Digital Commons Network^™

Conditional Quantization For Uniform Distributions On Line Segments And Regular Polygons, Tsianna Danielle Dominguez

Theses and Dissertations

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are preselected, then the quantization is called a conditional quantization. In this thesis, we have investigated the conditional quantization for the uniform distributions defined on the unit line segments and m-sided regular polygons, where m ≥ 3, inscribed in a unit circle.

A Study Of Quantitative Reasoning Instructors’ Choices And Motivations When Teaching Quantitative Reasoning For The First Time, Trish Ann Harding

Theses and Dissertations

This qualitative study delves into the instructional decision-making processes of post-secondary instructors teaching quantitative reasoning (QR) courses for the first time. The study aims to address the gap in understanding how first-time QR instructors navigate the complexities of curriculum design and pedagogical strategies, and how these experiences contribute to their professional development. The research questions center on identifying the instructional decisions made by these instructors, exploring the factors influencing their decision-making, and understanding the impact of exercising agency has on their professional development. Through in-depth exploration, this study seeks to shed light on the challenges and opportunities faced by first-time …

How Mathematics Instructors Foster The Development Of Black Students' Mathematics Identity In Undergraduate Active Learning Mathematics Courses, Ashly J. Olusanya

Theses and Dissertations

Black students must overcome unique challenges to succeed in mathematics. Educators are tasked with identifying equitable teaching practices to support these students. Active learning (AL) is a teaching pedagogy that engages students in rigorous mathematical activities and encourages student participation. This research study will explore the professors’ beliefs about how students learn mathematics and why they use active learning in their collegiate mathematics courses. The study explores the connections between these beliefs and their reported use of instructional practices. The study also identifies the instructors’ beliefs about developing students’ mathematics identities, particularly their Black …

A Study On A Vector Complex Modified Korteweg-De Vries Equation, Changyan Shi

Theses and Dissertations

In this thesis, we systematically study a vector complex modified Kordeweg-de Vries equation by combining Hirota's bilinear method and the the Kadomtsev–Petviashvili (KP) reduction method. This vector nonlinear equation is a multi-component generalization of the well-known modified Kordeweg-de Vries (mKdV) equation and can be reduced to the known Hirota equation, Sasa-Satsuma (SS) equation, Sasa-Satsuma-mKdV equation as well as coupled Sasa-Satsuma equation. First, we bilinearize the vector complex mKdV equation under both the zero and nonzero boundary conditions by introducing auxiliary tau functions. Then, starting from two sets of bilinear equations of multi-component KP hierarchy and single-component KP-Toda …

Representation Learning For Generative Models With Applications To Healthcare, Astronautics, And Aviation, Van Minh Nguyen

Theses and Dissertations

This dissertation explores applications of representation learning and generative models to challenges in healthcare, astronautics, and aviation.

The first part investigates the use of Generative Adversarial Networks (GANs) to synthesize realistic electronic health record (EHR) data. An initial attempt at training a GAN on the MIMIC-IV dataset encountered stability and convergence issues, motivating a deeper study of 1-Lipschitz regularization techniques for Auxiliary Classifier GANs (AC-GANs). An extensive ablation study on the CIFAR-10 dataset found that Spectral Normalization is key for AC-GAN stability and performance, while Weight Clipping fails to converge without Spectral Normalization. Analysis of the training dynamics provided further …

A Post-Quantum Mercurial Signature Scheme, Madison Mabe

All Theses

This paper introduces the first post-quantum mercurial signature scheme. We also discuss how this can be used to construct a credential scheme, as well as some practical applications for the constructions.

