Mathematics Commons^™

An Automatic Solver For Optimal Control Problems, Marcel Efren Benitez

Theses and Dissertations

Optimal control theory is a study that is used to find a control for a dynamical system over a period of time such that a objection function is optimized. In this study we will be looking at optimal control problems for ordinary differential equations or ODEs and see that we can use an automatic solver using the forward-backward sweep using Matlab to solve for them from an 1 dimension to bounded cases and to nth dimension cases.

How An Instructor's Noticing For Equity Can Foster Students' Sense Of Belonging And Mathematical Confidence, Sthefania Espinosa

Theses and Dissertations

There are many aspects a teacher can notice inside the mathematics classroom, and the more a teacher notices, the more difficult it is to teach. In this study, I particularly focus on noticing for equity, which describes the role of the teacher in attending to students’ mathematical thinking through an equity lens that can allow the instructor to notice the aspects of classroom mathematical activity that can make students feel less or more empowered in their mathematical practices (van Es et al., 2017). There exists few research about how students perceive their instructor’s effort to promote equity and …

Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp

Theses and Dissertations

This thesis obtains a number of results in stochastic optimal control for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the uniqueness of the solutions and derive a relevant version of Itô's formula. We provide the dynamic programming principle and prove the associated verification theorem. A stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle. Additionally, we utilize our stochastic maximum principle result for a mean-variance portfolio selection problem.

Machine Learning And Causality For Interpretable And Automated Decision Making, Maria Lentini

Theses and Dissertations

This abstract explores two key areas in decision science: automated and interpretable decision making. In the first part, we address challenges related to sparse user interaction data and high item turnover rates in recommender systems. We introduce a novel algorithm called Multi-View Interactive Collaborative Filtering (MV-ICTR) that integrates user-item ratings and contextual information, improving performance, particularly for cold-start scenarios. In the second part, we focus on Student Prescription Trees (SPTs), which are interpretable decision trees. These trees use a black box "teacher" model to predict counterfactuals based on observed covariates. We experiment with a Bayesian hierarchical binomial regression model as …

Leveraging Galois Theory And Computational Results In The Search For Legendre Pairs, David M. Arquette

Theses and Dissertations

With applications spanning myriad disciplines, Hadamard matrices have tremendous utility. Infinitely many have been discovered, but there is no general proof of their existence. Proving the Hadamard conjecture would provide a significant technological edge. Hadamard matrices are difficult to construct in general; however, they can be created directly from Legendre pairs (LPs). While LPs are not trivial to find, a breakthrough in this area would be pivotal in the quest to prove the Hadamard conjecture. Most recent efforts rely upon refined search algorithms, and we seek to either develop a better such algorithm or discover an altogether new theoretical construction. …

Signings Of Graphs And Sign-Symmetric Signed Graphs, Ahmad Asiri

Theses and Dissertations

In this dissertation, we investigate various aspects of signed graphs, with a particular focus on signings and sign-symmetric signed graphs. We begin by examining the complete graph on six vertices with one edge deleted ($K_6$\textbackslash e) and explore the different ways of signing this graph up to switching isomorphism. We determine the frustration index (number) of these signings and investigate the existence of sign-symmetric signed graphs. We then extend our study to the $K_6$\textbackslash 2e graph and the McGee graph with exactly two negative edges. We investigate the distinct ways of signing these graphs up to switching isomorphism and demonstrate …

Matrix Completion Problems For The Positiveness And Contraction Through Graphs, Louis C. Christopher

Theses and Dissertations

In this work, we study contractive and positive real matrix completion problems which are motivated in part by studies on sparce (or dense) matrices for weighted sparse recovery problems and rating matrices with rating density in recommender systems. Matrix completions problems also have many applications in probability and statistics, chemistry, numerical analysis (e.g. optimization), electrical engineering, and geophysics. In this paper we seek to connect the contractive and positive completion property to a graph theoretic property. We then answer whether the graphs of real symmetric matrices having loops at every vertex have the contractive completion property if and only if …

Deep Learning Methods For Some Problems In Scientific Computing, Yuankai Teng

Theses and Dissertations

Deep learning has emerged as a powerful approach for solving complex problems in scientific computing due to the increasing availability of large-scale data and computational resources. This thesis explores the potential of deep learning methods for three specific problems in scientific computing: (i) reducing the dimensions of variables in function approximation, (ii) solving linear reaction-diffusion equations, and (iii) finding the parametric representations of parameters in the numerical schemes for solving time-dependent partial differential equations.

