Physical Sciences and Mathematics Commons^™

Towards Simulation Of Complex Ocean Flows: Analysis And Algorithm For Computation Of Coupled Partial Differential Equations, Wenbin Dong

Dissertations and Theses

The hybrid CFD models which usually consist of 2 sub-models, develop our capability to simulate many emerging problems with multiphysics and multiscale flows, especially for the coastal ocean flows interacted with local phenomena of interest. For most cases, the sub-models are connected with direct interpolation which is easy and workable. It becomes urgently needed to investigate the inner mechanism of such model integration as this simple method does not work well if the two sub-models are different in governing equations, numerical methods, and computational grids. Also, it can not treat complex flow structures as well as the balance in mass …

Error Propagation And Algorithmic Design Of Contour Integral Eigensolvers With Applications To Fiber Optics, Benjamin Quanah Parker

Dissertations and Theses

In this work, the finite element method and the FEAST eigensolver are used to explore applications in fiber optics. The present interest is in computing eigenfunctions u and propagation constants β satisfing [sic] the Helmholtz equation Δu + k²n²u = β²u. Here, k is the freespace wavenumber and n is a spatially varying coefficient function representing the refractive index of the underlying medium. Such a problem arises when attempting to compute confinement losses in optical fibers that guide laser light. In practice, this requires the computation of functions u referred to as …

From Mdp To Alphazero, David Robert Sewell

Dissertations and Theses

In this paper I will explain the AlphaGo family of algorithms starting from first principles and requiring little previous knowledge from the reader. The focus will be upon one of the more recent versions AlphaZero but I hope to explain the core principles that allowed these algorithms to be so successful. I will generally refer to AlphaZero as theses [sic] core set of principles and will make it clear when I am referring to a specific algorithm of the AlphaGo family. AlphaZero in short combines Monte Carlo Tree Search (MCTS) with Deep learning and self-play. We will see how these …

A New Mathematical Theory For The Dynamics Of Large Tumor Populations, A Potential Mechanism For Cancer Dormancy & Recurrence And Experimental Observation Of Melanoma Progression In Zebrafish, Adeyinka A. Lesi

Dissertations and Theses

Cancer, a family of over a hundred disease varieties, results in 600,000 deaths in the U.S. alone. Yet, improvements in imaging technology to detect disease earlier, pharmaceutical developments to shrink or eliminate tumors, and modeling of biological interactions to guide treatment have prevented millions of deaths. Cancer patients with initially similar disease can experience vastly different outcomes, including sustained recovery, refractory disease or, remarkably, recurrence years after apparently successful treatment. The current understanding of such recurrences is that they depend on the random occurrence of critical mutations. Clearly, these biological changes appear to be sufficient for recurrence, but are they …

Exploring The Potential Of Sparse Coding For Machine Learning, Sheng Yang Lundquist

Dissertations and Theses

While deep learning has proven to be successful for various tasks in the field of computer vision, there are several limitations of deep-learning models when compared to human performance. Specifically, human vision is largely robust to noise and distortions, whereas deep learning performance tends to be brittle to modifications of test images, including being susceptible to adversarial examples. Additionally, deep-learning methods typically require very large collections of training examples for good performance on a task, whereas humans can learn to perform the same task with a much smaller number of training examples.

In this dissertation, I investigate whether the use …

Mechanisms Of Value-Biased Prioritization In Fast Sensorimotor Decision Making, Kivilcim Afacan-Seref

Dissertations and Theses

In dynamic environments, split-second sensorimotor decisions must be prioritized according to potential payoffs to maximize overall rewards. The impact of relative value on deliberative perceptual judgments has been examined extensively, but relatively little is known about value-biasing mechanisms in the common situation where physical evidence is strong but the time to act is severely limited. This research examines the behavioral and electrophysiological indices of how value biases split-second perceptual decisions and the possible mechanisms underlying the process. In prominent decision models, a noisy but statistically stationary representation of sensory evidence is integrated over time to an action-triggering bound, and value-biases …

