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Torus Surgery, Fibrations, Multisections, And Spun 4-Manifolds, Nicholas Paul Meyer

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

A compact n-manifold X is fibered if it is a fiber bundle where the fiber F and base space B are manifolds. Fibered manifolds are particularly nice, as they are essentially classified by their monodromy maps. Two common examples of 4-dimensional fibered manifolds are surface bundles over surfaces and 3-manifold bundles over the circle.

The main focus of this dissertation is to investigate fibered 4-manifolds whose boundaries are the 3-torus and how these manifolds glue together to give new closed, fibered 4-manifolds. In particular, suppose W is diffeomorphic to S¹ × E_Y (K) where Y …

On Laudenbach-Type Exact Sequences, Jorge Andres Robinson Arrieta

Graduate Theses and Dissertations

Laudenbach proved that the mapping class group of the connected sum of $n$ copies of $S^2 \times S^1$ is an extension of $\text{Out}(F_n)$ by a finite group. Brendle, Broaddus and Putman proved that this exact sequence splits. We provide an explicit section $s$ of this split exact sequence. Given a locally finite graph $\Gamma$, Udall proved that the mapping class group of the doubled handlebody associated to $\Gamma$ is an extension of $\map(\Gamma)$ by a possibly infinite direct product of $\Z_2$, and proved that this exact sequence splits. We provide an explicit formula for this section $s$ of $\Psi$ restricted …

A Portable Numerical Library For The Calculation Of Multi-Dimensional Integrals, Ioannis Sakiotis

Computer Science Theses & Dissertations

Multi-dimensional numerical integration is a prevalent task in physics and other scientific fields, e.g., in the simulation of particle-beam dynamics and Bayesian parameter estimation. Scientific computing applications that simulate complex phenomena may require the solution to numerous multi-variate integrals. However, functions that have features such as sharp peaks or oscillations in high dimensional spaces, can result in an exorbitant number of computations. For many cases, convergence to accurate results in a reasonable amount of time is infeasible with existing numerical libraries. One approach towards making multi-dimensional integration viable is to parallelize existing algorithms. No commonly available algorithms or libraries exist …

Parallel-In-Time Implicit Schemes For Nonlinear Pdes, Subhash Paudel

Mathematics & Statistics Theses & Dissertations

An accurate prediction of unsteady physical phenomena arising in various applications (e.g., rotorcraft and turbomachinery flows, fluid-structure interaction, maneuvering flight conditions, etc.) requires a very large number of time steps, thus considerably increasing the total computational time, because conventional time integrators are inherently sequential. Parallel-in-time methods offer a promising direction for drastically reducing the computational time and achieving such scalability that is required for solving these unsteady problems on modern supercomputers with hundreds of thousands of computing cores. The parallel performance of existing parallel-in-time algorithms for nonlinear equations especially of the hyperbolic or mixed type is far from being satisfactory. …

Using Chatgpt As A Thought Partner In Writing Relevant Proportional Reasoning Word Problems, Andrea Berryhill, Lendon Chandler, Liza Bondurant, Bima Sapkota

School of Mathematical & Statistical Sciences Faculty Publications

In this article, we, two preservice mathematics teachers (PSTs) and two mathematics teacher educators (MTEs), explore the potential of using ChatGPT, a large language model (LLM), as a thought partner to create relevant proportional reasoning word problems. We detail our iterative process of refining our inputs and critically evaluating ChatGPT's outputs. Our takeaways from this journey offer valuable insights for educators seeking to leverage the capabilities of LLMs in their lesson-planning endeavors.

On Angles In Higher Order Brillouin Tessellations And Related Tilings In The Plane, Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss, Morteza Saghafian

School of Mathematical & Statistical Sciences Faculty Publications

For a locally finite set in R 2 , the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R 2 is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in …

Bivariate Polynomials Of Low Degree And Small Mahler Measure, Souad El Otmani

BAU Journal - Science and Technology

In this work, we highlight that many of the known limit points of the Mahler measure of univariate polynomials can be obtained as the Mahler measure of low-degree bivariate polynomials. To this end, we provide for each relevant measure the corresponding original bivariate polynomial found in the literature, along with the corresponding low-degree polynomial with an analogous measure.

