Modeling The Effect Of Observational Social Learning On Parental Decision-Making For Childhood Vaccination And Diseases Spread Over Household Networks, Tamer Oraby, Andras Balogh

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we introduce a novel model for parental decision-making about vaccinations against a childhood disease that spreads through a contact network. This model considers a bilayer network comprising two overlapping networks, which are either Erdős–Rényi (random) networks or Barabási–Albert networks. The model also employs a Bayesian aggregation rule for observational social learning on a social network. This new model encompasses other decision models, such as voting and DeGroot models, as special cases. Using our model, we demonstrate how certain levels of social learning about vaccination preferences can converge opinions, influencing vaccine uptake and ultimately disease spread. In addition, …

Flow And Stability Of Three-Dimensional Rotating Viscoelastic Jet, Daniel N. Riahi

School of Mathematical & Statistical Sciences Faculty Publications

We consider rotationally driven nonlinear viscoelastic jet. In contrast to previous unrealistic planar studies with no gravity effect, we investigate here realistic three-dimensional jet with gravity effect. Using theoretical and computational methods, we develop models for such jet and its stability and determine the solutions. We find three-dimensional jet with gravity effect leads to faster and thinner jet. For jet arc length higher than its exit diameter, our calculation with typical parameter values shows that jet radius is smaller by a factor of more than 1.4 and jet speed is higher by factor of more than 2 as are compared …

Exploring International Educators' Learning About Local And Global Social Justice In A Virtual Community Of Practice, Bima Sapkota, Xuwei Luo, Muna Sapkota, Murat Akarsu, Emmanuel Deogratias, Daphne Fauber, Rose Mbewe, Fidelis Mumba, Ram Krishna Panthi, Jill Newton

School of Mathematical & Statistical Sciences Faculty Publications

In this chapter, the authors report themes that emerged when a cross-cultural team of researchers involved in a virtual international community of practice (Global Social Justice in Education-GSJE) investigated reflections on activities focused on social justice in local and global contexts. The findings suggested that the activities elicited GSJE community members' understandings of the complexities of social justice associated with naming practices, privilege, and the arts within their own and across contexts. The authors discuss implications of the activities to advance diverse educators' understanding of social justice in global and local contexts. They also unpack the opportunities and challenges that …

Assessing Concepts, Procedures, And Cognitive Demand Of Chatgpt-Generated Mathematical Tasks, Bima Sapkota, Liza Bondurant

School of Mathematical & Statistical Sciences Faculty Publications

In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises concerns, such as outputs that are inaccurate, nonsensical, or vague. We, two mathematics teacher educators, engaged in a collaborative self-study using qualitative descriptive approaches to investigate the procedures, concepts, and cognitive demand of ChatGPT-generated mathematical tasks focused on fraction multiplication using the area model approach. We found that the ChatGPT-generated tasks were …

Ivermectin, Colleen Aldous, Eleftherios Gkioulekas, Philip Oldfield

School of Mathematical & Statistical Sciences Faculty Publications

No abstract provided.

Brillouin Zones Of Integer Lattices And Their Perturbations, Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss, Morteza Saghafian, Mathijs Wintraecken

School of Mathematical & Statistical Sciences Faculty Publications

For a locally finite set, 𝐴⊆ℝ𝑑 , the 𝑘 th Brillouin zone of 𝑎∈𝐴 is the region of points 𝑥∈ℝ𝑑 for which ‖𝑥−𝑎‖ is the 𝑘 th smallest among the Euclidean distances between 𝑥 and the points in 𝐴 . If 𝐴 is a lattice, the 𝑘 th Brillouin zones of the points in 𝐴 are translates of each other, and together they tile space. Depending on the value of 𝑘 , they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our …

Development Of Probabilistic Dynamic Model Building And Bayesian Machine Learning Approaches, Samuel Oladayo Adeyemo

Graduate Theses, Dissertations, and Problem Reports (ETD)

Abstract

Development of Probabilistic Dynamic Model Building and Bayesian Machine Learning Approaches

Samuel Adeyemo

The recent years have seen a tremendous increase in the use of artificial intelligence (AI) and machine learning (ML) for the development of data-driven mathematical models needed for performing real-time optimization, model-based control, performance optimization, dynamic data reconciliation, and process performance monitoring. However, the development of data-driven models is faced with some challenges including lack of model interpretability, sensitivity of algorithm to noise in training data, limited extrapolation capabilities and violation of conservation laws. Drawing motivation from these existing gaps, this work aims to develop robust …

Advanced Techniques In Time Series Forecasting: From Deterministic Models To Deep Learning, Xue Bai

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation discusses three instances of temporal prediction, applied to population dynamics and deep learning.

