Digital Commons Network^™

Causalmodels: An R Library For Estimating Causal Effects, Joshua Wolff Anderson

Computational and Data Sciences (MS) Theses

Free and open source software for statistical modeling and machine learning have advanced productivity in data science significantly. Packages such as SciPy in Python and caret in R provide fundamental tools for statistical modeling and machine learning in the two most popular programming languages used by data scientists. Unfortunately, robust tools similar to these are limited in terms of causal inference. The tools in R that exist lack consistent and standardized methodologies and inputs. R lacks a comprehensive package that offers traditional causal inference methods such as standardization, IP weighting, G-estimation, outcome regression, and propensity matching in one common package. …

Mathematical Modeling Suggests Cooperation Of Plant-Infecting Viruses, Joshua Miller, Vitaly V. Ganusov, Tessa Burch-Smith

Chancellor’s Honors Program Projects

No abstract provided.

Linear Nearest Neighbor Flocks With All Distinct Agents, Robert G. Lyons

Dissertations and Theses

This dissertation analyzes the global dynamics of 1-dimensional agent arrays with nearest neighbor linear couplings. The equations of motion are second order linear ODE's with constant coefficients. The novel part of this research is that the couplings are different for each agent. We allow the forces to depend on the relative position and relative velocity (damping terms) of the agents, and the coupling magnitudes differ for each agent. Further, we do not assume that the forces are "Newtonian'" (i.e., the force due to A on B equals minus the force of B on A) as this assumption does not apply …

The Effects Of Stem And Non-Stem Mathematics Corequisite Courses On Student Success At Public Institutions In West Virginia, Vanessa S. Keadle

Theses, Dissertations and Capstones

This study explored the differences in student success outcomes between students enrolled in non-STEM and STEM corequisite mathematics courses at 18 postsecondary institutions across five academic years in West Virginia, using de-identified student data. The researcher analyzed this extant data to determine if student characteristics were predictors of success, as defined as passing the mathematics corequisite course, retention to the next semester, and earning a GPA of 2.0 or higher. The researcher also conducted analyses to understand if the differences in those outcomes between STEM and non-STEM courses were significant. This study identified statistically significant gaps in success for students …

On Loop Commutators, Quaternionic Automorphic Loops, And Related Topics, Mariah Kathleen Barnes

Electronic Theses and Dissertations

This dissertation deals with three topics inside loop and quasigroup theory. First, as a continuation of the project started by David Stanovský and Petr Vojtĕchovský, we study the commutator of congruences defined by Freese and McKenzie in order to create a more pleasing, equivalent definition of the commutator inside of loops. Moreover, we show that the commutator can be characterized by the generators of the inner mapping group of the loop. We then translate these results to characterize the commutator of two normal subloops of any loop.

Second, we study automorphic loops with the desire to find more examples of …

Local-Global Results On Discrete Structures, Alexander Lewis Stevens

Electronic Theses and Dissertations

Local-global arguments, or those which glean global insights from local information, are central ideas in many areas of mathematics and computer science. For instance, in computer science a greedy algorithm makes locally optimal choices that are guaranteed to be consistent with a globally optimal solution. On the mathematical end, global information on Riemannian manifolds is often implied by (local) curvature lower bounds. Discrete notions of graph curvature have recently emerged, allowing ideas pioneered in Riemannian geometry to be extended to the discrete setting. Bakry- Émery curvature has been one such successful notion of curvature. In this thesis we use combinatorial …

Topics In Moufang Loops, Riley Britten

Electronic Theses and Dissertations

We will begin by discussing power graphs of Moufang loops. We are able to show that as in groups the directed power graph of a Moufang loop is uniquely determined by the undirected power graph. In the process of proving this result we define the generalized octonion loops, a variety of Moufang loops which behave analogously to the generalized quaternion groups. We proceed to investigate para-F quasigroups, a variety of quasigroups which we show are antilinear over Moufang loops. We briefly depart from the context of Moufang loops to discuss solvability in general loops. We then prove some results on …

