Mathematics Commons^™

Approval Gap Of Weighted K-Majority Tournaments, Jeremy Coste, Breeann Flesch, Joshua D. Laison, Erin Mcnicholas, Dane Miyata

Theory & Applications of Graphs

A $k$-majority tournament $T$ on a finite set of vertices $V$ is defined by a set of $2k-1$ linear orders on $V$, with an edge $u \to v$ in $T$ if $u>v$ in a majority of the linear orders. We think of the linear orders as voter preferences and the vertices of $T$ as candidates, with an edge $u \to v$ in $T$ if a majority of voters prefer candidate $u$ to candidate $v$. In this paper we introduce weighted $k$-majority tournaments, with each edge $u \to v$ weighted by the number of voters preferring $u$.

We define the …

Representations Of Solutions Of Time-Fractional Multi-Order Systems Of Differential-Operator Equations, Sabir Umarov

Mathematics Faculty Publications

This paper is devoted to the general theory of systems of linear time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order is known through the matrix-valued Mittag-Leffler function. Multi-order (incommensurate) systems with rational components can be reduced to single-order systems, and, hence, representation formulas are also known. However, for arbitrary fractional multi-order (not necessarily with rational components) systems of differential equations, the representation formulas are still unknown, even in the case of fractional-order ordinary differential equations. In this paper, we obtain representation formulas for the solutions of arbitrary fractional multi-order …

Topics In The Study Of The Pragmatic Functions Of Phonetic Reduction In Dialog, Nigel G. Ward, Carlos A. Ortega

Departmental Technical Reports (CS)

Reduced articulatory precision is common in speech, but for dialog its acoustic properties and pragmatic functions have been little studied. We here try to remedy this gap. This technical report contains content that was omitted from the journal article (Ward et. al, submitted). Specifically, we here report 1) lessons learned about annotating for perceived reduction, 2) the finding that, unlike in read speech, the correlates of reduction in dialog include high pitch, wide pitch range, and intensity, and 3) a baseline model for predicting reduction in dialog, using simple acoustic/prosodic features, that achieves correlations with human perceptions of 0.24 for …

How To Make A Neural Network Learn From A Small Number Of Examples -- And Learn Fast: An Idea, Chitta Baral, Vladik Kreinovich

Departmental Technical Reports (CS)

Current deep learning techniques have led to spectacular results, but they still have limitations. One of them is that, in contrast to humans who can learn from a few examples and learn fast, modern deep learning techniques require a large amount of data to learn, and they take a long time to train. In this paper, we show that neural networks do have a potential to learn from a small number of examples -- and learn fast. We speculate that the corresponding idea may already be implicitly implemented in Large Language Models -- which may partially explain their (somewhat mysterious) …

Counting Hamming-Graceful Labelings Of Paths, Ashka Dalal

Mathematical Sciences Technical Reports (MSTR)

Let Γ be a graph of m edges and n vertices. A Hamming-graceful labeling of Γ labels vertices with binary strings of length m and the edge labels are induced by the Hamming distance between vertex labels. It is known that all paths have Hamming-graceful labelings, thus the question arises, how many possible labelings exist for a path of a given size. We develop an algebraic way to generate labelings, conjecture a method for counting, prove this for small examples, and verify larger examples using a Python program.

Statistical Modeling Of Right-Censored Spatial Data Using Gaussian Random Fields, Fathima Z. Sainul Abdeen, Akim Adekpedjou, Sophie Dabo Niang

Mathematics and Statistics Faculty Research & Creative Works

Consider a Fixed Number of Clustered Areas Identified by their Geographical Coordinates that Are Monitored for the Occurrences of an Event Such as a Pandemic, Epidemic, or Migration. Data Collected on Units at All Areas Include Covariates and Environmental Factors. We Apply a Probit Transformation to the Time to Event and Embed an Isotropic Spatial Correlation Function into Our Models for Better Modeling as Compared to Existing Methodologies that Use Frailty or Copula. Composite Likelihood Technique is Employed for the Construction of a Multivariate Gaussian Random Field that Preserves the Spatial Correlation Function. the Data Are Analyzed using Counting Process …

