Mathematics Commons^™

Survey Of Lebesgue And Hausdorff Measures, Jacob N. Oliver

Graduate Theses/Dissertations

Measure theory is fundamental in the study of real analysis and serves as the basis for more robust integration methods than the classical Riemann integrals. Measure theory allows us to give precise meanings to lengths, areas, and volumes which are some of the most important mathematical measurements of the natural world. This thesis is devoted to discussing some of the major proofs and ideas of measure theory. We begin with a study of Lebesgue outer measure and Lebesgue measurable sets. After a brief discussion of non-measurable sets, we define Lebesgue measurable functions and the Lebesgue integral. In the last chapter …

Ridge Regression And Lasso Estimators For Data Analysis, Dalip Kumar

Graduate Theses/Dissertations

An important problem in data science and statistical learning is to predict an outcome based on data collected on several predictor variables. This is generally known as a regression problem. In the field of big data studies, the regression model often depends on a large number of predictor variables. The data scientist is often dealing with the difficult task of determining the most appropriate set of predictor variables to be employed in the regression model. In this thesis we adopt a technique that constraints the coefficient estimates which in effect shrinks the coefficient estimates towards zero. Ridge regression and lasso …

Variational Inference For Quantile Rgression, Bufei Guo

Arts & Sciences Graduate Student Theses and Dissertations

Quantile regression (QR) (Koenker and Bassett, 1978), is an alternative to classic lin- ear regression with extensive applications in many fields. This thesis studies Bayesian quantile regression (Yu and Moyeed, 2001) using variational inference, which is one of the alternative methods to the Markov chain Monte Carlo (MCMC) in approximating intractable posterior distributions. The lasso regularization is shown to be effective in improving the accuracy of quantile regression (Li and Zhu, 2008). This thesis developed variational inference for quantile regression and regularized quantile regression with the lasso penalty. Simulation results show that variational inference is a computationally more efficient alternative …

Estimating Controlled Direct Effects Through Marginal Structural Models, Silvia Michelle Torres Pacheco

Arts & Sciences Graduate Student Theses and Dissertations

When working with panel data, many researchers wish to estimate the direct effects of time-varying factors on future outcomes. However, when a baseline treatment affects both the confounders of further stages of the treatment and the outcome, the estimation of controlled direct effects using traditional regression methods faces a bias trade-off between confounding bias and post-treatment control. Drawing on research from the field of epidemiology, in this thesis I present a marginal structural modeling (MSM) approach that allows scholars to generate unbiased estimates of controlled direct effects. Further, I detail the characteristics and implementation of MSMs, compare the performance of …

Bifurcation Analysis Of A Photoreceptor Interaction Model For Retinitis Pigmentosa, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka

Biology and Medicine Through Mathematics Conference

No abstract provided.

Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mental Geometry For Estimating Relative 3d Size, Akihito Maruya, Qasim Zaidi Dr.

MODVIS Workshop

No abstract provided.

On A Hypothesis For ℵ0-Bounded Groups, Marion Scheepers

Mathematics Faculty Publications and Presentations

We show that it is consistent, relative to the consistency of a strongly inaccessible cardinal, that an instance of the generalized Borel Conjecture introduced in [6] holds while the classical Borel Conjecture fails.

A Q-Analogue And A Symmetric Function Analogue Of A Result By Carlitz, Scoville And Vaughan, Yifei Li

Arts & Sciences Graduate Student Theses and Dissertations

We derive an equation that is analogous to a well-known symmetric function identity: $\sum_{i=0}^n(-1)^ie_ih_{n-i}=0$. Here the elementary symmetric function $e_i$ is the Frobenius characteristic of the representation of $\mathcal{S}_i$ on the top homology of the subset lattice $B_i$, whereas our identity involves the representation of $\cS_n\times \cS_n$ on the top homology of Segre product of $B_n$ with itself. We then obtain a q-analogue of a polynomial identity given by Carlitz, Scoville and Vaughan through examining the Segre product of the subspace lattice $B_n(q)$ with itself. We recognize the connection between the Euler characteristic of the Segre product of $B_n(q)$ with …

Market Research On Student Concert Attendance At Bgsu's College Of Musical Arts, Mary Solomon

Honors Projects

Bowling Green State University boasts a well established College of Musical Arts which holds concerts performed by esteemed faculty, prestigious guest artists, and students. The school hosts these events in Kobacker Hall and Bryan Recital Hall which can accommodate up to 800 and 250 audience members, respectively. However, performances in Kobacker hall only fill one- fourth of the 800 seats, on average. Why is this so? This project aims to investigate the factors that influence students’ decisions to attend concerts at the College of Musical Arts (CMA). By methodology of survey research and statistical analysis, this project will look into …

Limits And Singularities Of Normal Functions., Tokio Sasaki

Arts & Sciences Graduate Student Theses and Dissertations

On a projective complex variety $X$, constructing indecomposable higher Chow cycles is an interesting question toward the Hodge conjecture, motives, and other arithmetic applications. A standard method to determine whether a given higher cycle is indecomposable or not is to consider it as a general fiber of a degenerate family of higher cycles, and observe the asymptotic behaviors of the associated higher normal functions. In this thesis, we introduce some known examples of indecomposable cycles and a new method to detect the linearly independence of $\mathbb{R}$-regulator indecomposable $K_1$-cycles which is based on the singularities and limits of admissible normal functions …