Banach Spaces On Topological Ramsey Structures, Cheng-Chih Ko

Electronic Theses and Dissertations

A Banach space T₁(d, θ) with a Tsirelson-type norm is constructed on the top of the topological Ramsey space T₁ defined by Dobrinen and Todorcevic [6]. Finite approximations of the isomorphic subtrees are utilised in constructing the norm. The subspace on each “branch” of the tree is shown to resemble the structure of an ℓ_∞ⁿ⁺¹ -space where the dimension corresponds to the number of terminal nodes on that branch. The Banach space T₁(d, θ) is isomorphic to (∑_n∊ℕ⊕ℓ_∞ⁿ⁺¹)_p , where d ∈ ℕ with d ≥ 2, …

Counting The Moduli Space Of Pentagons On Finite Projective Planes, Maxwell Hosler

Senior Independent Study Theses

Finite projective planes are finite incidence structures which generalize the concept of the real projective plane. In this paper, we consider structures of points embedded in these planes. In particular, we investigate pentagons in general position, meaning no three vertices are colinear. We are interested in properties of these pentagons that are preserved by collineation of the plane, and so can be conceived as properties of the equivalence class of polygons up to collineation as a whole. Amongst these are the symmetries of a pentagon and the periodicity of the pentagon under the pentagram map, and a generalization of …

Fourth-Dimensional Education In Virtual Reality, Jesse P. Hamlin-Navias

Senior Projects Spring 2022

This project was driven by an interest in mathematics, visualization, and the budding field of virtual reality. The project aimed to create virtual reality software to allow users to interact and play with three-dimensional representations of four-dimensional objects. The chosen representation was a perspective projection. Much like three-dimensional shapes cast two-dimensional shadows, four-dimensional shapes cast three-dimensional shadows. Users of the software developed in this project could interact and experiment with these three-dimensional shadows using hand controlled inputs. The hypothesis put forward is that virtual reality is currently the best medium to teach three-dimensional and four-dimensional geometry.

Grade K-5 Teachers’ Perceptions Of Professional Development That Supports Mathematics Instruction, Shannon Annette Manley

Walden Dissertations and Doctoral Studies

Many Grade K-5 teachers in the United States do not receive the mathematics support they need from the professional development (PD) activities offered by their school districts. The purpose of this qualitative research was to explore the perceptions of Grade K-5 teachers on the PD activities they received from their school district to support mathematics instruction. The conceptual framework that supported this study was andragogy, an adult learning theory that takes the learner’s needs into account and values the connection to real-world situations. The research question addressed how Grade K-5 teachers perceive the PD that they were offered by their …

Wildfire Simulation Using Agent Based Modeling: Expanding Controlled Burn Season, Morgan C. Kromer

Senior Independent Study Theses

The United States is home to many different and unique forests. Prior to the 21st century, the United States Forests Service assumed that the best way to protect these forests was to put all efforts to keeping them alive. An enemy to these efforts were wildfires, thus the US adopted a complete fire suppression approach. At the turn of the century, the US realized that wildfires are a necessary part of a forest ecosystem, as they help return nutrients to the soil and reduce ground fuels. However, after suppressing all fires for over 100 years, the forests evolved into a …

Highlights Generation For Tennis Matches Using Computer Vision, Natural Language Processing And Audio Analysis, Alon Liberman

Senior Independent Study Theses

This project uses computer vision, natural language processing and audio analysis to automatize the highlights generation task for tennis matches. Computer vision techniques such as camera shot detection, hough transform and neural networks are used to extract the time intervals of the points. To detect the best points, three approaches are used. Point length suggests which points correspond to rallies and aces. The audio waves are analyzed to search for the highest audio peaks, which indicate the moments where the crowd cheers the most. Sentiment analysis, a natural language processing technique, is used to look for points where the commentators …

The Infinity Conundrum: Understanding Topics In Set Theory And The Continuum Hypothesis, Sabrina Grace Helck

Senior Independent Study Theses

This project is concerned with articulating the necessary background in order to understand the famous result of the undecidability of the continuum hypothesis. The first chapter of this independent study discusses the foundations of set theory, stating fundamental definitions and theorems that will be used throughout the remainder of the project. The second chapter focuses on ordinal and cardinal numbers which will directly relate to the final chapter. First, there is a clear explanation of the notion of order and what it means for a set to be well-ordered. Then ordinal numbers are defined and some properties are listed and …

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib

Senior Independent Study Theses

Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.

