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Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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  • 15 2020

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Items (1-15) out of 15 results

A modeling investigation of the calcium dynamics underlying human EEG signals

Description:
Electroencephalography (EEG) signals are created by electrical currents from pyramidal neurons in the outer layer of the brain. These signals are easy to obtain and …
Year:
2020
Contributor:
Pugliese, Sarah M. (creator)
Jones, Stephanie (thesis advisor)
Harrison, Matthew (reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Dendrites--Mathematical models
Calcium channels
Electroencephalography
Computational neuroscience
Neurons--Mathematical models
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Ablation study of named entity recognition (NER) taxonomies on the de-identification of free-text medical records

Description:
Electronic Health Records (EHRs) have become the primary form of medical data-keeping across the United States. Federal law restricts the sharing of any EHR data …
Year:
2020
Contributor:
Ahmed, Abdullah (creator)
Eickhoff, Carsten (thesis advisor)
Shin, Yeonjong (reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Artificial intelligence--Medical applications
Medical records--Data processing
Natural language processing (Computer science)
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Available to Brown-affiliated users only
Full Record

Brain Connectivity Analysis using fMRI Data

Description:
In many real-world applications, e.g., brain imaging and or weather patterns, data are captured over particular periods or intervals, which we call time series. Time …
Year:
2020
Contributor:
Cao, Xuefei (creator)
Sandstede, Björn (Advisor)
Luo, Xi (Reader)
Harrison, Matthew (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Statistics
fmri
Computational neuroscience
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Data Applications of Space Filling Curves

Description:
A space filling curve (or mapping) is a parametric map from a one-dimensional unit interval to a n-dimensional hypercube that traverses every point in its …
Year:
2020
Contributor:
Kwon, Oh Joon (creator)
Harrison, Matthew (thesis advisor)
Tompkin, James (reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Available to Brown-affiliated users only
Full Record

Data-driven uncertainty quantification for problems in systems biology

Description:
A number of problems of interest in applied mathematics and biology involve the quantification of uncertainty in computational and real-world models. A recent approach to …
Year:
2020
Contributor:
Larson, Karen Ruth (creator)
Matzavinos, Anastasios (Advisor)
Maxey, Martin (Reader)
Olson, Sarah (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Biology--Mathematical models
Parameter estimation
Applied mathematics
Uncertainty Quantification
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Elliptic Boundary Value Problems on Irregular Domains

Description:
In this thesis, we study the elliptic boundary value problems on irregular domains. We first obtain the $W^{2,p}$ and $C^2$ regularity theories for second-order, non-divergence …
Year:
2020
Contributor:
Li, Zongyuan (creator)
Dong, Hongjie (Advisor)
Guo, Yan (Reader)
Dafermos, Constantine (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Mathematics
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Exact Smooth Piecewise Polynomial Sequences on Powell-Sabin and Worsey-Farin Splits

Description:
The problem of forming exact sequences of finite element spaces that discretize Hilbert complexes is central to the finite element exterior calculus. This framework offers …
Year:
2020
Contributor:
Lischke, Anna (creator)
Guzman, Johnny (Advisor)
Neilan, Michael (Reader)
Shu, Chi-Wang (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Scientific Computation
Numerical analysis
Finite element method
Algebra, Homological
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Nonlinear waves in the fifth-order Korteweg-de Vries equation

Description:
Solitary waves are localized disturbances that maintain their shape as they propagate at a constant velocity. They have applications in diverse fields such as fluid …
Year:
2020
Contributor:
Parker, Ross Hamilton (creator)
Sandstede, Bjorn (Advisor)
Mallet-Paret, John (Reader)
Goh, Ryan (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
dynamical systems
Nonlinear waves
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Persistent Reflective Ocean Particulates of Biologic Origin: a Geoengineering Strategy

Description:
This thesis project examines a novel method of geoengineering, a means to ameliorate the effects of anthropogenic climate change. As discussed in the first chapter …
Year:
2020
Contributor:
Nicklas, John Matthew (creator)
Lawrence, Charles (thesis advisor)
Fox-Kemper, Baylor (reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Climate change mitigation
Greenhouses--Climate--Mathematical models
Kalman filtering--Mathematical models
Environmental geotechnology
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Preconditioning the p-FEM Mass Matrix: Theory, Implementation, and Applications

Description:
The finite element method (FEM) is an extremely successful approach to numerically approximating solutions to partial differential equations arising from many real-world scenarios. While the …
Year:
2020
Contributor:
Jiang, Shuai (creator)
Ainsworth, Mark (Advisor)
Shu, Chi-Wang (Reader)
Sarkis, Marcus (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
preconditioners
Finite element method
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Quantifying Patterns in Dynamical Systems and Biological Data

Description:
From data clusters to fish swarms, patterns are widespread in both the natural world and in the era of big data. Across a range of …
Year:
2020
Contributor:
McGuirl, Melissa Rose (creator)
Sandstede, Bjorn (Advisor)
Blumberg, Andrew (Reader)
Harrison, Matthew (Reader)
Ramachandran, Sohini (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Genetics
Patterns
agent-based models
spiral waves
topological data analysis
pattern quantification
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

State-space Models and Gaussian Processes in Paleoceanography and Paleoclimatology

Description:
For the recent decades, statistical (machine) learning and Bayesian modelling have emerged as popular frameworks for various fields of area, regardless of academy or industry. …
Year:
2020
Contributor:
Lee, Taehee (creator)
Lawrence, Charles (Advisor)
Lisiecki, Lorraine (Reader)
Harrison, Matthew (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Paleoclimatology
Gaussian processes
State-space models
Machine learning--Statistical methods
Bayesian Machine Learning
Paleoceanography
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

The Incompressible Navier-Stokes Equations: Two Regularity Criteria

Description:
This dissertation presents new regularity criteria of the incompressible Navier-Stokes equations and derive further results, including extensions of the Ladyzhenskaya-Prodi-Serrin condition in high dimensional critical …
Year:
2020
Contributor:
Wang, Kunrui (creator)
Dong, Hongjie (Advisor)
Shu, Chi-Wang (Advisor)
Guo, Yan (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Differential equations, Partial
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Theory and Applications of Harish-Chandra Integrals

Description:
This thesis studies the integral of an exponential function over an adjoint orbit of a compact Lie group. These integrals are named after Harish-Chandra, who …
Year:
2020
Contributor:
McSwiggen, Colin Smith (creator)
Menon, Govind (Advisor)
Zuber, Jean-Bernard (Reader)
Novak, Jonathan (Reader)
Ramanan, Kavita (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Combinatorics
Applied mathematics
Mathematical physics
Representations of Lie algebras
Random matrices
Functions, Special
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Theory, Algorithms, and Software for Physics-Informed Deep Learning

Description:
This dissertation is centered around the broad topic of physics-informed deep learning (DL). Specifically, it covers the following three fronts: Algorithms. Recent developments of DL, …
Year:
2020
Contributor:
Lu, Lu (creator)
Karniadakis, George (Advisor)
Harrison, Matthew (Reader)
Stinis, Panos (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Differential equations, Partial
Deep Learning
computational physics
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Items (1-15) out of 15 results