In population modeling, dynamic processes are frequently represented by systems of differential equations, allowing for the analysis of various phenomena. The first application explores modeling cloned hematopoiesis in chronic myeloid leukemia (CML) via a nonlinear system of differential equations. By tracking the evolution of different cell compartments, including cycling and quiescent stem cells, progenitor cells, differentiated cells, and terminally differentiated cells, the model captures the transition from normal hematopoiesis to the chronic and accelerated-acute phases of CML. Three distinct non-zero steady states are identified, representing …

On Cyclically 4-Connected Cubic Graphs, R. J. Kingan, S. R. Kingan

Publications and Research

A 3-connected cubic graph is cyclically 4-connected if it has at least n ≥ 8 vertices and when removal of a set of three edges results in a disconnected graph, only one component has cycles. By introducing the notion of cycle spread to quantify the distance between pairs of edges, we get a new characterization of cyclically 4-connected graphs. Let Q_n and V_n denote the ladder and Möbius ladder on n ≥ 8 vertices, respectively. We prove that a 3-connected cubic graph G is cyclically 4-connected if and only if G is either the Petersen graph, Q …

Heuristics For Anti-Cyclotomic ℤp-Extensions, Debanjana Kundu, Lawrence C. Washington

School of Mathematical & Statistical Sciences Faculty Publications

This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this by proposing two heuristics supported by computations. First we propose the Intersection Heuristics: these model “how often” the p-Hilbert class field of an imaginary quadratic field intersects the anti-cyclotomic tower and to what extent. Second we propose the Invariants Heuristics: these predict that the Iwasawa invariants 𝜆 and 𝜇 usually vanish for imaginary quadratic fields where p is non-split.

On The Center And The Antipode Of The Super-Yangian Of Q(1), Elena Poletaeva

School of Mathematical & Statistical Sciences Faculty Publications

For the queer Lie superalgebra Q(1), we explicitly describe the center of the super-Yangian Y Q(1) of Q(1) in terms of generators of Y Q(1). We also describe the square of the antipodal map on Y Q(1) and use the antipode to construct an involutive automorphism of Y Q(1).

GröBner Bases With An Application To Tame Functions, Jessica D. Marconi

UNF Graduate Theses and Dissertations

Grobner bases are essential tools in algebraic geometry, used to simplify and solve systems of polynomial equations. These bases revolutionized computational methods in various branches of mathematics after being introduced in 1965 by Bruno Buchberger. This thesis explores the foundational concepts of Grobner bases, including their formation and properties. It also demonstrates their use in solving mathematical problems in algebraic geometry, including the ideal membership problem. As an application, we show how Grobner bases can be used to determine whether a polynomial mapping is tame. This concept is crucial for analyzing the topology near singular points and establishing whether a …

Enumeration Of Lattice Paths With Restrictions, Vince White

College of Graduate Studies: Theses & Dissertations

Lattice path enumeration, through the lens of Catalan numbers, plays a crucial role in combinatorics. This thesis delves into enumerations of some of the most common lattice paths – north-east paths, up-down paths, and Dyck paths – with restrictions applied. The first restriction is counting north-east lattice paths that only cross the diagonal line, y=x, once. The second form of lattice paths with restrictions is up-down paths that cross the x-axis exactly once and fall to a fixed depth of k. While working through this module, a novel proof for a known integer sequence was used, then applied to generate …

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 …

Problems In Graph Theory With Applications To Topology And Modeling Rna, Rayan K. Ibrahim

Theses and Dissertations

In this thesis, we explore four projects. In the first project, we explore $r$-neighbor bootstrap percolation on a graph $G$. We establish upper bounds for the number of vertices required to percolate in the case that $r=2$ for particular classes of graphs. In the second project, we study the structure of graphs with independence number two. We prove a lower bound on the number of edges of such graphs, related to an upper bound on the number of edges in a triangle-saturated graph, and give a sufficient forbidden induced subgraph condition for independence number two graphs. In the third project, …

Torricelli's Law And The Turn-Up Number, Bianca K. Hampel

Theses and Dissertations

We investigate Torricelli's differential law for solids of revolution. Computing the ratio of times of drainage under the same circumstances (same existing requirements) but rotating the solids 180 degrees allows us to define a "Torricelli turn-up number" associated with the solid. For various solids, we calculate this turn-up number and construct solids that are not symmetric under the 180-degree rotation but with a turn-up number of 1. That allows us to construct nonsymmetric clepsydra.

