Physical Sciences and Mathematics Commons^™

Restrictions On Topological Symmetry Groups Of The 3-Rung Möbius Ladder On The Torus, Logan Willhoite

Electronic Theses and Dissertations

In this work, we discuss properties of the 3-rung Möbius ladder embedded on the surface of a torus. We present proofs on restrictions of topological symmetry groups of the Möbius ladder with and without the assumption of preserving orientation. Specifically, we show that Z₂ is the only possible non-trivial orientation-preserving topological symmetry groups, and also that Z₂ and D₂ are the only possible nontrivial topological symmetry groups.

Constructing Spanning Sets Of Affine Algebraic Curvature Tensors, Stephen J. Kelly

Rose-Hulman Undergraduate Mathematics Journal

In this paper, we construct two spanning sets for the affine algebraic curvature tensors. We then prove that every 2-dimensional affine algebraic curvature tensor can be represented by a single element from either of the two spanning sets. This paper provides a means to study affine algebraic curvature tensors in a geometric and algebraic manner similar to previous studies of canonical algebraic curvature tensors.

A Note On The Involutive Concordance Invariants For Certain (1,1)-Knots, Anna Antal, Sarah Pritchard

Rose-Hulman Undergraduate Mathematics Journal

A knot K is a smooth embedding of the circle into the three-dimensional sphere; two knots are said to be concordant if they form the boundary of an annulus properly embedded into the product of the three-sphere with an interval. Heegaard Floer knot homology is an invariant of knots introduced by P. Ozsváth and Z. Szabó in the early 2000's which associates to a knot a filtered chain complex CFK(K), which improves on classical invariants of the knot. Involutive Heegaard Floer homology is a variant theory introduced in 2015 by K. Hendricks and C. Manolescu which additionally considers a chain …

On The Superabundance Of Singular Varieties In Positive Characteristic, Jake Kettinger

Department of Mathematics: Dissertations, Theses, and Student Research

The geproci property is a recent development in the world of geometry. We call a set of points Z\subseq\P_k^3 an (a,b)-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point P to a plane is a complete intersection of curves of degrees a and b. Examples known as grids have been known since 2011. Previously, the study of the geproci property has taken place within the characteristic 0 setting; prior to the work in this thesis, a procedure has been known for creating an (a,b)-geproci half-grid for 4\leq a\leq b, but it was not …

Partitions Of R^N With Maximal Seclusion And Their Applications To Reproducible Computation, Jason Vander Woude

Department of Mathematics: Dissertations, Theses, and Student Research

We introduce and investigate a natural problem regarding unit cube tilings/partitions of Euclidean space and also consider broad generalizations of this problem. The problem fits well within a historical context of similar problems and also has applications to the study of reproducibility in randomized computation.

Given $k\in\mathbb{N}$ and $\epsilon\in(0,\infty)$, we define a $(k,\epsilon)$-secluded unit cube partition of $\mathbb{R}^{d}$ to be a unit cube partition of $\mathbb{R}^{d}$ such that for every point $\vec{p}\in\R^d$, the closed $\ell_{\infty}$ $\epsilon$-ball around $\vec{p}$ intersects at most $k$ cubes. The problem is to construct such partitions for each dimension $d$ with the primary goal of minimizing …

The Future Is Now In Twisted Coil Polymer Actuators (Tcpa), Ryan Ronquillo

Electronic Theses and Dissertations

This thesis aimed to fabricate and test twisted coiled polymer actuators (TCPA) to understand the mechanical and thermal aspects of this artificial muscle fiber. The purpose of this thesis was to find a linear relationship using the LVDT sensor, fabricating TCPA fibers, and interpreting the data. The project tested whether nylon/polymer could be used as a better artificial muscle fiber.

This research accomplished three goals: (1) designing and fabricating a system capable of creating supercoiled muscle fibers consistently, (2) calibrating the Linear Variable Differential Transformer (LVDT) and Core, and (3) analyzing/interpreting the data of the Twisted Coiled Polymer Actuators (TCPA) …

What Is A Number?, Nicholas Radley

HON499 projects

This essay is, in essence, an attempt to make a case for mathematical platonism. That is to say, that we argue for the existence of mathematical objects independent of our perception of them. The essay includes a somewhat informal construction of number systems ranging from the natural numbers to the complex numbers.

Gordian Distance And Complete Alexander Neighbors, Ana Wright

Department of Mathematics: Dissertations, Theses, and Student Research

We call a knot K a complete Alexander neighbor if every possible Alexander polynomial is realized by a knot one crossing change away from K. It is unknown whether there exists a complete Alexander neighbor with nontrivial Alexander polynomial. We eliminate infinite families of knots with nontrivial Alexander polynomial from having this property and discuss possible strategies for unresolved cases.

