Physical Sciences and Mathematics Commons^™

Subsystems Of Transitive Subshifts With Linear Complexity, Andrew Dykstra, Nicholas Ormes, Ronnie Pavlov

Mathematics: Faculty Scholarship

We bound the number of distinct minimal subsystems of a given transitive subshift of linear complexity, continuing work of Ormes and Pavlov [On the complexity function for sequences which are not uniformly recurrent. Dynamical Systems and Random Processes (Contemporary Mathematics, 736). American Mathematical Society, Providence, RI, 2019, pp. 125--137]. We also bound the number of generic measures such a subshift can support based on its complexity function. Our measure-theoretic bounds generalize those of Boshernitzan [A unique ergodicity of minimal symbolic flows with linear block growth. J. Anal. Math.44(1) (1984), 77–96] and are closely related to those of Cyr and Kra …

Quantum Markov Maps: Structureand Asymptotics., Vijaya Kumar U. Dr.

Doctoral Theses

No abstract provided.

Essays In Social Choice Theory., Dipjyoti Majumdar Dr.

Doctoral Theses

The purpose of this thesis is to explore some issues in social choice theory and decision theory. Social choice theory provides the theoretical foundations for the field of public choice and welfare economics. It tries to bring together normative aspects like perspective value judgements and positive aspects, like strategic con- siderations. The second feature which is our focus, is closely related to the problem of providing appropriate incentives to agents, an issue of prime importance in eco- nomics.Consider for example, a set of agents who must elect one among a set of can- didates. These candidates may be physical agents …

Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, Al Cuoco, E. Paul Goldenberg

Journal of Humanistic Mathematics

How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and …

On Subshifts With Slow Forbidden Word Growth, Ronnie Pavlov

Mathematics: Faculty Scholarship

In this work, we treat subshifts, defined in terms of an alphabet A and (usually infinite) forbidden list F, where the number of n-letter words in F has ‘slow growth rate’ in n. We show that such subshifts are well behaved in several ways; for instance, they are boundedly supermultiplicative in the sense of Baker and Ghenciu [Dynamical properties of S-gap shifts and other shift spaces. J. Math. Anal. Appl.430(2) (2015), 633–647] and they have unique measures of maximal entropy with the K-property and which satisfy Gibbs bounds on large (measure-theoretically) sets. The main tool in our proofs is a …

Aps March Meeting 2021 (Online) Updates On Scientific Research During Pandemic Times, Vianney Gimenez-Pinto

Title III Professional Development Reports

While the ongoing global pandemic continues to affect our everyday lives, researchers in Science, Technology, Engineering and Math found a way to come together at the American Physical Society (APS) March Meeting 2021. The conference was online-only and had more than 11,000 registered attendants who actively participated in the program during March 14- 19, 2021.

An Axiomatic Construction Of The Real Number System, Leonard Van Wyk

Libraries

Starting from the Peano Axioms, we construct the natural numbers, the integers, the rationals, and the reals.

Math Department 2020-2021 Newsletter, Mathematics Department

Mathematics Newsletter

This was an unusual year for our department as the coronavirus pandemic continued. However, we made the best of the situation and did as many activities as we could -- In the Fall, we inaugurated our new math major with three tracks: the traditional track, actuarial science track, and data science track -- Faculty changes -- Graduating seniors -- Pi Mu Epsilon Induction Ceremony and Awards Night -- Alumni Page -- Faculty spotlight -- Noyce grant -- Alumni night -- Coming attractions.

Applying Cognitive Measures In Counterfactual Prediction, Lori A. Mahoney

Browse all Theses and Dissertations

Counterfactual reasoning can be used in task-switching scenarios, such as design and planning tasks, to learn from past behavior, predict future performance, and customize interventions leading to enhanced performance. Previous research has focused on external factors and personality traits; there is a lack of research exploring how the decision-making process relates to both task-switching and counterfactual predictions. The purpose of this dissertation is to describe and explain individual differences in task-switching strategy and cognitive processes using machine learning techniques and linear ballistic accumulator (LBA) models, respectively, and apply those results in counterfactual models to predict behavior. Applying machine learning techniques …

Regression Analysis: Graduation Rate In Kentucky Public High Schools, Rebecca Price

Mahurin Honors College Capstone Experience/Thesis Projects

Kentucky’s Public High School graduation rates vary widely across the rural and urban regions in the state. In addition to their graduation rates, each of these schools have their own unique demographics, funding, teacher-student ratio, etc. that define said school’s identity. This research aims to analyze the aforementioned variables, as well as other variables listed on each school state report card, in order to create a model to predict any school’s graduation rate.

