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Articles 1 - 16 of 16
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Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp
Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp
Theses and Dissertations
This thesis obtains a number of results in stochastic optimal control for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the uniqueness of the solutions and derive a relevant version of Itô's formula. We provide the dynamic programming principle and prove the associated verification theorem. A stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle. Additionally, we utilize our stochastic maximum principle result for a mean-variance portfolio selection problem.
Low Reynolds Number Locomotion Near Interfaces In Two-Fluid Media, Avriel Rowena Mae Cartwright
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
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 …
Advanced Prognostic Modeling For Breast Cancer Patients: Leveraging Data-Driven Approaches For Survival Analysis, Theophilus Gyedu Baidoo
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 …
Identification Of Heart Disorders With Symbolic Aggregate Approximation, Moses K. Owusu
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 …
Failure Distributions For Parallel Dependent Identical Weibull Components, Gina S. Sigler
Failure Distributions For Parallel Dependent Identical Weibull Components, Gina S. Sigler
Theses and Dissertations
For a parallel system, when one component fails, the failure distribution of the remaining components will have an increased failure rate. This dissertation takes a novel approach to finding the associated failure distribution of the full system using ordinal statistic distributions for correlated Weibull components, allowing for unknown correlations between the dependent components. A Taylor series approximation is presented for the two component; system failure time distributions are also derived for two failures in a two component system, two failures in an n component system, three failures in a three component system, and k failures in an n component system. …
Monolithic Multiphysics Simulation Of Hypersonic Aerothermoelasticity Using A Hybridized Discontinuous Galerkin Method, William Paul England
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
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 …
Numerical Study Of A One-Dimensional Poisson-Nernst–Planck Ion Channel Model By Finite Element Backward And Forward Euler Methods, Michel Stanislas Korfhage
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 …
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 …
Global Upper Bounds For The Landau Equation Of Plasma Physics In The Very Soft Potentials Case, Caleb Solomon
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.
Modeling And Simulation Of Ion-Induced Volume Phase Transitions In Chemically-Active Polyelectrolyte Gels, Bindi Mahesh Nagda
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 …
Comparative Study Of Variable Selection Methods For Genetic Data, Anna-Lena Kubillus
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 …
Student Performance In Traditional In-Person Vs. Online Sections Of An Introductory Graduate Mathematics Course, Lauran E. Kittle
Student Performance In Traditional In-Person Vs. Online Sections Of An Introductory Graduate Mathematics Course, Lauran E. Kittle
Theses and Dissertations
The growth of technology impacts nearly every aspect of everyday life, to include education and learning. The availability of distance learning (online) classes has increased drastically in the last few decades, expanding access to education for millions of people. However, it is imperative to consider exactly how the growth of technology impacts education – whether it is a positive, negative, or neutral impact. Previous research comparing distance learning and in-residence (traditional) classes have widely mixed, disparate conclusions. This type of research, two-stage analysis, and modeling has yet to be conducted on a graduate school level. For this reason, a detailed …
Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, Andres P. Hyer
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 …
Effects Of Slip On Highly Viscous Thin-Film Flows Inside Vertical Tubes (Constant Radius, Constricted And Flexible), Mark S. Schwitzerlett
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 …