Mathematics Commons^™

Algebraic Properties Of Boolean Models, Harrison Fisher

All Theses

Boolean models are n-tuples of polynomial functions in n variables over the finite field of order 2. These models define finite dynamical systems which are used for modeling many different biological systems such as gene regulatory networks. These systems can be defined by updating every function synchronously, or by updating one function at a time asynchronously. In this project, we discuss a method for reverse engineering the model space of all Boolean models which fit a set of partial asynchronous data. This method is a generalization of a known method for synchronous data. In addition, we show that given the …

Constructing Binary Encoding Matrices From Joined Graphs, Joshua Avalos

Electronic Theses, Projects, and Dissertations

Codes and technology are part of our daily lives and allow the modern world to function, and for us to have conveniences in our lives such as smartphones that can be used to privately call people on the other side of the planet, and for secure access to the internet. In this thesis we will explore the construction of binary codes created by vertex-edge incidence matrices of planar graphs. The Hamming (7,4) code was an incredible code that allowed the detection and correction of errors after receiving them through a transmission. We will explore the possibility of the creation of …

Efficient Fully Bayesian Approach To Brain Activity Mapping With Complex-Valued Fmri Data, Zhengxin Wang, Daniel B. Rowe, Xinyi Li, D. Andrew Brown

Mathematical and Statistical Science Faculty Research and Publications

Functional magnetic resonance imaging (fMRI) enables indirect detection of brain activity changes via the blood-oxygen-level-dependent (BOLD) signal. Conventional analysis methods mainly rely on the real-valued magnitude of these signals. In contrast, research suggests that analyzing both real and imaginary components of the complex-valued fMRI (cv-fMRI) signal provides a more holistic approach that can increase power to detect neuronal activation. We propose a fully Bayesian model for brain activity mapping with cv-fMRI data. Our model accommodates temporal and spatial dynamics. Additionally, we propose a computationally efficient sampling algorithm, which enhances processing speed through image partitioning. Our approach is shown to be …

The Food Truck: A Multi-Product Newsvendor With Trans-Shipment Cost, Samuel Ajibola

Electronic Theses and Dissertations

The Newsvendor Problem is a key model in supply chain management that focuses on determining the optimal order quantity to minimize costs under uncertain demand. This thesis introduces the Food Truck Problem, an extension of the Newsvendor model that incorporates nonlinear transshipment costs for inventory transportation. In this context, a Food Truck must determine the optimal stock levels for multiple products while minimizing costs related to stock shortages, excess inventory, and transportation. Unlike traditional Newsvendor models, our approach explicitly considers a quadratic transshipment cost, which necessitates the use of Lagrangian duality and Karush-Kuhn-Tucker (KKT) conditions for analysis. Moreover, we apply …

2-Segal Sets And Pseudomonoids In The Bicategory Of Spans, Sophia E. Marx, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

In this survey article, we give an introduction to the notion of a 2-Segal set and prove that 2-Segal sets are equivalent to pseudomonoids in the bicategory of spans. The proof utilizes graphical techniques for 2-Segal sets and spans that should be useful in more general settings.
There are procedures for obtaining an associative algebra from a 2-Segal set (satisfying finiteness conditions). We describe these procedures and give several examples of algebras arising from 2-Segal sets.
Wherever possible, we avoid higher category theory so as to make the paper accessible to a wide audience.

A Numerical Study Of Self-Assembling Amphiphilic Systems, Joshua Albert Sackey

Open Access Theses & Dissertations

Mixing processes in ternary mixtures involve immiscible fluids such as oil and water, and a surface-active molecule called surfactant. These physical processes find applications in various fields, including enhanced oil recovery, drug delivery design systems, and the formulation of cleaning products. Even though this process has several applications, the mathematical models describing it and the numerical methods solving it are not well understood. The underlying mathematical model is a nonlinear initial-boundary value problem involving sixth-order derivatives and belongs to the class of sixth-order Cahn-Hilliard equations. Authors Sharma and Tierra recently proposed a numerical method to approximate its solutions in two …

Equity Vs. Excellence: Dichotomy Or Duo?, Nadjia I. Logans

Honors Program: Senior Projects (Public)

In this thesis, I investigate recent changes in mathematics education and how these developments connect to the principles of equity and excellence. I place a special focus on “active learning” methods. My methodology primarily consisted of interviews with educators, along with analyzing literature from math education researchers. I first define and explain the motivations behind active learning instruction methods. Next, I explore not only how instructors define equity and excellence but how educators perceive the role of the two principles within education. Finally, I challenge the pervasive media portrayal of equity and excellence as being mutually exclusive. Instead, I find …

Culture And Context: How Frames Of Teaching And Of Learning Mathematics Form And Change For Graduate Student Instructors, Johan Benedict Arroyo Cristobal

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

Why do instructors teach the way that they do? This question is key in understanding how and why asset-based or deficit-based practices are enacted in the classroom. In consequence, this question also gives insight into how the environment where students learn is shaped. Mathematics education research, in particular, has been concerned with how instructors respond to students’ contributions in the classroom and how these ways of responding can (dis)empower students.

