Browsing Applied mathematics by Title
Now showing items 52-71 of 117
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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 ... -
Multiscale Financial Signal Processing and Machine Learning
Financial time series such as market indices and asset prices are shown to be driven by multiscale factors, ranging from long-term market regimes to rapid fluctuations. Multiscale analysis and signal processing not only ... -
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 ... -
Neural Networks for Nonlinear Dynamical Systems
Nonlinear dynamical systems are ubiquitous in many fields of sciences and engineering. Throughout the history, differential equations were widely accepted as effective tools for describing the evolution of such systems in ... -
Nonconvex and Nonsmooth Inverse Problems
Optimization approaches to inverse problems and parameter estimation have wide-ranging applications, from classical physics and biology to recently developed topics in statistical computing. Here, we focus on solving ... -
Nonconvex Optimization Methods with Applications to Portfolio Selection and Hybrid Systems
This thesis focuses on formulating selection problems using continuous optimization, and solving them by specialized algorithms. Problems involving selection, i.e., selecting ``best" candidate(s) out of a given set, occur ... -
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 ... -
Numerical Modeling of Poroelastic-Fluid Systems Using High-Resolution Finite Volume Methods
(2013-06-24)Poroelasticity theory models the mechanics of porous, uid-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 ...