Problem-Based Learning Model Assisted With A Humanistic-Merdeka Belajar Approach Improved Biology Students’ Learning Ownership, Dita Tri Mulyani, Dwi Listyorini

Jurnal Pendidikan Sains

Fostering ownership over learning constitutes a pivotal aspect for students to cultivate a comprehensive understanding, employ cognitive strategies effectively, hone essential skills, and refine learning methodologies. Preliminary studies have underscored a prevalent deficiency in the learning ownership among biology students, categorizing it as notably low. The purpose of this study is to ascertain the effect of the Project Based Learning (PBL) model assisted with a Humanistic-Merdeka Belajar (HMB) approach, in nurturing students’ ownership of their learning endeavors. Employing a quasi-experimental design, the research adopts a pre-test post-test non-equivalent control group configuration, administered both prior to and following the intervention within …

Asistensi Mengajar (Am) Program In Merdeka Belajar Kampus Merdeka (Mbkm) As A Pedagogical Mastery Accelerator For Vocational High School Teacher Candidates, Muhammad Idris Effendi, Yoto Yoto, Widiyanti Widiyanti

Jurnal Pendidikan Sains

This research delves into the issue of inadequate pedagogical proficiency among vocational high school (SMK) teacher candidates, primarily stemming from the constrained timeframe of educational internships, typically spanning a mere two months. As an option, this study suggests the implementation of an Asistensi Mengajar (AM) initiative within the framework of the Merdeka Belajar Kampus Merdeka Program (MBKM), extending over a semester’s duration. Employing a literature review methodology, the research highlights that the brevity of conventional two-month internships poses a significant impediment to the development of pedagogical acumen among SMK teacher candidates. The proposed option entails an AM program under MBKM, …

Analysis Of Genetic Engineering Material Misconceptions In Biology Textbooks For Ninth-Grade In Yogyakarta, Silfi Pratiwi, Purwanti Pratiwi Purbosari, Oktira Roka Aji, Rinaldi Rizal Putra

Jurnal Pendidikan Sains

Textbooks play a pivotal role in the pedagogical landscape, serving as indispensable aids for learning, founts of knowledge, and platforms for practical application. This study endeavors to scrutinize the content of textbooks, specifically focusing on ninth-grade biology textbooks within the educational milieu of Yogyakarta City, and to juxtapose these contents with existing literature to discern potential misconceptions. Employing a descriptive qualitative approach, the investigation centers on printed biology textbooks utilized in ninth-grade curricula across junior high schools in Yogyakarta. The selection of textbooks for analysis was based on their prevalence as instructional materials, as determined through survey data. Genetic engineering …

Students’ Science Literacy On Discussion-Based Contextual Approaches Of Human Reproductive System Learning, Yeni Mulyaningsih, Chaerul Rochman, Adam Malik, Tri Wahyu Agustina, Yulia Sukmawardani, Nur Hamidah, Nurul Annisa

Jurnal Pendidikan Sains

The aim of this study was to enhance students’ science literacy through a discussion-based contextual approach in the learning of the human reproductive system. This quantitative research employed an experimental method with a quasi-experimental posttest-only design. The study involved 60 students, with 30 students each in class XI MIPA 4 serving as the experimental group and class XI MIPA 5 serving as the control group. The control group received instruction through a conceptual approach-based lecture method, whereas the experimental group engaged in learning through a contextual approach-based discussion method. The research instrument comprised 10 open-ended science literacy questions pertaining to …

Identify Resources Activated By Students When Solving Straight Motion Kinematics Problems With Different Representation, Nur Utami Amaliah, Sutopo Sutopo, Eny Latifah, Hutkemri Zulnaidi

Jurnal Pendidikan Sains

This research aims to explore kinematic resources in linear kinematics by utilizing different forms of problem representation. The study was conducted by administering 15 reasoned multiple-choice questions to 146 high school students from three districts in Central Sulawesi, Indonesia. The research instrument covers topics in linear kinematics, including distance, displacement, speed, and velocity, presented through diagrammatic representations, graphs, and mathematical equations. The students’ written answers were analyzed both quantitatively and qualitatively. Quantitative analysis was conducted to determine descriptive statistics from the data, while qualitative analysis identified the resources students activated when solving these questions. The findings reveal that the various …