One way to answer this question is to understand how instructors frame their own teaching and their students’ learning. Frames are mental constructs which help individuals filter details, interpret information, …

Countering Deficit Narratives Through A Blackcrit Lens By Examining Case Studies Of Black College Mathematics Students’ Classroom Experiences, Akhenaton Wilbourn

All Dissertations

This dissertation examines the lived experiences of 11 Black college mathematics students at their predominantly white institution (PWI) through the lens of Black Critical Theory (BlackCrit) to counter deficit narratives about the racial achievement gap (RAG) in mathematics education courses. Deficit narratives often attribute disparities between Black and white students’ mathematical performance to assumed deficiencies in Black students’ abilities rather than systemic inequities, historical marginalization, and ongoing anti-Blackness in educational settings (Cobb & Russell, 2015; Kress, 2021). Using multiple case studies, this study explores how anti-Blackness manifests in mathematics classrooms, how students navigate tensions between multiculturalism, neoliberal educational policies, and …

The Impact Of Corporate Profits On Gdi Estimates: Forecasting And Data Revisions, Peterson Haas

Honors Theses

The National Income and Product Accounts (NIPAs) produced by the U.S. Bureau of Economic Analysis (BEA) provide key measures of U.S. economic activity, including gross domestic product (GDP) and gross domestic income (GDI). Although conceptually equivalent, GDP and GDI often diverge due to differences in source data and revision timing. This study focuses on corporate profits—a small but volatile component of GDI that is frequently revised, especially during the BEA’s annual (A1) and benchmark (C1) revisions. I examine how revisions to corporate profits influence GDI revisions and whether they can improve real-time estimates of GDI. First, I document the size …

Ritt’S Theorem And The Chebyshev Polynomials, Eric Neuhaus

Honors Theses

We explore polynomial composition through Ritt’s Theorem and mondromy groups. J.F. Ritt asked the question of when a polynomial can be written as the composition of two other polynomials of smaller, nontrivial degree. Ritt’s Theorem provides a method for determining whether or not a polynomial is composite by observing the actions of its associated monodromy group, a group of permutations acting upon the roots of a given polynomial. In this work, we study the monodromy groups of the Chebyshev polynomials of the first and second kinds to uncover their compositional properties.

A Dg-Algebra Structure With Divided Powers On The Generalized Taylor Resolution, Raul F, Alvarez

Theses and Dissertations

This thesis investigates the construction of a DG Γ-algebra structure on the Generalized Taylor Resolution (GTR) associated with monomial ideals. The classical Taylor resolution is known for providing a free but generally non-minimal resolution, leading to computational challenges and inefficiencies in algebraic analysis. In contrast, the GTR preserves essential algebraic structures while optimizing the resolution process, offering a more efficient and comprehensive framework for studying monomial ideals.

We introduce a novel DG Γ-structure that incorporates divided powers into the GTR, enhancing its multiplicative and homological properties. This structure preserves strict graded commutativity and is fully compatible with the differential graded …

Graph Codes, Jacquelyn Franqui

Theses, Dissertations and Culminating Projects

The concept of graph codes, introduced in recent work by Alon, applies coding theory to graphs by defining codewords as graphs and measuring distances between them through structural differences. In ordinary coding theory, the distance between two words is the number of positions in which the two words differ. In graph codes, each word is a graph and the distance between two graphs is measured by structural properties of their difference. For a fixed graph H, an H-code is a collection F of graphs on vertex set [n] = {1, 2, . . . , n} such that the symmetric …

Car Price Prediction Using Machine Learning: Analyzing The Dvm-Car Dataset, Yaman Abu Ghareebaih

Electronic Theses and Dissertations

The objective of this study is to predict car prices using machine learning models and the DVM-CAR dataset, which includes over 1.4 million images and car specifi- cations from 899 car models. Key factors such as mileage, engine power, and year of registration were analyzed for their correlation with car prices. Extensive data cleaning was performed, including filling missing values, identifying outliers, and normalizing numerical variables. Discrete variables like car make and body type were encoded using one-hot encoding. Linear relationships were analyzed with Multiple Logistic Regression, and Random Forest models were used for nonlinear patterns. Model performance was evaluated …