Additionally, we use a condition on determinants of knots one crossing change away from unknotting number one knots to improve KnotInfo’s unknotting number data on 11 and 12 crossing knots. Lickorish introduced an obstruction to unknotting number one, which proves …

Formula 101 Using 2022 Formula One Season Data To Understand The Race Results, Christopher Garcia, Oliver Lopez

Student Scholar Symposium Abstracts and Posters

The reason why I am interested in Formula One is that my friend showed me what Formula One was all about. It became interesting to see the action of the sport, including the battles the drivers have during the race and how fast they go through a corner. Also, when qualifying comes around, they push their car to the absolute limit to gain a few seconds off their opponents. The drivers only in the top 10 receive points from the winner getting 25 points, the last driver in the top 10 getting 1 point, and those below the top ten …

Fractal Newton Methods, Ali Akgül, David E. Grow

Mathematics and Statistics Faculty Research & Creative Works

We introduce fractal Newton methods for solving (Formula presented.) that generalize and improve the classical Newton method. We compare the theoretical efficacy of the classical and fractal Newton methods and illustrate the theory with examples.

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 …

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.

Fully Decoupled Energy-Stable Numerical Schemes For Two-Phase Coupled Porous Media And Free Flow With Different Densities And Viscosities, Yali Gao, Xiaoming He, Tao Lin, Yanping Lin

Mathematics and Statistics Faculty Research & Creative Works

In this article, we consider a phase field model with different densities and viscosities for the coupled two-phase porous media flow and two-phase free flow, as well as the corresponding numerical simulation. This model consists of three parts: a Cahn-Hilliard-Darcy system with different densities/viscosities describing the porous media flow in matrix, a Cahn-illiard-Navier-Stokes system with different densities/viscosities describing the free fluid in conduit, and seven interface conditions coupling the flows in the matrix and the conduit. Based on the separate Cahn-Hilliard equations in the porous media region and the free flow region, a weak formulation is proposed to incorporate the …

Why Inverse Layers In Pavement? Why Zipper Fracking? Why Interleaving In Education? A General Explanation, Edgar Daniel Rodriguez Velasquez, Aaron Velasco, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, if we split our efforts into two disconnected chunks, we get better results: a pavement is stronger if instead of a single strengthening layer, we place two parts of this layer separated by no-so-strong layers; teaching is more effective if instead of concentrating a topic in a single time interval, we split it into two parts separated in time, etc. In this paper, we provide a general explanation for all these phenomena.

Fast -- Asymptotically Optimal -- Methods For Determining The Optimal Number Of Features, Saied Tizpaz-Niari, Luc Longpré, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In machine learning -- and in data processing in general -- it is very important to select the proper number of features. If we select too few, we miss important information and do not get good results, but if we select too many, this will include many irrelevant ones that only bring noise and thus again worsen the results. The usual method of selecting the proper number of features is to add features one by one until the quality stops improving and starts deteriorating again. This method works, but it often takes too much time. In this paper, we propose …

Investigating The Effect Of Greediness On The Coordinate Exchange Algorithm For Generating Optimal Experimental Designs, William Thomas Gullion

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Design of Experiments (DoE) is the field of statistics concerned with helping researchers maximize the amount of information they gain from their experiments. Recently, researchers have been turning to optimal experimental designs instead of classical/catalog experimental designs. One of the most popular algorithms used today to generate optimal designs is the Coordinate Exchange (CEXCH) Algorithm. CEXCH is known to be a greedy algorithm, which means it tends to favor immediate, locally best designs instead of globally optimal designs. Previous research demonstrated that this tradeoff was efficacious in that it reduced the cost of a single run of CEXCH and allowed …

Flexible Models For The Estimation Of Treatment Effect, Habeeb Abolaji Bashir

Open Access Theses & Dissertations

Estimation of treatment effect is an important problem which is well studied in the literature. While the regression models are one of the most commonly used techniques for the estimation of treatment effect, they are prone to model misspecification. To minimize the model misspecification bias, flexible nonparametric models are introduced for the estimation. Continuing this line of research, we propose two flexible nonparametric models that allow the treatment effect to vary across different levels of covariates. We provide estimation algorithms for both these models. Using simulations and data analysis, we illustrate the usefulness of the proposed methods.

