Browsing Applied mathematics by Title
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PolynomialBased Methods for TimeIntegration
This thesis is divided into two parts: The first introduces a new time integration framework that is based on interpolating polynomials, and the second extends exponential integration to the spectral deferred correction ... 
Reproducing color images with custom inks
(1998)This dissertation investigates the general problem of reproducing color images on an offset printing press using custom inks in any combination and number. Many mathematical and algorithmic challenges arise when printing ... 
RiemannHilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions
(20131114)The computation of special functions has important implications throughout engineering and the physical sciences. Nonlinear special functions include the solutions of integrable partial differential equations and the ... 
Robust RealTime Image Processing Through Dynamic Mode Decomposition
(20131114)In many areas of research, robust and efficient datamining, and datadriven modeling, have become essential to progressing our understanding of increasingly complex and nonlinear relations often embedded in cluttered ... 
SelfOptimizing Metamaterial Antennas
The reconfigurable holographic metamaterial antenna is an attractive new technology for satellite communications, particularly in mobile applications. This antenna is thin, lightweight, consumes little power to operate, ... 
Singlecolumn and mixedlayer model analysis of subtropical stratocumulus response mechanisms relevant to climate change
(20131114)Subtropical stratocumulus clouds are important part of the Earth's energy budget. The response of low clouds to Earth's changing climate is one of the dominant uncertainties in global warming projections, due primarily ... 
Skewt Information Matrix: Evaluation and Use
Azzalini’s skewt distributions, described in detail in Azzalini [2013], have become very popular because of their practical usefulness and the complete R package sn for skewnormal distributions that include extensive ... 
Some BoundaryValue Problems for Water Waves
(20120913)Euler's equations describe the evolution of waves on the surface of an ideal incompressible fluid. In this dissertation, I discuss some boundaryvalue problems associated with Euler's equations. My approach is motivated ... 
Some Problems in Stochastic Dynamics and Statistical Analysis of SingleCell Biology of Cancer
With the development of experimental apparatus and data processing softwares, one now has easy access to cancer related data on a single cell, its genome and/or molecular compositions. At this level of description, ... 
Spectral Methods for Partial Dierential Equations that Model Shallow Water Wave Phenomena
Mathematical models for waves on shallow water surfaces has been of interest to researchers dating back to the 1800's. These models are governed by partial differential equations, and many of them have rich mathematical ... 
A splitting algorithm for multistage stochastic programming with application to hydropower scheduling
(1997)With water in short supply and utility deregulation imminent, the problem of longterm scheduling on a hydroelectric power system has become increasingly important.Many of the algorithms developed for this largescale ... 
Statistical, Stochastic, and Dynamical Models of Neural Decision Making
(20130225)Models of decision making provide a direct link between behavior and neurobiology. How does the encoding and accumulation of evidence by neural circuits impact decision making performance? Through datadriven and ... 
Stochastic Dynamics: Markov Chains, Random Transformations and Applications
Stochastic dynamical systems, as a rapidly growing area in applied mathematics, has been a successful modeling framework for biology, chemistry and data science. Depending upon the origin of uncertainties in an application ... 
Stochastic Modeling of Reversible Biochemical ReactionDiffusion Systems and HighResolution ShockCapturing Methods for Fluid Interfaces
My thesis contains two parts, both of which are motivated by biological problems. One is on stochastic reactiondiffusion for biochemical systems and the other on shockcapturing methods for fluid interfaces. In both parts, ... 
The stability and instabilities of stationary solutions to the nonlinear Schroedinger equation and the sineGordon equation
I present an analysis of the stability spectrum of all stationary elliptictype solutions to the focusing Nonlinear Schroedinger equation and the sineGordon equation. An analytical expression for the spectrum is given. ... 
This Brain Is a Mess: Inference, Random Graphs, and Biophysics to Disentangle Neuronal Networks
At first glance, the neuronal network seems like a tangled web in many areas throughout the nervous system. Often, our best guess is that such “messy” connections are close to random, while obeying certain statistical ... 
Towards PatientSpecific Mathematical Radiation Oncology
(20131114)The war against cancer continues to take its toll on society, even after many decades of focused, intensive research into its origins and cures. Increasingly, efforts are being made to incorporate physical sciences and ... 
Uncertainty Quantification Problems in Tsunami Modeling and Reduced Order Models for Hyperbolic Partial Differential Equations
In this thesis, we consider an uncertainty quantification (UQ) problem that arises from tsunami modeling, namely the probabilistic tsunami hazard assessment (PTHA) problem. The goal of PTHA is to compute the probability ... 
Value function approximation methods for Linearlysolvable Markov Decision Process
(20140224)Optimal control provides an appealing machinery to complete complicated control tasks with limited prior knowledge. Both global methods and online trajectory optimization methods are powerful techniques for solving optimal ... 
Variability in Modified Estimators of VaR and ES
Modified ValueatRisk (mVaR) and Modified Expected Shortfall (mES) are risk estimators that can be calculated without modelling the distribution of asset returns. These modifided estimators use skewness and kurtosis ...