For the first problem, a novel deep learning architecture is developed for reducing the dimensions of variables in function approximation. The proposed method achieves state-of-the-art performance …

Widely Digitally Delicate Brier Primes And Irreducibility Results For Some Classes Of Polynomials, Thomas David Luckner

Theses and Dissertations

This dissertation considers three different sections of results. In the first part of the dissertation, a result on consecutive primes which are widely digitally delicate and Brier numbers is discussed. Making use of covering systems and a theorem of D. Shiu, M. Filaseta and J. Juillerat showed that for every positive integer k, there exist k consecutive widely digitally delicate primes. They also noted that for every positive integer k, there exist k consecutive primes which are Brier numbers. We show that for every positive integer k, there exist k consecutive primes that are both widely digitally …

Computation Offloading Design For Deep Neural Network Inference On Iot Devices, Asmika Boosarapu

Theses and Dissertations

In recent times, advances in the technologies of Internet-of-Things (IoT) and Deep Neural Networks (DNN) have significantly increased the accuracy and speed of a variety of smart applications. However, one of the barriers to deploying DNN to IoT is the computational limitations of IoT devices as compared with the computationally expensive task of DNN inference. Computation offloading is an approach that addresses this problem by offloading DNN computation tasks to cloud servers. In this thesis we propose a collaborative computation offloading solution, in which some of the work is done on the IoT device, and the remainder of the work …

An Investigative Study Of Potential Factors That Contribute To High Under-Five Mortality Rate In Africa, David Banahene

Theses and Dissertations

Under-Five Mortality remains a significant challenge in developing countries, especially in Africa. The United Nations has implemented various measures, such as the Millennium Development Goals (MDGs) and Sustainable Development Goals (SDGs), to combat this issue. However, the success of these initiatives is uncertain. Our study investigates the social, economic, and environmental factors contributing to high Under-Five Mortality rates in African countries, using data from 1985 to 2020.We analyzed 53 African countries, partitioning them into training (45 countries) and testing data (8 countries). We conducted Multiple Linear Regression analysis and assessed the model performance using R-squared values and Root-Mean-Squared-Error (RMSE) values. …

Creation Of A College Math Club For High School Students, Lilian N. Chavez

Theses and Dissertations

This study aimed to investigate the variables that contribute to high school students' desire to join a math club, specifically the FMiM VIP Club, which is an extension of UTRGV's Follow Me into Math research project. The research utilized multiple questionnaire s to examine the combination of factors that contribute to the students' attitudes toward the math club. The participants were high school Algebra 2 students from two different schools, and the study was conducted in two stages. The first stage was conducted in the Spring of 2022, focusing on girls' math identity and their interactions with the FMiM VIP …

Data Science For Hospital Antibiotic Stewardship, Saikou Jawla

Theses and Dissertations

Antibiotics are widely used to treat bacterial infections, but their misuse leads to antibiotic resistance. Antibiotic resistance is one of the biggest threats to global health, food security, and development today. Antibiotic resistance leads to higher medical costs, prolonged hospital stays, and increased mortality. Antimicrobial stewardship is an approach to measure and improve the appropriate use of antibiotics in healthcare settings. Data science has the potential to support these programs by providing insights into antibiotic prescribing patterns, identifying areas for improvement, and predicting patient outcomes. We explored the role of data science in hospital antibiotic stewardship programs, including statistical methods …

An Analysis Of Antichimeral Ramanujan Type Congruences For Quotients Of The Rogers-Ramanujan Functions, Ryan A. Mowers

Theses and Dissertations

This paper proves the existence of antichimeral Ramanujan type congruences for certain modular forms These modular forms can be represented in terms of Klein forms and the Dedekind eta function. The main focus of this thesis is to introduce the necessary theory to characterize these specific Ramanujan type congruences and prove their antichimerality.

An Investigation Into Optimal Descent Trajectories For Multipurpose Long Range Space Vehicles Under Advanced Conditions, John M. Levis

Theses and Dissertations

In this work, we investigate the problem of fuel-optimal control of space vehicle descent trajectories. The main tool we use to establish optimality is Pontryagin’s Maximum Principle. We present a variety of scenarios with increasing complexities, including drag, wind, and moving landing platforms in the context of differing atmospheric and gravitational conditions. Throughout the paper, we use a balance of analytical and numerical techniques. Finally, observations and conclusions drawn from the investigation form the basis for suggestions into additional areas of analysis.