In order to create this model, data was taken on all public high schools in Kentucky from the Kentucky Department of Education’s School Report Card. Data were …

Multivariate Distributions Of Correlated Binary Variables Generated By Pair-Copulas, Huihui Lin, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Correlated binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. The generalized estimating equations (GEEs) and the multivariate probit (MP) model are two of the popular methods for analyzing such data. However, both methods have some significant drawbacks. The GEEs may not have an underlying likelihood and the MP model may fail to generate a multivariate binary distribution with specified marginals and bivariate correlations. In this paper, we study multivariate binary distributions that are based on D-vine pair-copula models as a superior alternative to these methods. We elucidate the construction of these binary distributions …

Computational Simulation And Analysis Of Neuroplasticity, Madison E. Yancey

Browse all Theses and Dissertations

Homeostatic synaptic plasticity is the process by which neurons alter their activity in response to changes in network activity. Neuroscientists attempting to understand homeostatic synaptic plasticity have developed three different mathematical methods to analyze collections of event recordings from neurons acting as a proxy for neuronal activity. These collections of events are from control data and treatment data, referring to the treatment of neuron cultures with pharmacological agents that augment or inhibit network activity. If the distribution of control events can be functionally mapped to the distribution of treatment events, a better understanding of the biological processes underlying homeostatic synaptic …

Applying Cognitive Measures In Counterfactual Prediction, Lori A. Mahoney

Browse all Theses and Dissertations

Counterfactual reasoning can be used in task-switching scenarios, such as design and planning tasks, to learn from past behavior, predict future performance, and customize interventions leading to enhanced performance. Previous research has focused on external factors and personality traits; there is a lack of research exploring how the decision-making process relates to both task-switching and counterfactual predictions. The purpose of this dissertation is to describe and explain individual differences in task-switching strategy and cognitive processes using machine learning techniques and linear ballistic accumulator (LBA) models, respectively, and apply those results in counterfactual models to predict behavior. Applying machine learning techniques …

On The Characteristics Of A Data-Driven Multi-Scale Frame Convergence Algorithm, Beverly K. Grunden

Browse all Theses and Dissertations

In recent years, data-driven representation methods have been introduced to improve compressed sensing image reconstruction. This research explores a recently proposed algorithm that utilizes a data-driven multi-scale Parseval frame for image compression. Because a sensing matrix by itself may be insufficient to obtain a sparse representation for an image, a frame is combined with the compressed sensing matrix to increase flexibility in obtaining a sparse representation. The two-step algorithm optimizes the representation by alternating between adjusting a sparse coefficient vector and tuning a small filterbank which determines the frame. The structure of the frame and its relationship with the underlying …

Statistical And Machine Learning Approaches To Depressive Disorders Among Adults In The United States: From Factor Discovery To Prediction Evaluation, Minhwa Lee

Senior Independent Study Theses

According to the National Institutes of Mental Health (NIMH), depressive disorders (or major depression) are considered one of the most common and serious health risks in the United States. Our study focuses on extracting non-medical factors of depressive disorders diagnosis, such as overall health states, health risk behaviors, demography, and healthcare access, using the Behavioral Risk Factor Surveillance System (BRFSS) data set collected by the Centers for Disease Control and Prevention (CDC) in 2018.

We set the two objectives of our study about depressive disorders diagnosis in the United States as follows. First, we aim to utilize machine learning algorithms …

Teacher Understanding Of Instructional Strategies In Elementary Mathematics, Erica Boatwright Glover

Walden Dissertations and Doctoral Studies

Synergizing Elementary School (pseudonym) consistently experiences low state-required mathematics test scores in grades 3 and 4 below district and state proficiency rates in mathematics. The purpose of this qualitative case study was to investigate what instructional practices used by Grade 3 and Grade 4 teachers are, aligned or not aligned, with research-based planning, standards-based instruction, attention to conditions of learning, and professional responsibilities of teachers to support students’ achievement in mathematics. This study's conceptual framework was grounded in Robert Marzano's model of teaching effectiveness called the focus teacher evaluation model. Data for this case study were gathered from semi-structured interviews …

Option Implied Volatility's Predictability On Monthly Stock Returns, Hung T. Dao

Senior Independent Study Theses

Since the trading of options is based on underlying stocks, it is reasonable to assume that information from the options market can be used to explain the returns in the stock market. Our independent study investigates the relationship between options implied volatility and stock returns. Previous studies have found significant results in using implied volatility in predicting stock returns. This paper provides a discussion of such studies, the theoretical framework for the research topic, and the Black-Scholes model, which is famous for its application in implied volatility calculation. Monthly returns of 20 large US firms are regressed against implied volatility …

Zn Orbifolds Of Vertex Operator Algebras, Daniel Graybill

Electronic Theses and Dissertations

Given a vertex algebra V and a group of automorphisms of V, the invariant subalgebra V^G is called an orbifold of V. This construction appeared first in physics and was also fundamental to the construction of the Moonshine module in the work of Borcherds. It is expected that nice properties of V such as C2-cofiniteness and rationality will be inherited by V^G if G is a finite group. It is also expected that under reasonable hypotheses, if V is strongly finitely generated and G is reductive, V^G will also be strongly finitely generated. This is an analogue …

Cross-Model Parameter Estimation In Epidemiology, Julia R. Fitzgibbons

Honors Theses and Capstones

No abstract provided.

