Applied Mathematics Commons^™

Creating The Optimal Wedding Seating Chart, Madison Lane

Theses/Capstones/Creative Projects

The purpose of this project is to develop an effective seating arrangement for a wedding reception that enhances the comfort of guests. The ultimate aim is to create a harmonious and enjoyable atmosphere for all attendees. To achieve this, an integer program was designed to optimize the seating arrangement for the author’s upcoming wedding on May 27th, 2023. To ensure accuracy and feasibility, actual feedback was gathered from the guests to evaluate their compatibility and preferences. The proposed seating chart optimization not only addresses the placement of guests but also determines the number of tables required for the reception. The …

Topological Data Analysis Of Weight Spaces In Convolutional Neural Networks, Adam Wagenknecht

Dissertations

Convolutional Neural Networks (CNNs) have become one of the most commonly used tools for performing image classification. Unfortunately, as with most machine learning algorithms, CNNs suffer from a lack of interpretability. CNNs are trained by using a training data set and a loss function to tune a set of parameters known as the layer weights. This tuning process is based on the classical method of gradient descent, but it relies on a strong stochastic component, which makes the weight behavior during training difficult to understand. However, since CNNs are governed largely by the weights that make up each of the …

Project Based Learning, Christopher Imm

Sabbatical Projects

Project-based learning (PBL) is a pedagogy which encourages students to be actively involved in their learning process through gaining information to solve real-world problems with projects. In areas of STEM education, PBL can supplement the traditional classroom lecture, where students have a predominantly passive role in the learning process. Through practical activities, interactive discussions, independent reflection and/or team cooperation, students achieve the desired learning outcomes.

Viscous Thin-Film Models Of Nanoscale Self-Organization Under Ion Bombardment, Tyler Evans

Mathematics Theses and Dissertations

For decades, it has been observed that broad-beam irradiation of semiconductor surfaces can lead to spontaneous self-organization into highly regular patterns, sometimes at length scales of only a few nanometers. Initial theory was largely based on erosion and redistribution of material occurring on fast time scales, which are able to produce good agreement with certain aspects of surface evolution. However, further experimental and theoretical work eventually led to the realization that numerous effects are active in the irradiated target, including stresses associated with ion-implantation and the accumulation of damage leading to the development of a disordered, amorphous layer atop the …

Practical Implementation Of The Immersed Interface Method With Triangular Meshes For 3d Rigid Solids In A Fluid Flow, Norah Hakami

Mathematics Theses and Dissertations

When employing the immersed interface method (IIM) to simulate a fluid flow around a moving rigid object, the immersed object can be replaced by a virtual fluid enclosed by singular forces on the interface between the real and virtual fluids. These forces represent the impact of the rigid motion on the fluid flow and cause jump discontinuities across the interface in the whole flow field. Then, the IIM resolves the fluid flow on a fixed computational domain by directly incorporating the jump conditions across the interface into numerical schemes. Previous development of the method is limited to simple smooth boundaries. …

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 …

An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu

OUR Journal: ODU Undergraduate Research Journal

This paper presents an alternate proof of the divergence of the unique maximizer sequence {𝑥∗ 𝑛} of a function sequence {𝐹𝑛(𝑥)} that is derived from an adaptive algorithm based on the now classic optimal stopping problem, known by many names but here ‘the secretary problem’. The alternate proof uses a result established by Nguyen, Xu, and Zhao (n.d.) regarding the uniqueness of maximizer points of a generalized function sequence {𝑆𝜇,𝜎 𝑛 } and relies on the strict monotonicity of 𝐹𝑛(𝑥) as 𝑛 increases in order to show divergence of {𝑥∗ 𝑛}. Towards this, limits of the exponentiated Gaussian CDF are …

Quantum Computing And Its Applications In Healthcare, Vu Giang

OUR Journal: ODU Undergraduate Research Journal

This paper serves as a review of the state of quantum computing and its application in healthcare. The various avenues for how quantum computing can be applied to healthcare is discussed here along with the conversation about the limitations of the technology. With more and more efforts put into the development of these computers, its future is promising with the endeavors of furthering healthcare and various other industries.