A Corona Theorem For Multipliers On The Dirichlet Space, Alea Wittig

Electronic Theses & Dissertations (2024 - present)

An analogue to Wolff's ideal problem for the multiplier algebra of the Dirichlet space, the main theorem provides sufficient conditions to classify membership of an arbitrary function in an infinitely generated ideal of the multiplier algebra.

Random Forests Regression For Soft Interval Data, Paul Gaona-Partida, Chih-Ching Yeh, Yan Sun, Adele Cutler

Mathematics and Statistics Faculty Publications

Analyzing soft interval data for uncertainty quantification has attracted much attention recently. Within this context, regression methods for interval data have been extensively studied. As most existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and the development of nonlinear regression tools for interval data is crucial. This paper proposes an interval-valued random forests model that defines the splitting criterion of variance reduction based on an L₂ type metric in the space of compact intervals. The model simultaneously considers the centers and ranges of the interval data as …

On The Structure Of Repeated-Root Polycyclic Codes Over Local Rings, Maryam Bajalan, Edgar Martinez-Moro, Reza Sobhani, Steve Szabo, Guelsuem Goezde Yilmazguc

EKU Faculty and Staff Scholarship

This paper provides the Generalized Mattson Solomon polynomial for repeated-root polycyclic codes over local rings that gives an explicit decomposition of them in terms of idempotents. It also states some structural properties of repeated-root polycyclic codes over finite fields in terms of matrix product codes. Both approaches provide a description of the perpendicular to 0-dual code for a given polycyclic code. (c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Paley Graphs, Prime Graphs, And Crossword Puzzles, Robert D. Jacobs Jr.

Theses and Dissertations

In this paper, we will talk about many different mathematical concepts. We will prove theorems about Paley graphs, prime graphs, and crossword puzzles. It will be very fun.

The results in the section about Paley graphs include structure theorems about the subgraph induced by the quadratic residues, the subgraph induced by the non-residues and a few related subgraphs. The main is to better understand the “independence structure” of the Paley graph itself. No good upper bound on the independence number of Paley graphs is known. Theorems about these subgraphs, and various counts aim at future improvement of upper bounds for …

Gwid: An R Package And Shiny Application For Genome-Wide Analysis Of Ibd Data, Soroush Mahmoudiandehkordi, Mehdi Maadooliat, Steven J. Schrodi

Mathematical and Statistical Science Faculty Research and Publications

Summary

Genome-wide identity by descent (gwid) is an R package developed for the analysis of identity-by-descent (IBD) data pertaining to dichotomous traits. This package offers a set of tools to assess differential IBD levels for the two states of a binary trait, yielding informative and meaningful results. Furthermore, it provides convenient functions to visualize the outcomes of these analyses, enhancing the interpretability and accessibility of the results. To assess the performance of the package, we conducted an evaluation using real genotype data derived from the SNPs to investigate rheumatoid arthritis susceptibility from the Marshfield Clinic Personalized Medicine Research Project.

Availability …

A Journey From Univariate To Multivariate Functional Time Series: A Comprehensive Review, Hossein Haghbin, Mehdi Maadooliat

Mathematical and Statistical Science Faculty Research and Publications

Functional time series (FTS) analysis has emerged as a potent framework for modeling and forecasting time-dependent data with functional attributes. In this comprehensive review, we navigate through the intricate landscape of FTS methodologies, meticulously surveying the core principles of univariate FTS and delving into the nuances of multivariate FTS. The journey commences with an exploration of the foundational aspects of univariate FTS analysis. We delve into representation, estimation, and modeling, spotlighting the effectiveness of various parametric and nonparametric models at our disposal. The stage then transitions to multivariate FTS analysis, where we confront the intricacies posed by high-dimensional data. We …

