Physical Sciences and Mathematics Commons^™

Graph Coloring Reconfiguration, Reem Mahmoud

Theses and Dissertations

Reconfiguration is the concept of moving between different solutions to a problem by transforming one solution into another using some prescribed transformation rule (move). Given two solutions s₁ and s₂ of a problem, reconfiguration asks whether there exists a sequence of moves which transforms s₁ into s₂. Reconfiguration is an area of research with many contributions towards various fields such as mathematics and computer science.
The k-coloring reconfiguration problem asks whether there exists a sequence of moves which transforms one k-coloring of a graph G into another. A move in this case is a type …

Combinatorial Problems Related To Optimal Transport And Parking Functions, Jan Kretschmann

Theses and Dissertations

In the first part of this work, we provide contributions to optimal transport through work on the discrete Earth Mover's Distance (EMD).We provide a new formula for the mean EMD by computing three different formulas for the sum of width-one matrices: the first two formulas apply the theory of abstract simplicial complexes and result from a shelling of the order complex, whereas the last formula uses Young tableaux. Subsequently, we employ this result to compute the EMD under different cost matrices satisfying the Monge property. Additionally, we use linear programming to compute the EMD under non-Monge cost matrices, giving an …

A Combinatorial Proof Of Supercranks For Partitions With A Fixed Number Of Parts, Jacob J. Gutierrez

Theses and Dissertations

In a previous paper by Eichhorn and Kronholm, a selection of supercranks for p(n,m) was established by generating functions. In this paper we will reprove this result with combinatorial witnesses for the selection of supercranks via integer lattice points.

Attitudes Towards Mathematics Of Developmental Mathematics Students In A Community College, Benjamin Ortiz

Theses and Dissertations

Reformations to developmental mathematics aim to remove barriers for students entering higher education. Challenges like costly multi-course sequences and high failure rates prohibit students’ access to college-level math courses and prevent degree or certification completion. Understanding factors that foster student success is critical to increase student success. This study focuses on students’ attitudes towards mathematics, utilizing the novice-expert continuum through Code et al.’s Mathematical Attitude and Perceptions Survey (MAPS) instrument. Student expertise scores, including all MAPS dimensions and specific dimension scores, were assigned. Kruskal-Wallis Rank-Sum tests identified differences in student populations by course and attitude dimension. …

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 …

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.

Case Studies Of Algebra 1 Teachers Selection And Implementation Of Mathematics Tasks Toward Situated Learning, Luis Román Sauceda

Theses and Dissertations

Mathematical tasks are vital in active learning, especially in situated learning. Adequate selection and appropriate implementation of tasks are steps toward success in engaging students for active learning. This study explored how a professional development (PD) workshop influences teacher participants’ capabilities in selecting, redesigning, implementing, and reflecting on mathematical tasks to promote situated and active learning. The teacher participants were Algebra 1 teachers from a South Texas secondary school. During the workshop, participants developed and implemented activities after being shown situated learning strategies to promote student-centered learning. They were required to design hypothetical dialogues to simulate their class practice before …

Strategies Community College Mexican American Adult College Algebra Students Use When Graphing Function Transformations, Roxana Pamela Jimenez

Theses and Dissertations

This qualitative case study pursued to describe the different strategies Mexican American adult students in a local community college used to graph function transformations. Participants in the study were purposefully selected using a criterion sampling to ensure participants were atypical, above average students between the ages 18-22, and had a final course average of 89.5-100 in College Algebra. Three research questions were examined 1) In what ways do Mexican American adult college students graph a function transformation? 2) Which strategies do students implement when graphing a function transformation? Qualitative research methods using think aloud semi-structured interviews were used in this …

Quasipolynomials And The Unimodality Of Gaussian Polynomials, Paul Marsh

Theses and Dissertations

We illustrate a method to prove the unimodality of Gaussian polynomials ${N+m \brack m}$ for $m = 5$ and $6$, building upon Dr. Brandt Kronholm's work, which proved unimodality for $m = 2,3,$ and $4$. Our approach involves viewing coefficients $p(n,m,N)$ of Gaussian polynomials $N+m \brack m$ based on how far away $n$ is from the central coefficient $p(\lfloor\frac{mN}{2}\rfloor,m,N)$ and then creating generating functions for those coefficients. We then take the difference of neighboring generating functions and change those generating functions into quasipolynomials to verify that their coefficients are non-negative. While the generalization of these generating functions for the coefficients …

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 …

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 …

Enumerative Problems Of Doubly Stochastic Matrices And The Relation To Spectra, Julia A. Vandenlangenberg

Theses and Dissertations

This work concerns the spectra of doubly stochastic matrices whose entries are rational numbers with a bounded denominator. When the bound is fixed, we consider the enumeration of these matrices and also the enumeration of the orbits under the action of the symmetric group.