Koszul Cohomology Of Canonical Products, Alexander Scott Duncan

Graduate Theses and Dissertations

In this thesis, we give a complete classification of the Koszul cohomology groups K_p,₁(C, B, ω_C ⊗ B) on a smooth curve C of genus g ≥ 2 with B p-very ample. Such a classification in the case B = ω_C has been incomplete until [5]. The classification follows easily from our main result which precisely calculates K_p,1(C, B, B ω_C ⊗ B) in terms of h⁰(C, B). This result also handles the case B = ω_C. A straightforward …

Reuben Hersh's What Is Mathematics, Really? (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reuben Hersh’s 1997 book What is Mathematics, Really? popularized a trend in the philosophy of mathematics that was gaining some traction at the time it was written. This essay examines Hersh’s work within the broader historical context of 19th- and 20th-century developments in mathematics and philosophy of mathematics. It also focuses on Hersh’s antagonism toward the influence of religion on (philosophy of) mathematics, concluding by briefly considering two positions taken by Christian mathematicians associated with ACMS in defense of such a connection.

Bibliography Of Christianity And Mathematics Update, Calvin Jongsma

Faculty Work Comprehensive List

This was a banquet talk given at the Twenty-fourth Biennial Conference of the Association of Christians in the Mathematical Sciences held at Dordt University on May 28-June 1, 2024.

It provides an update on the progress being made in the author’s project of producing a second edition of Bibliography of Christianity and Mathematics. This work is now being developed as a Zotero database with a slightly broader focus on Religious Faith and the Mathematical Sciences and with a much expanded list of books, articles, and blog posts on the topic. The author hopes to make the database public sometime …

Setting Up Students For Success: Analysis Of Effectiveness For Mathematics Placement, Jeff Carvell, Jason N.E. Ho, Dave Klanderman, Sarah Klanderman

Faculty Work Comprehensive List

How do we effectively and equitably place students into math classes in a way that provides them the best chance of success? As many higher education institutions veer away from placement based on standardized testing, many departments are seeking placement alternatives that will properly support students. Additionally, math placement determines not only a student’s mathematics courses but also influences their progress in related fields, including physics, chemistry, engineering, and more. This paper will describe three different existing placement systems at each of our liberal arts institutions as well as the affordances and constraints of each approach. Further, we analyze data …

Relaxation Maximum-Based Iteration Method For Solving The Generalized Absolute Value Equation, Ximing Fang, Zhidong Wang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The generalized absolute value equation (GAVE) has wide applications in scientific computing. Establishing a high performance computing method to solve the GAVE is a hot research topic in recent years. In this paper, with the aid of the maximum function, the GAVE is decomposed of two equations, and then we present the relaxation maximum-based (RM) iteration method. To see the feasibility of the method, we discuss the necessary and sufficient conditions for the GAVE to have a unique solution. Next, the convergence analysis of the RM iteration is discussed under some convergence conditions. Moreover, some numerical examples of low and …

The Improved New Intersection Theorem Revisited, Lars Winther, Luigi Ferraro

School of Mathematical & Statistical Sciences Faculty Publications

We prove a generalized version of Evans and Griffith’s improved new intersection theorem: Let I be an ideal in a local ring R. If a finite free R-complex, concentrated in nonnegative degrees, has I-torsion homology in positive degrees, and the homology in degree 0 has an I-torsion minimal generator, then the length of the complex is at least dimR−dimR/I. This improves the bound htI obtained by Avramov, Iyengar, and Neeman in 2018.

Yield Prediction Of Pv Solar Energy Systems And Its Application In The Energy Grid For Operational Efficiency, Pablo Bustamante

Open Access Theses & Dissertations

The generation of power from photovoltaic (PV) solar panels is influenced by a multitude of factors. These include the tilt and orientation of the solar panels, the latitude of their location, and the prevailing climate and weather conditions. Additionally, shading at specific locations, particularly if the panels are not part of a solar facility, can significantly impact their efficiency. The quality and efficiency of the panels themselves, along with the preventive maintenance of both the solar panels and associated components such as inverters and trackers, are also critical. Finally, the overall system design and installation play a vital role in …

Multiscale Integration Of Receptor-Ligand Dynamics Into Discrete And Continuous Tumor Growth Models With Application To Tyrosine Kinase Inhibitor Treatment, Romasa Qasim

Open Access Theses & Dissertations

The epidermal growth factor (EGF) receptor cascade plays a crucial role in the survival and proliferation of tumor cells. Tyrosine kinase inhibitors (TKIs) are a class of drugs that inhibit epidermal growth factor receptors (EGFRs), thereby preventing the downstream signal transduction. Despite their importance, models that link spatial receptor dynamics to tumor growth remain scarce. Further, TKIs act through selective mechanisms, inhibiting active, inactive, or all receptor states, which poses a challenge to traditional modeling approaches.

