this paper is focused on exploring. Such research began as a theoretical study, however over time the applied benefits were discovered and utilized and have since been expanded on, …

Towards Constructing Vertex Algebroids, Nicholas J. Klecki

Theses and Dissertations

The notion of vertex algebroids were introduced in the late 1990's as a crucial tool for the study of chiral differential operators and chiral de Rham complex. Vertex algebroids play vital role in the study of N-graded vertex algebra. Also, they have deep connection with representation theory of Leibniz algebras. However, the classification of irreducible modules of vertex algebroids is not completed.

The aim of this thesis is to investigate the possibility of using the simple Lie algebra G_2 and its irreducible modules to construct vertex A-algebroids B that contain G_2 as their Levi factor. Under very mild and natural …

Lie Groups And Euler-Bernoulli Beam Equation, Medeu Amangeldi

Theses and Dissertations

Lie groups approach in differential equations was a breakthrough subject in the late nineteenth century. Sophus Lie, a Norwegian mathematician, introduced the systematic approach to study the solutions of differential equations. The main goal of this thesis is to study, using Lie's approach, the Euler-Bernoulli beam equation subject to swelling force, the fourth-order nonlinear differential equation used to describe the beam deflection under the swelling force. In particular, we will classify the symmetry groups of this equation, obtain several reductions, and demonstrate both analytical and numerical solutions.

Embedding Factorizations, Anna Johnsen

Theses and Dissertations

Let $V$ be a set of $n$ vertices for some $n\in\mathbb{N}$ and let $E$ be a collection of $h$-subsets of $V$. Then $\mathscr G = (V,E)$ is an $h$-unifrom hypergraph and we refer to $V$ as its vertex set and to $E$ as its edge set. We say that $\mathscr G$ is complete and denote it by $K_n^h$ if every $h$-subset of $V$ is contained in $E$. If every edge in $E$ is repeated $\lambda$ times, we say $G$ is $\lambda$-fold. Specifically, $\lambda K_n^h$ is the complete $\lambda$-fold $n$-vertex $h$-uniform hypergraph with an edge set containing $\lambda$ copies of every …