In the case where the bound is two, we investigate the symmetric case. Such matrices are in fact doubly stochastic, and have a nice characterization when we are in the special case where the diagonal is zero. As a central tool to this investigation, we utilize Birkhoff's theorem that asserts that the doubly stochastic matrices are …

The Vanishing Discount Method For Stochastic Control: A Linear Programming Approach, Brian Hospital

Theses and Dissertations

Under consideration are convergence results between optimality criteria for two infinite-horizon stochastic control problems: the long-term average problem and the $\alpha$-discounted problem, where $\alpha \in (0,1]$ is a given discount rate. The objects under control are those stochastic processes that arise as (relaxed) solutions to a controlled martingale problem; and such controlled processes, subject to a given budget constraint, comprise the feasible sets for the two stochastic control problems.

In this dissertation, we define and characterize the expected occupation measures associated with each of these stochastic control problems, and then reformulate each problem as an equivalent linear program over a …

Collapsibility And Z-Compactifications Of Cat(0) Cube Complexes, Daniel L. Gulbrandsen

Theses and Dissertations

We extend the notion of collapsibility to non-compact complexes and prove collapsibility of locally-finite CAT(0) cube complexes. Namely, we construct such a cube complex $X$ out of nested convex compact subcomplexes $\{C_i\}_{i=0}^\infty$ with the properties that $X=\cup_{i=0}^\infty C_i$ and $C_i$ collapses to $C_{i-1}$ for all $i\ge 1$.

We then define bonding maps $r_i$ between the compacta $C_i$ and construct an inverse sequence yielding the inverse limit space $\varprojlim\{C_i,r_i\}$. This will provide a new way of Z-compactifying $X$. In particular, the process will yield a new Z-boundary, called the cubical boundary.

Non-Hyperbolic Right-Angled Coxeter Groups With Menger Curve Boundary, Cong He

Theses and Dissertations

We find a class of simplicial complexes as nerves of non-hyperbolic right-angled Coxetergroups, with boundary homeomorphic to the Menger curve. The nerves are triangulations of compact orientable surfaces with boundary. In particular, the nerves are non-graphs.

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 …

Random Quotients Of Hyperbolic Groups And Property (T), Prayagdeep Parija

Theses and Dissertations

What does a typical quotient of a group look like? Gromov looked at the density model of quotients of free groups. The density parameter $d$ measures the rate of exponential growth of the number of relators compared to the size of the Cayley ball. Using this model, he proved that for $d<1/2$, the typical quotient of a free group is non-elementary hyperbolic. Ollivier extended Gromov's result to show that for $d<1/2$, the typical quotient of many hyperbolic groups is also non-elementary hyperbolic.

Żuk and Kotowski--Kotowski proved that for $d>1/3$, a typical quotient of a free group has Property (T). We show that (in a closely related density model) for $1/3

An Optimal Decay Estimation Of The Solution To The Airy Equation, Ashley Scherf

Theses and Dissertations

In this thesis, we investigate the initial value problem to the Airy equation \begin{align} \partial_t u + \partial_{x}^3 u &= 0\\ u(0,x) &= f(x). \end{align}

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 …

Explorations In Baseball Analytics: Simulations, Predictions, And Evaluations For Games And Players, Katelyn Mongerson

Theses and Dissertations

From statistics being reported in newspapers in the 1840s, to present day, baseballhas always been one of the most data-driven sports. We make use of the endless publicly available baseball data to build models in R and Python that answer various baseball- related questions regarding predicting and optimizing run production, evaluating player effectiveness, and forecasting the postseason. To predict and optimize run production, we present three models. The first builds a common tool in baseball analysis called a Run Expectancy Matrix which is used to give a value (in terms of runs) to various in-game decisions. The second uses the …

Modeling Wlan Received Signal Strengths Using Gaussian Process Regression On The Sodindoorloc Dataset, Fabian Hermann Josef Fuchs

Theses and Dissertations

While any wireless technology can be used for indoor localization purposes, WLANhas the advantage of having a huge existing infrastructure. A radio map that matches specific locations to received signal strength is needed, to enable most of these indoor localization methods. To create these radio maps, with enough detail to achieve sufficient localization accuracy, is expensive and time consuming. Therefore, methods to interpolate and extrapolate more detailed maps from sparse radio maps are being developed. One recent approach is to use Gaussian process regression. Even though some papers already studied Gaussian process regression, most studied only the basic model with …

Applying The Efficiency Gap To Wisconsin Politics, Joseph Robert Szydlik

Theses and Dissertations

Gerrymandering is a plague on modern democracy, blatantly violating the democratic principle of “one person, one vote.” Here we will methodically examine the 2018 Wisconsin state assembly election, and using a metric known as the efficiency gap demonstrate the extent to which gerrymandering played a role. Through this metric, and a probabilistic simulation of our own, we will show that in this election the Republican party benefited from systematic partisan gerrymandering. Additionally, we will use these findings to suggest methods for correcting this undemocratic practice that both parties utilize in order to disenfranchise opposition voters.

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 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.

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.

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 …

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 …

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.