Enhancing Tumor Classification Through Machine Learning Algorithms For Breast Cancer Diagnosis, Lawrence Agbota, Edmund F. Agyemang, Priscilla Kissi-Appiah, Lateef Moshood, Akua Osei- Nkwantabisa, Vincent Agbenyeavu, Abraham Nsiah, Augustina Adjei

School of Mathematical & Statistical Sciences Faculty Publications

In cancer diagnosis, machine learning helps improve cancer detection by providing doctors with a second perspective and allowing for faster and more accurate determination and decisions. Numerous studies have used both classic machine learning approaches and deep learning to address cancer classification. In this study, we examine the efficacy of five commonly used machine learning algorithms; both traditional and deep learning models namely, Logistic Regression, Support Vector Machines (SVM), Random Forest (RF), Decision Tree and Deep Neural Networks (DNN). We analyze their ability to properly classify tumors as Benign or Malignant using the Wisconsin breast cancer dataset (WBCD). Random Forest …

On The Size Of Maximal Binary Codes With 2, 3, And 4 Distances, Alexander Barg, Alexey Glazyrin, Wei-Jiun Kao, Ching-Yi Lai, Pin-Chieh Tseng, Wei-Hsuan Yu

School of Mathematical & Statistical Sciences Faculty Publications

We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths n≥6 as well as the exact size of maximal binary constant weight codes with 2, 3, and 4 distances for several values of the weight and for all but small lengths.

Some Problems In Harmonic Analysis, Anastasios Fragkos

Arts & Sciences Graduate Student Theses and Dissertations

One the most central questions in harmonic analysis of whether the Fourier series of a square integrable function on the torus $\mathbb T$ converges Lebesgue a.e.\ $ x\in\mathbb T$ was answered positively by L.\ Carleson in 1966 \cite{C}, by means of a weak-$L^2$ inequality for the maximal operator \begin{equation} \label{carleson0} \mathcal C f(x) =\sup_{N\in \mathbb Z} \Bigg| \sum_{|\xi|\leq N} \widehat f(\xi) \exp(ix\xi) \Bigg|, \qquad x\in \mathbb T. \end{equation} The argument of \cite{C} estimates $\mathcal C $ pointwise as a maximal modulated Hilbert transform, outside appropriately constructed exceptional sets whose mass is controlled by almost-orthogonality. The implicit distributional estimate in \cite{C} …

Post-Baccalaureate Research Experiences For Students At Two Hispanic-Serving Institutions (Experience), Dessaray Monique Gorbett, Benjamin C. Flores, Cristina Villalobos, Sara E. Rodriguez, Ariana (Ari) Arciero, Josef A. Sifuentes

School of Mathematical & Statistical Sciences Faculty Publications

This study examines the implementation of a one-year program that offered post-baccalaureate research experiences to a cohort of recent STEM graduates from two large Hispanic-serving institutions. Both institutions are collaborators in an NSF Louis Stokes Alliance for Minority Participation (LSAMP) grant, which is dedicated to enhancing the academic experience of historically underrepresented minorities. Applicants were either self-nominated or were nominated by faculty to participate in the post-baccalaureate program. Following an application process that included an interview, selected participants were matched to research faculty and committed to engage in a high-impact research project for at least one semester and for up …

A Note On Surfaces In ℂℙ² And ℂℙ²#ℂℙ², M. Marengon, Allison N. Miller, A. Ray, A. I. Stipsicz

Mathematics & Statistics Faculty Works

In this brief note, we investigate the ℂℙ²-genus of knots, i.e., the least genus of a smooth, compact, orientable surface in ℂℙ² \ \mathringB⁴ bounded by a knot in 𝑆³. We show that this quantity is unbounded, unlike its topological counterpart. We also investigate the ℂℙ²-genus of torus knots. We apply these results to improve the minimal genus bound for some homology classes in ℂℙ²#ℂℙ².

