Name
|
Dissertation Title
|
Advising Professor(s)
|
2022
|
|
|
| Yuying Liu |
Neural Networks for Nonlinear Dynamical Systems |
Nathan Kutz & Steven Brunton |
| Jianghong Shi |
Representations of Biological and Artificial Neural Networks |
Eric Shea-Brown |
2021
|
|
|
| Bobby Baraldi |
A Proximal Quasi-Newton Trust-Region Method for Nonsmooth Regularized Optimization |
Aleksandr Aravkin |
| Yu-Chen Cheng |
Asymptotic Behaviors and Perturbation Analysis of Stochastic Dynamics and Applications to Complex Systems |
Hong Qian |
| Kenan Li |
Crouzeix’s Conjecture and Beyond for Special Classes of Matrices |
Anne Greenbaum |
| Benjamin Liu |
Invasions with Fat-Tailed and Long-Distance Dispersal |
Mark Kot |
| Kelsey Maass |
Optimization Formulations and Algorithms for Cancer Therapy |
Aleksandr Aravkin |
| Megan Morrison |
From worms to wars, modeling and controlling networked dynamical systems |
Nathan Kutz |
| Diya Sashidhar |
Data-Driven Methods for Time Series Forecasting, Classification, and Uncertainty Quantification |
Nathan Kutz |
| Lowell Thompson |
Affine structures and stochastic thermodynamics on the space of measures |
Hong Qian |
| Xin Yang |
On the Riemann-Hilbert approach to the numerical solution of boundary-value problems for evolution partial differential equations |
Bernard Deconinck & Thomas Trogdon |
| Yang Zhou |
Stochastic Control Methods for Dynamic Futures Portfolios |
Tim Leung |
2020
|
|
|
| Matthew Farrell |
Revealing structure in trained neural networks through dimensionality based methods |
Eric Shea-Brown |
| Andreas L. Freund |
Wavelet-spectral analysis and large-eddy simulation using neural networks of droplet-laden decaying isotropic turbulence |
Antonio Ferrante |
| Yuan Gao |
Generalized Matrix-fractional Functions and Their Applications |
James Burke |
| Kelsey Marcinko |
Mathematical Analysis of Host–Parasitoid Dynamics |
Mark Kot |
| Sean Santos |
Time Step Sensitivity and Process Coupling in Climate Models |
Chris Bretherton/Peter Caldwell |
| Brian de Silva |
Data-driven discovery and model reduction of complex systems |
Nathan Kutz/Steven Brunton |
| Jeremy Upsal |
Stability of solutions of integrable partial differential equations |
Bernard Deconinck |
| Xin Yang |
On the Riemann-Hilbert approach to the numerical solution of boundary-value problems for evolution partial differential equations |
Bernard Deconinck/Tom Trogdon |
| Jize Zhang |
Nonconvex Optimization Methods with Applications to Portfolio Selection and Hybrid Systems |
Aleksandr Aravkin |
| Yang Zhou |
Stochastic control methods for dynamic futures portfolios |
Tim Leung |
2019
|
|
|
| Weston D. Barger |
A Partial Differential Equation Approach to Three Problems in Finance: Barrier Option Pricing, Optimal Asset Liquidation and Insider Trading |
Matthew Lorig |
| Kathleen P. Champion |
From data to dynamics: discovering governing equations from data |
Nathan Kutz |
| Samuel H. Rudy |
Computational methods for system identification and data-driven forecasting |
Nathan Kutz/Steven Brunton |
| Peng Zheng |
Algorithm design for nonconvex and nonsmooth problems and its applications |
Aleksandr Aravkin |
2018
|
|
|
| Tommaso Buvoli |
Polynomial-Based Methods for Time Integration |
Randall LeVeque |
| Krithika Manohar |
Data-Driven Sensor Placement Methods |
Nathan Kutz/Steven Brunton |
| Jacob Price |
Multiscale Techniques for Nonlinear Dynamical Systems: Applications and Theory |
Panos Stinis |
| Yue Wang |
Some Problems in Stochastic Dynamics and Statistical Analysis of Single-Cell Biology of Cancer |
Hong Qian |
| Felix Xiaofeng Ye |
Stochastic Dynamics: Markov Chains, Random Transformations and Applications |
Hong Qian |
2017
|
| Kameron Decker Harris |
This Brain is a Mess: Inference, Random Graphs, and Biophysics to Disentangle Neuronal Networks |
Eric Shea-Brown |
