Applied Mathematics Commons^™

Simulation Based Inference In Epidemic Models, Tejitha Dharmagadda

Theses, Dissertations and Culminating Projects

From ancient times to the modern day, public health has been an area of great interest. Studies on the nature of disease epidemics began around 400 BC and has been a continuous area of study for the well-being of individuals around the world. For over 100 years, epidemiologists and mathematicians have developed numerous mathematical models to improve our understanding of infectious disease dynamics with an eye on controlling and preventing disease outbreak and spread. In this thesis, we discuss several types of mathematical compartmental models such as the SIR, and SIS models. To capture the noise inherent in the real-world, …

Increasing Performance Of Classifiers For Ssvep-Based Brain-Computer Interfaces Using Extension Methods, Ethan Douglas Webster

Legacy Theses & Dissertations (2009 - 2024)

Brain-computer interfaces (BCI) provide an alternative communication method that does not require standard physical mediums (speech, typing, etc.). These systems have been implemented to provide additional communication and control options for people with certain motor disabilities. Classification is an important part of BCI systems and consists of inferring user commands from brain activity. Supervised classification methods often achieve higher accuracy, but unsupervised classification methods are useful when training is not practical for the user. This thesis focuses on unsupervised classification algorithms used for a BCI speller application and presents extensions for two existing classifiers that improve classification accuracy and thus …

Maxwell's Equations And Yang-Mills Equations In Complex Variables : New Perspectives, Sachin Munshi

Legacy Theses & Dissertations (2009 - 2024)

Maxwell's equations, named after James C. Maxwell, are a U(1) gauge theory describing the interactions between electric and magnetic fields. They lie at the heart of classical electromagnetism and electrodynamics. Yang-Mills equations, named after C. N. Yang and Robert Mills, generalize Maxwell's equations and are associated with a non-abelian gauge theory called Yang-Mills theory. Yang-Mills theory unified the electroweak interaction with the strong interaction (QCD), and it is the foundation of the Standard Model in particle physics.

An Algorithm Based On Vanet Technology To Count Vehicles Stopped At A Traffic Light, Manuel Contreras, Eric Gamess

Research, Publications & Creative Work

Vehicular Ad hoc Networks (VANETs) have gained considerable attention in the past few years due to their promising applicability in relation to the Intelligent Transportation Systems (ITSs). This emerging new technology will provide timely information to develop adaptive traffic light control systems that will allow a significant optimization of the vehicular traffic flow. In this paper, we introduce a novel algorithm for counting vehicles stopped at a traffic light using VANET technology. The algorithm is based on the idea of the propagation of a count request message from the RSU (originating unit) toward the vehicles that are at the end …

Missing Data Imputation Of High-Resolution Temporal Climate Time Series Data, Eben Afrifa-Yamoah, Ute A. Mueller, S. M. Taylor, A. J. Fisher

Research outputs 2014 to 2021

© 2020 The Authors. Meteorological Applications published by John Wiley & Sons Ltd on behalf of the Royal Meteorological Society. Analysis of high-resolution data offers greater opportunity to understand the nature of data variability, behaviours, trends and to detect small changes. Climate studies often require complete time series data which, in the presence of missing data, means imputation must be undertaken. Research on the imputation of high-resolution temporal climate time series data is still at an early phase. In this study, multiple approaches to the imputation of missing values were evaluated, including a structural time series model with Kalman smoothing, …

An Exploration Of 5g Wireless Network Attenuation Using Finite Element Analysis In Comsol Multiphysics, Matthew Johnson

CMC Senior Theses

5G, ultra-high frequency wireless networks face numerous hurdles due to significant signal attenuation in materials and large path loss. Empirical research on signal attenuation has been limited to low frequencies or very select high frequencies. This paper utilizes Finite Element Analysis in COMSOL Multiphysics to analyze signal attenuation in materials over a range of the frequency spectrum, from 100Mhz to 40Ghz, which is inclusive of 5G wireless frequencies. The focus of this paper is on glass and dry wood, as well as wet wood (representative of trees), as these materials are some of the most likely to stand in the …