On Implementing And Testing The Rsa Algorithm, Kien Trung Le

Senior Independent Study Theses

In this work, we give a comprehensive introduction to the RSA cryptosystem, implement it in Java, and compare it empirically to three other RSA implementations. We start by giving an overview of the field of cryptography, from its primitives to the composite constructs used in the field. Then, the paper presents a basic version of the RSA algorithm. With this information in mind, we discuss several problems with this basic conception of RSA, including its speed and some potential attacks that have been attempted. Then, we discuss possible improvements that can make RSA runs faster and more secure. On the …

Multicolor Ramsey And List Ramsey Numbers For Double Stars, Jake Ruotolo

Honors Undergraduate Theses

The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. For a graph H, the k-color Ramsey number r(H; k) of H is the smallest integer n such that every k-edge-coloring of K_n contains a monochromatic copy of H. Despite active research for decades, very little is known about Ramsey numbers of graphs. This is especially true for r(H; k) when k is at least 3, also known as the multicolor Ramsey number of …

A Brief Treatise On Bayesian Inverse Regression., Debashis Chatterjee Dr.

Doctoral Theses

Inverse problems, where in a broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific disciplines. However, apart from the class of traditional inverse problems, there exists another class of inverse problems, which qualify as more authentic class of inverse problems, but unfortunately did not receive as much attention.In a nutshell, the other class of inverse problems can be described as the problem of predicting the covariates corresponding to given responses and the rest of the data. …

Secret Sharing And Its Variants, Matroids,Combinatorics., Shion Samadder Chaudhury Dr.

Doctoral Theses

The main focus of this thesis is secret sharing. Secret Sharing is a very basic and fundamental cryptographic primitive. It is a method to share a secret by a dealer among different parties in such a way that only certain predetermined subsets of parties can together reconstruct the secret while some of the remaining subsets of parties can have no information about the secret. Secret sharing was introduced independently by Shamir [139] and Blakely [20]. What they introduced is called a threshold secret sharing scheme. In such a secret sharing scheme the subsets of parties that can reconstruct a secret …

Error Propagation And Algorithmic Design Of Contour Integral Eigensolvers With Applications To Fiber Optics, Benjamin Quanah Parker

Dissertations and Theses

In this work, the finite element method and the FEAST eigensolver are used to explore applications in fiber optics. The present interest is in computing eigenfunctions u and propagation constants β satisfing [sic] the Helmholtz equation Δu + k²n²u = β²u. Here, k is the freespace wavenumber and n is a spatially varying coefficient function representing the refractive index of the underlying medium. Such a problem arises when attempting to compute confinement losses in optical fibers that guide laser light. In practice, this requires the computation of functions u referred to as …

Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.

Doctoral Theses

No abstract provided.

Some Topics In Leavitt Path Algebras And Their Generalizations., Mohan R. Dr.

Doctoral Theses

The purpose of this section is to motivate the historical development of Leavitt algebras, Leavitt path algebras and their various generalizations and thus provide a context for this thesis. There are two historical threads which resulted in the definition of Leavitt path algebras. The first one is about the realization problem for von Neumann regular rings and the second one is about studying algebraic analogs of graph C ∗ -algebras. In what follows we briefly survey these threads and also introduce important concepts and terminology which will recur throughout.

Scaling Limits Of Some Random Interface Models., Biltu Dan Dr.

Doctoral Theses

In this thesis, we study some probabilistic models of random interfaces. Interfaces between different phases have been topic of considerable interest in statistical physics. These interfaces are described by a family of random variables, indexed by the ddimensional integer lattice, which are considered as a height configuration, namely they indicate the height of the interface above a reference hyperplane. The models are defined in terms of an energy function (Hamiltonian), which defines a Gibbs measure on the set of height configurations. More formally, letÏ• = {Ï•x}x∈Z dbe a collection of real numbers indexed by the d-dimensional integer lattice Z d. …

On The Inertia Conjecture And Its Generalizations., Soumyadip Das Dr.