Analysis And Construction Of Artificial Neural Networks For The Heat Equations, And Their Associated Parameters, Depths, And Accuracies., Shakil Ahmed Rafi

Graduate Theses and Dissertations

This dissertation seeks to explore a certain calculus for artificial neural networks. Specifi- cally we will be looking at versions of the heat equation, and exploring strategies on how to approximate them. Our strategy towards the beginning will be to take a technique called Multi-Level Picard (MLP), and present a simplified version of it showing that it converges to a solution of the equation �� ∂ ud�� (t, x) = (∇2xud) (t, x). ∂t We will then take a small detour exploring the viscosity super-solution properties of so- lutions to such equations. It is here that we will first encounter …

Local Existence Of Solutions To A Nonlinear Autonomous Pde Model For Population Dynamics With Nonlocal Transport And Competition, Michael R. Lindstrom

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Highlights

• Partial differential equation models are ubiquitous in applied sciences.

• A partial differential equation based in ecology is studied for solution existence.

• Energy methods and convergence analysis lead to local classical solutions.

Abstract

In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to qualitatively describe temporal changes in population densities over space through accounting for location desirability and fast, long-range travel. Beginning with sufficiently regular initial conditions, through smoothing the PDE and employing energy arguments, we obtain a sequence …

Art And Math Via Cubic Polynomials, Polynomiography And Modulus Visualization, Bahman Kalantari

LASER Journal

Throughout history, both quadratic and cubic polynomials have been rich sources for the discovery and development of deep mathematical properties, concepts, and algorithms. In this article, we explore both classical and modern findings concerning three key attributes of polynomials: roots, fixed points, and modulus. Not only do these concepts lead to fertile ground for exploring sophisticated mathematics and engaging educational tools, but they also serve as artistic activities. By utilizing innovative practices like polynomiography—visualizations associated with polynomial root finding methods—as well as visualizations based on polynomial modulus properties, we argue that individuals can unlock their creative potential. From crafting captivating …

An Investigation Into The Causes Of Home Field Advantage In Professional Soccer, Paige E. Tomer

Mathematics, Statistics, and Computer Science Honors Projects

Home-field advantage is the sporting phenomenon in which the home team outperforms the away team. Despite its widespread occurrence across sports, the underlying reasons for home-field advantage remain uncertain. In this paper, we employ a range of statistical methods to explore the causal relationships of potential determinants of home-field advantage. We measure home-field advantage using match outcomes and differential metrics (e.g., differences in yellow cards received). In an attempt to narrow the research disparity between men’s and women’s sports, we utilize data from the National Women’s Soccer League (NWSL) and the English Premier League (EPL) to investigate potential causes of …

Classification Of Topological Defects In Cosmological Models, Abigail Swanson

Student Research Submissions

In nature, symmetries play an extremely significant role. Understanding the symmetries of a system can tell us important information and help us make predictions. However, these symmetries can break and form a new type of symmetry in the system. Most notably, this occurs when the system goes through a phase transition. Sometimes, a symmetry can break and produce a tear, known as a topological defect, in the system. These defects cannot be removed through a continuous transformation and can have major consequences on the system as a whole. It is helpful to know what type of defect is produced when …

A Discussion On Estimation Of The Best Constant For Spherical Restriction Inequalities, Hongyi Liu

Mathematics, Statistics, and Computer Science Honors Projects

The restriction conjecture asks for a meaningful restriction of the Fourier transform of a function to a sufficiently curved lower dimensional manifold. It then conjectures certain size estimates for this restriction in terms of the size of the original function. It has been proven in 2 dimensions, but it is open in dimensions 3 and larger, and is an area of much recent active effort. In our study, instead of aiming to prove the restriction conjecture, we target understanding its worst-case scenarios within known estimates. Specifically, we investigate the extension operator applied to antipodally concentrating profiles, examining the ratio of …

Representation Theory And Burnside's Theorem, Nathan Fronk

Senior Seminars and Capstones

In this paper we give a brief introduction to the representation theory of finite groups, and by extension character theory. These tools are extensions of group theory into linear algebra, that can then be applied back to group theory to prove propositions that are based entirely in group theory. We discuss the importance of simple groups and the Jordan-Hölder theorem in order to prepare for the statement of Burnside’s pq theorem. Lastly, we provide a proof of Burnside’s theorem that utilizes the character theory we covered earlier in the paper.

