Physical Sciences and Mathematics Commons^™

Penalized Interpolating B-Splines And Their Applications, Kylee L. Hartman-Caballero

Theses and Dissertations

One of the most studied data analysis techniques in Numerical Analysis is interpolation. Interpolation is used in a variety of fields, namely computer graphic design and biomedical research. Among interpolation techniques, cubic splines have been viewed as the standard since at least the 1960s, due to their ease of computation, numerical stability, and the relative smoothness of the interpolating curve. However, cubic splines have notable drawbacks, such as their lack of local control and necessary knowledge of boundary conditions. Arguably a more versatile interpolation technique is the use of B-splines. B-splines, a relative of Bézier curves, allow local control through …

Symmetry Analysis Of The Canonical Connection On Lie Groups:Co-Dimension Two Abelian Nilradical With Abelian And Non Abelian Complement, Nouf Alrubea Almutiben

Theses and Dissertations

We consider the symmetry algebra of the geodesic equations of the canonical
connection on a Lie groups. We mainly consider the solvable indecomposable four,
five and six-dimensional Lie algebras with co-dimension two abelian nilradical, that
have an abelian and not abelian complement. In this particular case, we have only
one algebra in dimension four namely; A4,12 , and three algebras in dimension five
namely; A5,33, A5,34, and A5,35 In dimension six, based on the list of Lie algebras in
Turkowski’s list, there are nineteen such algebras namely; A6,1- A6,19 that have an
abelian complement, and there are eight algebras that …

Mathematical Modeling And Analysis Of Inflammation And Tissue Repair: Lung Inflammation And Wound Healing In Corals Under Stress, Quintessa Hay

Theses and Dissertations

A variety of insults, including tissue injury and/or exposure to pathogen, elicit an immune response in many organisms. An improperly regulated immune response can result in deleterious effects to the organism. Here we present models for lung injury in young and old mice and models for wound healing in coral reefs.

It is well known that the immune response becomes less effective in older individuals. This is of particular interest in pulmonary insults such as ventilator induced lung injury (VILI) or lung infection. We extended a mathematical model for the inflammatory response to VILI and used experimental data to select …

Low Reynolds Number Locomotion Near Interfaces In Two-Fluid Media, Avriel Rowena Mae Cartwright

Theses and Dissertations

Microorganisms often swim within complex fluid environments composed of multiple materials with very different properties. Biological locomotion, including swimming speed, is significantly impacted by the physical composition and rheology of the surrounding fluid environment, as well as the presence of phase boundaries and free interfaces, across which physical properties of the fluid media may vary greatly. Through computational simulations, we first investigate the classical Taylor’s swimming sheet problem near interfaces within multi-fluid environments using a two-fluid immersed boundary method. The accuracy of the methodology is illustrated through comparisons with analytical solutions. Our simulation results indicate that the interface dynamics and …

Mathematical Evaluation Of Ulnar Nerve Somatosensory Evoked Potentials (Sseps), Maribel Carmen Gomez

Theses and Dissertations

As the number of individuals suffering with low back and neck pain rises, we find people undergoing spinal procedures more often. In means, of safeguarding the patient and their neurological structures during the procedure intraoperative neuro-physiological monitoring (I.O.M) has been more widely used amongst surgeons orthopedic and neuro alike. During these procedures, a modality widely used for both low back and neck surgery is somatosensory evoked potentials (SSEPs). The aim of neuro-technicians is to obtain a baseline waveform that can be considered present and reliable. When obtaining SSEPs the technician can encounter obstacles with ’noisy’ wave-forms due to …

Identification Of Heart Disorders With Symbolic Aggregate Approximation, Moses K. Owusu

Theses and Dissertations

This project is an application of the Symbolic Aggregate Approximation (SAX) to 1000 fragments of ECG signals for 45 patients (42% females aged between 23 and 89 years and 58% males aged 32 to 89 years) using data obtained from the MIH-BIH Arrhythmia database to recognize cardiac health disorders. Data include a normal sinus rhythm, pacemaker rhythm and ECG readings for 15 heart disorders, making 17 in total. The aim is to use SAX to classify heart disorders using ECG signal, that analyzes QRS-complexes by first splitting the time series into smaller equally sized segments using the Piecewise Aggregate Approximation …

Advanced Prognostic Modeling For Breast Cancer Patients: Leveraging Data-Driven Approaches For Survival Analysis, Theophilus Gyedu Baidoo

Theses and Dissertations

Breast cancer is the second most prevalent form of cancer in women in the United States. Each year, about 264,000 cases of breast cancer are diagnosed in women and of this number, about 42,000 women lose their lives as reported by the Centers for Disease Control and Prevention. Early detection and effective treatment are crucial for improving survival rates and reducing mortality. This study aimed to explore the influential factors that may risk the survival of women with the disease and compare their predictive abilities using several error and performance metrics. The study uses a dataset from the National Cancer …