| Benjamin Lansdell |
On neural encoding: its estimation, application, and development |
Adrienne Fairhall |
| Yian Ma |
Irreversibility in Stochastic Dynamic Models and Efficient Bayesian Inference
|
Hong Qian |
| Susan C. Massey |
Multi-scale modeling of paracrine PDGF-driven glioma growth and invasion |
Kristin Swanson |
| Scott Moe |
High order shock capturing methods with compact stencils for use with adaptive mesh refinement and mapped grids |
Randall LeVeque |
| Donsub Rim |
Uncertainty quantification problems in tsunami modeling and reduced order models for hyperbolic partial differential equations |
Randall LeVeque |
| Daniel Shapero |
Data assimilation problems in glaciology |
Randall LeVeque/Ian Joughin |
| Timothy B. Oleskiw |
On computing shape: a study of the neural processes concerning naturalistic boundary conformation within the ventral visual pathway |
Eric Shea-Brown |
| Niket Thakkar |
Energy and Charge Transfer in Open Plasmonic Systems |
David Masiello |
| Benjamin Segal |
The stability and instabilities of stationary solutions to the nonlinear Schroedinger and sine-Gordon equation |
Bernard Deconinck |
2016
|
| Xing Fu |
Integrating Data-Driven Methods in Nonlinear Dynamical Systems: Control, Sparsity, and Machine Learning |
Nathan Kutz |
| Jakob Kotas |
Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing |
Archis Ghate |
| Bethany Lusch |
Machine learning and data decompositions for complex networked dynamical systems |
Nathan Kutz |
| Syuzanna Sargsyan |
Dimensionality hyper-reduction and machine learning for dynamical systems with varying parameters |
Nathan Kutz |
| Mauricio del Razo Sarmina |
Stochastic Modeling of Reversible Biochemical Reaction-Diffusion Systems and High-Resolution Shock-Capturing Methods for Fluid Interfaces |
Randall LeVeque/Hong Qian |
2015
|
| Natasha A. Cayco Gajic |
Coordinated Neural Activity: Mechanistic Origins and Impact on Stimulus Coding |
Eric Shea-Brown |
| Kathleen M. Curtius |
Multiscale Modeling of Esophageal Adenocarcinoma |
Georg Luebeck |
| Mikala C. Johnson |
Self-Optimizing Metamaterial Antennas |
Nathan Kutz |
| Pedro D. Maia |
Mathematical Modeling of Focal Axonal Swellings Arising in Traumatic Brain Injuries and Neurodegenerative Diseases |
Nathan Kutz |
| Natalie E. Sheils |
Interface Problems Using the Unified Transform Method |
Bernard Deconinck |
| Olga Trichtchenko |
On the Instability of Water Waves with Surface Tension |
Bernard Deconinck |
2014
|
| Meng-Huo Chen |
Analysis of an Aggregation-based Algebraic Multigrid Method and its Parallelization |
Anne Greenbaum |
| Yu Hu |
Collective Activity in Neural Networks: the Mathematical Structure of Connection Graphs and Population Codes |
Eric Shea-Brown |
| Jihwan Kim |
Finite Volume Method for Tsunamis Generated by Submarine Landslides |
Randall LeVeque |
| Guillaume Lajoie |
On Driven Neural Assemblies: Synchrony, Chaos and Entropy |
Eric Shea-Brown |
2013
|
| Jacob R. Grosek |
Robust Real-Time Image Processing Through Dynamic Mode Decomposition |
Nathan Kutz |
| Christopher R. Jones |
Single-column and mixed-layer model analysis of subtropical stratocumulus response mechanisms relevant to climate change |
Christopher Bretherton |
| Grady I. Lemoine |
Numerical Modeling of Poroelastic-Fluid Systems Using High-Resolution Finite Volume Methods |
Randall LeVeque |
| Russell C. Rockne |
Patient-Specific Mathematical Radiation Oncology |
Kristin Swanson |
| Thomas D. Trogdon |
Riemann-Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions |
Bernard Deconinck |
| Mingyuan Zhong |
Value function approximation methods for Linearly-solvable Markov Decision Process |
Emo Todorov |
| Ying Zhou |
Geographic Range Shifts under Climate Warming |
Mark Kot |
2012
|
| Nicholas Cain |
Probabilistic, Statistical, and Dynamical Models of Neural Decision Making |