A Tale Of Two Toroidal Graphs, Akshat Gulgulia

Honors Theses

A graph is toroidal if it can be embedded on a torus which is a doughnut-shaped surface. Two well-known examples of toroidal graphs are the complete graph K5 and the complete bipartite graph K3,3. In this thesis we elucidate the association of the subject matter with two renowned enigmas in graph theory, namely the Five Princes Problem and the Three Utilities Problems. Additionally, we look at their association with several renowned theorems in topological graph theory. We explore the link between these two graphs and a contemporary labeling concept.

Largeness And Accessibility Of Sparse Sets, Oscar Quester

Honors Program Theses and Projects

One of the main goals in the study of Ramsey Theory is to find “order” in seemingly “random” structures. For example, Van der Waerden’s Theorem tells us that given any r-coloring of the positive integers, there will exist arbitrarily long monochromatic arithmetic progressions. The theorem places no requirement on the gap (common difference), d, of the arithmetic progression – it can be any natural number. With this in mind, we ask if we are still guaranteed arbitrarily long monochromatic arithmetic progressions when we restrict the possible values of d to some subset D ⊆ N. We also ask a similar …

Numerical Investigation To Produce A Fundamental Polygon, Elizabeth Sipes

Honors College Theses

There exist multiple types of geometry, differing in the postulates they are based on, and therefore the theorems and proofs that make up said geometry. Hyperbolic geometry differs from others by allowing there to exist multiple lines through a single point not on a given line, that are parallel to the given line. Every geometry has the idea of distance and isometries, distance preserving maps. By considering special collections of isometries called discrete groups, we can construct interesting surfaces, such as the torus and genus-g surface. The connection between the surface and the discrete group can be understood through …

Euler Archive Spotlight: Multiple Search Options, Christopher Goff

Euleriana

The Euler Archive houses PDF versions of almost all of Euler's original publications. While most visitors search the archive via a work's Eneström number, the Archive can be searched via source publication name, date written, or decade of publication. The Archive also provides context for Euler's publications through short pieces of historical information.

Euler And A Proof Of The Functional Equation For The Riemann Zeta-Function He Could Have Given, Alexander Aycock

Euleriana

We explain how Euler could have proved a functional equation, which is equivalent to the one for the Riemann zeta-function, that he conjectured in his paper {\it ``Remarques sur un beau rapport entre les series des puissances tant directes que reciproques"} \cite{E352} (E352: ``Remarks on the beautiful relation between the series of the direct and reciprocal powers").

Euler And The Gaussian Summation Formula For The Hypergeometric Series, Alexander Aycock

Euleriana

We show that in his paper {\it ``Plenior expositio serierum illarum memorabilium, quae ex unciis potestatum binomii formantur"} \cite{E663} (E663: ``A more thorough exposition of those memorable series that are formed from the binomial coefficients") Euler could have found the Gaussian summation formula for the hypergeometric series from his own formulas in that same paper, if he actually set the task for himself.

Euler And Homogeneous Difference Equations With Linear Coefficients, Alexander Aycock

Euleriana

We present a method outlined by Euler in his paper{\it ``De fractionibus continuis observationes"} \cite{E123} (E123: ``Observations on continued fractions") that can be used to solve homogeneous difference equations with linear coefficients. We will illustrate his ideas by applying it to two familiar examples and explain how it can be understood from a more modern point of view.

On The Cases In Which The Formula X^4+Kxxyy+Y^4 Can Be Reduced To A Square, Georg Ehlers

Euleriana

Euler’s key idea for equating the Quartic in the title to a square is to set k=P+surd(Q). From this he derives P=f·x^2 and Q=4f·y^2+4 and solves the Pell equation for y. He then discusses various extensions to rational numbers that leave k an integer. Euler provides incomplete tables for integers k with |k|square.

