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Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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Items (1-20) out of 22 results

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

Confluence in Chip-Firing and Related Combinatorial Processes

Description:
Confluence is an important property in many combinatorial processes. A globally confluent process is one in which a fixed initial state always leads to a …
Year:
2022
Contributor:
Liscio, Patrick Hirsch (creator)
Klivans, Caroline (Advisor)
Guzman, Johnny (Reader)
Chan, Melody (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Combinatorics
Applied mathematics
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 Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice

Description:
Abstract of Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice, by Rebecca Santorella Ph.D., Brown University, May 2022. As data becomes …
Year:
2022
Contributor:
Santorella, Rebecca (creator)
Sandstede, Bjorn (Advisor)
Singh, Ritambhara (Reader)
Harrison, Matthew (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
dynamical systems
Computational biology
Fair Machine Learning
federal sentencing
data science
Collection:
Applied Mathematics
Theses and Dissertations
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

Homoclinic Snaking of Spatiotemporal Patterns in Reaction Diffusion Systems

Description:
Abstract of Homoclinic Snaking of Spatiotemporal Patterns in Reaction Diffusion Equations, by Timothy V Roberts, Ph.D., Brown University, May 2024. Spiral and target waves are …
Year:
2024
Contributor:
Roberts, Timothy Victor (creator)
Sandstede, Bjorn (Advisor)
Beck, Margaret (Reader)
Menon, Govind (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Differential equations, Partial
Applied mathematics
Pattern formation (Biology)
dynamical systems
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Identifying Diabetic Kidney Disease Risk Factors in the U.S. Population with Type 2 Diabetes Mellitus

Description:
Diabetes is the leading cause of chronic kidney disease and kidney failure worldwide, causing 44 percent of new cases of kidney failure each year. Although …
Year:
2019
Contributor:
Webb, Katherine (creator)
Aubert, Ronald (thesis advisor)
Sandstede, Bjorn (reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Biology
Diabetes
Diabetic nephropathies
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Available to Brown-affiliated users only
Full Record

Infectious Disease Spread on Context-Specific Interaction Networks: Influenza and COVID-19

Description:
The spread of infectious disease is strongly influenced by human interaction. In order to understand this connection and develop effective strategies against future outbreaks, it …
Year:
2021
Contributor:
Mallory, Kristina (creator)
Sandstede, Bjorn (Advisor)
Maxey, Martin (Reader)
Harrison, Matthew (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Epidemiology
Biology--Mathematical models
Applied mathematics
Infection
Influenza
Communicable diseases
COVID-19
Coronavirus infections
Contact tracing (Epidemiology)
Social distancing (Public health)
Influenza--Prevention
SARS-CoV-2
Emerging infectious diseases
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Interpretable Probabilistic Methods for Genetic Association Mapping and Shape Generation

Description:
As data structures become larger and more complex, methods of data analysis must evolve to harness the most accurate insights. Inspired by the challenges presented …
Year:
2024
Contributor:
Winn-Nunez, Emily Taylor (creator)
Crawford, Lorin (Advisor)
Sandstede, Bjorn (Reader)
Wong, Ian (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Applied mathematics
Shape
Computational biology
nonlinear model fitting
topological data analysis
Quantitative genetics
Bayesian Statistics
Computational modeling
Generative Models
Shapes
Ranking and selection (Statistics)
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Patterns in Network Dynamics

Description:
Many real-world complex systems exhibit dynamics on network structures. Within such systems, patterns emerge in various ways and motivate diverse approaches towards understanding the formation …
Year:
2024
Contributor:
Tian, Moyi (creator)
Sandstede, Björn (Advisor)
Harrison, Matthew (Reader)
Bramburger, Jason (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Nonlinear systems
Applied mathematics
dynamical systems
data science
Lattice dynamics
Reaction-diffusion equations
Pattern formation
Network science
Community robustness
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Play by the Rules: How a Game-Playing GPT Learns

Description:
Creating and studying a GPT that plays tic-tac-toe
Year:
2025
Contributor:
Parekh, Rajen N. (creator)
Shenfeld, Yair (thesis advisor)
Singh, Ritambhara (reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Predicting Utilization of LVC Services using Machine Learning

Description:
Each year, as much as $100 billion is wasted on low-value care (LVC) procedures that offer little or no benefit to patients and may even …
Year:
2021
Contributor:
Kumar, Soryan P. (creator)
Panagiotou, Orestis (thesis advisor)
Wang, Hui (reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Machine learning
Public health
Clinical medicine--Decision making
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Problems at the interface of high dimensional probability and random matrix theory

Description:
Abstract of “Problems at the interface of high dimensional probability and random matrix theory”, by Xiaoyu Xie, Ph.D., Brown University, May 2024 In this thesis, …
Year:
2024
Contributor:
Xie, Xiaoyu (creator)
Ramanan, Kavita (Advisor)
Dupuis, Paul (Reader)
Paouris, Grigoris (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Probability
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Problems at the Interface of Probability and Convex Geometry: Random Projections and Constrained Processes

Description:
Convex sets in high-dimensional linear spaces are classical objects of study that have long enjoyed rich connections with probability theory. Interest in these connections has …
Year:
2017
Contributor:
Kim, Steven Soon (creator)
Ramanan, Kavita (Advisor)
Dupuis, Paul (Reader)
Wang, Hui (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Limit theorems (Probability theory)
Large deviations
Convex geometry
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Regularity for $p$-Laplace Type Equations with Applications in Composite Materials

Description:
In this dissertation, we study regularity theory for equations of $p$-Laplace type. In the first part of the dissertation, we address elliptic and parabolic $p$-Laplace …
Year:
2024
Contributor:
Zhu, Hanye (creator)
Dong, Hongjie (Advisor)
Guo, Yan (Reader)
Pausader, Benoit (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Regularity Theory of Elliptic and Parabolic Equations and Systems

Description:
In this dissertation, we study regularity theory of elliptic and parabolic equations and systems with irregular coefficients. In the first part of the dissertation, we …
Year:
2017
Contributor:
Zhang, Hong (creator)
Dong, Hongjie (Advisor)
Guo, Yan (Reader)
Dafermos, Constantine (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Differential equations, Elliptic
Differential equations, Parabolic
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Riemannian Langevin Equation and Its Applications in Random Matrix Theory and Gibbs Sampling Problems

Description:
The Riemannian Langevin Equation is a natural extension of Langevin equation on Riemannian manifolds. As a stochastic relaxation of gradient flow, Riemannian Langevin equation serves …
Year:
2024
Contributor:
Yu, Tianmin (creator)
Menon, Govind (Advisor)
Darbon, Jerome (Reader)
Shenfeld, Yair (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
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

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

Uncertainty Quantification in Scientific Machine Learning: Theory, Methods, and Software

Description:
Uncertainty quantification (UQ) is a critical component in scientific machine learning (SciML), addressing the challenges of modeling, predicting, and interpreting complex systems under incomplete or …
Year:
2024
Contributor:
Zou, Zongren (creator)
Karniadakis, George (Advisor)
Darbon, Jerome (Reader)
Owhadi, Houman (Reader)
Tartakovsky, Daniel (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Items (1-20) out of 22 results