Eric Shea-Brown |
| Joshua Jacobs |
Vortex Dynamics of Geostrophically Adjusted Density Perturbations in Stratified, Incompressible Fluids |
Randall LeVeque/Pascale Lelong |
| Laura Matarajt Arbetman |
Optimal Vaccine Allocation for Pandemic Influenza |
Mark Kot/Ira Longini |
| Vishal Vasan |
Some Boundary-Value Problems for Water Waves |
Bernard Deconinck |
| Matthew Williams |
Exploiting Low Dimensionality in Nonlinear Optics and Other Physical Systems |
Nathan Kutz |
| Yun Zhang |
ETG-ETL Portfolio Optimization |
James Burke |
| Jiansong Zhou |
Climate Response to Solar Variation: Cyclic and Secular |
Ka Kit Tung |
2011
|
| Lisa Bishop |
The Origin of Noise-Induced Phenomena: A Mathematical Analysis of Mesoscopic Chemical and Biochemical Dynamics |
Hong Qian |
| Jonathan Claridge |
Numerical methods and studies of parabolic problems, operator splitting, and adaptive mesh refinement |
Randall LeVeque |
| Joshua Goldwyn |
Mathematical modeling of cochlear implants -- from single neurons to psychoacoustics |
Eric Shea-Brown |
| Edwin Ding |
Modeling High-Energy Temporal and Spatial Mode-Locking |
Nathan Kutz |
| Woo Hyun Kim |
On the Behavior of the Entropy Production Rate of a Diffusion Process in Nonequilibrium Steady State |
Hong Qian |
| Eleftherios Kirkinis |
Renormalization Group Methods in Applied Mathematics |
Robert O'Malley |
| Christine Lind |
Mathematical Models for Molecular Motors |
Hong Qian |
| Kyle Mandli |
Finite Volume Methods for the Multilayer Shallow Water Equations with Applications to Storm Surges |
Randall LeVeque |
| Peizhe Shi |
The Coupled Process and its Applications in Cellular Molecular Biology |
Hong Qian |
2010
|
| Kirsten Fagnan |
High-resolution Finite Volume Methods for Extracorporeal Shock Wave Therapy |
Randall LeVeque |
| Minsun Kim |
A mathematical framework for spatiotemporal optimality in radiotherapy |
Archis Ghate |
| Eric MacHorro |
A study of several numerical methods for the Boltzmann transport problems |
Anne Greenbaum |
| Junya Uchida |
Mixed-Layer Models and Large-Eddy Simulations of Stratocumulus-Topped Marine Boundary Layers: Their Nonlinear Dynamics and Sensitivity to Cloud Droplet Concentration |
Chris Bretherton |
2009
|
| Christopher Curtis |
Exact and approximate methods for computing the spectral stability of traveling-wave solutions |
Bernard Deconinck |
| Dean Gull |
Steady State Analysis of Chemical Reaction Systems |
Hong Qian |
| Larry Jean |
Stochastic multi-scale modeling of carcinogenesis |
Georg Luebeck |
| David Ketcheson |
High Order Strong Stability Preserving Time Integrators and Numerical Wave Propagation Methods for Hyperbolic PDEs |
Randall LeVeque |
| Michael Nivala |
Nonlinear Stability in Integrable Hamiltonian Systems |
Bernard Deconinck |
| Katie Oliveras |
Stability of periodic surface gravity water waves |
Bernard Deconinck |
| Yiyi Shi |
Theory of Random Networks and Their Applications |
Hong Qian |
| Melissa Vellela |
Mesoscopic dynamics of biochemical kinetic equations |
Hong Qian |
2008
|
| Brandon Bale |
Modeling the stability and dynamics of mode-locked fiber lasers |
Nathan Kutz |
| Miguel Gomez |
Optimization-based Analysis of Rigid Mechanical Systems with Unilateral Contact and Kinetic Friction." |
Anne Greenbaum |
| Gunog Seo |
The dynamics of simple predator-prey models with Holling functional responses |
Mark Kot |
| Jason Slemons |
Toward the solution of the eigenproblem: Nonsymmetric tridiagonal matrices |
Loyce Adams |
2007
|
| Jihyoun Jeon |
Mathematical modeling of pre-malignant lesions in multistage carcinogenesis |
Suresh Moolgavkar |
| Matthew Patterson |
Algebro-geometric algorithms for integrable systems |
Bernard Deconinck |
| Santosh Srivastava |
Bayesian Minimum Expected Risk Estimation of Distributions for Statistical Learning |