Key Benefits Of Small Group Instruction For Diverse Learners, Lydia Mcevoy

Master's Theses

Utilizing a mixed method approach this research study investigated the effects of small group instruction on the learning of diverse learners. Informed by a preliminary literature review that supports the use of small-group instruction, the researcher conducted a small-scale action research project to focus on three diverse learners in a 1st-grade classroom over four weeks. One of the findings of this project shows that small group instruction helps promote social and emotional skills as students feel more comfortable interacting with peers in a small group rather than in a whole group. Another finding indicates that students feel more encouraged by …

On Distortion Of Surface Groups In Right-Angled Artin Groups, Lucas Bridges

Mathematical Sciences Undergraduate Honors Theses

Surfaces have long been a topic of interest for scholars inside and outside of mathe- matics. In a topological sense, surfaces are spaces which appear flat on a local scale. Surfaces in this sense have a restricted set of properties, including the behavior of loops around a surface, codified in the fundamental group.

All but 3 surface groups have been shown to embed into a class of groups called right-angled Artin groups. The method through which these embeddings are created places large restrictions on all homomorphisms from surface groups to right-angled Artin groups.

One such restriction on these homomorphisms is …

Fundamental 2-Quandles Of The M(1/2, 1/3, 1/3; K) Montesino Knots, Alex Abrams

Mathematics Theses

Every oriented knot has an associated fundamental quandle. Except in two simple cases, these quandles have infinite order. For every integer n>1, there is a quotient of the fundamental quandle called the n-quandle of the knot. In some cases, these n-quandles may be finite. In the case of the M(1/2,1/3,1/3; k) Montesino knot family, the 2-quandle is finite. In this paper, we investigate the structure of the 2-quandle and prove its size.

Murmurations And Root Numbers, Alexey Pozdnyakov

University Scholar Projects

We report on a machine learning investigation of large datasets of elliptic curves and L-functions. This leads to the discovery of murmurations, an unexpected correlation between the root numbers and Dirichlet coefficients of L-functions. We provide a formal definition of murmurations, describe the connection with 1-level density, and provide three examples for which the murmuration phenomenon has been rigorously proven. Using our understanding of murmurations, we then build new machine learning models in search of a polynomial time algorithm for predicting root numbers. Based on our models and several heuristic arguments, we conclude that it is unlikely for …

How Can We Explain Empirical Formulas For Shrinkage Cracking Of Cement-Stabilized Pavement Layers, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

In pavement construction, one of the frequent defects is shrinkage cracking of the cement-stabilized pavement layer. To minimize this defect, it is important to be able to predict how this cracking depends on the quantities describing the pavement layer and the corresponding environment. Cracking is usually described by two parameters: the average width of the crack and the crack spacing. Empirical analysis shows that the dependence of the width on all related quantities is described by a power law. Power laws are ubiquitous in physics, they describe a frequent case when the dependence is scale-invariant -- i.e., does not change …

Understanding Perspectives Of Power In A College Mathematics Classroom, Laura Seeberger

Honors College Theses

Power is embedded in teacher and student actions within mathematics classrooms, whether that power is known or not. Incorporating equity and inclusiveness requires a deeper understanding of this power behind actions. In this study, we developed and administered a three part survey questioning college faculty and college students how they perceive power related to common actions within a college mathematics classroom. For example, participants were asked whether a college math teacher assigning homework increased, decreased, or did both to the teacher’s power; then whether this action increased, decreased, or did both to a student’s power. Analysis of 16 faculty and …

Multicolor Bipartite Ramsey Numbers Of Balanced Double Stars, Ella Oren-Dahan

Theses, Dissertations and Culminating Projects

Given an integer n ≥ 1, the balanced double star Sn,n is a tree consisting of two vertex disjoint stars with n leaves each, connected at their central vertices by an edge. Given r ≥ 2, we consider the problem of finding the smallest integer N such that every r-colored complete bipartite graph KN,N contains a monochromatic copy of the balanced double star Sn,n. This question is an instance of a problem within Ramsey theory. In this thesis, we cover the history of Ramsey theory and our problem in general, provide an alternative approach to prove the two colored case, …

Coarctation Duration And Severity Predict Risk Of Hypertension Precursors In A Preclinical Model And Hypertensive Status Among Patients, Arash Ghorbannia, Hilda Jurkiewicz, Lith Nasif, Abdillahi Ahmed, Jennifer Co-Vu, Mehdi Maadooliat, Ronald K. Woods, John F. Ladisa Jr.