Effects Of Missing Data Imputation Methods On Univariate Time Series Forecasting With Arima And Lstm, Nicholas Niako

Theses and Dissertations

Missing data are common in real-life studies and missing observations within the univariate time series cause analytical problems in the flow of the analysis. Imputation of missing values is an inevitable step in the analysis of every incomplete univariate time series data. The reviewed literature has shown that the focus of existing studies is on comparing the distribution of imputed data. There is a gap of knowledge on how different imputation methods for univariate time series data affect the fit and prediction performance of time series models. In this work, we evaluated the predictive performance of autoregressive integrated moving average …

Evaluation Of Black Holes In An Evolving Universe, John P. Naan

Theses and Dissertations

There are various solutions to the Einstein field equations that represent different physical assumptions, but how to represent multiple black holes within an expanding universe remains an area of open interest. The first step to resolving this question involves evaluating spacetime models that contain a single black hole in an expanding universe. Here, we are primarily interested in understanding the energy distribution of black hole models by solving Einstein's equations using the associated spacetime metric and comparing the propagation of waves within the model against other known spacetime models. Specifically, we will evaluate the combined Schwarschild-de Sitter solution under a …

Congruences For Quotients Of Rogers-Ramanujan Functions, Maria Del Rosario Valencia Arevalo

Theses and Dissertations

In 1919 the mathematician Srinivasa Ramanujan conjectured congruences for the partition function p(n) modulo powers of the primes 5,7,11. In this work, we study Ramanujan type congruences modulo powers of primes p = 7,11,13,17,19,23 satisfied by the Fourier coefficients of quotients the Rogers-Ramanujan Functions G(τ) and H(τ) and the Dedekind eta function η(5τ). In addition to deriving new congruences, we develop the foundational theory of modular forms to motivate and prove the results. The work includes proofs of congruences facilitated by Python/SageMath code.

Propuesta De Un Modelo De Enseñanza En Las Matemáticas Enfocado En La Solución De Problemas En El Nivel Secundario En Puerto Rico, Carlos J. Colon Rivera

Theses and Dissertations

El propósito del estudio fue proponer un modelo educativo enfocado en la solución de problemas matemáticos en el nivel secundario, y se realizó la revisión sistemática para evaluarlo. El marco teórico incluyó teorías heurísticas y modelos educativos. La metodología de seis fases que se empleó en este estudio, incluyendo la formulación de preguntas investigativas, búsqueda de literatura, selección de investigaciones, levantamiento de información, análisis y resumen de resultados y exposición y discusión de estos. Se siguieron guías para revisiones sistemáticas y criterios de inclusión y exclusión para evaluar la efectividad de modelos didácticos en la disciplina de matemáticas con énfasis …

On The Algebraic And Geometric Multiplicity Of Zero As A Hypergraph Eigenvalue, Grant Ian Fickes

Theses and Dissertations

We consider the algebraic and geometric multiplicity of hypergraph eigenvalues, paying particular attention to nullities of hypertrees. Conjecture surrounds the relationship between these two multiplicites, but little work appears in the literature on this topic. Predominantly, we are interested in identifying the geometric structure of the nullvariety of certain hypergraph classes by listing the irreducible components and their accompanying dimensions. When applicable, we use this description to verify a conjecture relating the algebraic and geometric nullity. Furthermore, we refine these geometric structure tools to graph theoretic trees, defining a matroid on trees and relating skew zero forcing to the existence …

Extreme Covering Systems, Primes Plus Squarefrees, And Lattice Points Close To A Helix, Jack Robert Dalton

Theses and Dissertations

This dissertation considers three different topics.

In the first part, we prove that if the least modulus of a distinct covering system is 4, its largest modulus is at least 60; also, if the least modulus is 3, the least common multiple of the moduli is at least 120; finally, if the least modulus is 4, the least common multiple of the moduli is at least 360. The constants 60, 120, and 360 are best possible, they cannot be replaced by larger constants. We also show that there do not exist distinct covering systems with all of the moduli in …

Regular Simplices Within Doubly Transitive Equiangular Tight Frames, Evan C. Lake

Theses and Dissertations

An equiangular tight frame (ETF) yields an optimal way to pack a given number of lines into a given space of lesser dimension. Every ETF has minimal coherence, and this makes it potentially useful for compressed sensing. But, its usefulness also depends on its spark: the size of the smallest linearly dependent subsequence of the ETF. When formed into a sensing matrix, a larger spark means a lower chance that information is lost when sensing a sparse vector. Spark is difficult to compute in general, but if an ETF contains a regular simplex, then every such simplex is a linearly …

Induced Correlation And Its Effects In The Performance Of Fused Classification Systems, Mary K. Collins

Theses and Dissertations

Classification systems are abundant in modern-day life. The United States Air Force uses classification systems across many applications such as radar, satellite, and infrared sensing just to name a few. Combining classification systems allows an opportunity to get more accurate results. Using the known information from already built and tested systems that can be mathematically combined can give insight into the performance of the fused system without having to build a combined system. Leveraging this can save time, resources, and money. This work examines the correlation effects of fusing two classifier systems, each with only two labels, using the Boolean …

Minimal Sets, Union-Closed Families, And Frankl's Conjecture, Christopher S. Flippen

