Browsing Dissertations and Theses by Subject "applied mathematics"
Now showing items 1-20 of 28
-
Analysis of an Aggregation-based Algebraic Multigrid Method and its Parallelization
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), ... -
Closing the Loop: Optimal Stimulation of Neuronal Networks via Adaptive Control Algorithms
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 ... -
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 ... -
Dimensionality hyper-reduction and machine learning for dynamical systems with varying parameters
This work demonstrates methods for hyper reduction and efficient computation of solutions of dynamical systems using optimization and machine learning techniques. We consider nonlinear partial differential equations that ... -
Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing
Medical treatment commonly involves the administration of drug doses at multiple time-points. Intuitively, the higher the doses, the higher the likelihood of disease control as well as the risk of adverse effects and of ... -
Finite volume methods for Tsunamis generated by submarine landslides
(2014-04-30)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
(2013-07-25)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 ... -
Integrating Data-Driven 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 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 ... -
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 self-driving 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 ... -
Multi-scale modeling of paracrine PDGF-driven 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 ... -
Numerical Modeling of Poroelastic-Fluid Systems Using High-Resolution Finite Volume Methods
(2013-07-25)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 ... -
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.
(2014-02-24)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 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 ... -
Riemann-Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions
(2013-11-14)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 ...