Monolithic Multiphysics Simulation Of Hypersonic Aerothermoelasticity Using A Hybridized Discontinuous Galerkin Method, William Paul England

Theses and Dissertations

This work presents implementation of a hybridized discontinuous Galerkin (DG) method for robust simulation of the hypersonic aerothermoelastic multiphysics system. Simulation of hypersonic vehicles requires accurate resolution of complex multiphysics interactions including the effects of high-speed turbulent flow, extreme heating, and vehicle deformation due to considerable pressure loads and thermal stresses. However, the state-of-the-art procedures for hypersonic aerothermoelasticity are comprised of low-fidelity approaches and partitioned coupling schemes. These approaches preclude robust design and analysis of hypersonic vehicles for a number of reasons. First, low-fidelity approaches limit their application to simple geometries and lack the ability to capture small scale flow …

Variational And Adaptive Non-Local Image Denoising Using Edge Detection And K − Means Clustering, Shiraz Mujahid

Theses and Dissertations

With the increased presence of image-based data in modern applications, the need for robust methods of image denoising grows greater. The work presented herein considers two of the most ubiquitous approaches towards image denoising: variational and non-local methods. The effectiveness of these methods is assessed using quantitatively using peak signal-to-noise ratio and structural similarity index measure metrics. This study employs ��−means clustering, an unsupervised machine learning algorithm, to isolate the most dominant cluster centroids within the incoming data and propose the introduction of a new adaptive parameter into the non-local means framework. Motivated by the fact that a majority of …

Global Upper Bounds For The Landau Equation Of Plasma Physics In The Very Soft Potentials Case, Caleb Solomon

Theses and Dissertations

This paper explores global upper bounds for solutions of the Landau equation in the soft potentials case (γ < −2). In particular, this paper explores the case of γ ∈ [−3,−2). Working with a classical solution to the Landau equation weighted by a cut-off function χ and using the Moser iteration, an upper bound for the L∞v norm of the solution to the Landau equation f is obtained proportianally to the L2 v norm of f with the assumptions of positive, essentially bounded coefficients. The supremum of f for t ∈ [0, T], x ∈ R3, v ∈ BR for some large radius R is shown to be bounded polynomially in R.

Comparative Study Of Variable Selection Methods For Genetic Data, Anna-Lena Kubillus

Theses and Dissertations

Association studies for genetic data are essential to understand the genetic basis of complex traits. However, analyzing such high-dimensional data needs suitable feature selection methods. For this reason, we compare three methods, Lasso Regression, Bayesian Lasso Regression, and Ridge Regression combined with significance tests, to identify the most effective method for modeling quantitative trait expression in genetic data. All methods are applied to both simulated and real genetic data and evaluated in terms of various measures of model performance, such as the mean absolute error, the mean squared error, the Akaike information criterion, and the Bayesian information criterion. The results …

Numerical Study Of A One-Dimensional Poisson-Nernst–Planck Ion Channel Model By Finite Element Backward And Forward Euler Methods, Michel Stanislas Korfhage

Theses and Dissertations

This thesis presents a numerical study of a one-dimensional Poisson-Nernst-Planck (PNP) ion channel model,which describes the transport of charged species in an electrolyte under the influence of an electric field. We develop a new numerical scheme for solving the PNP model by combining the method of lines with the finite element and Euler's forward and backward methods. We then implement the scheme based on the finite element library from the FEniCS project. To validate the accuracy of our numerical scheme, we construct an analytical solution of the PNP model with source terms. We find in numerical tests that the backward …

Modeling And Simulation Of Ion-Induced Volume Phase Transitions In Chemically-Active Polyelectrolyte Gels, Bindi Mahesh Nagda

Theses and Dissertations

Ion-induced volume phase transitions in polyelectrolyte gels play an important role in physiological processes such as mucus storage and secretion in the gut, nerve tissue excitation, and DNA packaging. Biological experiments show that polyelectrolyte gels may swell or collapse rapidly due to changes in external conditions such as ionic composition. The volume phase transition is accompanied by a monovalent/ divalent ion exchange between the polymer network and the solvent that make up the gel. We propose a 2D computational method for simulating mucus swelling and deswelling with a two-fluid mixture model. The model includes electro-diffusive transport of ionic species, the …

A Machine Learning Approach To Evaluate The Effect Of Sodium-Glucose Cotransporter-2 Inhibitors On Chronic Kidney Disease In Diabetes Patients, Solomon Eshun