Laboratories In Mathematical Experimentation: A Bridge To Higher Mathematics, 2nd Edition, J. William Bruce, George Cobb, Giuliana Davidoff, Christopher Dugaw, Alan Durfee, Art M. Duval, Janice Gifford, Helmut Knaust, Donal O’Shea, Mark Peterson, Harriet Pollatsek, Margaret Robinson, Lester Senechal, Robert Weaver

Textbooks and Manuals Series

This second edition is composed of a set of sixteen laboratory investigations which allow the student to explore rich and diverse ideas and concepts in mathematics. The approach is hands-on and experimental, an approach that is very much in the spirit of modern pedagogy. The course is typically offered in one semester, at the sophomore (second year) level of college. It requires prior exposure to calculus and provides a transition to the study of higher, abstract mathematics. Most of the laboratories require the use of a computer for experimentation, but the text is written independent of any particular software.

Note …

Stochastic Analytical Predictive Models For Life Sciences And Crop Production Process, Erasmus Tetteh-Bator

USF Tampa Graduate Theses and Dissertations

Analytical predictive modeling uses algorithm-based mathematical, probabilistic and statistical methods to anticipate future events by identifying patterns in past data. It is a technique for predicting outcomes and a key application of statistical analysis in real-world scenarios. Real data-driven predictive models in various fields, such as life sciences, economics,or production industry, help individuals and institutions make data-driven informed decisions, which is essential for business success, providing companies with a competitive edge.

One of every five adult deaths is caused by heart disease and one person dies every 33 from cardiovascular disease in the United States according to the Center for …

Mathematical Modeling Of Tumor Response Dynamics To Predict Progression-Free Survival In Patients With Recurrent High-Grade Glioma, Daniel James Glazar

USF Tampa Graduate Theses and Dissertations

In this dissertation, I aim to develop a mathematical model describing tumor volume response dynamics to perform individual dynamic predictions of progression-free survival (PFS) on patients with recurrent high-grade glioma (rHGG).

Patients with rHGG have a dismal prognosis with median overall survival (OS) of <12 months and median PFS of <7 months. However, there is a wide heterogeneity in treatment responses. Therefore, to aid clinicians with making decisions to alter therapeutic protocol, I would like to predict patient-specific PFS.

To perform individual dynamic predictions, I employ the Claret tumor growth inhibition (TGI) model. I further develop this model by coupling it with two different survival models. Inter-patient heterogeneity is also taken into account through mixed effects, including covariate effects. Model PFS predictions were evaluated using receiver operating characteristic (ROC) curve analysis as well as Brier …

Bounds For The Regularity Radius Of Delone Sets, Nikolay Dolbilin, Alexey Garber, Egon Schulte, Marjorie Senechal

School of Mathematical & Statistical Sciences Faculty Publications

Delone sets are discrete point sets X in Rd characterized by parameters (r, R), where (usually) 2r is the smallest inter-point distance of X, and R is the radius of a largest “empty ball” that can be inserted into the interstices of X. The regularity radius ρ^d is defined as the smallest positive number ρ such that each Delone set with congruent clusters of radius ρ is a regular system, that is, a point orbit under a crystallographic group. We discuss two conjectures on the growth behavior of the regularity radius. Our “Weak Conjecture” states that ρ^d=O(d2log2d)R as d→∞ , …

Optimal Selection Of Good Polynomials And Constructions Of Locally Recoverable Codes Via Galois Theory, Austin Dukes

USF Tampa Graduate Theses and Dissertations

To keep up with the ever-growing demand for reliable and efficient availability of data,locally recoverable codes (LRCs) have been the focus of much study due to their applications in cloud and distributed storage systems. A fundamental construction of LRCs was given in [36] based on polynomials which relied on the existence of r-good polynomials. In the same paper some constructions of good polynomials were given, but these constructions did not cover every configuration of parameters. Naturally this led to research into constructing good polynomials for what was not addressed in [36], but new ponderings were also posed, such as the …

Supplementary Files For "Using Digitized Building And Weather Records To Improve The Accuracy Of Ground To Roof Snow Load Ratio Estimations", Gideon Parry, Brennan Bean