Machine Learning-Based Data And Model Driven Bayesian Uncertanity Quantification Of Inverse Problems For Suspended Non-Structural System, Zhiyuan Qin

All Dissertations

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and …

Tribute To Gene Chase, Calvin Jongsma

Faculty Work Comprehensive List

Gene’s academic work was always one of service to God, his students, and his colleagues, and his intellectual passion was to promote the development of Christian perspectives on various aspects of the field. His contributions to the ACMS have been much appreciated and, God willing, may still bear fruit into the future.

Incorporating Perspectival Elements In A Discrete Mathematics Course, Calvin Jongsma

Faculty Work Comprehensive List

Discrete mathematics is a vast field that can be explored along many different paths. Opening with a unit on logic and proof and then taking up some additional core topics (induction, set theory, combinatorics, relations, Boolean algebra, graph theory) allows one to bring in a wealth of relevant material on history, philosophy, axiomatics, and abstraction in very natural ways. This talk looks at how my 2019 textbook on discrete mathematics, focused in this way, came to be, and it highlights the various perspectival elements the book includes.

Effects Of Factors On The Market Price Of The Shares Using Design Of Experiment, Amir Ahmad Dar, Mohammad Shahfaraz Khan, Imran Azad, Tanveer Ahmad Tarray, N. Anuradha, Qaiser Farroq Dar

Applied Mathematics & Information Sciences

When the cost of capital, dividends and the price of the share at the beginning is known, Modigliani and Miller’s model can be used to estimate the price of the share at the end of the period. A design of experiment (Taguchi’s orthogonal array) is used in order to investigate the impact of three parameters on the price of the share at the end of the period. The main aim of this research article is to find which parameter is more significant on the price of the share at the end of the period. Taguchi’s methodology of design of the …

Knot Equivalence, Jacob Trubey

Electronic Theses, Projects, and Dissertations

A knot is a closed curve in R3. Alternatively, we say that a knot is an embedding f : S1 → R3 of a circle into R3. Analogously, one can think of a knot as a segment of string in a three-dimensional space that has been knotted together in some way, with the ends of the string then joined together to form a knotted loop. A link is a collection of knots that have been linked together.

An important question in the mathematical study of knot theory is that of how we can tell when two knots are, or are …

Listening For Common Ground In High School And Early Collegiate Mathematics, Gail Burrill, Henry Cohn, Yvonne Lai, Dev P. Sinha, Ji Y. Son, Katherine F. Stevenson

Department of Mathematics: Faculty Publications

Solutions to pressing and complex social challenges require that we reach for common ground. Only through cooperation among people with a broad range of backgrounds and expertise can progress be made on issues as challenging as improving student success in mathematics. In this spirit, the AMS Committee on Education held a forum in May 2022 entitled The Evolving Curriculum in High School and Early Undergraduate Mathematical Sciences Education.¹ This article is a report on that forum by the authors listed above, who were among the organizers and presenters.

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 …

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 …

A Frobenius-Schur Extension For Real Projective Representation, Levi Gagnon‐Ririe

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many problems in physics have explicit mathematical descriptions. This thesis aims to provide the mathematical tools for a particular problem in physics, that of Quantum Mechanical symmetries. In essence, we extend the known mathematics to a more general setting and provide a wider view of Real projective representation theory. The work done in this thesis contributes to the subfield of mathematics known as representation theory and to the subfield of physics concerned with time reversal symmetry.

A Study In The Freeness Of Finitely Generated Anp-Modules Upon Restriction To Principal Subalgebras, Luke Manford Flattery

Mathematics Dissertations

We are interested in quantitative information on the freeness of modules over a truncated polynomial ring when restricting to subalgebras generated by a linear form. After investigating the structure of the truncated polynomial ring, subalgebras generated by a linear form, and corresponding vector spaces, we construct a generic representation and discuss its connection to a certain affine space. We quantify the abundance of freeness of modules using a certain variety called the rank variety. For any possible dimension we construct a module whose rank variety has that dimension. Finally, we define another variety, called the module variety, and show that …

Adaptive And Topological Deep Learning With Applications To Neuroscience, Edward Mitchell

Doctoral Dissertations

Deep Learning and neuroscience have developed a two way relationship with each informing the other. Neural networks, the main tools at the heart of Deep Learning, were originally inspired by connectivity in the brain and have now proven to be critical to state-of-the-art computational neuroscience methods. This dissertation explores this relationship, first, by developing an adaptive sampling method for a neural network-based partial different equation solver and then by developing a topological deep learning framework for neural spike decoding. We demonstrate that our adaptive scheme is convergent and more accurate than DGM -- as long as the residual mirrors the …