Mathematical and Statistical Science Faculty Research and Publications

BACKGROUND:

Coarctation of the aorta (CoA) often leads to hypertension posttreatment. Evidence is lacking for the current >20 mm Hg peak-to-peak blood pressure (BP) gradient (BPGpp) guideline, which can cause aortic thickening, stiffening, and dysfunction. This study sought to find the BPGpp severity and duration that avoid persistent dysfunction in a preclinical model and test if predictors translate to hypertension status in patients with CoA.

METHODS:

Rabbits (n=75; 5–12/group) were exposed to mild, intermediate, or severe CoA (≤12, 13–19, ≥20 mm Hg BPGpp) for ≈1, 3, or 22 weeks using dissolvable and permanent sutures with thickening, stiffening, contraction, and endothelial …

Influence Of Parsimony And Work-Related Psychological Constructs In Predicting Turnover Intention When Using Machine Learning Vs Regression, Diego Figueiras

Theses, Dissertations and Culminating Projects

This dissertation explores the ongoing debate between traditional statistical regression models and machine learning (ML) algorithms in predictive modeling, focusing on the impact of sample size and the number of variables. Study 1 investigates the relationship between sample size and predictive accuracy, proposing hypotheses regarding the advantages of ML over regression as sample size increases. Additionally, the study examines the influence of the number of variables on predictive accuracy, emphasizing the trade-off between ML and regression models. Using data from the Federal Employee Viewpoint Survey, the research aims to contribute insights into the conditions favoring each modeling approach. Study 2 …

On The Number Of Strong Dominating Sets In A Graph, Frankie Mennicucci

Theses, Dissertations and Culminating Projects

This thesis investigates various problems related to the number of strong dominating sets in a graph. Given a graph G, a set of vertices D is said to be dominating if every vertex outside of D has a neighbor in D. Bród and Skupién proved that the number of dominating sets in a tree T on n vertices is at most 2ⁿ⁻¹ + 1. A set S of vertices in a graph G is a strong dominating set if every vertex x outside of S has a neighbor y ∈ S with d(y) ≥ d(x). We investigate the number of …

Formalization Of A Security Framework Design For A Health Prescription Assistant In An Internet Of Things System, Thomas Rolando Mellema

Electronic Theses and Dissertations

Security system design flaws will create greater risks and repercussions as the systems being secured further integrate into our daily life. One such application example is incorporating the powerful potential of the concept of the Internet of Things (IoT) into software services engineered for improving the practices of monitoring and prescribing effective healthcare to patients. A study was performed in this application area in order to specify a security system design for a Health Prescription Assistant (HPA) that operated with medical IoT (mIoT) devices in a healthcare environment. Although the efficiency of this system was measured, little was presented to …

A Central Limit Theorem For The Number Of Excursion Set Components Of Gaussian Fields, Dmitry Beliaev, Michael Mcauley, Stephen Muirhead

Articles

For a smooth stationary Gaussian field f on R^d and level ℓ ∈ R, we consider the number of connected components of the excursion set {f ≥ ℓ} (or level set {f = ℓ}) contained in large domains. The mean of this quantity is known to scale like the volume of the domain under general assumptions on the field. We prove that, assuming sufficient decay of correlations (e.g. the Bargmann-Fock field), a central limit theorem holds with volume-order scaling. Previously such a result had only been established for ‘additive’ geometric functionals of the excursion/level sets (e.g. the volume or …