Tropical Cyclone Hazards In Relation To Propagation Speed, Jiehao Huang

Dissertations and Theses

As the population and infrastructure along the US East Coast increase, it becomes increasingly important to study the characteristics of tropical cyclones that can impact the coast. A recent study shows that the propagation speed of tropical cyclones has slowed over the past 60 years, which can lead to greater accumulation of precipitation and greater storm surge impacts. The study presented herein is meant to examine and analyze the relationships that exist between the propagation speed of tropical cyclones, their surface wind strength, displacement angles, and cyclone averaged winds. This analysis is focused on tropical cyclones spanning from 1950-2015 in …

Spacetime Numerical Techniques For The Wave And Schrödinger Equations, Paulina Ester Sepùlveda Salas

Dissertations and Theses

The most common tool for solving spacetime problems using finite elements is based on semidiscretization: discretizing in space by a finite element method and then advancing in time by a numerical scheme. Contrary to this standard procedure, in this dissertation we consider formulations where time is another coordinate of the domain. Therefore, spacetime problems can be studied as boundary value problems, where initial conditions are considered as part of the spacetime boundary conditions.

When seeking solutions to these problems, it is natural to ask what are the correct spaces of functions to choose, to obtain wellposedness. This motivates the study …

Computational Algorithms For Improved Representation Of The Model Error Covariance In Weak-Constraint 4d-Var, Jeremy A. Shaw

Dissertations and Theses

Four-dimensional variational data assimilation (4D-Var) provides an estimate to the state of a dynamical system through the minimization of a cost functional that measures the distance to a prior state (background) estimate and observations over a time window. The analysis fit to each information input component is determined by the specification of the error covariance matrices in the data assimilation system (DAS). Weak-constraint 4D-Var (w4D-Var) provides a theoretical framework to account for modeling errors in the analysis scheme. In addition to the specification of the background error covariance matrix, the w4D-Var formulation requires information on the model error statistics and …

Accuracy Of Wave Speeds Computed From The Dpg And Hdg Methods For Electromagnetic And Acoustic Waves, Nicole Michelle Olivares

Dissertations and Theses

We study two finite element methods for solving time-harmonic electromagnetic and acoustic problems: the discontinuous Petrov-Galerkin (DPG) method and the hybrid discontinuous Galerkin (HDG) method.

The DPG method for the Helmholtz equation is studied using a test space normed by a modified graph norm. The modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter. We find that, as the parameter approaches zero, better results are obtained, under some circumstances. A dispersion analysis on the multiple interacting stencils that form the DPG method shows that the discrete wavenumbers of the method are complex, explaining …

Introducing Complex Systems Analysis In High School Mathematics Using System Dynamics Modeling: A Potential Game-Changer For Mathematics Instruction, Diana Marie Fisher

Dissertations and Theses

Complex systems abound on this planet, in the composition of the human body, in ecosystems, in social interaction, in political decision-making, and more. Analytical methods allowing us to better understand how these systems operate and, consequently, to have a chance to intervene and change the undesirable behavior of some of the more pernicious systems have developed and continue to be enhanced via quickly changing technology. Some of these analytical methods are accessible by pre-college students, but have not been widely used at that level of education. Jay Forrester, the founder of one of the methodologies, System Dynamics (SD), used to …

Discrete Stability Of Dpg Methods, Ammar Harb

Dissertations and Theses

This dissertation presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, for triangular meshes, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree. Finally, for rectangular meshes, the test space is …

Finite Sample Properties Of Minimum Kolmogorov-Smirnov Estimator And Maximum Likelihood Estimator For Right-Censored Data, Jerzy Wieczorek

Dissertations and Theses

MKSFitter computes minimum Kolmogorov-Smirnov estimators (MKSEs) for several different continuous univariate distributions, using an evolutionary optimization algorithm, and recommends the distribution and parameter estimates that best minimize the Kolmogorov-Smirnov (K-S) test statistic. We modify this tool by extending it to use the Kaplan-Meier estimate of the cumulative distribution function (CDF) for right-censored data. Using simulated data from the most commonly-used survival distributions, we demonstrate the tool's inability to consistently select the correct distribution type with right-censored data, even for large sample sizes and low censoring rates. We also compare this tool's estimates with the right-censored maximum likelihood estimator (MLE). While …