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Author:

Chen, Long

Title:

Robust and Accurate Algorithms for Solving Anisotropic Singularities

Graduate Program:

Mathematics

Keywords:

mesh adaptation
anisotropic error estimate
convection dominated problem
singularly perturbed problem
optimal Delaunay triangulation
nonlinear approximation

File:

Download MyThesis.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Qiang Du, Committee Member
Chun Liu, Committee Member
James Z Wang, Committee Member
Ludmil Tomov Zikatanov, Committee Member

Author:

Chen, Jianyu

Title:

Coexistence of Hyperbolic and Non-hyperbolic Behavior in Smooth Dynamical Systems

Graduate Program:

Mathematics

Keywords:

Dynamical systems
Ergodic theory
Lyapunov exponents

File:

Download Jianyu_Chen-Dissertation.pdf

Committee Members:

Yakov B Pesin, Dissertation Advisor/Co-Advisor
Yakov B Pesin, Committee Chair/Co-Chair
Svetlana Katok, Committee Member
Mark Levi, Committee Member
Mark Strikman, Committee Member

Author:

Chen, Yao

Title:

Algebraic Multilevel Methods for Graph Laplacians

Graduate Program:

Mathematics

Keywords:

Algebraic Multigrid Methods
Graph Laplacians
Parallel Algorithms

File:

Download main.pdf

Committee Members:

James Joseph Brannick, Committee Chair/Co-Chair
Ludmil Tomov Zikatanov, Dissertation Advisor/Co-Advisor
Jinchao Xu, Committee Member
Jesse Louis Barlow, Special Member

Author:

Chen, William Y

Title:

Moduli Interpretations for Noncongruence Modular Curves

Graduate Program:

Mathematics

Keywords:

number theory
arithmetic geometry
algebraic geometry
modular curves
galois theory
noncongruence subgroups
modular forms
unbounded denominators conjecture
elliptic curves
moduli problems

File:

Download Will_Chen_Dissertation.pdf

Committee Members:

Wen Ching Li, Dissertation Advisor/Co-Advisor

Author:

Chen, Dong

Title:

On some problems in Lagrangian Dynamics and Finsler Geometry

Graduate Program:

Mathematics

Keywords:

KAM theory
Finsler metric
duel lens map Hamiltonian flow
perturbation
metric entropy
duel lens map
Hamiltonian flow
perturbation
metric entropy

File:

Download Dong_Chen-Dissertation_V2.pdf

Committee Members:

Dmitri Yu Burago, Dissertation Advisor/Co-Advisor
Dmitri Yu Burago, Committee Chair/Co-Chair
Federico Juan Rodriguez Hertz, Committee Member
Mark Levi, Committee Member
Runze Li, Outside Member

Author:

Chen, Qipin

Title:

Nonlinear computations in neural networks and applications

Graduate Program:

Mathematics

Keywords:

Homotopy
Neural Network
Initialization

File:

Download Qipin-Chen-Dissertation.pdf

Committee Members:

Wenrui Hao, Dissertation Advisor/Co-Advisor
Wenrui Hao, Committee Chair/Co-Chair
John Harlim, Committee Member
Wen Shen, Committee Member
Xiang Gao, Outside Member
Carina Pamela Curto, Program Head/Chair

Author:

Chen, Jianhong

Title:

Reducing Model Complexity and Overcoming Overfitting: Deep Learning Algorithms and Medical Applications

Graduate Program:

Mathematics

Keywords:

Deep learning
Compressed sensing
Medical application

File:

Download JianhongChen-Dissertation.pdf

Committee Members:

Jinchao Xu, Dissertation Advisor/Co-Advisor
Wenrui Hao, Committee Member
Xiantao Li, Committee Member
Ludmil Tomov Zikatanov, Committee Member
Xiang Zhang, Outside Member
Alexei Novikov, Program Head/Chair
Jinchao Xu, Committee Chair/Co-Chair