Browse all Datasets

Reliability targeted snow loads (RTLs) measure the weight in accumulated snow (i.e. snow load) that a roof is required to support to ensure the probability of failure is suf- ficiently low. This calculation has historically relied upon a probability distribution that characterizes the ratio between the annual maximum ground snow load to the annual max- imum roof snow load, a quantity referred to as Gr. The best available data for estimating Gr comes from Canadian case studies from the 1950s and 1960s. However, much of the data was never digitized, with only approximations of data being made available in scanned …

Numerical Issues For A Non-Autonomous Logistic Model, Marina Mancuso, Kaitlyn M. Martinez, Carrie Manore, Fabio Milner

CODEE Journal

The user-friendly aspects of standardized, built-in numerical solvers in
computational software aid in the simulations of many problems solved using
differential equations. The tendency to trust output from built-in numerical
solvers may stem from their ease-of-use or the user’s unfamiliarity with the
inner workings of the numerical methods. Here, we show a case where the
most frequently used and trusted built-in numerical methods in Python’s
SciPy library produce incorrect, inconsistent, and even unstable approxima-
tions for a the non-autonomous logistic equation, which is used to model
biological phenomena across a variety of disciplines. Some of the most com-
monly used …

Cellular Automata Modeling Approach Of Addiction, Ruba Hameed

Thesis/ Dissertation Defenses

This thesis develops a mathematical model and cellular automata simulations to study the spread of drug addiction in populations, incorporating key factors like peer influence, substance availability, support networks, and awareness campaigns. The model describes transitions between non-use, experimental use, recreational use, and addiction states. Mathematical analysis establishes model properties, while an irregular graph cellular automata framework analyzes emerging spatial patterns and behaviors. Extensive scenario simulations explore peer influence, isolation, substance availability, support networks, and awareness campaign impacts, enabling visualization of model evolution over time and determining thresholds, tipping points, and intervention effectiveness. The findings provide an actionable understanding of …

Mixed Uncertainty Analysis On Pumping By Peristaltic Hearts Using Dempster-Shafer Theory, Yanyan He, Nicholas A. Battista, Lindsay D. Waldrop

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster–Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief …

Combinatorial Problems On The Integers: Colorings, Games, And Permutations, Collier Gaiser

Electronic Theses and Dissertations

This dissertation consists of several combinatorial problems on the integers. These problems fit inside the areas of extremal combinatorics and enumerative combinatorics.

We first study monochromatic solutions to equations when integers are colored with finitely many colors in Chapter 2. By looking at subsets of {1, 2, . . . , n} whose least common multiple is small, we improved a result of Brown and Rödl on the smallest integer n such that every 2-coloring of {1, 2, . . . , n} has a monochromatic solution to equations with unit fractions. Using a recent result of Boza, …

Building Blocks For W-Algebras Of Classical Types, Vladimir Kovalchuk

Electronic Theses and Dissertations

The universal 2-parameter vertex algebra W_∞ of type W(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type W(2, 3, . . . ,N) for some N in the sense that under mild hypothesis, all such vertex algebras arise as quotients of W_∞. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as Y-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all W-algebras in type A, i.e, every W-(super) algebra in …

Circling The Square: Computing Radical Two, Isaiah Mellace, Joshua Kroeker

NEXUS: The Liberty Journal of Interdisciplinary Studies

Discoveries of equations for irrational numbers are not new. From Newton’s Method to Taylor Series,there are many ways to calculate the square root of two to arbitrary precision. The following method is similar in this way, but it is also a fascinating derivation from geometry that has applications to other irrationals. Additionally, the equation derived has some properties that may lead to fast computation. The first part of this paper is dedicated to deriving the equation, and the second is focused on computer science implementations and optimizations.

Mathematical Modeling Of An Epidemic In Scale-Free Network With Imperfect Vaccination, Heba Hameed

Thesis/ Dissertation Defenses

In light of the recent COVID-19 pandemic, the mathematical epidemiological model has proven to be essential for understanding the disease dynamic and finding the best control tool to help contain the disease and minimize its impact. This thesis investigates the dynamics of an infectious disease spread with latent infection and vaccination. The aim is to study this model's dynamic in a network that reflects the heterogeneity of the environment where the disease spreads. The vaccination is assumed to be not perfect, which means that vaccinated persons are likely to be infected and that the vaccinated person could lose their immunity, …