K-Means Stock Clustering Analysis Based On Historical Price Movements And Financial Ratios, Shu Bin

CMC Senior Theses

The 2015 article Creating Diversified Portfolios Using Cluster Analysis proposes an algorithm that uses the Sharpe ratio and results from K-means clustering conducted on companies' historical financial ratios to generate stock market portfolios. This project seeks to evaluate the performance of the portfolio-building algorithm during the beginning period of the COVID-19 recession. S&P 500 companies' historical stock price movement and their historical return on assets and asset turnover ratios are used as dissimilarity metrics for K-means clustering. After clustering, stock with the highest Sharpe ratio from each cluster is picked to become a part of the portfolio. The economic and …

How Machine Learning And Probability Concepts Can Improve Nba Player Evaluation, Harrison Miller

CMC Senior Theses

In this paper I will be breaking down a scholarly article, written by Sameer K. Deshpande and Shane T. Jensen, that proposed a new method to evaluate NBA players. The NBA is the highest level professional basketball league in America and stands for the National Basketball Association. They proposed to build a model that would result in how NBA players impact their teams chances of winning a game, using machine learning and probability concepts. I preface that by diving into these concepts and their mathematical backgrounds. These concepts include building a linear model using ordinary least squares method, the bias …

Certified Functions For Mesh Generation, Andrey N. Chernikov

Chemistry & Biochemistry Faculty Publications

Formal methods allow for building correct-by-construction software with provable guarantees. The formal development presented here resulted in certified executable functions for mesh generation. The term certified means that their correctness is established via an artifact, or certificate, which is a statement of these functions in a formal language along with the proofs of their correctness. The term is meaningful only when qualified by a specific set of properties that are proven. This manuscript elaborates on the precise statements of the properties being proven and their role in an implementation of a version of the Isosurface Stuffing algorithm by Labelle and …

Spectral Analysis Of Complex Dynamical Systems, Casey Lynn Johnson

CGU Theses & Dissertations

The spectrum of any differential equation or a system of differential equations is related to several important properties about the problem and its subsequent solution. So much information is held within the spectrum of a problem that there is an entire field devoted to it; spectral analysis. In this thesis, we perform spectral analysis on two separate complex dynamical systems. The vibrations along a continuous string or a string with beads on it are the governed by the continuous or discrete wave equation. We derive a small-vibrations model for multi-connected continuous strings that lie in a plane. We show that …

Multiplicative Noise Removal: Nonlocal Low-Rank Model And It's Proximal Alternating Reweighted Minimization Algorithm, Xiaoxia Liu, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Mathematics & Statistics Faculty Publications

The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By exploiting this low-rank prior with application to multiplicative noise removal, we propose a nonlocal low-rank model for this task and develop a proximal alternating reweighted minimization (PARM) algorithm to solve the optimization problem resulting from the model. Specifically, we utilize a generalized nonconvex surrogate of the rank function to regularize the patch matrices and develop a new nonlocal low-rank model, which is a nonconvex …

Unitary And Symmetric Structure In Deep Neural Networks, Kehelwala Dewage Gayan Maduranga

Theses and Dissertations--Mathematics

Recurrent neural networks (RNNs) have been successfully used on a wide range of sequential data problems. A well-known difficulty in using RNNs is the vanishing or exploding gradient problem. Recently, there have been several different RNN architectures that try to mitigate this issue by maintaining an orthogonal or unitary recurrent weight matrix. One such architecture is the scaled Cayley orthogonal recurrent neural network (scoRNN), which parameterizes the orthogonal recurrent weight matrix through a scaled Cayley transform. This parametrization contains a diagonal scaling matrix consisting of positive or negative one entries that can not be optimized by gradient descent. Thus the …

Orthogonal Recurrent Neural Networks And Batch Normalization In Deep Neural Networks, Kyle Eric Helfrich