Doctoral Theses

This thesis concerns problems related to the ramification behaviour of the branched Galois covers of smooth projective connected curves defined over an algebraically closed field of positive characteristic. Our first main problem is the Inertia Conjecture proposed by Abhyankar in 2001. We will show several new evidence for this conjecture. We also formulate a certain generalization of it which is our second problem, and we provide evidence for it. We give a brief overview of these problems in this introduction and reserve the details for Chapter 4.Let k be an algebraically closed field, and U be a smooth connected affine …

Commuting Isometries And Invariant Subspaces In Several Variables., Sankar T. R. Dr.

Doctoral Theses

A very general and fundamental problem in the theory of bounded linear operators on Hilbert spaces is to find invariants and representations of commuting families of isometries.In the case of single isometries this question has a complete and explicit answer: If V is an isometry on a Hilbert space â„‹, then there exists a Hilbert space Hu and a unitary operator U on â„‹u such that V on â„‹u and[ S ⊗ IW 0 0 U] ∈ B((l 2 (ℤ+) ⊗ W) ⊕ â„‹u),are unitarily equivalent, whereW = ker V∗ ,is the wandering subspace for V and S is the …

Partial Representations For Ternary Matroids, Ebony Perez

Electronic Theses, Projects, and Dissertations

In combinatorics, a matroid is a discrete object that generalizes various notions of dependence that arise throughout mathematics. All of the information about some matroids can be encoded (or represented) by a matrix whose entries come from a particular field, while other matroids cannot be represented in this way. However, for any matroid, there exists a matrix, called a partial representation of the matroid, that encodes some of the information about the matroid. In fact, a given matroid usually has many different partial representations, each providing different pieces of information about the matroid. In this thesis, we investigate when a …

Essays In Behavioral Social Choice Theory., Sarvesh Bandhu Dr.

Doctoral Theses

This thesis comprises four essays on social choice theory. The first three essays/chapters consider models where voters follow “non-standard” rules for decision making. The last chapter considers the binary social choice model and analyzes the consequences of a new axiom. The first chapter introduces a new axiom for manipulability when voters incur a cost if they misreport their true preference ordering. The second chapter considers the random voting model with strategic voters where standard stochastic dominance strategy-proofness is replaced by strategy-proofness under two lexicographic criteria. The third chapter also considers the random voting model but from a non-strategic perspective. It …

An Exploratory Analysis Of The Bgsu Learning Commons Student Usage Data, Emily Eskuri

Honors Projects

The purpose of this study was to explore past student usage data in individualized tutoring sessions from the Learning Commons from two academic years. The Bowling Green State University (BGSU) Learning Commons is a learning assistance center that offers various services, such as individualized tutoring, math assistance, writing assistance, study hours, and academic coaching. There have been limited research studies into how big data and analytics can have an impact in higher education, especially research utilizing predictive analytics.

This project applied analytics to individualized tutoring data in the Learning Commons to create a better understanding of why those trends happen …

On Tests Of Independence Among Multiplerandom Vectors Of Arbitrary Dimensions., Angshuman Roy Dr.

Doctoral Theses

Measures of dependence among several random vectors and associated tests of independence play a major role in different statistical applications. Blind source separation or independent component analysis (see, e.g., Hyv¨arinen et al., 2001; Shen et al., 2009), feature selection and feature extraction (see, e.g., Li et al., 2012), detection of serial correlation in time series (see, e.g., Ghoudi et al., 2001) and finding the causal relationships among the variables (see, e.g., Chakraborty and Zhang, 2019) are some examples of their wide-spread applications. Tests of independence has vast applications in other areas of sciences as well. For instance, to characterize the …

Matrix Product Structure Of A Permuted Quasi Cyclic Code And Its Dual, Perian Perdhiku

Dissertations

In my Dissertation I will work mostly with Permuted Quasi Cyclic Codes. They are a generalization of Cyclic Codes, one of the most important families of Linear Codes in Coding Theory. Linear Codes are very useful in error detection and correction. Error Detection and Correction is a technique that first detects the corrupted data sent from some transmitter over unreliable communication channels and then corrects the errors and reconstructs the original data. Unlike linear codes, cyclic codes are used to correct errors where the pattern is not clear and the error occurs in a short segment of …