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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
New numerical algorithms are devised for high-order, efficient quadrature in domains arising from the intersection of a hyperrectangle and a manifold implicitly defined by level sets. By casting the manifold locally as the graph of a...
We perform linear and nonlinear stability analyses for thermal convection in a fluid overlying a saturated porous medium, in addition to conducting novel numerical simulations. We use a coupled system, with the Navier-Stokes equations...
In the first part of this thesis, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion (AJD) model. Let log stock price under risk-neutral measure follow an AJD model, we show that an explicit form of...
Next generation sequencing can rapidly analyze entire genomes in just hours. However, due to the nature of the sequencing process, errors may arise which limit the accuracy of the reads obtained. Luckily, modern sequencing technologies...
In this work, several nonlocal problems are studied. Analysis and computation have been done for these problems. Firstly, we consider the time-dependent nonlocal diffusion and wave equations, formulated in the peridynamics setting....
Overcoming Geometric Limitations in the Finite Element Method by Means of Polynomial Extension: Application to Second Order Elliptic Boundary Value and Interface Problems
In this dissertation, we present a new approach for approximating the solution of second order partial differential equations and interface problems. This approach is based on the classical finite element method, where instead of using...
Recently nonlocal continuum models have gained interest as alternatives to traditional PDE models due to their capability of handling solutions with discontinuities and their ease of modeling anomalous diffusion. The typical approach...
Mass Conserving Hamiltonian-Structure-Preserving Reduced Order Modeling for the Rotating Shallow Water Equations Discretized by a Mimetic Spatial Scheme
Ocean modeling, in a climate-modeling context, requires long time-horizons over global scales, which when combined with accurate resolution in time and space makes simulations very time-consuming. While high-resolution ocean-modeling...
The diagnosis and treatment of gliomas continues to pose a significant challenge for oncologists who not only have to contend with managing acute neurological symptoms, but also the almost inevitable development of resistance to...
Living systems consist of several complex interacting components. Depending on the complexity of the organism, these components can span from molecules to tissues and organs. Systems biology is the interdisciplinary field of study that...
Diffusion Tensor Imaging (DTI) provides a unique contrast based on the restricted directionality of water movement in an anisotropic environment. As such, DTI-based tractography can be used to characterize and quantify the structural...
Unsteady fluid flows have complex dynamics due to the nonlinear interactions amongst vortical elements. In this thesis, a network-theoretic framework is developed to describe vortical and modal (coherent structure) interactions in...
This dissertation research extends and simplfiies existing piecewise-linear homotopy (PL) methods to solve G(x) = 0, with G : ℝⁿ → ℝ[superscript m]. Existing PL methods are designed to solve F(x) = 0, with F : ℝⁿ → ℝⁿ and some related...
In many composite materials, rigid fibers are distributed throughout the material to tune the mechanical, thermal, and electric properties of the composite. The orientation and distribution of the fibers play a critical role in the...
Groundwater is a vital natural resource, and our ability to protect and manage this resource efficiently and effectively relies heavily on our ability to perform reliable and accurate computer modeling and simulation of subsurface...
This dissertation uses Riemannian optimization theory to increase our understanding of the role extraction problem and algorithms. Recent ideas of using the low-rank projection of the neighborhood pattern similarity measure and our...
Dissertation focuses on exploring the capabilities of the SRSF statistical shape analysis framework through various applications. Each application gives rise to a specific mathematical shape analysis model. The theoretical investigation...
The central purpose of this thesis is to explore the behavior of the numerical solution of the Cold- Ion model with shock forming conditions in one and two dimensions. In the one dimensional case, a comparison between the numerical...
In our work we analyze and implement numerical schemes for the infinite Prandtl number model for convection. This model describes the convection that is a potential driving force behind the flow and temperature of the Earth's mantle....
This study explores whether or not tropical cyclone (TC) structure information may be retrieved from satellite total ozone observations and how to link total ozone with analysis fields for potential application to TC vortex...
Computer vision principles enable the analysis of fire, wind, and plume behavior from visual and infrared (IR) video as opposed to sparse measurements obtained with expensive instrumentation. Data that quantifies the transport of heat...
This thesis investigates nonlinear systems that are dispersive and conservative in nature and well-approximated by the nonlinear Schrödinger (NLS) equation. The NLS equation is the prototypical equation for describing such phenomena and...
Computational neuroscience is a relatively new area that utilizes the computational analyses of neural systems as well as development of mathematical models. Analyses of neural systems help us to gain a deeper understanding of how...
Nonlocal models differ from traditional partial differential equation (PDE) models because they contain no spatial derivatives; instead an appropriate integral is used. Nonlocal models are especially useful in the case where there are...
Carbon fiber reinforced composites (CFRC) have several desirable traits that can be exploited in the design of advanced structures and systems. The applications requiring high strength- to-weight ratio and high stiffness-to-weight ratio...
