Models for particles interacting with compressible fluids are useful to several areas of science. This dissertation considers some of the mathematical issues of the Navier-Stokes-Smoluchowski and Euler-Smoluchowski models ...

This thesis deals with two approaches to building efficient representations of data. The first is a study of compressive sensing and improved data acquisition. We outline the development of the theory, and proceed into ...

Recorded images are usually contaminated by blur and noise. The restoration of such altered images is an ill-posed problem. Even if the blur is known, the unknown noise leads to uncertainty in the restored image. The ...

Statistical learning is widely used in business analytics to discover structure or exploit patterns from historical data, and build models that capture relationships between an outcome of interest and a set of variables. ...

We compute and compare three types of vectors frequently used to explore the instability properties of dynamical models, Lyapunov vectors (LVs), singular vectors (SVs), and bred vectors (BVs). The first model is the Lorenz ...

We describe a module for the <italic>Athena</italic> code that solves the gray equations of radiation hydrodynamics (RHD), based on the first two moments of the radiative transfer equation. We combine explicit Godunov ...

The magnetohydrodynamics (MHD) model describes the flow of electrically conducting fluids in the presence of magnetic fields. A principal application of MHD is the modeling of plasma physics, ranging from plasma confinement ...

Multi-scale problems appear in many contexts. In this thesis, we study two dif- ferent subjects involving multi-scale problems: (i) collective dynamics, and (ii) image processing. For collective dynamics, we concentrate ...

The rise of human interaction in digital environments has lead to an abundance of behavioral traces. These traces allow for model-based investigation of human-human and human-machine interaction `in the wild.' Stochastic ...

Two price economy provides a new approach to describe incomplete markets. Unlike the classical economy theory, in which the law of one price prevails, a two price economy determines prices by the directions of the trades. ...