Browsing Applied mathematics by Title
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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 ... 
Irreversibility in Stochastic Dynamic Models and Efficient Bayesian Inference
This thesis is the summary of an excursion around the topic of reversibility. We start the journal from a classical mechanical view of the “time reversal symmetry”: we look into the details to track the movements of all ... 
Kspectral Sets and Functions of Nonnormal Matrices
In this thesis, we study Kspectral sets and use them to bound norms of functions of nonnormal matrices. For a fixed constant K > 0, the set Ω is said to be a Kspectral set for a matrix A if the spectrum Λ(A) is contained ... 
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 ... 
Machine learning and data decompositions for complex networked dynamical systems
Machine learning has become part of our daily lives. Its applications include personalized advertisements, stock price predictions, and selfdriving cars. The goal of this thesis is to study ways to apply machine learning ... 
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 paracrine PDGFdriven glioma growth and invasion
The most common primary brain tumor in adults, glioma claims thousands of lives each year. Despite efforts to improve survival rates, the standard of care has remain unchanged for more than a decade. Recent research has ... 
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 ... 
Multiscale Techniques for Nonlinear Dynamical Systems: Applications and Theory
Most interesting real world systems can be understood at multiple scales of detail. A physical system such as a closed container of gas particles can be understood in terms of hydrodynamic flows, molecules and atoms exerting ... 
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 ... 
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 ... 
On computing shape: a study of the neural processes concerning naturalistic boundary conformation within the ventral visual pathway
The perception of shape is a remarkable computation, solved rapidly by the brain to extract boundary features within natural scenes while being robust against many visual obstacles. Interestingly, while observers typically ... 
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 ... 
On neural encoding: its estimation, application, and development
The spiking activity of neurons encodes information about sensory stimuli and about planned or executed motor outputs. An important problem in computational neuroscience is the development of predictive models that describe ... 
On the asymptotic behavior of internal layer solutions of advectiondiffusionreaction equations
(2001)We study the behavior of solutions of certain parabolic partial differential equations of the form ut = epsilon2 uxx + epsilong(u) ux + h(u) in the limit epsilon → 0+. Solutions of advectiondiffusion and reactiondiffusion ... 
On the instability of water waves with surface tension.
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 ...