The interests of this thesis are twofold. First, a two-grid convergence analysis based on the paper [ \textit{Algebraic analysis of aggregation-based multigrid } by A. Napov and Y. Notay, Numer. Lin. Alg. Appl. 18 (2011), ...
The radiation emitted by the Sun varies both cyclically and secularly. We first study in this thesis the response of the Earth's temperature to the 11-year solar cycle at the surface and in the troposphere. Then we study ...
Correlated, or synchronized, spiking activity among pairs of neurons is widely observed across the nervous system. How do these correlations arise from the dynamics of neural networks? The interconnectivity of neurons is ...
Modern Portfolio Theory dates back to 1950s, when Markowitz proposed mean-variance portfolio optimization to construct portfolios. It provided a systematic approach to determine portfolio allocation when one is facing ...
Dimensionality reduction techniques have long been used in a number of fields including nonlinear optics and fluid dynamics. Regardless of the specific technique, the underlying idea is to generate a reduced order model ...
Submarine landslides can generate tsunamis, and the generated waves can be catastrophic when a large volume of landslide material is involved. Moreover, large earthquakes are often accompanied by submarine landslides that ...
Rapid climate warming has caused species across the globe to shift their geographic ranges, and ecologists are increasingly concerned about whether species are able to track climate warming. Early efforts to predict species ...
The goal of my thesis is to provide a theoretical demonstration of how dimension reduc- tion, control and machine learning techniques can be applied to optimize the performance of complex nonlinear systems. Specifically, ...
Dynamics of inertial particles in two-dimensional planar flow have been investigated by evaluating finite-time Lyapunov exponents (FTLE). The first part of our work deals with inertial particle dynamics. The Maxey-Riley ...
There is a broad need in the neuroscience, neurological and biomedical engineering communities to better classify, quantify and diagnose Focal Axonal Swellings (FAS) and their impact on cognitive deficits and/or neural ...
This work studies the problem of model-based hand posture estimation via monocular camera. Generally, a model-based posture estimation method manipulates a 3D hand model whose posture is determined by a set of parameters. ...
Poroelasticity theory models the mechanics of porous, fluid-saturated, deformable solids. It was originally developed by Maurice Biot to model geophysical problems, such as seismic waves in oil reservoirs, but has also ...
In this dissertation, I address mathematical problems arising from the field of theo- retical neuroscience that share a common theme: temporally driven neural networks treated as perturbed, coupled nonlinear dynamical ...
We analyze the stability of solutions to Euler's equations in the presence of surface tension. First we compute stationary solutions to periodic Euler's equations in a travelling frame of reference and then we analyze their ...
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 ...
In many areas of research, robust and efficient data-mining, and data-driven modeling, have become essential to progressing our understanding of increasingly complex and nonlinear relations often embedded in cluttered ...
The reconfigurable holographic metamaterial antenna is an attractive new technology for satellite communications, particularly in mobile applications. This antenna is thin, light-weight, consumes little power to operate, ...
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 ...
Euler's equations describe the evolution of waves on the surface of an ideal incompressible fluid. In this dissertation, I discuss some boundary-value problems associated with Euler's equations. My approach is motivated ...
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 ...