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Self-Repelling Elastic Manifolds With Low Dimensional Range, Carl Mueller, Eyal Neumann 2022 University of Rochester, Rochester, NY 14627, USA

Self-Repelling Elastic Manifolds With Low Dimensional Range, Carl Mueller, Eyal Neumann

Journal of Stochastic Analysis

No abstract provided.


Induced Matrices: Recurrences And Markov Chains, Philip Feinsilver 2022 Southern Illinois University, Carbondale, Illinois 62901, USA

Induced Matrices: Recurrences And Markov Chains, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.


Using Graph Theoretical Methods And Traceroute To Visually Represent Hidden Networks, Jordan M. Sahs 2022 University of Nebraska at Omaha

Using Graph Theoretical Methods And Traceroute To Visually Represent Hidden Networks, Jordan M. Sahs

Student Research and Creative Activity Fair

Within the scope of a Wide Area Network (WAN), a large geographical communication network in which a collection of networking devices communicate data to each other, an example being the spanning communication network, known as the Internet, around continents. Within WANs exists a collection of Routers that transfer network packets to other devices. An issue pertinent to WANs is their immeasurable size and density, as we are not sure of the amount, or the scope, of all the devices that exists within the network. By tracing the routes and transits of data that traverses within the WAN, we can identify ...


Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs 2022 University of Nebraska at Omaha

Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs

Student Research and Creative Activity Fair

The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.

Now there are three difficulty tiers to POW problems, roughly corresponding ...


Implementation Of A Least Squares Method To A Navier-Stokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'Nya Breeden 2022 Francis Marion University

Implementation Of A Least Squares Method To A Navier-Stokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden

Rose-Hulman Undergraduate Mathematics Journal

The Navier-Stokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the Navier-Stokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares ...


Estimating Glutamate Transporter Surface Density In Mouse Hippocampal Astrocytes, Anca R. Radulescu, Annalisa Scimemi 2022 State University of New York at New Paltz

Estimating Glutamate Transporter Surface Density In Mouse Hippocampal Astrocytes, Anca R. Radulescu, Annalisa Scimemi

Biology and Medicine Through Mathematics Conference

No abstract provided.


Optimal Time-Dependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley 2022 Johns Hopkins University

Optimal Time-Dependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.


Sheltered Math Curriculum For Middle School English Learners, Jasmine Ercink 2022 Minnesota State University Moorhead

Sheltered Math Curriculum For Middle School English Learners, Jasmine Ercink

Dissertations, Theses, and Projects

Language barriers have shown a need for differentiation and sheltered instruction in the classroom for English Learners (ELs) to be successful in the United States public school system. This project proposes a mathematics curriculum using SIOP so that both groups of students in the middle school level can increase their proficiency in the mathematics content area as well as experience opportunities for academic and social language development. The purpose of this report is to describe the processes, methods, data, and intent of the mathematics curriculum for these learners. The curriculum acts as an effective intervention to fill gaps in both ...


The Mathematical Foundation Of The Musical Scales And Overtones, Michaela DuBose-Schmitt 2022 Mississippi State University

The Mathematical Foundation Of The Musical Scales And Overtones, Michaela Dubose-Schmitt

Theses and Dissertations

This thesis addresses the question of mathematical involvement in music, a topic long discussed going all the way back to Plato. It details the mathematical construction of the three main tuning systems (Pythagorean, just intonation, and equal temperament), the methods by which they were built and the mathematics that drives them through the lens of a historical perspective. It also briefly touches on the philosophical aspects of the tuning systems and whether their differences affect listeners. It further details the invention of the Fourier Series and their relation to the sound wave to explain the concept of overtones within the ...


3-Uniform 4-Path Decompositions Of Complete 3-Uniform Hypergraphs, Rachel McCann 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, v7}}. We provide the necessary and sufficient conditions for the existence of a decomposition of Kv ...


Improved First-Order Techniques For Certain Classes Of Convex Optimization, Trevor Squires 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 ...


The Decomposition Of The Space Of Algebraic Curvature Tensors, Katelyn Sage Risinger 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 ...


Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton 2022 Utah State University

Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton

All Graduate Plan B and other Reports

Using Natural Language Processing (NLP), we are able to analyze text from suicidal individuals. This can be done using a variety of methods. I analyzed a dataset of a girl named Victoria that died by suicide. I used a machine learning method to train a different dataset and tested it on her diary entries to classify her text into two categories: suicidal vs non-suicidal. I used topic modeling to find out unique topics in each subset. I also found a pattern in her diary entries. NLP allows us to help individuals that are suicidal and their family members and close ...


Computational Complexity Reduction Of Deep Neural Networks, Mee Seong Im, Venkat Dasari 2022 United States Naval Academy

Computational Complexity Reduction Of Deep Neural Networks, Mee Seong Im, Venkat Dasari

Mathematica Militaris

Deep neural networks (DNN) have been widely used and play a major role in the field of computer vision and autonomous navigation. However, these DNNs are computationally complex and their deployment over resource-constrained platforms is difficult without additional optimizations and customization.

In this manuscript, we describe an overview of DNN architecture and propose methods to reduce computational complexity in order to accelerate training and inference speeds to fit them on edge computing platforms with low computational resources.


How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli 2022 St. John Fisher College

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, Yu Wan 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, Daniel Alpay, Kamal Diki, Irene Sabadini 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.


Varieties Of Nonassociative Rings Of Bol-Moufang Type, Ronald E. White 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 $x=0$.


Remotely Close: An Investigation Of The Student Experience In First-Year Mathematics Courses During The Covid-19 Pandemic, Sawyer Smith 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, University of Nebraska-Lincoln

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 and ...


Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture, Reid Taylor 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 ...


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