A Statistical Look Into How Common Soccer Metrics Influence Expected Goal Measures In The Professional Game, Tristan George Rumsey

Undergraduate Honors Thesis Collection

The advent of sports analytics has ignited a fervor across all sporting disciplines, particularly soccer, where clubs are sprinting to harness vast data reserves to elevate team performance, spearhead effective marketing endeavors, and bolster financial gains crucial for club expansion. Much like Billy Beane's transformative "Moneyball" approach, soccer clubs are in pursuit of innovative strategies to transcend financial limitations and achieve triumph. In soccer, where goals are scarce commodities, heightened offensive efficacy becomes imperative. Presently, one metric stands out as pivotal in gauging a team's goal-scoring success: expected goals (xG). This metric quantifies the likelihood of a given shot or …

New Algorithms For The Multiplication Table Problem, Evan Blom

Undergraduate Honors Thesis Collection

In 1955, Paul Erdős initiated the study of a function that counts the number of distinct integers in an (n × n) multiplication table. That is, he studied M(n) = |{i · j, 1 ≤ i, j ≤ n}|. Much research has been done in regards to both asymptotic and exact approximations of M(n) for increasingly large values of n. Recently, Brent et. al. investigated the algorithmic cost in computing this function. Instead of computing M(n) directly, their approach was to compute it incrementally. That is, given M(n−1), they could quickly compute M(n) using another function δ(n) to count the …

Elasticity Of Orders In Quadratic Rings Of Integers, Jared Kettinger

All Theses

This project explores elasticity in quadratic rings of integers, specifically, those of the form Z[pω] where p is a rational prime which remains prime in Z[w]. For these rings, we establish an upper bound on the elasticity which is attained in many cases. We also prove that this upper bound is an equality in the case when the ring of integers is a unique factorization domain. During this process, we also prove theorems about the class group of quadratic rings of integers and develop a useful method for calculating a constant similar to the Davenport constant.

Asteroidal Sets And Dominating Targets In Graphs, Oleksiy Al-Saadi

School of Computing: Dissertations, Theses, and Student Research

The focus of this PhD thesis is on various distance and domination properties in graphs. In particular, we prove strong results about the interactions between asteroidal sets and dominating targets. Our results add to or extend a plethora of results on these properties within the literature. We define the class of strict dominating pair graphs and show structural and algorithmic properties of this class. Notably, we prove that such graphs have diameter 3, 4, or contain an asteroidal quadruple. Then, we design an algorithm to to efficiently recognize chordal hereditary dominating pair graphs. We provide new results that describe the …

Error Estimates For A Mixed Finite Element Method For The Maxwell's Transmission Eigenvalue Problem, Chao Wang, Jintao Cui, Jiguang Sun

Michigan Tech Publications

In this paper, we analyze a numerical method combining the Ciarlet-Raviart mixed finite element formulation and an iterative algorithm for the Maxwell's transmission eigenvalue problem. The eigenvalue problem is first written as a nonlinear quad-curl eigenvalue problem. Then the real transmission eigenvalues are proved to be the roots of a non-linear function. They are the generalized eigenvalues of a related linear self-adjoint quad-curl eigenvalue problem. These generalized eigenvalues are computed by a mixed finite element method. We derive the error estimates using the spectral approximation of compact operators, the theory of mixed finite element method for quad-curl problems, and the …

Mathematical And Computational Analysis Of Certain Regularizations For The 3d Navier-Stokes Equations And Nonlocal Peridynamic Conservation Laws, Isabel Safarik

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Voigt regularization is a technique used to model turbulent flows, offering advantages such as sharing steady states with the Navier-Stokes equations and requiring no modification of boundary conditions. We explore a modification to the Voigt regularization technique by introducing fractional dissipation into the system, specifically incorporating a fractional power, r. In this work, the proofs are in the context of periodic boundary conditions. The resulting fractional Navier-Stokes-Voigt (fNSV) and fractional Euler-Voigt (fEV) equations are studied for global well-posedness in three dimensions. It is shown that global well-posedness holds in the 3D case for fEV when the fractional power r …