Theses and Dissertations

Chronic kidney disease (CKD) is a significant complication that contributes to diabetes-related mortality in the United States, and there is growing evidence that sodium-glucose cotransporter 2 inhibitors (SGLT2i) can slow its progression. However, observational studies may suffer from confounding by indication, where patient characteristics and disease severity influence the decision to prescribe SGLT2i. This study utilized electronic health records of individuals with diabetes (from TriNetX) to investigate the effectiveness of SGLT2i on CKD progression. The database provided detailed information on patients’ CKD status, demographics, diagnosis, procedures, and medications, along with corresponding dates of diagnosis and prescription. The study comprised of …

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 …

Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, Andres P. Hyer

Theses and Dissertations

Axisymmetric Drop Shape Analysis (ADSA) is a technique commonly used to determine surface or interfacial tension. Applications of traditional ASDA methods to process analytical technologies are limited by computational speed and image quality. Here, we address these limitations using a novel machine learning approach to analysis. With a convolutional neural network (CNN), we were able to achieve an experimental fit precision of (+/-) 0.122 mN/m in predicting the surface tension of drop images at a rate of 1.5 ms^-1 versus 7.7 s^-1, which is more than 5,000 times faster than the traditional method. The results are validated on real images …

Automated Feature Extraction From Large Cardiac Electrophysiological Data Sets, And A Population Dynamics Approach To The Distribution Of Space Debris In Low-Earth Orbit, John Jurkiewicz

Theses and Dissertations

We present two applications of mathematics to relevant real-world situations.

In the first chapter, we discuss an automated method for the extraction of useful data from large file-size readings of cardiac data. We begin by describing the history of electrophysiology and the background of the work's setting, wherein a new multi-electrode array-based application for the long-term recording of action potentials from electrogenic cells makes large-scale readings of relevant data possible, opening the way for exciting cardiac electrophysiology studies in health and disease. With hundreds of simultaneous electrode recordings being acquired over a period of days, the main challenge becomes achieving …

On Clinical Use Of Infrared Cameras For Video-Based Estimation Of 3d Facial Kinematics, William Mackenzie Harrington

Theses and Dissertations

Neurological and neurodegenerative disorders such as Parkinson’s disease (PD), amyotrophic lateral sclerosis (ALS), and stroke can cause speech and orofacial motor impairments with devastating effects on quality of life. Analysis of orofacial movement provides vital information for early diagnosis and tracking disease progression, but current clinical practice relies on perceptual assessments performed by clinicians, which are unreliable and insensitive to early symptoms. New methods in machine learning have enabled automatic and objective assessment of orofacial kinematics from color and depth videos, hence we introduce MEADepthCamera, a mobile application for RGB-D video and audio recording and automatic estimation of 3D facial …

Gmres Convergence Of Block Preconditioners For Nonsymmetric Matrices, Miguel A. Mascorro

Theses and Dissertations

GMRES is an iterative method for solving linear systems that minimizes the residual over the k-dimensional Krylov subspace at iteration k. Murphy, Golub and Wathen in [11] show that saddle point type matrices can be preconditioned so that GMRES converges in two or three steps. Ipsen in [10] extends this work to matrixes where the (2,2) block is nonzero. However, the three step convergence result no longer holds in this case. In this thesis we investigate how many more steps are needed for convergence as a function of the size of that (2,2) block.

Leveraging Subject Matter Expertise To Optimize Machine Learning Techniques For Air And Space Applications, Philip Y. Cho

Theses and Dissertations

We develop new machine learning and statistical methods that are tailored for Air and Space applications through the incorporation of subject matter expertise. In particular, we focus on three separate research thrusts that each represents a different type of subject matter knowledge, modeling approach, and application. In our first thrust, we incorporate knowledge of natural phenomena to design a neural network algorithm for localizing point defects in transmission electron microscopy (TEM) images of crystalline materials. In our second research thrust, we use Bayesian feature selection and regression to analyze the relationship between fighter pilot attributes and flight mishap rates. We …

Could Cultures Determine The Course Of Epidemics And Explain Waves Of Covid-19?, Md Salman Rahman

Theses and Dissertations

Coronavirus Disease (COVID-19), caused by the SARS-CoV-2 virus, is an infectious disease that quickly became a pandemic spreading with different patterns in each country. Travel bans, lockdowns, social distancing, and non-essential business closures caused significant economic disruptions and stalled growth worldwide in the pandemic’s first year. In almost every country, public health officials forced and/or encouraged Nonpharmaceutical Interventions (NPIs) such as contact tracing, social distancing, masks, and quarantine. Human behavioral decision-making regarding social isolation significantly impedes global success in containing the pandemic. This thesis focuses on human behaviors and cultures related to the decision-making of social isolation during the pandemic. …