Maya Gupta |
2006
|
| David George |
Finite volume methods and adaptive refinement for tsunami propagation and inundation |
Randall LeVeque |
| Eleftherios Gkioulekas |
A theoretical study of the cascades of 3D, 2D, and QG turbulence |
Ka Kit Tung |
| Rafael Meza |
Some Extensions and Applications of Multistage Carcinogenesis Models |
Suresh Moolgavkar |
| Damon Toth |
Analysis of Age-Structured Chemostat Models |
Mark Kot |
2005
|
| Edward Farnum |
Stability and Dynamics of Solitary Waves in Nonlinear Optical Materials |
Nathan Kutz |
| William Heuett |
New Methods for Modeling Large-Scale Biochemical Networks |
Hong Qian |
| Rie Komuro |
Multi-Objective Evolutionary Algorithms for Ecological Process Models |
E. David Ford |
| Marica Pelanti |
Wave Propagation Algorithms for Multicomponent Compressible Flows with Applications to Volcanic Jets |
Randall LeVeque |
| Matthew Peters |
Moist convection and the large scale tropical circulation |
Christopher Bretherton |
| David Williams |
Solving singular perturbation problems: An amplitude equation approach |
Robert O'Malley |
2004
|
| Sarah Hewitt |
Dynamics and Stability of Periodic Spatial Patterns in the Optical Parametric Oscillator |
Nathan Kutz |
| Viktoria Hsu |
Ion Transport through Biological Cell Membranes: From Electro-Diffusion to Hodgkin-Huxley via a Quasi Steady-State Approach |
Hong Qian |
| Jan Medlock |
Integro-differential-Equation Models in Ecology and Epidemiology |
Mark Kot |
| Timothy Reluga |
Some results on temporal and spatial heterogeneity in theoretical ecology |
Mark Kot |
2003
|
| Kathleen Coughlin |
Stratospheric and Tropospheric Signals Extracted Using the Empirical Mode Decomposition Method |
Ka Kit Tung |
| Rebecca Crabb |
A Dynamic Game for Managing a Conservative Pollutant in an Estuary |
Thomas Leschine |
| Steven Kusiak |
The Scattering Support and the Inverse Scattering Problem at Fixed Frequency |
John Sylvester |
2002
|
| Derek Bale |
Wave Propagation Algorithms On Curved Manifolds With Applications to Relativistic Hydrodynamics |
Randall LeVeque |
| Eric Dolven |
Seaquake Waves - Standing Wave Dynamics with Faraday Excitation and Radiative Loss |
Harry Yeh |
| Long Lee |
Immersed Interface Methods for Incompressible Flow with Moving Interfaces |
Randall LeVeque |
| Blessing Mudavanhu |
A New Ronormalization Method for the Asymptotic Solution of Multiple Scale Singular Perturbation Problems |
Robert O'Malley |
| James Rossmanith |
A Wave Propagation Method with Constrained Transport for Ideal and Shallow Water Magnetohydrodynamics |
Randall LeVeque |
2001
|
| Tiernan Fogarty |
Finite Volume Methods for Acoustics and Elasto-plasticity with Damage in a Heterogeneous Medium |
Randall LeVeque |
| Karl Knaub |
On the Asymptotic Behavior of Internal Layer Solutions of Advection-Diffusion-Reaction Equations |
Robert O'Malley |
| David Luke |
Analysis of Optical Wavefront Reconstruction and Deconvolution in Adaptive Optics |
James Burke |
2000
|
| Arnold Kim |
Optical Pulse Propagation, Diffusion and Depolarization in Discrete Random Media |
Akira Ishimaru |
| Mark Martin |
The Influence of Seasonal and Climatic Environmental Changes on Plankton in the Marine Mixed Layer |
Mark Kot |
| Benjamin Moskowitz |
An Analysis of Frictional Feedback in the Madden-Julian Oscillation |
Christopher Bretherton |
| Dominik Obrist |
On the stability of the swept leading-edge boundary layer |
Peter Schmid |
| Darryl Yong |
Solving boundary-value problems for systems of hyperbolic conservation laws with rapidly varying coefficients |
Jirair Kevorkian |
1999
|
| Donna Calhoun |
A Cartesian Grid Method for Solving the Streamfunction Vorticity Equations in Irregular Geometries |
Randall LeVeque |
| Kristin Swanson |
Mathematical Modeling of the Growth and Control of Tumors |
James Murray |
1998
|
