Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, 2023 University of Nebraska at Omaha

#### Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, Jordan M. Sahs, Brad Horner

*UNO Student Research and Creative Activity Fair*

Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy …

On Variants Of Sliding And Frank-Wolfe Type Methods And Their Applications In Video Co-Localization, 2022 Clemson University

#### On Variants Of Sliding And Frank-Wolfe Type Methods And Their Applications In Video Co-Localization, Seyed Hamid Nazari

*All Dissertations*

In this dissertation, our main focus is to design and analyze first-order methods for computing approximate solutions to convex, smooth optimization problems over certain feasible sets. Specifically, our goal in this dissertation is to explore some variants of sliding and Frank-Wolfe (FW) type algorithms, analyze their convergence complexity, and examine their performance in numerical experiments. We achieve three accomplishments in our research results throughout this dissertation. First, we incorporate a linesearch technique to a well-known projection-free sliding algorithm, namely the conditional gradient sliding (CGS) method. Our proposed algorithm, called the conditional gradient sliding with linesearch (CGSls), does not require the …

Modeling Our World With Mathematics: Incorporating Math Modeling Into A General Education Curriculum, 2022 Illinois State University

#### Modeling Our World With Mathematics: Incorporating Math Modeling Into A General Education Curriculum, Brittany Stephenson

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Dynamics Of A Diffusive Vaccination Model With Therapeutic Impact And Non-Linear Incidence Rates, 2022 Illinois State University

#### Dynamics Of A Diffusive Vaccination Model With Therapeutic Impact And Non-Linear Incidence Rates, Md Shahriar Mahmud

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

An Agent-Based Model Of Covid-19 Transmission At Lewis University, 2022 Lewis University

#### An Agent-Based Model Of Covid-19 Transmission At Lewis University, Austin Kind, Brittany Stephenson Phd

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Compilación De Procesos Investigativos En Educación Matemática, 2022 Universidad de Cundinamarca

#### Compilación De Procesos Investigativos En Educación Matemática, Martha Lidia Barreto Moreno, Yeferson Castellanos Novoa, María Alejandra Mayorga Henao, Diana Marcela Contento Sarmiento, Jesús Antonio Villarraga Palomino, Andrés Alberto Gutiérrez Morales, Juan David Firigua Bejarano, Yineth Marleidy Parra Ubaque, Lady Johanna Silva Marín

*Educación*

En el libro Compilación de procesos de investigación en educación matemática, consta de cuatro capítulos donde se presentan los procesos desarrollados en el marco de proyectos de investigación a nivel de pregrado y postgrado en Educación.

El primer capítulo consiste en la sistematización de la acción docente desarrollada en el marco de los Talleres Itinerantes de Alfabetización Computacional en la provincia de Sumapaz, propuesta de innovación para implementar procesos didácticos que contribuyan al desarrollo del pensamiento matemático computacional en educación básica primaria rural.

El segundo capítulo contiene el proceso investigativo que dio continuidad al trabajo realizado en la Fase1, sobre …

Lecture Note On Delay Differential Equation, 2022 Western University

#### Lecture Note On Delay Differential Equation, Wenfeng Liu

*Undergraduate Student Research Internships Conference*

Delay differential equation is an important field in applied mathematics since it concerns more situations than the ordinary differential equation. Moreover, it makes the equations more applicable to the object's movement in real life.

My project is the lecture note on the delay differential equation provides a basic introduction to the delay differential equation, its application in real life, improving the ordinary differential equation, the primary method and definition for solving the delay differential equation and the use of the way in the ordinary differential equation to estimate the periodic solution to the delay differential equation.