A Novel Chebyshev Wavelet Method For Solving Fractional-Order Optimal Control Problems, Ghodsieh Ghanbari

Theses and Dissertations

This thesis presents a numerical approach based on generalized fractional-order Chebyshev wavelets for solving fractional-order optimal control problems. The exact value of the Riemann– Liouville fractional integral operator of the generalized fractional-order Chebyshev wavelets is computed by applying the regularized beta function. We apply the given wavelets, the exact formula, and the collocation method to transform the studied problem into a new optimization problem. The convergence analysis of the proposed method is provided. The present method is extended for solving fractional-order, distributed-order, and variable-order optimal control problems. Illustrative examples are considered to show the advantage of this method in comparison …

A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker

Theses and Dissertations

The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit …

Dirichlet Type Boundary Value Problems For Linear And Quasi{Linear Hyperbolic Equations Of Higher Order, Reemah Alhuzally

Theses and Dissertations

Dirichlet type problems for quasi-linear hyperbolic equations are considered. For two-dimensional boundary value problems there are established:

(i) Unimprovable sufficient conditions of unique solvability and well-posedness of linear problems in piecewise smooth domains;

(ii) Unimprovable Sufficient conditions of unique solvability of linear problems in smooth convex domains.

(iii) Optimal Sufficient conditions of solvability, unique solvability and strong well-posedness of quasi-linear problems in piecewise smooth domains;

(iv) Optimal sufficient conditions of solvability and unique solvability of quasi- linear problems in smooth convex domains.

For three-dimensional linear boundary value problems there are established:

(i) Unimprovable sufficient conditions of unique solvability and well-posedness …

Relaxation Of Variational Principles For Z-Problems In Effective Media Theory, Kenneth Beard

Theses and Dissertations

In this thesis, we consider a class of Z-problems and their associated effective operators on Hilbert spaces which arise in effective media theory, especially within the theory of composites. We provide a unified approach to obtaining solutions of the Z-problem, formulas for the effective operator in terms of generalized Schur complements, and their associated variational principles (e.g., the Dirichlet minimization principle), while allowing for relaxation of the standard hypotheses on positivity and invertibility for the classes of operators usually considered in such problems. The Hilbert space framework developed here is inspired by the methods of orthogonal projections and Hodge decompositions. …

Mathematical And Statistical Modeling With Deep Neural Networks, Albert Romero

Theses and Dissertations

General adversarial networks (GANs) are a form of machine learning that includes two neural networks competing in a zero-sum game. One network produces artificial, while the other tries to distinguish artificial data from real. The Wasserstein general adversarial network with gradient penalty (WGAN-GP) variant of this technique is used to produce solutions for ordinary and partial differential equations.

Classification And Keyword Identification Of Covid 19 Misinformation On Social Media: A Framework For Semantic Analysis, Grace Y. Smith

Theses and Dissertations

The growing surge of misinformation among COVID-19 communication can pose great hindrance to truth, magnify distrust in policy makers and/or degrade authorities’ credibility, and it can even harm public health. Classification of textual context on social media data relating to COVID-19 is an effective tool to combat misinformation on social media platforms. In this research, Twitter data was leveraged to 1) develop classification methods to detect misinformation and identify Tweet sentiment with respect to COVID-19 and 2) develop a human-in-the-loop interactive framework to enable identification of keywords associated with social context, here, being misinformation regarding COVID-19. 1) Six fusion-based classification …

Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft

Theses and Dissertations

Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …

Mathematical Models Of Infection Prevention Programs In Hospital Settings, Kelly A. Reagan

Theses and Dissertations

Hospitals play a vital role in providing for the healthcare needs of a community. Patients can develop hospital-acquired infections (HAIs) during their hospitalization due to exposure to foreign bacteria, viruses, and fungi. Infection prevention programs target and reduce HAIs, but implementing the infection prevention programs often comes with a cost. The goal of my research is to use mathematical models to quantify the impact of infection prevention programs on cases of HAIs and total healthcare costs. First, I use a Markov chain model to quantify how one infection prevention program reduces general HAIs in the hospital. Then, I calculate the …

Estimating The Statistics Of Operational Loss Through The Analyzation Of A Time Series, Maurice L. Brown

Theses and Dissertations

In the world of finance, appropriately understanding risk is key to success or failure because it is a fundamental driver for institutional behavior. Here we focus on risk as it relates to the operations of financial institutions, namely operational risk. Quantifying operational risk begins with data in the form of a time series of realized losses, which can occur for a number of reasons, can vary over different time intervals, and can pose a challenge that is exacerbated by having to account for both frequency and severity of losses. We introduce a stochastic point process model for the frequency distribution …