Estimating Glutamate Transporter Surface Density In Mouse Hippocampal Astrocytes, 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, 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, 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 ...

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 K_{v} 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 P_{7}, a path with vertex set {v_{1}, v_{2}, v_{3}, v_{4}, v_{5}, v_{6}, v_{7}} and edge set {{v_{1}, v_{2}, v_{3}}, {v_{2}, v_{3}, v_{4}}, {v_{4}, v_{5}, v_{6}}, {v_{5}, v_{6}, v_{7}}}. We provide the necessary and sufficient conditions for the existence of a decomposition of K_{v ...}

Analyzing Suicidal Text Using Natural Language Processing, 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 ...

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 ...

Computational Complexity Reduction Of Deep Neural Networks, 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, 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, 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.

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 $x=0$.

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, 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, 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 the form ...

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 ...

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, University of Nebraska-Lincoln*

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.