A New Sir Model With Mobility., 2022 University of Louisville

#### A New Sir Model With Mobility., Ciana Applegate

*Electronic Theses and Dissertations*

In this paper, a mobility-based SIR model is built to understand the spread of the pandemic. A traditional SIR model used in epidemiology describes the transition of particles among states, such as susceptible, infected, and recovered states. However, the traditional model has no movement of particles. There are many variations of SIR models when it comes to the factor of mobility, the majority of studies use mobility intensity or population density as a measure of mobility. In this paper, a new dynamical SIR model, including the spatial motion of three-type particles, is constructed and the long-time behavior of the first …

Dimension And Ramsey Results In Partially Ordered Sets., 2022 University of Louisville

#### Dimension And Ramsey Results In Partially Ordered Sets., Sida Wan

*Electronic Theses and Dissertations*

In this dissertation, there are two major parts. One is the dimension results on different classes of partially ordered sets. We developed new tools and theorems to solve the bounds on interval orders using different number of lengths. We also discussed the dimension of interval orders that have a representation with interval lengths in a certain range. We further discussed the interval dimension and semi dimension for posets. In the second part, we discussed several related results on the Ramsey theory of grids, the results involve the application of Product Ramsey Theorem and Partition Ramsey Theorem

Optimal First Order Methods For Reducing Gradient Norm In Unconstrained Convex Smooth Optimization, 2022 Clemson University

#### Optimal First Order Methods For Reducing Gradient Norm In Unconstrained Convex Smooth Optimization, Yunheng Jiang

*All Theses*

In this thesis, we focus on convergence performance of first-order methods to compute an $\epsilon$-approximate solution of minimizing convex smooth function $f$ at the $N$-th iteration.

In our introduction of the above research question, we first introduce the gradient descent method with constant step size $h=1/L$. The gradient descent method has a $\mathcal{O}(L^2\|x_0-x^*\|^2/\epsilon)$ convergence with respect to $\|\nabla f(x_N)\|^2$. Next we introduce Nesterov’s accelerated gradient method, which has an $\mathcal{O}(L\|x_0-x^*\|\sqrt{1/\epsilon})$ complexity in terms of $\|\nabla f(x_N)\|^2$. The convergence performance of Nesterov’s accelerated gradient method is much better than that of the gradient descent method but still not optimal. We also …

Efficiency Of Homomorphic Encryption Schemes, 2022 Clemson University

#### Efficiency Of Homomorphic Encryption Schemes, Kyle Yates

*All Theses*

In 2009, Craig Gentry introduced the first fully homomorphic encryption scheme using bootstrapping. In the 13 years since, a large amount of research has gone into improving efficiency of homomorphic encryption schemes. This includes implementing leveled homomorphic encryption schemes for practical use, which are schemes that allow for some predetermined amount of additions and multiplications that can be performed on ciphertexts. These leveled schemes have been found to be very efficient in practice. In this thesis, we will discuss the efficiency of various homomorphic encryption schemes. In particular, we will see how to improve sizes of parameter choices in homomorphic …

Cross-Validation For Autoregressive Models., 2022 University of Louisville

#### Cross-Validation For Autoregressive Models., Christina Han

*Electronic Theses and Dissertations*

There are no set rules for choosing the lag order for autoregressive (AR) time series models. Currently, the most common methods employ AIC or BIC. However, AIC has been proven to be inconsistent and BIC is inefficient. Racine proposed an estimator based on Shao's work which he hypothesized would also be consistent, but left the proof as an open problem. We will show his claim does not follow immediately from Shao. However, Shao offered another consistent method for cross validation of linear models called APCV, and we will show that AR models satisfy Shao's conditions. Thus, APCV is a consistent …

#### Computational Models To Detect Radiation In Urban Environments: An Application Of Signal Processing Techniques And Neural Networks To Radiation Data Analysis, Jose Nicolas Gachancipa

*Beyond: Undergraduate Research Journal*

Radioactive sources, such as uranium-235, are nuclides that emit ionizing radiation, and which can be used to build nuclear weapons. In public areas, the presence of a radioactive nuclide can present a risk to the population, and therefore, it is imperative that threats are identified by radiological search and response teams in a timely and effective manner. In urban environments, such as densely populated cities, radioactive sources may be more difficult to detect, since background radiation produced by surrounding objects and structures (e.g., buildings, cars) can hinder the effective detection of unnatural radioactive material. This article presents a computational model …

A Network Analysis Of Covid-19 In The United States, 2022 California Polytechnic State University, San Luis Obispo

#### A Network Analysis Of Covid-19 In The United States, Joseph C. Mcguire

*Master's Theses*

Through methods in network theory and time-series analysis, we will analyze the spread of COVID-19 in the United States by determining trends in state-by-state daily cases through a network construction. Previous researchers have found frameworks for approximating the spread of the COVID-19 pandemic and identifying potential rises in cases by a network construction based on correlation of cases between regions [1]. Applying this network construction we determine how this network and its structure act as a predictor for overall COVID-19 cases in the United States by preforming a trend analysis on a variety of network statistics and US COVID-19 cases.