Theses and Dissertations--Mathematics

Despite the recent success of various machine learning techniques, there are still numerous obstacles that must be overcome. One obstacle is known as the vanishing/exploding gradient problem. This problem refers to gradients that either become zero or unbounded. This is a well known problem that commonly occurs in Recurrent Neural Networks (RNNs). In this work we describe how this problem can be mitigated, establish three different architectures that are designed to avoid this issue, and derive update schemes for each architecture. Another portion of this work focuses on the often used technique of batch normalization. Although found to be successful …

Filtered-Dynamic-Inversion Control For Unknown Minimum-Phase Systems With Unknown Relative Degree, Sumit Suryakant Kamat

Theses and Dissertations--Mechanical and Aerospace Engineering

We present filtered-dynamic-inversion (FDI) control for unknown linear time-invariant systems that are multi-input multi-output and minimum phase with unknown-but-bounded relative degree. This FDI controller requires limited model information, specifically, knowledge of an upper bound on the relative degree and knowledge of the first nonzero Markov parameter. The FDI controller is a single-parameter high-parameter-stabilizing controller that is robust to uncertainty in the relative degree. We characterize the stability of the closed-loop system. We present numerical examples, where the FDI controller is implemented in feedback with mathematical and physical systems. The numerical examples demonstrate that the FDI controller for unknown relative degree …

Three Point Boundary Value Problems For Ordinary Differential Equations, Uniqueness Implies Existence, Paul W. Eloe, Johnny Henderson, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We consider a family of three point n − 2, 1, 1 conjugate boundary value problems for nth order nonlinear ordinary differential equations and obtain conditions in terms of uniqueness of solutions imply existence of solutions. A standard hypothesis that has proved effective in uniqueness implies existence type results is to assume uniqueness of solutions of a large family of n−point boundary value problems. Here, we replace that standard hypothesis with one in which we assume uniqueness of solutions of large families of two and three point boundary value problems. We then close the paper with verifiable conditions on the …

Description Of Income And Substitution Effects Using Slutsky Identity, Julius N. Esunge, Dali Magrakvelidze

Mathematics Articles

In the paper we describe how income and price changes affect consumer's decision making using the Slutsky Identity. We also investigate economical meaning of curve turn-movements of consumer's budget. For analyzing the changes of consumer's choice we are using two step movements (turn, then parallel movement) of budget curve.

Hybrid Electric Vehicle Energy Management Strategy With Consideration Of Battery Aging, Bin Zhou

Dissertations, Master's Theses and Master's Reports

The equivalent consumption minimization strategy (ECMS) is a well-known energy management strategy for Hybrid Electric Vehicles (HEV). ECMS is very computationally efficient since it yields an instantaneous optimal control. ECMS has been shown to minimize fuel consumption under certain conditions. But, minimizing the fuel consumption often leads to excessive battery damage. The objective of this dissertation is to develop a real-time implementable optimal energy management strategy which improves both the fuel economy and battery aging for Hybrid Electric Vehicles by using ECMS. This work introduces a new optimal control problem where the cost function includes terms for both fuel consumption …

The Singular Value Expansion For Compact And Non-Compact Operators, Daniel Crane

Dissertations, Master's Theses and Master's Reports

Given any bounded linear operator T : X → Y between separable Hilbert spaces X and Y , there exists a measure space (M, Α, µ) and isometries V : L²(M) → X, U : L²(M) → Y and a nonnegative, bounded, measurable function σ : M → [0, ∞) such that

T = Um_σV ^†,

with m_σ : L²(M ) → L²(M ) defined by m_σ(f ) = σf for all f …

Sub-Sampled Matrix Approximations, Joy Azzam

Dissertations, Master's Theses and Master's Reports

Matrix approximations are widely used to accelerate many numerical algorithms. Current methods sample row (or column) spaces to reduce their computational footprint and approximate a matrix A with an appropriate embedding of the data sampled. This work introduces a novel family of randomized iterative algorithms which use significantly less data per iteration than current methods by sampling input and output spaces simultaneously. The data footprint of the algorithms can be tuned (independent of the underlying matrix dimension) to available hardware. Proof is given for the convergence of the algorithms, which are referred to as sub-sampled, in terms of numerically tested …

On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov

Articles

A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are …