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#### Data Representation for Learning and Information Fusion in Bioinformatics

(2013)

This thesis deals with the rigorous application of nonlinear dimension reduction and data organization techniques to biomedical data analysis. The Laplacian Eigenmaps algorithm is representative of these methods and has ...

#### Compact-Reconstruction Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

(2013)

A new class of non-linear compact interpolation schemes is introduced in this dissertation that have a high spectral resolution and are non-oscillatory across discontinuities. The Compact-Reconstruction Weighted Essentially ...

#### Network Algorithms for Complex Systems with Applications to Non-linear Oscillators and Genome Assembly

(2013)

Network and complex system models are useful for studying a wide range of phenomena, from disease spread to traffic flow. Because of the broad applicability of the framework it is important to develop effective simulations ...

#### The Hunt Variance Gamma Process with Applications to Option Pricing

(2013)

In this dissertation we develop a spatially inhomogeneous Markov process as a model for financial asset prices. This model is called the Hunt variance gamma process. We define it via its infinitesimal generator and prove ...

#### Small fluctuations in epitaxial growth via conservative noise

(2012)

We study the combined effect of growth (material deposition from above) and
nearest-neighbor entropic and force-dipole interactions in a stochastically perturbed
system of N line defects (steps) on a vicinal crystal ...

#### Linear Stability Analysis Using Lyapunov Inverse Iteration

(2012)

In this dissertation, we develop robust and efficient methods for linear stability analysis of large-scale dynamical systems, with emphasis on the incompressible Navier-Stokes equations. Linear stability analysis is a ...

#### Three Dimensional Edge Detection Using Wavelet and Shearlet Analysis

(2012)

Edge detection determines the boundary of objects in an image.
A sequence of images records a 2D representation of a scene changing over time, giving 3D data. New 3D edge detectors, particularly ones we developed using ...

#### Modeling and Solving Arc Routing Problems in Street Sweeping and Snow Plowing

(2012)

In arc routing problems, the goal is to determine an optimal path, or set of paths, that traverse a required subset of arcs on a graph with respect to a set of constraints and objective function. The Chinese Postman Problem ...

#### Using a Discriminator to Improve Compressive Sensing Efficiency

(2012)

Our work defines, implements, and evaluates a modification to a spectrum-based compression scheme for data streams coming from jet aircraft health-monitoring sensors. The modification consists of the addition of a ...

#### Image representation and compression via sparse solutions of systems of linear equations

(2012)

We are interested in finding sparse solutions to systems of linear equations $mathbf{A}mathbf{x} = mathbf{b}$, where $mathbf{A}$ is underdetermined and fully-ranked. In this thesis we examine an implementation of the {em ...