Unique Signed Minimal Wiring Diagrams And The Stanley-Reisner Correspondence, 2022 California Polytechnic State University, San Luis Obispo

#### Unique Signed Minimal Wiring Diagrams And The Stanley-Reisner Correspondence, Vanessa Newsome-Slade

*Master's Theses*

Biological systems are commonly represented using networks consisting of interactions between various elements in the system. Reverse engineering, a method of mathematical modeling, is used to recover how the elements in the biological network are connected. These connections are encoded using wiring diagrams, which are directed graphs that describe how elements in a network affect one another. A signed wiring diagram provides additional information about the interactions between elements relating to activation and inhibition. Due to cost concerns, it is optimal to gain insight into biological networks with as few experiments and data as possible. Minimal wiring diagrams identify the …

Fine-Tuning A 𝑘-Nearest Neighbors Machine Learning Model For The Detection Of Insurance Fraud, 2022 The University of Southern Mississippi

#### Fine-Tuning A 𝑘-Nearest Neighbors Machine Learning Model For The Detection Of Insurance Fraud, Alliyah Stout

*Honors Theses*

Billions of dollars are lost within insurance companies due to fraud. Large money losses force insurance companies to increase premium costs and/or restrict policies. This negatively affects a company’s loyal customers. Although this is a prevalent problem, companies are not urgently working toward bettering their machine learning algorithms. Underskilled workers paired with inefficient computer algorithms make it difficult to accurately and reliably detect fraud.

The goal of this study is to understand the idea of -Nearest Neighbors ( -NN) and to use this classification technique to accurately detect fraudulent auto insurance claims. Using -NN requires choosing a value and a …

A Novel Correction For The Adjusted Box-Pierce Test, 2022 Chapman University

#### A Novel Correction For The Adjusted Box-Pierce Test, Sidy Danioko, Jianwei Zheng, Kyle Anderson, Alexander Barrett, Cyril S. Rakovski

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

The classical Box-Pierce and Ljung-Box tests for auto-correlation of residuals possess severe deviations from nominal type I error rates. Previous studies have attempted to address this issue by either revising existing tests or designing new techniques. The Adjusted Box-Pierce achieves the best results with respect to attaining type I error rates closer to nominal values. This research paper proposes a further correction to the adjusted Box-Pierce test that possesses near perfect type I error rates. The approach is based on an inflation of the rejection region for all sample sizes and lags calculated *via* a linear model applied to simulated …

Cooccurrr - Applying Glcm Analysis Techniques To Non-Image Objects Such As Fitness Landscapes, 2022 Cleveland Clinic Lerner Research Institute

#### Cooccurrr - Applying Glcm Analysis Techniques To Non-Image Objects Such As Fitness Landscapes, Steph J. Owen

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Empirical And Computational Approaches To Explore The Underlying Neuromodulatory Mechanisms Of Social Status Regulation On Zebrafish Motor Circuits, 2022 East Carolina University

#### Empirical And Computational Approaches To Explore The Underlying Neuromodulatory Mechanisms Of Social Status Regulation On Zebrafish Motor Circuits, Sungwoo Ahn, Choongseok Park, Fadi Issa

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Age-Dependent Ventilator-Induced Lung Injury, 2022 Virginia Commonwealth University

#### Age-Dependent Ventilator-Induced Lung Injury, Quintessa Hay, Christopher Grubb, Rebecca L. Heise, Sarah Minucci, Michael S. Valentine, Jennifer Van Mullekom, Angela M. Reynolds

*Biology and Medicine Through Mathematics Conference*

No abstract provided.