We propose to numerically study two mathematical models incorporating receptor-dynamics into cancer models to describe the impact of EGFR overexpression and TKIs. The first …

Stochastic Analysis With Operational Calculus In Reliability, Hend Hamdan Al-Jahani

Theses and Dissertations

Our dissertation models several reliability systems subject to occasional random shocks of random magnitudes W1,W2,..occurring at times tau0, tau2,..In Model 1, the underlying system becomes inoperational if it wears out due to aging specified by a monotone increasing continuous function Delta identifying system's wear at any time t>=0 . The system is deemed inoperational if delta crosses a sustainability threshold at some moment T=(delta )^-1(D). The precise time T is difficult to identify making the realistic failure time randomly delayed and thus identified at some opportune observation epoch. The system can also fail due to damages by external shocks, …

Math Course Placement Models At Csbsju Using Data Analysis, Josephine Jackson

Celebrating Scholarship and Creativity Day (2018-)

Many majors at the College of Saint Benedict and Saint John’s University (CSBSJU) require students to complete a course in calculus or statistics, however incoming students have various levels of preparation for these courses. This research investigates strategies for predicting student success in these courses and potential recommendations for remediation courses, e.g., pre-calculus or pre-statistics. The research uses data analysis to make this determination based on their previous math coursework and other data incoming students provide. Trends for success in math classes at CSBSJU have previously been based on outdated and inequitable methods. This project identifies correlations between prior coursework …

Analysis And Derivation Of The Compressible Euler System With Nonlinear Velocity Alignment: An Investigation Into Collective Behavior, Mckenzie Meredith Black

Theses and Dissertations

Collective behavior refers to the observable patterns, actions, or movements that emerge within a group of entities, such as individuals, animals, or particles, when they interact with each other. In this study, we concentrate on the pressureless compressible Euler system, expanding it to incorporate a family of nonlinear velocity alignment. This extension represents a nonlinear iteration of the Euler-alignment system within collective dynamics, revealing intriguing asymptotic emergent phenomena such as alignment and flocking. Our investigation explores different types of nonlinearity and nonlocal communication protocols, unveiling a diverse spectrum of asymptotic behaviors within the system.

In focusing on the derivation, we …

Generation And Dimension For Derived Categories, Pat Lank

Theses and Dissertations

This work focuses on problems regarding derived categories arising in algebraic geometry and commutative algebra. There are six chapters regarding generation in the bounded derived category of coherent sheaves over a Noetherian scheme. The targeted topics involve explicitly identifying generators, proving existence results thereof, and producing estimates on Rouquier dimension.

Symmetries Of Del Pezzo Surfaces, Jonathan Smith

Theses and Dissertations

For each del Pezzo surface X of degree d, the action of the automorphism group Aut(X) on the exceptional curves of X induces a map ρ : Aut(X) → W(R_d), where W(R_d) is the Weyl group of a root system R_d dependent on the degree of X. The image of ρ is well defined up to conjugacy in W(R_d), so we say that a group G acts by automorphisms on a del Pezzo surface X of degree d if a representative of the …

On Finite Groups With Essential Dimension 2 Over ℚ, Michael Huggins

Theses and Dissertations

We determine all finite subgroups of Aut(X) which have essential dimension 2 over ℚ, where X is a minimal Del Pezzo surface of degree at least 5. Additionally, finite groups with essential dimension 2 whose order is divisible only by the prime numbers 2 and 3 are classified with the exception of the groups dic ₁₂ , C₁₂, and Dih₂₄, whose essential dimensions remain unknown, but may possibly be equal to 2.

Generalized Sierpiński Numbers And New Irreducibility Criteria On Legendre Polynomials, Robert Scottfield Groth

Theses and Dissertations

A Sierpiński number is an odd positive integer k such that k·2n +1 is composite for all n ∈ Z+. Similarly, a Riesel number is an odd positive integer k such that k · 2n − 1 is composite for all n ∈ Z+, and a Brier number is a number that is both Sierpiński and Riesel. In this dissertation, we consider a generalization of a Sierpiński number and establish their existence by showing, for every fixed A ≥ 2, there are infinitely many odd positive integers k such that the k · an + 1 is composite for every …

Supershift Properties For Nonanalytic Signals, Fabrizio Colombo, Irene Sabadini, Daniele Carlo Struppa, Alain Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

The phenomenon of superoscillations is of great interest in microscopy, antenna design, and material sciences. This phenomenon has been generalized and has given rise to the concept of supershift, which is a far reaching extension that applies to functions that may present discontinuous derivatives. From this perspective, this is a notion that might have significant applications. This paper will provide an up to date report on the complex connections between the concept of supershift and that of analyticity.