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 ...
The Caenorhabditis elegans (C. elegans) worm is a well-studied biological organism model. The nervous system of C. elegans is particularly appealing to study, since it is a tractable fully functional neuronal network for ...
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 ...
How does the activity of populations of neurons encode the signals they receive? Since neurons in vivo are inherently variable, each fixed input to a population will elicit not a deterministic response, but rather a ...
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, ...
Interface problems for partial differential equations are initial boundary value problems for which the solution of an equation in one domain prescribes boundary conditions for the equations in adjacent domains. These ...
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. ...
Over the past three to four decades, esophageal adenocarcinoma (EAC) incidence has increased dramatically in the Western world due to causes that are not well understood. Current screening strategies for early detection ...
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 ...