Topics In Complex And Large-Scale Data Analysis, Guanshengrui Hao

Arts & Sciences Graduate Student Theses and Dissertations

Past few decades have witnessed skyrocketed development of modern technologies. As a result, data collected from modern technologies are evolving towards a direction with more complicated structure and larger scale, driving the traditional data analysis methods to develop and adapt. In this dissertation, we study three statistical issues rising in data with complicated structure and/or in large scale. In Chapter 2, we propose a Bayesian framework via exponential random graph models (ERGM) to estimate the model parameters and network structures for networks with measurement errors; In Chapter 3, we design a novel network sampling algorithm for large-scale networks with community …

Necessary Conditions For Stability Of Vehicle Formations, Pablo Enrique Baldivieso Blanco

Dissertations and Theses

Necessary conditions for stability of coupled autonomous vehicles in R are established in this thesis. The focus is on linear arrays with decentralized vehicles, where each vehicle interacts with only a few of its neighbors. Decentralized means that there is no central authority governing the motion. Instead, each vehicle registers only velocity and position relative to itself and bases its acceleration only on those data. Explicit expressions are obtained for necessary conditions for asymptotic stability in the cases that a system consists of a periodic arrangement of two or three different types of vehicles, i.e. configurations as follows: ...2-1-2-1 or …

Theory Of Linear Models For Estimating Regression Parameters With Applications To Two-Factor Studies With Unequal Sample Sizes, Zenan Sun

Honors Program Theses and Projects

In this thesis we explored some topics in regression analysis. In particular, we studied what linear regression is from a matrix theory perspective, and applied analysis of variance in a setting with two factors and unbalanced sample sizes. In addition, we applied Box-Cox variable transformation as a solution when the regression model violated the normality and equal variance (also called homoscedasticity) assumption. Our main goal is to use these theories to construct models and investigate questions related to lifetime earnings of people living in America by using real data. In doing so, we used the statistical software R to perform …

Finite Field Dynamics: Exploring Isomorphic Graphs And Cycles Of Length P, Catlain Mccarthy

Honors Program Theses and Projects

For this project, we explore nite eld dynamics and the various patterns of cycles of elements that emerge from the manipulation of a function and eld. Given a function f : Fp ��! Fp, we can create a directed graph with an edge from c to f(c) for all c 2 Fp. We especially consider polynomials of the form f(x) = xd + c and investigate how varying the values of d and c affect the cycles in a given nite eld, Fp. We analyze data to look for graphs that result in cycles of length p. We also identify …

On The Intersection Number Of Finite Groups, Humberto Bautista Serrano

Math Theses

Let G be a finite, nontrivial group. In a paper in 1994, Cohn defined the covering number of a finite group as the minimum number of nontrivial proper subgroups whose union is equal to the whole group. This concept has received considerable attention lately, mainly due to the importance of recent discoveries. In this thesis we study a dual concept to the covering number. We define the intersection number of a finite group as the minimum number of maximal subgroups whose intersection is equal to the Frattini subgroup. Similarly we define the inconjugate intersection number of a finite group as …

Behind The Tiles: Mathematics Of Carcassonne, Emilia Dewyngaert

Across the Bridge: The Merrimack Undergraduate Research Journal

Carcassonne is a tile-placing game where players take turns choosing a tile from a stack and attempting to create a city, road or a meadow. In addition to this, there is a river expansion pack that has river tiles to be placed. This paper focuses on how many different layouts or configurations of the river expansion pack can be created. It also discusses the Matlab code adapted to create a simulation of possible configurations of the river expansion pack.

Bounding The Rates Of Convergence Towards The Extreme Value Distributions, James Palmer

Honors Program Theses and Projects

Extreme value theory is a branch of probability which examines the extreme outliers of probability distributions. Three extreme value distributions arise as the limits of the maxima of sequences of random variables with certain properties. In this paper, we will first give information about these three distributions and prove that they are the only limit distributions of maxima. After that, we switch to a discussion about Stein's method. Stein's method is commonly used to prove central limit theorems. Stein's method also develops bounds on the distance between probability distributions with regards to a probability metric. There are three essential steps …

Black Swamp Pub And Bistro Analysis, Sara Aniol

Honors Projects

The Black Swamp Pub and Bistro is a full-service restaurant located in the Union on the Bowling Green State University Campus. We mainly do sit-down service, but we also do take-out orders and have a full bar with draft beers as well as mixed drinks. Our menu tends to change a lot, with new additions as well as some of the items being deleted. My goal of this project is to try to give some insight on the patterns that are too big to see with day-to-day operations as well as give some recommendations for the future that is backed …

Software For Conformal Boundary Operators, T-Curvatures, And Conformal Fractional Laplacians Of Odd Order, Lawrence Peterson

Datasets

The author has developed some new computer software and has used it, together with Mathematica and John M. Lee's Ricci software package, to construct and verify many of the symbolic formulae in the article "Conformal boundary operators, T-curvatures, and conformal fractional Laplacians of odd order," by the author and A. Rod Gover. This software is posted here, along with the Ricci package.

The author has also prepared a special guidelines file describing the new software. This guidelines file briefly describes Mathematica and Ricci as well. One should read Section 3 of the guidelines file before saving the main software file …

An Analysis Of The Telegrapher Equation With A Bifurcation Parameter To Model Relativistic Diffusion, Hunter R. Wages

Student Scholarship

In this paper, we derive a solution to the telegrapher equation. We then apply a bifurcation parameter to the telegrapher equation in order to analyze the behavior of the solution as it changes classification. In order to obtain the solution to both the telegrapher and modified telegrapher equation, we derive the heat equation and telegrapher equation using a continuous random walk. We also solve the heat equation using invariant properties of a particular solution, a random walk analysis, and a Fourier-Laplace transform. The solution to the telegrapher equation contains modified Bessel functions, so we also derive the solutions to both …

Modified Ramsey Numbers, Meaghan Mahoney

Honors Program Theses and Projects

Ramsey theory is a eld of study named after the mathematician Frank P. Ramsey. In general, problems in Ramsey theory look for structure amid a collection of unstructured objects and are often solved using techniques of Graph Theory. For a typical question in Ramsey theory, we use two colors, say red and blue, to color the edges of a complete graph, and then look for either a complete subgraph of order n whose edges are all red or a complete subgraph of order m whose edges are all blue. The minimum number of vertices needed to guarantee one of these …

Portfolio Optimization Methods: The Mean-Variance Approach And The Bayesian Approach, Hoang Nguyen

Honors Theses

This thesis is a discussion on the mean-variance approach to portfolio optimization and an introduction of the Bayesian approach, which is designed to solve certain limitations of the classical mean-variance analysis. The primary goal of portfolio optimization is to achieve the maximum return from investment given a certain level of risk. The mean-variance approach, introduced by Harry Markowitz, sought to solve this optimization problem by analyzing the means and variances of a certain collection of stocks. However, due to its simplicity, the mean-variance approach is subject to various limitations. In this paper, we seek to solve some of these limitations …

Firefighter Problem Played On Infinite Graphs, Sarah Days-Merrill

Honors Program Theses and Projects

The Firefighter Problem was introduced over 30 years ago and continues to be studied by researchers today. The problem consists of a graph of interest where a fire breaks out at time t = 0 on any given vertex of thegraph G. The player, then, gets to place a firefighter to “protect” a vertex from the fire. Each consecutive turn,the fire spreads to adjacent vertices. These vertices are then referred to as “burned”. The firefighter also gets tomove to protect an additional, unburned vertex, completing the first round. Each vertex that the firefighter “defends” stays protected for the remainder …

#Whyididntreport: Using Social Media As A Tool To Understand Why Sexual Assault Victims Do Not Report, Abby Garrett

Honors Theses

Sexual assault has gone largely under-reported, and social media movements, like #WhyIDidntReport, have brought great awareness to this issue. In order to take advantage of the large amounts of data the #WhyIDidntReport movement has generated, the study uses tweets to explore reasons why victims do not report their assault. The thesis cites current research on the topic of assault to generate a list of explanations victims use to describe their lack of reporting and compares the distributions with existing studies. We use a supervised learning technique to automatically categorize tweets into one of eight categories. This approach uses social sensing …

Maximum Oriented Forcing Number For Complete Graphs, Yair Caro, Ryan Pepper

Theory & Applications of Graphs

The maximum oriented k-forcing number of a simple graph G, written MOF_k(G), is the maximum directed k-forcing number among all orientations of G. This invariant was recently introduced by Caro, Davila and Pepper in [6], and in the current paper we study the special case where G is the complete graph with order n, denoted K_n . While MOF_k(G) is an invariant for the underlying simple graph G, MOF_k(K_n) can also be interpreted as an interesting property for tournaments. Our main results …

On Monochromatic Pairs With Nondecreasing Diameters, Adam O'Neal, Michael W. Schroeder

Mathematics Faculty Research

Let n m r t be positive integers and Δ : [n] → [r]. We say Δ is (m, r, t) - permissible if there exist t disjoint m-sets B₁,…,B_t contained in [n] for which

1. |Δ(B_i)| = 1 for each i = 1,2,…, t.
2. max(B_i) < min(B_i+1) for each i = 1,2,…, t − 1, and
3. max(B_i) − min(B_i) ≤ max(B_i+1) − max(B_i+1) for each i = …

Matching Preclusion Of The Generalized Petersen Graph, Ajay Arora, Eddie Cheng, Christopher Melekian

Theory & Applications of Graphs

The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph with no perfect matchings. In this paper we determine the matching preclusion number for the generalized Petersen graph P(n,k) and classify the optimal sets.

Impartial Achievement Games For Generating Nilpotent Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben

Mathematics Faculty Publications

We study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for finite groups of the form T×H, where T is a 2-group and H is a group of odd order. This includes all nilpotent and hence abelian groups.