Mathematics Teachers’ Pedagogical Content Knowledge And Its Relation To Student Achievement, Michelle Emmalyn Peters-George

Walden Dissertations and Doctoral Studies

Students' performance in national assessments of mathematics at Grades 2, 4, and 6 has been a cause for concern in the Eastern Caribbean. Researchers have called for studies to focus on primary mathematics teachers' pedagogies rather than on laptops and curriculum; however, it is unclear how primary mathematics teachers' pedagogical knowledge influences these student’s achievement. The purpose of this quantitative study was to investigate the relationship between primary mathematics teachers' pedagogical content knowledge (mathematical knowledge for teaching, quality of instruction, and pedagogical qualifications) and student achievement, measured by national assessment scores in Grenada, controlling for teachers’ age, gender, and experience. …

Exponential Random Graphs And A Generalization Of Parking Functions, Ryan Demuse

Electronic Theses and Dissertations

Random graphs are a powerful tool in the analysis of modern networks. Exponential random graph models provide a framework that allows one to encode desirable subgraph features directly into the probability measure. Using the theory of graph limits pioneered by Borgs et. al. as a foundation, we build upon the work of Chatterjee & Diaconis and Radin & Yin. We add complexity to the previously studied models by considering exponential random graph models with edge-weights coming from a generic distribution satisfying mild assumptions. In particular, we show that a large family of two-parameter, edge-weighted exponential random graphs display a phase …

Applied Topology Ams 528, Harrison Dekker

Library Impact Statements

No abstract provided.

The Beautiful Math Of Everything And You Included, E. Ozie

The Transdisciplinary STEAM+ Journal

This a reflection on how there is beautiful math to everything. An author's interpretation of matrices and mechanics in its relationship to someone's identity.

Factors Impacting Students’ Perceptions Of Mathematics, Amber Souza

Honors Program Theses and Projects

I want to be able to present math in a positive light to all of my future students, regardless of race, gender, and math background. However, for teachers as a whole to be able to take this important step, they must first develop a deeper understanding of why math is a sore spot for many students.

Parametric Art, Shaun Pollard, Daanial Ahmad, Satyanand Singh

Publications and Research

Lissajous curves, named after Jules Antoine Lissajous (1822-1880) are generated by the parametric equations ��=��������(����) and ��=��������(����) in its simplistic form. Others have studied these curves and their applications like Nathaniel Bowditch in 1815, and they are often referred to as Bowditch curves as well. Lissajous curves are found in engineering, mathematics, graphic design, physics, and many other backgrounds. In this project entitled “Parametric Art” this project will focus on analyzing these types of equations and manipulating them to create art. We will be investigating these curves by answering a series of questions that elucidate their purpose. Using Maple, which …

Introduction To Data Science, Joanna Burkhardt

Library Impact Statements

No abstract provided.

Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

Electronic Theses, Projects, and Dissertations

In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …

An Exploration Of The Numeracy Skills Required For Safe, Quality Nursing Practice, Anna Wendel

UNLV Theses, Dissertations, Professional Papers, and Capstones

The purpose of this study was to explore the numeracy skills required for safe, quality nursing practice. Using a descriptive mixed methods design, this study answered two research questions: 1) What numeracy skills do nurses perceive as important for providing safe, quality nursing care in the first three years of practice? 2) How do nurses incorporate numeracy skills into daily patient care during the first three years of practice? Early career nurses from a not-for-profit health care organization in the mid-Atlantic region of the United States (n=109) responded to an online survey tool developed by the student investigator that ranked …

Lis Online Graduate Certificate In Data Science, Joanna Burkhardt

Library Impact Statements

No abstract provided.

The Decline Of The Mid-Range Jump Shot In Basketball: A Study Of The Impact Of Data Analytics On Shooting Habits In The Nba, Shawn Kilcoyne

Honors Projects in Mathematics

The purpose of this thesis paper is to investigate the strategic shift away from the mid-range jump shot in basketball over the past decade. This paper will cover the rationale for the decline of the mid-range, as well as the general impact of data analytics on the way the game of basketball is played at the professional level. Following a review of the existing literature relating to the use of analytics in the NBA, this paper will analyze the differences in shooting habits between two seven-season periods. Data visualization tools, including boxplots, statistical trends, and distribution plots, will be used …