Browsing Applied mathematics by Title
Now showing items 43-62 of 117
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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 ... -
Impact Investing: Performance Analysis and Comparison Across Themes
Social impact themes prioritized by the United Nations’ “The 2030 Agenda for Sustainable Development” such as clean energy, workplace equality, and industrial innovation share similar characteristics in terms of correlation ... -
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 ... -
Interpretation and Optimization of Recurrent Neural Network Performance Through Lyapunov Exponents Methodology
Common deep learning models for learning multivariate time series data are Recurrent Neural Networks (RNN). These models are ubiquitous computing systems which have been studied for decades. The propagation of gradients ... -
Invasions with Fat-Tailed and Long-Distance Dispersal
Ecologists have recognized fat-tailed and long-distance dispersal (LDD) as critical to our understanding of population spread and invasions; heavy- and fat-tailed kernels fit empirical dispersal data better than classical ... -
Investigating longitudinal evolution of liquid cancers using computational and mathematical models
Cancer can result from a series of driver mutations, alterations in the genome sequence that confer a fitness advantage to cells containing them, resulting in their net proliferation. Mutations that have a neutral fitness ... -
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 ... -
K-spectral Sets and Functions of Nonnormal Matrices
In this thesis, we study K-spectral 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 K-spectral 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 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 ... -
Lanczos Algorithm and Conjugate Gradient
We review results from the literature on the conjugate gradient algorithm for solving symmetric positive definite linear systems and the related Lanczos algorithm. We derive the conjugate gradient algorithm from the more ... -
Lanczos-based methods for matrix functions
We study Lanczos-based methods for tasks involving matrix functions. We begin by resurfacing a range of ideas regarding matrix-free quadrature which, to the best of our knowledge, have not been treated simultaneously. This ... -
Learning to Predict in Networks with Heterogeneous and Dynamic Synapses
A salient difference between artificial and biological neural networks is the complexity and diversity of individual units in the latter (Tasic et al., 2018). This remarkable diversity is present in the cellular and synaptic ... -
Life Together: Modeling the Collective Behavior of Cellular Communities
Our lives as eukaryotic organisms are defined by the collective behaviors of cellular systems. Together groups of cells form intricate structures and accomplish complex tasks. Where an individual cell cycles through growth, ... -
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 Analysis of Host–Parasitoid Dynamics
Host and parasitoid systems are of great interest to ecologists, both because of the global prevalence of insect parasitoids and the impact of parasitoids in regulating their hosts. The direct connection between parasitized ... -
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
(2011-08-31)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 ... -
Model-Based Hand Posture Estimation Using Monocular Camera
(2013-02-25)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. ... -
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 ...