Improved First-Order Techniques For Certain Classes Of Convex Optimization, 2022 Clemson University
Improved First-Order Techniques For Certain Classes Of Convex Optimization, Trevor Squires
All Dissertations
The primary concern of this thesis is to explore efficient first-order methods of computing approximate solutions to convex optimization problems. In recent years, these methods have become increasingly desirable as many problems in fields such as machine learning and imaging science have scaled tremendously. Our aim here is to acknowledge the capabilities of such methods and then propose new techniques that extend the reach or accelerate the performance of the existing state-of-the-art literature.
Our novel contributions are as follows. We first show that the popular Conditional Gradient Sliding (CGS) algorithm can be extended in application to objectives with H\"older continuous …
3-Uniform 4-Path Decompositions Of Complete 3-Uniform Hypergraphs, 2022 University of Arkansas, Fayetteville
3-Uniform 4-Path Decompositions Of Complete 3-Uniform Hypergraphs, Rachel Mccann
Mathematical Sciences Undergraduate Honors Theses
The complete 3-uniform hypergraph of order v is denoted as Kv and consists of vertex set V with size v and edge set E, containing all 3-element subsets of V. We consider a 3-uniform hypergraph P7, a path with vertex set {v1, v2, v3, v4, v5, v6, v7} and edge set {{v1, v2, v3}, {v2, v3, v4}, {v4, v5, v6}, {v5, v6 …
The Decomposition Of The Space Of Algebraic Curvature Tensors, 2022 California State University - San Bernardino
The Decomposition Of The Space Of Algebraic Curvature Tensors, Katelyn Sage Risinger
Electronic Theses, Projects, and Dissertations
We decompose the space of algebraic curvature tensors (ACTs) on a finite dimensional, real inner product space under the action of the orthogonal group into three inequivalent and irreducible subspaces: the real numbers, the space of trace-free symmetric bilinear forms, and the space of Weyl tensors. First, we decompose the space of ACTs using two short exact sequences and a key result, Lemma 3.5, which allows us to express one vector space as the direct sum of the others. This gives us a decomposition of the space of ACTs as the direct sum of three subspaces, which at this point …
How To Guard An Art Gallery: A Simple Mathematical Problem, 2022 St. John Fisher University
How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli
The Review: A Journal of Undergraduate Student Research
The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …
Additional Fay Identities Of The Extended Toda Hierarchy, 2022 University of Minnesota, Twin Cities
Additional Fay Identities Of The Extended Toda Hierarchy, Yu Wan
Rose-Hulman Undergraduate Mathematics Journal
The focus of this paper is the extended Toda Lattice hierarchy, an infinite system of partial differential equations arising from the Toda lattice equation. We begin by giving the definition of the extended Toda hierarchy and its explicit bilinear equation, following Takasaki’s construction. We then derive a series of new Fay identities. Finally, we discover a general formula for one type of Fay identity.
Fock And Hardy Spaces: Clifford Appell Case, 2022 Chapman University
Fock And Hardy Spaces: Clifford Appell Case, Daniel Alpay, Kamal Diki, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we study a specific system of Clifford–Appell polynomials and, in particular, their product. Moreover, we introduce a new family of quaternionic reproducing kernel Hilbert spaces in the framework of Fueter regular functions. The construction is based on a general idea which allows us to obtain various function spaces by specifying a suitable sequence of real numbers. We focus on the Fock and Hardy cases in this setting, and we study the action of the Fueter mapping and its range.
Remotely Close: An Investigation Of The Student Experience In First-Year Mathematics Courses During The Covid-19 Pandemic, 2022 University of Nebraska - Lincoln
Remotely Close: An Investigation Of The Student Experience In First-Year Mathematics Courses During The Covid-19 Pandemic, Sawyer Smith
Honors Theses
The realm of education was shaken by the onset of the COVID-19 pandemic in 2020. It had drastic effects on the way that courses were delivered to students, and the way that students were getting their education at the collegiate level. At the University of Nebraska – Lincoln, the pandemic dramatically changed the way that first-year mathematics courses looked for students. By Spring 2021, students had the opportunity to take their first-year math courses either in-person or virtually. This project sought to identify differences between the two methods of course delivery during the Spring 2021 semester, regarding interaction with peers …
A New Metaphor: How Artificial Intelligence Links Legal Reasoning And Mathematical Thinking, 2022 Marquette University Law School
A New Metaphor: How Artificial Intelligence Links Legal Reasoning And Mathematical Thinking, Melissa E. Love Koenig, Colleen Mandell
Marquette Law Review
Artificial intelligence’s (AI’s) impact on the legal community expands exponentially each year. As AI advances, lawyers have more powerful tools to enhance their ability to research and analyze the law, as well as to draft contracts and other legal documents. Lawyers are already using tools powered by AI and are learning to shift their methodologies to take advantage of these enhancements. To continue to grow into their shifting role, lawyers should understand the relationship between AI, mathematics, and legal reasoning.
Finite Subdivision Rules For Matings Of Quadratic Thurston Maps With Few Postcritical Points, 2022 Bellarmine University
Finite Subdivision Rules For Matings Of Quadratic Thurston Maps With Few Postcritical Points, Jeremiah Zonio
Undergraduate Theses
A finite subdivision rule is set of instructions for repeatedly subdividing a partitioning of a given space. This turns out to be incredibly useful when attempting to describe a process known as polynomial mating. Polynomial mating is a way of gluing together two spaces which two polynomials may act upon such that the glued borders of each space respects the dynamics described by each polynomial. For matings of Misiurewicz polynomials, the spaces we are gluing together are 1-dimensional and are thus all border. This poses a conceptual difficulty which this paper attempts to resolve by using finite subdivison rules to …
Varieties Of Nonassociative Rings Of Bol-Moufang Type, 2022 Northern Michigan University
Varieties Of Nonassociative Rings Of Bol-Moufang Type, Ronald E. White
All NMU Master's Theses
In this paper we investigate Bol-Moufang identities in a more general and very natural setting, \textit{nonassociative rings}.
