Browsing Applied mathematics by Title
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Climate Response to Solar Variation: Cyclic and Secular
(20130225)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 11year solar cycle at the surface and in the troposphere. Then we study ... 
Closing the Loop: Optimal Stimulation of Neuronal Networks via Adaptive Control Algorithms
The Caenorhabditis elegans (C. elegans) worm is a wellstudied biological organism model. The nervous system of C. elegans is particularly appealing to study, since it is a tractable fully functional neuronal network for ... 
Collective Activity in Neural Networks: the Mathematical Structure of Connection Graphs and Population Codes
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 ... 
Coordinated neural activity: Mechanistic origins and impact on stimulus coding
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 ... 
ETGETL Portfolio Optimization
(20130225)Modern Portfolio Theory dates back to 1950s, when Markowitz proposed meanvariance portfolio optimization to construct portfolios. It provided a systematic approach to determine portfolio allocation when one is facing ... 
Exploiting Low Dimensionality in Nonlinear Optics and Other Physical Systems
(20120913)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 ... 
Finite Volume Methods for the Multilayer Shallow Water Equations with Applications to Storm Surges
(20110711)Coastal hazards related to strong storms such as hurricanes and typhoons are one of the most frequently recurring and wide spread hazards to coastal communities. Storm surges are among the most devastating effects of these ... 
Finite volume methods for Tsunamis genereated by submarine landslides
(20140430)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 ... 
Geographic Range Shifts under Climate Warming
(20130725)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 immersed interface method: a numerical approach for partial differential equations with interfaces
(1994)This thesis describes the Immersed Interface Method (IIM) for interface problems, in which the partial differential equations have discontinuities and singularities in the coefficients and the solutions. A typical example ... 
Integrating DataDriven Methods in Nonlinear Dynamical Systems: Control, Sparsity and Machine Learning
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 using the Fokas Method
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 ... 
Lagrangian coherent structures and the dynamics of inertial particles
Dynamics of inertial particles in twodimensional planar flow have been investigated by evaluating finitetime Lyapunov exponents (FTLE). The first part of our work deals with inertial particle dynamics. The MaxeyRiley ... 
Mathematical modeling of focal axonal swellings arising in traumatic brain injuries and neurodegenerative diseases
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 ... 
Mathematical Models for Facilitated Diffusion and the Brownian Ratchet
(20110831)In this dissertation, mathematical models for two biophysically related topics are investigated: facilitated diffusion and the Brownian ratchet. Both phenomena exhibit counterintuitive behavior: in the case of facilitated ... 
ModelBased Hand Posture Estimation Using Monocular Camera
(20130225)This work studies the problem of modelbased hand posture estimation via monocular camera. Generally, a modelbased posture estimation method manipulates a 3D hand model whose posture is determined by a set of parameters. ... 
Multiscale Modeling of Esophageal Adenocarcinoma
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 ... 
Numerical Modeling of PoroelasticFluid Systems Using HighResolution Finite Volume Methods
(20130624)Poroelasticity theory models the mechanics of porous, uidsaturated, deformable solids. It was originally developed by Maurice Biot to model geophysical problems, such as seismic waves in oil reservoirs, but has also ... 
Numerical Modeling of PoroelasticFluid Systems Using HighResolution Finite Volume Methods
(20130725)Poroelasticity theory models the mechanics of porous, fluidsaturated, deformable solids. It was originally developed by Maurice Biot to model geophysical problems, such as seismic waves in oil reservoirs, but has also ... 
On driven neural assemblies: synchrony, chaos and entropy.
(20140224)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 ...