The nonlocal models considered are free of spatial derivatives and thus are suitable for modeling problems with solutions exhibiting defects such as fractures in solids. Those models feature a horizon parameter that specifies the maximum...
Human life and diseases are inseparable. For millions of years, humans and their ancestors suffered from diseases, caused by infectious pathogens (e.g., bacteria, viruses, parasites) and caused by our own bodies as they age and...
In this work, we propose a framework to develop testable hypotheses for the effects of changes in the experimental conditions on the dynamics of a biological system using mathematical models. We discuss the uncertainties present in this...
Novel Numerical Analysis Methods, Using the WENO and WENO-Z Algorithms, for Combining Observational Data with Model Predictions for Improving Forecasts
“Data assimilation is a mathematical discipline that seeks to optimally combine theory (usually in the form of a numerical model) with observations.” — Wikipedia Strong constraint 4D-Variational data assimilation (4D-Var) seeks to find...
This thesis directly deals with setting up all of the electrical components to create an inexpensive automatic dependent surveillance broadcast (ADS-B) receiver that can transmit the ADS-B data received to a ground control station (GCS)...
Artificial Neural Networks form the basis of very powerful learning methods. It has been observed that a naive application of fully connected neural networks often leads to overfitting. In an attempt to circumvent this issue, a prior...
The sensitivity analysis of options is as important as pricing in option theory since it is used for hedging strategies, hence for risk management purposes. This dissertation presents new sensitivities for options when the underlying...
The Hawkes process serves as a natural choice for modeling self-exciting dynamics, such as the behavior of an electronic exchange-hosted limit order book (LOB). However, due to the lack of analytical solutions, probability estimates of...
The identification of forensic cases often includes the use of skeletal elements to assess the age-at-death of an individual. The pubic symphysis is the preferred and most often used skeletal age indicator. Standard techniques, such as...
A functional relation between two chemical species puts observational constraints on attempts to model the atmosphere. For example, adequate representation of these relations is important when modeling the depletion of stratospheric...
The standard general equilibrium asset pricing models typically make two simplifying assumptions: homogeneous agents and the existence of a rational expectations equilibrium. This context sometimes yields outcomes that are inconsistent...
The default threshold framework for credit risk modeling developed by Garreau and Kercheval [SIAM Journal on Financial Mathematics, 7:642-673, 2016] enjoys the advantages of both the structural form models and the reduced form models, ...
Diseases such as tuberculosis, chronic pneumonia, and inner ear infections are caused by bacterial biofilms. Biofilms can form on any surface such as teeth, floors, or drains. Many studies show that it is much more difficult to kill the...
Many phenomena in ecology, evolution, and organismal biology relate to how a system changes through time. Unfortunately, most of the statistical methods that are common in these fields represent samples as static scalars or vectors....
We consider a classical risk process with arrival of claims following a non-stationary Hawkes process. We study the asymptotic regime when the premium rate and the baseline intensity of the claims arrival process are large, and claim...
Artificial neural networks (ANNs) are very popular nowadays and offer reliable solutions to many classification problems. Recent research indicates that these neural networks might be overparameterized and different solutions have been...
Symmetric positive definite (SPD) matrices have become fundamental computational objects in many areas. It is often of interest to average a collection of symmetric positive definite matrices. This dissertation investigates different...
Algorithmic Lung Nodule Analysis in Chest Tomography Images: Lung Nodule Malignancy Likelihood Prediction and a Statistical Extension of the Level Set Image Segmentation Method
Lung cancer has the highest mortality rate of all cancers in both men and women in the United States. The algorithmic detection, characterization, and diagnosis of abnormalities found in chest CT scan images can aid radiologists by...
In previous work, Striegel and Hurdal have developed a mathematical model for cortical folding pattern formation during development (Striegel). A Turing reaction-diffusion system and a prolate spheroid domain were used to model the shape...
We consider the heat equation forced by a space-time white noise and with periodic boundary conditions in one dimension. The equation is discretized in space using four different methods; spectral collocation, spectral truncation, finite...
Tolerant bacteria enmeshed in a biofilm causes several difficult to treat illnesses like tuberculosis, chronic pneumonia, and chronic inner ear infections. These diseases typically respond poorly to antibiotics due to high tolerance....
In this dissertation, we present several applications of polynomial chaos in Monte Carlo simulation.First, we investigate the use of polynomial chaos as a control variate method for Monte Carlo simulation. Specically, we analyze the mean...
Neuron morphology plays a central role in characterizing cognitive health and functionality of brain structures. The problem of quantifying neuron shapes, and capturing statistical variability of shapes, is difficult because axons and...
Pancreatic islet beta-cells play a vital role in regulating blood glucose levels by releasing insulin into the bloodstream. Insulin is released in pulses that parallel interacting beta-cell rhythms, including oscillatory glucose...
The definition of partial differential equation (PDE) models usually involves a set of parameters whose values may vary over a wide range. The solution of even a single set of parameter values may be quite expensive. In many cases, e.g., ...
Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