We first introduce and define common algebras. We then explore the varieties of nonassociative rings of Bol-Moufang type. We explore two separate cases, the first where we consider binary rings, rings in which we make no assumption of it's structure. The second case we explore are rings in which, $2x=0$ implies $x=0$.
Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture, 2022 University of South Carolina
Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture, Reid Taylor
Senior Theses
Current work in the field of deep learning and neural networks revolves around several variations of the same mathematical model for associative learning. These variations, while significant and exceptionally applicable in the real world, fail to push the limits of modern computational prowess. This research does just that: by leveraging high order tensors in place of 2nd order tensors, quadratic neural networks can be developed and can allow for substantially more complex machine learning models which allow for self-interactions of collected and analyzed data. This research shows the theorization and development of mathematical model necessary for such an idea to …
Superoscillating Sequences And Supershifts For Families Of Generalized Functions, 2022 Politecnico di Milano
Superoscillating Sequences And Supershifts For Families Of Generalized Functions, F. Colombo, I. Sabadini, Daniele Carlo Struppa, A. Yger
Mathematics, Physics, and Computer Science Faculty Articles and Research
We construct a large class of superoscillating sequences, more generally of F-supershifts, where F is a family of smooth functions in (t, x) (resp. distributions in (t, x), or hyperfunctions in x depending on the parameter t) indexed by λ ∈ R. The frame in which we introduce such families is that of the evolution through Schrödinger equation (i∂/∂t−H (x))(ψ) = 0 (H (x) = −(∂2/∂x2)/2+V (x)), V being a suitable potential). If F = {(t, x) → ϕλ(t, x) ; λ ∈ R}, where ϕλ is evolved from the initial datum x → eiλx , F-supershifts will be of …
High School Student Perspective: My Njit Stem For Success Internship Experience, 2022 STEM for Success
High School Student Perspective: My Njit Stem For Success Internship Experience, Michael Mora
STEM Month
During the 2020-2021 school year, I was a senior at the Academy for Mathematics, Science, and Engineering (AMSE) in Rockaway, NJ. At AMSE, a STEM-focused four-year magnet high school program hosted at Morris Hills High School, participating in an extended internship senior year is a cornerstone of the learning process. Required to complete a STEM-related internship to graduate, Academy students are encouraged to seek out an internship they’re passionate about in a field of their choice. The internship, which must be conducted under the mentorship of an industry professional, must meet the New Jersey-approved standards for a work-based learning experience …
Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, 2022 Università di Roma Tor Vergata, via Columbia 2, 00133 Roma, Italy
Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas
Journal of Stochastic Analysis
No abstract provided.
Construction Of The Canonical Representation From A Noncanonical Representation, 2022 Saga University, Saga, 8408502, JAPAN
Construction Of The Canonical Representation From A Noncanonical Representation, Yuji Hibino
Journal of Stochastic Analysis
No abstract provided.
Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, 2022 University of Nebraska - Lincoln
Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper
Honors Theses
Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of …
New Limit Theorems For Increments Of Birth-And-Death Processes With Linear Rates, 2022 University of Toronto, Toronto, ON, M5S 2E4, Canada
New Limit Theorems For Increments Of Birth-And-Death Processes With Linear Rates, Alexander Ya. Kreinin, Vladimir V. Vinogradov
Journal of Stochastic Analysis
No abstract provided.
Backward Stochastic Differential Equations With No Driving Martingale And Pseudo-Pdes, 2022 Université d’Évry Val d’Essonne, Laboratoire de Mathématiques et Modélisation, 23 Bd. de France, F-91037 Évry Cedex, France
Backward Stochastic Differential Equations With No Driving Martingale And Pseudo-Pdes, Adrien Barrasso, Francesco Russo
Journal of Stochastic Analysis
No abstract provided.
Prime Factors: America’S Prioritization Of Literacy Over Numeracy And Its Relationship To Systemic Inequity, 2022 The Graduate Center, City University of New York
Prime Factors: America’S Prioritization Of Literacy Over Numeracy And Its Relationship To Systemic Inequity, Troy Smith
Dissertations, Theses, and Capstone Projects
For much of American history, literacy has been prioritized in K-12 education and society, at large, at the expense of numeracy. This lack of numerical emphasis has established innumeracy as an American cultural norm that has resulted in America not producing a sufficient number of numerate citizens, and ranking poorly on mathematical performance in international comparisons. This paper investigates the decisions and circumstances that led to this under prioritization, along with the public and cultural impact of said actions. Toward this end, literature regarding contemporary and historical influences on American mathematics education (e.g., civic, policy, and parental) was reviewed. The …
Teiresias, Proportions, And Sexual Pleasure, 2022 National and Kapodistrian University of Athens
Teiresias, Proportions, And Sexual Pleasure, Spyros Missiakoulis
Journal of Humanistic Mathematics
In this short article, I claim that Teiresias, the blind prophet of Apollo, in order to answer the question of whether “in sexual intercourse the woman had a larger share of pleasure than the man did”, measured the abstract concept of sexual pleasure and acted as a present-day scholar. With the help of numerical, not geometrical, proportions, he ended up with the conclusion “a man enjoyed one-tenth of the pleasure and a woman nine-tenths”.