Theses and Dissertations

The most common statement of Frankl's conjecture is that for every finite family of sets closed under the union operation, there is some element which belongs to at least half of the sets in the family. Despite its apparent simplicity, Frankl's conjecture has remained open and highly researched since its first mention in 1979. In this paper, we begin by examining the history and previous attempts at solving the conjecture. Using these previous ideas, we introduce the concepts of minimal sets and minimally-generated families, some ideas related to viewing union-closed families as posets, and some constructions of families involving poset-defined …

Early Termination In Phase Ii Clinical Trials: Admissible Designs Using Decreasingly Informative Priors, Chen Wang

Theses and Dissertations

In Phase II clinical trials, Thall and Simon’s Bayesian posterior probability design is commonly implemented to allow for an early termination to determine whether a new treatment warrants further investigation in a larger-scale Phase III trial; this in turn requires a pre-selected prior distribution based on known clinical opinion or historical information. Moreover, this Bayesian approach can result in an issue of inflating type I error rate by monitoring interim data to inform early termination decisions. Alternatively, a Bayesian approach with the decreasingly informative prior (DIP), which is an informative yet skeptical prior, can be implemented to overcome the contentious …

Selected Problems In Graph Coloring, Hudson Lafayette

Theses and Dissertations

The Borodin–Kostochka Conjecture states that for a graph G, if ∆(G) ≥ 9 and ω(G) ≤ ∆(G) − 1, then χ(G) ≤ ∆(G) − 1. We prove the Borodin–Kostochka Conjecture for (P5, gem)-free graphs, i.e., graphs with no induced P5 and no induced K1 ∨P4.

For a graph G and t, k ∈ Z+ at-tone k-coloring of G is a function f : V (G) → [k] such that |f(v) ∩f (w)| < d(v,w) for all distinct v, w ∈ V(G). The t-tone chromatic number of G, denoted τt(G), is the minimum k such that G is t-tone k-colorable. For small values of t, we prove sharp or nearly sharp upper bounds on the t-tone chromatic number of various classes of sparse graphs. In particular, we determine τ2(G) exactly when mad(G) < 12/5 and also determine τ2(G), up to a small additive constant, when G is outerplanar. Finally, we determine τt(Cn) exactly when t ∈ {3, 4, 5}.

Effects Of Slip On Highly Viscous Thin-Film Flows Inside Vertical Tubes (Constant Radius, Constricted And Flexible), Mark S. Schwitzerlett

Theses and Dissertations

Viscous liquid film flows in a tube arise in numerous industrial and biological applications, including the transport of mucus in human airways. Previous modeling studies have typically used no-slip boundary conditions, but in some applications the effects of slip at the boundary may not be negligible. We derive a long-wave model based on lubrication theory which allows for slippage along the boundary. Linear stability analysis verifies the impact of slip-length on the speed, growth rate, and wavelength of the most unstable mode. Nonlinear simulations demonstrate the impact of slip-length on plug formation and wave dynamics. These simulations are conducted for …

Rainbow Turan Methods For Trees, Victoria Bednar

Theses and Dissertations

The rainbow Turan number, a natural extension of the well-studied traditional
Turan number, was introduced in 2007 by Keevash, Mubayi, Sudakov and Verstraete. The rainbow Tur ́an number of a graph F , ex*(n, F ), is the largest number of edges for an n vertex graph G that can be properly edge colored with no rainbow F subgraph. Chapter 1 of this dissertation gives relevant definitions and a brief history of extremal graph theory. Chapter 2 defines k-unique colorings and the related k-unique Turan number and provides preliminary results on this new variant. In Chapter 3, we explore the …

Investigations In The Semi-Strong Product Of Graphs And Bootstrap Percolation, Kevin J. Mccall

Theses and Dissertations

The semi-strong product of graphs G and H is a way of forming a new graph from the graphs G and H. The vertex set of the semi-strong product is the Cartesian product of the vertex sets of G and H, V(G) x V(H). The edges of the semi-strong product are determined as follows: (g₁,h₁)(g₂,h₂) is an edge of the product whenever g₁g₂ is an edge of G and h₁h₂ is an edge of H or g₁ = g₂ and h₁h_{2 …}

Quantization For A Nonuniform Triadic Cantor Distribution, Asha Barua

Theses and Dissertations

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. Let P be a Borel probability measure on R such that P := 1/4 P◦ S1−1 + 1\2 P◦ S2−1 + 1/4 P◦ S3−1, where S1, S2 and S3 are three contractive similarity mappings such that Sj(x) = 1/5x+2(j−1)/5, for all x ∈ R. For this probability measure, in this thesis, we determine the optimal sets of n-means and the nth quantization errors for …