Approximation Via Degree Reduction Of Nonlinearities With Applications To Turbulent Flows, Flame Fronts, And Magnetohydrodynamics, Matthew Enlow

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

We perform an analytical and computational investigation on the effectiveness of a locally bounded truncation function, which we call a calming function, when applied to the nonlinear terms of several dissipative partial differential equations. In particular, the 3D Navier-Stokes equations of incompressible fluid flow, the 2D Kuramoto-Sivashinsky equations of laminar flame fronts, and the 2D MHD-Boussinesq equations of magnetohydrodynamics. Each of these equations have open questions about the global existence and uniqueness of their solutions. These calming functions effectively reduce the algebraic degree of select nonlinear terms, thus one can verify global wellposedness for these "calmed systems." More specifically, in …

Spatiotemporal Negative Inventory Outlier Decomposition For Supply Chain Applications In Consumer-Packaged Goods (Cpg), Hayden Mcdonald

Data Science Undergraduate Honors Theses

Coca-Cola is a popular soft drink brand with sales occurring in every Walmart store across the world, which generates large quantities of data and requires a robust supply chain system. However, the company does not currently have a sophisticated, automated, and/or prescriptive system for detecting where, when, and why inventory outages occur and applying preventative measures to avoid loss of revenue from the absence of inventory on store shelves. This thesis proposes and applies a novel, prescriptive system for this purpose. An inventory outage can be seen as a ‘negative’ statistical outlier in a time series of inventory for an …

Bernstein Polynomials Method For Solving Multi-Order Fractional Neutral Pantograph Equations With Error And Stability Analysis, M. H. T. Alshbool

All Works

In this investigation, we present a new method for addressing fractional neutral pantograph problems, utilizing the Bernstein polynomials method. We obtain solutions for the fractional pantograph equations by employing operational matrices of differentiation, derived from fractional derivatives in the Caputo sense applied to Bernstein polynomials. Error analysis, along with Chebyshev algorithms and interpolation nodes, is employed for solution characterization. Both theoretical and practical stability analyses of the method are provided. Demonstrative examples indicate that our proposed techniques occasionally yield exact solutions. We compare the algorithms using several established analytical methods. Our results reveal that our algorithm, based on Bernstein series …

Mathematics Majors In Medical School Admissions: A Comparative Evaluation Of Mcat And Gpa Performance, Morgan Baker

Theses/Capstones/Creative Projects

Choosing a major as an incoming undergraduate student can be very stressful. This study investigates the differences in success that come with choice of undergraduate major, particularly focusing on the performance of mathematics majors. A large majority of medical school applicants come from a biological sciences background. Despite this preference, there is evidence that students from nontraditional majors produce higher Medical College Admission Test (MCAT) scores and superior grade point averages (GPAs). Utilizing data visualization and analysis through R programming, this research examines public data from the Association of American Medical Colleges (AAMC) to understand the benefits of pursuing a …

Geometric Principles In Architecture Aesthetics, Vincent Gemmiti

Architecture Undergraduate Honors Theses

This study focuses on geometric formalism in three major monuments across different architectural eras in time. The use of three distinct geometric principles to outline the use of pure or manufactured shapes and figures helps to discover and isolate an aesthetic component of architecture within which it is contained. A collection of studies are implemented and are focused on orthographic drawings from each monument in horizontality and verticality, consisting of a dual set of overlay and interpretative drawings for each type of orthographic representation for each monument. A discussion follows and highlights the changes or similarities over time the role …

An Analysis Of Instructor Feedback, Olga Hawranick

Boise State University Theses and Dissertations

Carless & Boud (2018) capture the definition of feedback best as “a process through which learners make sense of information… use it to enhance their work or learning strategies (p.1).” This definition goes beyond feedback solely being the role of instructors and highlights the student component in making sense of the feedback which we reference in this study as “actionable feedback.” Are instructors providing meaningful feedback to their students to encourage revision? Past studies offer inconsistent results on most features of feedback and little is known about how some of these factors benefit students’ interactions with feedback.

This study aims …