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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...
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...
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...
This dissertation is based on the structural model framework for default risk that was first introduced by garreau2016structural (henceforth: the "G-K model"). In this approach, the time of default is defined as the first time the log...
The problem of estimating trend and seasonality has been studied over several decades, although mostly using single time series setup. This dissertation studies the problem of estimating these components from a functional data point of...
Without proper treatment, direct analysis on data sets with missing or suppressed values can lead to biased results. Among all of the missing data handling methods, multiple imputation (MI) methods are regarded as the state of the art....
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 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...
This dissertation considers optimization problems on a Riemannian matrix manifold ℳ⊆ℝ[superscript m x n] with an additional rank inequality constraint. A novel technique for building new rank-related geometric objects from known...
The problem of optimal portfolio execution has become one of the most important problems in the area of financial mathematics. Over the past two decades, numerous researchers have developed a variety of different models to address this...
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...
This dissertation proposes a Riemannian approach for computing geodesics for closed curves in elastic shape space. The application of two Riemannian unconstrained optimization algorithms, Riemannian Steepest Descent (RSD) algorithm and...
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...
Deep learning has been widely used to predict price movements from the limit order book. In this paper, we design a consistently profitable trading system for predicting the bid-ask spread crossing. Our trading experiment is done on a...
Option pricing by the Fourier method has been popular for the past decade, many of its applications to Lévy processes has been applied especially for European options. This thesis focuses on exponential convergence Fourier method and its...
Diabetes mellitus type 2 has been described as a global epidemic characterized by the inability of the body to effectively control blood glucose levels. The liver is a central regulator of glucose homeostasis and stores or manufactures...
In this dissertation, we build several game-theoretic models to explore animal contest behavior. Classical game theory predicts that respect for ownership or "Bourgeois" behavior can arise as an arbitrary convention to avoid costly...
The Langevin algorithms are a collection of powerful optimization algorithms and Markov Chain Monte Carlo sampling algorithms that provide computational foundations for high dimensional data in machine learning. We first review variants...
In the foreseeable future, autonomous vehicles will have to drive alongside human drivers. In the absence of vehicle-to-vehicle communication, they will have to be able to predict the other road users' intentions. Equally importantly, ...
Improving the Accuracy of 3D Chromosome Structure Inference and Analyzing the Organization of Genome in Early Embryogenesis Using Single Cell Hi-C Data
This dissertation summarizes my graduate work on the structure and organization of mouse genome during preimplantation development. My research is divided into three different areas, which I will discuss in turn. To begin, I will discuss...
Computer modeling is extensively used to probe structure and evolution of stars and planets. These computations allow astrophysicists to connect theoretical models of star formation and evolution to astronomical observations. Because...
Chan-Vese is a level set method that simultaneously evolves a level set surface and fits locally constant intensity models for the interior and exterior regions to minimize a Mumford-Shah integral. However, the length-based contour...
Iterative methods are widely used to solve algebraic equations and matrix equations. In fact, they can also be used to solve differential equations. Unlike discretization methods which generate point solutions, iterative methods generate...
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