Research On Arithmetic, Erik R. Tou

Euleriana

In this English translation, some of Joseph-Louis Lagrange's early number theory is presented. Here, he laid out a theory of binary quadratic forms with special attention to the representation problem: determining those integers which may be represented by a given form, and cataloguing the possible forms of their divisors.

Number Theory And More, Christopher Goff, Erik Tou

Euleriana

An introduction to the contents in Issue 1, Volume 4 of Euleriana.

Finite State And Sequential Automata, Kriti Gulgulia

Honors Theses

No abstract provided.

Caterpillar, Lobster, X Graphs, Gerald Melin, Landon Seward, Will Mahowald, Xavier Jones

Celebrating Scholarship and Creativity Day (2018-)

We studied a combinatorial game played between two players ("Alpha", who goes first, and "Beta", who goes second). The idea is that there are a lot of lightbulbs in a large warehouse, and they take turns turning a light bulb on. When a light bulb is turned on, it illuminates the area directly by it as well as the areas immediately surrounding it. The player who is the one to make all of the warehouse illuminated is the winner. This can be modeled on a graph. The two players take turns (1) selecting a vertex that has not yet been …

The Mathematical And Historical Significance Of The Four-Color Theorem, Brock Bivens

Scholars Day Conference

Computers becoming more readily used in mathematics.

Blueberry Drone Ai: Estimating Crop Yield Using Deep Learning & Smart Drones, Luke Tonon, Brandon Mchenry, Anthony Thompson, Harper Zappone, Jacob Green, Hieu Nguyen, Thanh Nguyen

STEM Student Research Symposium Posters

This project seeks to assist blueberry growers in New Jersey estimate crop yield by developing software that allows autonomous drones to capture aerial images of blueberry bushes in the field, perform berry count, and identify blueberry conditions using deep learning models & computer vision.

Blueberry Drone Ai: Smart Farming Of Blueberries Using Artificial Intelligence And Autonomous Drones, Robert Czarnota, Anthony Segrest, Anthony Thompson, Harper Zappone, Hieu Nguyen, Nguyen Thanh, Ik Jae Lee, Lori Green, Tuan Le

STEM Student Research Symposium Posters

This project seeks to assist blueberry growers in New Jersey with preventing blueberry scorch disease. Plants can’t be cured of scorch, so they have to be removed to prevent the disease from spreading to other bushes. This project aims to use object detection and classifier machine learning models in order to detect scorch disease with photos from intelligent drones. Images are first tiled, then processed through and convolutional neural network that detects scorch symptoms. Lastly, a fully connected neural network is implemented to make a final prediction.

Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, Mahdiyeh Soltaninejad

Dissertations

The high prevalence of dental caries among children and adolescents, especially those from lower socio-economic backgrounds, is a significant nationwide health concern. Early prevention, such as dental sealants and fluoride varnish (FV), is essential, but access to this care remains limited and disparate. In this research, a national dataset is utilized to assess sealants' reach and effectiveness in preventing tooth decay, particularly focusing on 2nd molars that emerge during early adolescence, a current gap in the knowledge base. FV is recommended to be delivered during medical well-child visits to children who are not seeing a dentist. Challenges and facilitators in …

The Effect Of Fixed Time Delays On The Synchronization Phase Transition, Shaizat Bakhytzhan

USF Tampa Graduate Theses and Dissertations

Nature is full of synchronization phenomena, which are essential to many scientific fields like biology, chemistry, physics, and neuroscience. The Kuramoto model is a well-known theoretical model that helps explain the fundamental ideas behind synchronization dynamics [6]. Nevertheless, in practical situations, systems frequently display intrinsic latency, which can greatly impact their behavior during synchronization. This insight inspired our work, which looks at the results of adding temporal delays to the Kuramoto model. In particular, we investigate how the system’s synchronization dynamics are affected by delays. We shed light on the mechanisms underpinning synchronization in the face of temporal delays and …