Novel Architectures And Optimization Algorithms For Training Neural Networks And Applications, Vasily I. Zadorozhnyy

Theses and Dissertations--Mathematics

The two main areas of Deep Learning are Unsupervised and Supervised Learning. Unsupervised Learning studies a class of data processing problems in which only descriptions of objects are known, without label information. Generative Adversarial Networks (GANs) have become among the most widely used unsupervised neural net models. GAN combines two neural nets, generative and discriminative, that work simultaneously. We introduce a new family of discriminator loss functions that adopts a weighted sum of real and fake parts, which we call adaptive weighted loss functions. Using the gradient information, we can adaptively choose weights to train a discriminator in the direction …

Swarm Intelligence For Solving Some Nonlinear Differential Equations, Ahmed Elzaghal, Mohammed Mohammed Elgamal, Ahmed H. Eltanboly

Mansoura Engineering Journal

The Euler method is a well-known numerical technique employed for solving initial value problems of ordinary differential equations. The solution obtained through Euler's method is subject to significant inaccuracies, which tend to amplify with each successive iteration. The Particle Swarm Optimization (PSO) algorithm is a highly effective method for finding optimal solutions to both linear and nonlinear optimization problems. In this particular investigation, the PSO technique was utilized to solve initial value problems associated with ordinary differential equations. The Euler method, on the other hand, employs equidistant grid points to approximate solutions, which can result in significant errors and a …

Not Your Typical Tower Of Sauron, John Adam

Mathematics & Statistics Faculty Publications

The picture is of the tapering Chester Shot Tower, located in Chester, England. It was built in 1799 for the manufacture of lead shot for use in the Napoleonic Wars. Molten lead was poured through a sieve at the top of the tower, with the tiny droplets forming perfect spheres during the fall; these were then cooled in a vat of water at the base. This process was less labor intensive than an earlier method using molds. It is the oldest of the three remaining shot towers in the UK.

Question 1: Using the parked van at the base, estimate …

Effects Of Slip On Highly Viscous Thin-Film Flows Inside Vertical Tubes (Constant Radius, Constricted And Flexible), Mark S. Schwitzerlett

Theses and Dissertations

Viscous liquid film flows in a tube arise in numerous industrial and biological applications, including the transport of mucus in human airways. Previous modeling studies have typically used no-slip boundary conditions, but in some applications the effects of slip at the boundary may not be negligible. We derive a long-wave model based on lubrication theory which allows for slippage along the boundary. Linear stability analysis verifies the impact of slip-length on the speed, growth rate, and wavelength of the most unstable mode. Nonlinear simulations demonstrate the impact of slip-length on plug formation and wave dynamics. These simulations are conducted for …

Matemáticas Financieras Aplicadas, Odair Triana Calderón

Ciencias Administrativas, Económicas y Contables

Teniendo en cuenta que las matemáticas son una herramienta fundamental en las Ciencias Administrativas, especialmente en las finanzas. MATEMÁTICAS FINANCIERAS APLICADAS, busca dar solución a aquellos problemas de tipo económico y financiero que se presentan en una economía, organización o núcleo familiar, mediante la utilización de modelos matemáticos y la aplicación en Microsoft Excel.

El texto realiza un estudio de problemas de inversión y financiación, donde el cálculo de intereses con base en un capital y atendiendo a variables como el tiempo y las tasas de rendimiento, permite el desarrollo de casos utilizando el interés simple e interés compuesto.

Por …

Ambientes De Inclusión Para El Desarrollo Del Pensamiento Numérico Con Población Con Síndrome De Down, Luisa Valeria Escobar Buitrago, Ingry Yuliana Torres Garzón, Juan David Firigua Bejarano

Educación

La importancia de tratar sobre una educación inclusiva es hacer que la humanidad obtenga la aceptación hacia la diversidad, donde se encuentre un mundo lleno de posibilidades reconociendo todos los tipos de población entre ella las personas con Síndrome de Down, lo cual consiste en que la educación esté centrado en el respeto y la valoración de la diversidad, haciendo un enfoque general en las necesidades que esta población tiene, desarrollando habilidades para su desenvolvimiento tanto personal como laboral en determinada sociedad, por lo tanto el objetivo principal de este trabajo es desarrollar el pensamiento numérico de los estudiantes de …

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, 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, 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, Austin Kind, Brittany Stephenson Phd

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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 …

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

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 …

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 …

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, 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 …

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, 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.

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 …

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 …

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, Steph J. Owen

Biology and Medicine Through Mathematics Conference

No abstract provided.