Integrable Symplectic Maps With A Polygon Tessellation, T. Zolkin, Y. Kharkov, S. Nagaitsev

Physics Faculty Publications

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this …

Mixed Mechanisms Of Multi-Site Phosphorylation, Suha Jayyousi Dajani

Graduate Research Theses & Dissertations

Multi-site phosphorylation is an important mechanism in cell biology that regulates protein function and activity. It also plays a critical role in a wide variety of cellular processes that control intra-cellular signaling. Studies on mono- and dual-site phosphorylation have been conducted theoretically and experimentally by researchers. However, there is little research on triple-site and multi-site mixed mechanism phosphorylation.

The aim of this research is to study and identify the number of positive steady states (multistationarity) in a mathematical model of a triple-site mixed mechanism, processive and distributive, phosphorylation network. This research is accomplished by means of ordinary differential equations, Jacobian …

Univariate Extreme Value Analysis Of Quantitative Investment Management, George Agbenyega Zumanu

Graduate Research Theses & Dissertations

The evolution of product development within the variable annuity (VA) business have sparked interest in quantitative investment management, particularly as most VA issuers have integrated volatility-controlled funds into their annuity portfolios. Despite the existence of empirical research on statistical analysis of extreme values in conventional investments, there has been a notable gap in research focus towards risk modeling in volatility-controlled funds.

This study contributes by analyzing and modeling the extreme values of investments in volatility-controlled funds, comparing them to conventional equity funds. The financial returns of S&P Dow Jones Indices (SPDJI) indices - SPXTR, risk control SPXT18UT, and managed risk …

Explicit Proximal Gradient Methods: Bridging Theory And Practice In Optimization, Cassandra Mohr

Graduate Research Theses & Dissertations

Convex optimization problems are central to numerous fields, including machine learning, signal processing, and image reconstruction. The development and analysis of algorithms for solving splitting optimization problems constitutes a significant area of research. In particular, we investigate a proximal gradient splitting method (PGM) with an explicit linesearch for finding the solution of nonsmooth optimization problems, where the objective function is the sum of two convex functions.

We focus on cases where one of the functions is differentiable, without imposing any Lipschitz continuity assumption on its gradient. We establish the proper definition of the linesearch, and demonstrate that this version of …

Julia Limiting Directions Of Quasiregular Maps, Julie Marie Steranka

Graduate Research Theses & Dissertations

In this dissertation, we study the set of Julia limiting directions of quasiregular maps. The work combines the study of dynamics of quasiregular maps and applications of nonlinear potential theory to quasiregular maps. Our main result shows that the set of Julia limiting directions of a transcendental-type $K$-quasiregular map $f:\R^n\to \R^n$ must contain a component of a certain measure, depending on the dimension $n$, the maximal dilatation $K$, and the order of growth of $f$. In particular, we show that if the order of growth is small enough, then every direction is a Julia limiting direction. The main tool in …

Explicitly Counting Subspaces Of Given Height Defined Over A Field Of Rational Functions, Kakoli Bhuyan

Graduate Research Theses & Dissertations

A height function measures the complexity of mathematical objects, usually points on some projective variety. There are previous results that estimate the number of subspaces of bounded height defined over number fields and function fields over a finite field. These results are asymptotic estimates as the height bound tends to infinity. In this dissertation we derive an explicit counting of the number of subspaces of given height defined over a field of rational functions.

Snow Spheres And Ice Cubes, John Adam

Mathematics & Statistics Faculty Publications

This article, titled "Snow spheres and ice cubes," discusses the melting of snowballs and ice cubes. It explains that in standard calculus textbooks, it is shown that a snowball melting at a rate proportional to its surface area will have its radius decrease at a constant rate, assuming it remains spherical as it melts. The article then poses several questions related to this concept, including the proportion of a smaller snow sphere that remains when half of a larger one has melted, the value of p for which the smaller sphere first melts, and the volume reduction factor for cubes …

Preface, Mohamed Mahdi Tekitek, Manfred Krafczyk, Li-Shi Luo

Mathematics & Statistics Faculty Publications

[Introduction] Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications, a macroscopic or continuum description has usually been sufficient due to the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic …