Physical Sciences and Mathematics Commons^™

Cross-Participant Eeg-Based Assessment Of Cognitive Workload Using Multi-Path Convolutional Recurrent Neural Networks, Ryan G. Hefron, Brett J. Borghetti, Christine M. Schubert Kabban, James Christensen, Justin Estep

Faculty Publications

Applying deep learning methods to electroencephalograph (EEG) data for cognitive state assessment has yielded improvements over previous modeling methods. However, research focused on cross-participant cognitive workload modeling using these techniques is underrepresented. We study the problem of cross-participant state estimation in a non-stimulus-locked task environment, where a trained model is used to make workload estimates on a new participant who is not represented in the training set. Using experimental data from the Multi-Attribute Task Battery (MATB) environment, a variety of deep neural network models are evaluated in the trade-space of computational efficiency, model accuracy, variance and temporal specificity yielding three …

Properties And Computation Of The Inverse Of The Gamma Function, Folitse Komla Amenyou

Electronic Thesis and Dissertation Repository

We explore the approximation formulas for the inverse function of Γ. The inverse function of Γ is a multivalued function and must be computed branch by branch. We compare three approximations for the principal branch Γ̌ 0 . Plots and numerical values show that the choice of the approximation depends on the domain of the arguments, specially for small arguments. We also investigate some iterative schemes and find that the Inverse Quadratic Interpolation scheme is better than Newton’s scheme for improving the initial approximation. We introduce the contours technique for extending a real-valued function into the complex plane using two …

Simplicity And Sustainability: Pointers From Ethics And Science, Mehrdad Massoudi, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

In this paper, we explore the notion of simplicity. We use definitions of simplicity proposed by philosophers, scientists, and economists. In an age when the rapidly growing human population faces an equally rapidly declining energy/material resources, there is an urgent need to consider various notions of simplicity, collective and individual, which we believe to be a sensible path to restore our planet to a reasonable state of health. Following the logic of mathematicians and physicists, we suggest that simplicity can be related to sustainability. Our efforts must therefore not be spent so much in pursuit of growth but in achieving …

Uncertainty Evaluation In The Design Of Structural Health Monitoring Systems For Damage Detection, Christine M. Schubert Kabban, Richard P. Uber, Kevin J. Lin, Bin Lin, M. Bhuiyan, Victor Giurgiutiu

Faculty Publications

The validation of structural health monitoring (SHM) systems for aircraft is complicated by the extent and number of factors that the SHM system must demonstrate for robust performance. Therefore, a time- and cost-efficient method for examining all of the sensitive factors must be conducted. In this paper, we demonstrate the utility of using the simulation modeling environment to determine the SHM sensitive factors that must be considered for subsequent experiments, in order to enable the SHM validation. We demonstrate this concept by examining the effect of SHM system configuration and flaw characteristics on the response of a signal from a …

An Area Based Fan Beam Projection Model, Richard E. Steele, Jiehua Zhu

Honors College Theses

Area based projection models for computed tomography mitigate raw data errors by treating X-Rays as beams, whereas traditional line based projection models treat an X-Ray like a line, thus generating significant error. In an existing area based fan beam projection model, a rotation matrix, Q, simulates the rotation of the emitter detector pair to reduce computational load, but this introduces approximations by using an approximated rotation matrix. We eliminate approximations by deriving an exact formula for the entries of Q. Using a rotation of axes and by considering the neighboring cells' contributions to the area, the result has formulations for …

Using Random Forests To Describe Equity In Higher Education: A Critical Quantitative Analysis Of Utah’S Postsecondary Pipelines, Tyler Mcdaniel

Butler Journal of Undergraduate Research

The following work examines the Random Forest (RF) algorithm as a tool for predicting student outcomes and interrogating the equity of postsecondary education pipelines. The RF model, created using longitudinal data of 41,303 students from Utah's 2008 high school graduation cohort, is compared to logistic and linear models, which are commonly used to predict college access and success. Substantially, this work finds High School GPA to be the best predictor of postsecondary GPA, whereas commonly used ACT and AP test scores are not nearly as important. Each model identified several demographic disparities in higher education access, most significantly the effects …

Mathematical Modeling Of Tumor Immune Interactions: A Closer Look At The Role Of A Pd-L1 Inhibitor In Cancer Immunotherapy, Ami Radunskaya, Ruby Kim, Timothy Woods Ii

Spora: A Journal of Biomathematics

Monoclonal antibodies have shown promising results as a form of cancer immunotherapy used either alone or in combination with another treatment. We model a monoclonal antibody in combination with a dendritic cell (DC) vaccine in order to study treatment optimization. Certain proteins on tumor cells allow the tumor cells to bind to specific receptors on immune cells, rendering the immune cells ineffective. Experiments using mouse models show that a combination of antibodies to these proteins with tumor suppressing drugs improves the effectiveness of cancer vaccines. We create independent models of each of the two treatments in combination with DC therapy, …

Consensus And Clustering In Opinion Formation On Networks, Julia Bujalski, Grace Dwyer, Todd Kapitula, Quang Nhat Le

University Faculty Publications and Creative Works

Ideas that challenge the status quo either evaporate or dominate. The study of opinion dynamics in the socio-physics literature treats space as uniform and considers individuals in an isolated community, using ordinary differential equation (ODE) models. We extend these ODE models to include multiple communities and their interactions. These extended ODE models can be thought of as being ODEs on directed graphs. We study in detail these models to determine conditions under which there will be consensus and pluralism within the system. Most of the consensus/pluralism analysis is done for the case of one and two cities. However, we numerically …

On Central Branch/Reinsurance Risk Networks: Exact Results And Heuristics, Florin Avram, Sooie-Hoe Loke

Mathematics Faculty Scholarship

Modeling the interactions between a reinsurer and several insurers, or between a central management branch (CB) and several subsidiary business branches, or between a coalition and its members, are fascinating problems, which suggest many interesting questions. Beyond two dimensions, one cannot expect exact answers. Occasionally, reductions to one dimension or heuristic simplifications yield explicit approximations, which may be useful for getting qualitative insights. In this paper, we study two such problems: the ruin problem for a two-dimensional CB network under a new mathematical model, and the problem of valuation of two-dimensional CB networks by optimal dividends. A common thread between …

The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

Sandy Avila

No abstract provided.

Clark Measures And A Theorem Of Ritt, Isabelle Chalendar, Pamela Gorkin, Jonathan R. Partington, William T. Ross

Department of Math & Statistics Faculty Publications

We determine when a finite Blaschke product B can be written, in a non-trivial way, as a composition of two finite Blaschke products (Ritt's problem) in terms of the Clark measure for B. Our tools involve the numerical range of compressed shift operators and the geometry of certain polygons circumscribing the numerical range of the relevant operator. As a consequence of our results, we can determine, in terms of Clark measures, when two finite Blaschke products commute.

Highly Symmetric Multiple Bi-Frames For Curve And Surface Multiresolution Processing, Khulud Ziadi

Dissertations

Wavelets and wavelet frames are important and useful mathematical tools in numerous applications, such as signal and image processing, and numerical analysis. Recently, the theory of wavelet frames plays an essential role in signal processing, image processing, sampling theory, and harmonic analysis. However, multiwavelets and multiple frames are more flexible and have more freedom in their construction which can provide more desired properties than the scalar case, such as short compact support, orthogonality, high approximation order, and symmetry. These properties are useful in several applications, such as curve and surface noise-removing as studied in this dissertation. Thus, the study of …

Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, Yuezheng Gong, Jia Zhao, Qi Wang

Mathematics and Statistics Faculty Publications

We present second order, fully discrete, energy stable methods on spatially staggered grids for a hydrodynamic phase field model of binary viscous fluid mixtures in a confined geometry subject to both physical and periodic boundary conditions. We apply the energy quadratization strategy to develop a linear-implicit scheme. We then extend it to a decoupled, linear scheme by introducing an intermediate velocity term so that the phase variable, velocity field, and pressure can be solved sequentially. The two new, fully discrete linear schemes are then shown to be unconditionally energy stable, and the linear systems resulting from the schemes are proved …

Mathematics In Contemporary Society - Chapter 12 (Spring 2018), Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

Mathematics In Contemporary Society - Chapter 13 (Spring 2018), Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

Near-Optimal Control Of Switched Systems With Continuous-Time Dynamics Using Approximate Dynamic Programming, Tohid Sardarmehni

Mechanical Engineering Research Theses and Dissertations

Optimal control is a control method which provides inputs that minimize a performance index subject to state or input constraints [58]. The existing solutions for finding the exact optimal control solution such as Pontryagin’s minimum principle and dynamic programming suffer from curse of dimensionality in high order dynamical systems. One remedy for this problem is finding near optimal solution instead of the exact optimal solution to avoid curse of dimensionality [31]. A method for finding the approximate optimal solution is through Approximate Dynamic Programming (ADP) methods which are discussed in the subsequent chapters.

In this dissertation, optimal switching in switched …

Calculus For Business And Economics, Samuel Cartwright, Bhavana Burell, Patcharin Marion, Jianmin Zhu

Mathematics Grants Collections

This Grants Collection for Calculus for Business and Economics was created under a Round Six ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

A Mathematical Analysis Of The Game Of Chess, John C. White

Selected Honors Theses

This paper analyzes chess through the lens of mathematics. Chess is a complex yet easy to understand game. Can mathematics be used to perfect a player’s skills? The work of Ernst Zermelo shows that one player should be able to force a win or force a draw. The work of Shannon and Hardy demonstrates the complexities of the game. Combinatorics, probability, and some chess puzzles are used to better understand the game. A computer program is used to test a hypothesis regarding chess strategy. Through the use of this program, we see that it is detrimental to be the first …

Simulations And Queueing Theory: The Effects Of Priority And Vip Thresholds, Laura Schuck

Masters Theses & Doctoral Dissertations

Everyone has experienced waiting in lines, whether it is at the airport, the grocery store, or somewhere in-between. By developing queueing simulations based on mathematical models of airport security and customs, we explore a variety of questions related to optimal queue design with respect to efficiency, feasibility, priority, and other prescribed/variable constraints.

Simulations And Queueing Theory: The Effects Of Randomly Bypassing Security, Emily Ortmann

Masters Theses & Doctoral Dissertations

We discuss queueing theory in the setting of airport security and customs. By developing queueing simulations based on mathematical models, we explore a variety of questions related to optimal queue design with respect to efficiency, feasibility, priority, and other prescribed/variable constraints.

Swelling As A Stabilizing Mechanism During Ion Bombardment Of Thin Films: An Analytical And Numerical Study, Jennifer M. Swenson

Mathematics Theses and Dissertations

Irradiation of semiconductor surfaces often leads to the spontaneous formation of rippled structures at certain irradiation angles. However, at high enough energies, these structures are observed to vanish for all angles, despite the absence of any identified, universally-stabilizing physical mechanisms in operation. Here, we examine the effect on pattern formation of radiation-induced swelling, which has been excluded from prior treatments of stress in irradiated films. After developing a suitable continuum model, we perform a linear stability analysis to determine its effect on stability. Under appropriate simplifying assumptions, we find swelling indeed to be stabilizing at wavenumbers typical of experimental observations. …

Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle

Masters Theses & Specialist Projects

The Bernoulli distribution is a basic, well-studied distribution in probability. In this thesis, we will consider repeated Bernoulli trials in order to study runs of identical outcomes. More formally, for t ∈ N, we let Xt ∼ Bernoulli(p), where p is the probability of success, q = 1 − p is the probability of failure, and all Xt are independent. Then Xt gives the outcome of the tth trial, which is 1 for success or 0 for failure. For n, m ∈ N, we define Tn to be the number of trials needed to first observe n …

Rotordynamic Analysis Of Theoretical Models And Experimental Systems, Cameron R. Naugle

Master's Theses

This thesis is intended to provide fundamental information for the construction and

analysis of rotordynamic theoretical models, and their comparison the experimental

systems. Finite Element Method (FEM) is used to construct models using Timoshenko

beam elements with viscous and hysteretic internal damping. Eigenvalues

and eigenvectors of state space equations are used to perform stability analysis, produce

critical speed maps, and visualize mode shapes. Frequency domain analysis

of theoretical models is used to provide Bode diagrams and in experimental data

full spectrum cascade plots. Experimental and theoretical model analyses are used

to optimize the control algorithm for an Active Magnetic Bearing …

Controllability And Observability Of The Discrete Fractional Linear State-Space Model, Duc M. Nguyen

Masters Theses & Specialist Projects

This thesis aims to investigate the controllability and observability of the discrete fractional linear time-invariant state-space model. First, we will establish key concepts and properties which are the tools necessary for our task. In the third chapter, we will discuss the discrete state-space model and set up the criteria for these two properties. Then, in the fourth chapter, we will attempt to apply these criteria to the discrete fractional model. The general flow of our objectives is as follows: we start with the first-order linear difference equation, move on to the discrete system, then the fractional difference equation, and finally …

Score Test And Likelihood Ratio Test For Zero-Inflated Binomial Distribution And Geometric Distribution, Xiaogang Dai

Masters Theses & Specialist Projects

The main purpose of this thesis is to compare the performance of the score test and the likelihood ratio test by computing type I errors and type II errors when the tests are applied to the geometric distribution and inflated binomial distribution. We first derive test statistics of the score test and the likelihood ratio test for both distributions. We then use the software package R to perform a simulation to study the behavior of the two tests. We derive the R codes to calculate the two types of error for each distribution. We create lots of samples to approximate …

Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam

Masters Theses & Specialist Projects

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different …

Sabermetrics - Statistical Modeling Of Run Creation And Prevention In Baseball, Parker Chernoff

FIU Electronic Theses and Dissertations

The focus of this thesis was to investigate which baseball metrics are most conducive to run creation and prevention. Stepwise regression and Liu estimation were used to formulate two models for the dependent variables and also used for cross validation. Finally, the predicted values were fed into the Pythagorean Expectation formula to predict a team’s most important goal: winning.

Each model fit strongly and collinearity amongst offensive predictors was considered using variance inflation factors. Hits, walks, and home runs allowed, infield putouts, errors, defense-independent earned run average ratio, defensive efficiency ratio, saves, runners left on base, shutouts, and walks per …

Lozenge Tilings Of A Halved Hexagon With An Array Of Triangles Removed From The Boundary, Tri Lai

Department of Mathematics: Faculty Publications

Proctor's work on staircase plane partitions yields an enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi recently extended this tiling enumeration to a halved hexagon with a triangle removed from the boundary. In this paper, we prove a generalization of the results of Proctor and Rohatgi by enumerating lozenge tilings of a halved hexagon in which an array of an arbitrary number of adjacent triangles has been removed from the boundary.

Pricing Asian Options: Volatility Forecasting As A Source Of Downside Risk, Adam T. Diehl

Undergraduate Economic Review

Asian options are a class of derivative securities whose payoffs average movements in the underlying asset as a means of hedging exposure to unexpected market behavior. We find that despite their volatility smoothing properties, the price of an Asian option is sensitive to the choice of volatility model employed to price them from market data. We estimate the errors induced by two common schemes of forecasting volatility and their potential impact upon trading.

General Stochastic Integral And Itô Formula With Application To Stochastic Differential Equations And Mathematical Finance, Jiayu Zhai

LSU Doctoral Dissertations

A general stochastic integration theory for adapted and instantly independent stochastic processes arises when we consider anticipative stochastic differential equations. In Part I of this thesis, we conduct a deeper research on the general stochastic integral introduced by W. Ayed and H.-H. Kuo in 2008. We provide a rigorous mathematical framework for the integral in Chapter 2, and prove that the integral is well-defined. Then a general Itô formula is given. In Chapter 3, we present an intrinsic property, near-martingale property, of the general stochastic integral, and Doob-Meyer's decomposition for near-submartigales. We apply the new stochastic integration theory to several …