| Trachette Jackson |
Mathematical Models in Two-Step Cancer Chemotherapy |
James Murray |
| Patrick Nelson |
Mathematical Models of HIV Pathogenesis and Immunology |
James Murray |
| Eric Stollnitz |
Reproducing Color Images with Custom Inks |
David Salesin |
| Christopher Thompson |
A Linear, Stochastic, Dynamical Model of El Nino/Southern Oscillation |
Ka Kit Tung |
1997
|
| David Salinger |
A Splitting Algorithm for Multistage Stochastic Programming with Application to Hydropower Scheduling |
Terry Rockafellar |
1996
|
| Daphne Manoussaki |
Modelling formation of vascular networks in vitro |
James Murray |
| Wendell Orlando |
Nonlinear Baroclinic Adjustment and Wavenumber Selection as a Mechanism for Atmospheric Heat Transport |
Ka Kit Tung |
| Louis Stern |
An Explicitly Conservative Method for Time-Accurate Solution of Hyperbolic Partial Differential Equations on Embedded Chimera Grids |
Randall LeVeque |
| Rebecca Tyson |
Pattern formation by E. coli - mathematical and numerical investigation of a biological phenomenon |
James Murray |
| Zhiyun Yang |
A Cartesian Grid Method For Elliptic Boundary Value Problems in Irregular Regions |
Loyce Adams |
| Cynthia Young |
The two-frequency mutual conherence function of a Gaussian beam pulse in weak turbulence |
Akira Ishimaru |
| Chaoming Zhang |
Immersed interface methods for hyperbolic systems of partial differential equations with discontinuous coefficients |
Randall LeVeque |
1995
|
| Julian Cook |
Mathematical Models for Dermal Wound Healing: Wound Contraction and Scar Formation |
James Murray |
| Ming Fang |
On the Axisymmetric Circulation of the Atmosphere |
Ka Kit Tung |
| Paul Kulesa |
A Model Mechanism for the Initiation and Spatial Patterning of Teeth Primordia in the Alligator |
James Murray |
| Thomas Milac |
The Linear Elastostatics of Spherical Shells |
Frederic Wan |
| Hugh Rand |
Mesoscale Dynamics of the Marine Atmospheric Boundary Layer |
Christopher Bretherton |
| Lei Wang |
Asymptotic Analysis of a Class of Three-Degree-Of-Freedom Hamiltonian Systems Near Stable Equilibria |
Jirair Kevorkian |
| Katrin White |
Territoriality and Survival in Wolf-Deer Interactions |
James Murray |
1994
|
| Margaret Brown |
Geophysical inverse methods applied to the deduction of the emissions of atmospheric source gases |
Ka Kit Tung |
| George Chen |
Forward-Backward splitting techniques: Theory and Applications |
Terry Rockafellar |
| Chonghua Gu |
Shear Center of Plates with Variable Thickness |
Frederic Wan |
| Jacques Laforgue |
Using Exponential Asymptotics to Study the Metastability and Supersensitivity of Shock and Transition Layers |
Robert O'Malley |
| Zhilin Li |
The Immersed Interface Method - A Numerical Approach for Partial Differential Equations with Interfaces |
Randall LeVeque |
| Kristyn Maschhoff |
Methods for Solving Large Symmetric Eigenvalue Problems Associated with Configuration Interaction Electronic Structure Calculations |
Loyce Adams |
| William Mell |
An Investigation of Closure Models for Nonpremixed Turbulent Reacting Flow |
George Kosaly |
| Mike Neubert |
The Nonlinear Dynamics of Predator-Prey Growth and Dispersal |
Mark Kot |
| David Stevens |
An Adaptive Multilevel Method for Boundary Layer Meteorology |
Chris Bretherton |
| Mei Zhu |
Mechanisms for Biological Pattern Formation: Nonlinear Effects |
James Murray |
1993
|
| Charles Mannix |
An Investigation of Numerical Methods Applicable to a Certain Class of Singular Integral Equations |
Ka Kit Tung |
| Keh-Ming Shyue |
Front Tracking Methods based on Wave Propagation |
Randall LeVeque |
1991
|
| Yeng Bun |
Evolution of Three-Dimensional Disturbances in a Mixing Layer |
William Criminale |
| Kevin Gates |
Divide and Conquer Methods for the Symmetric Tridiagonal Eigenvalue Problem |
Loyce Adams |
| Jeffrey Greenough |
A Weakly Nonlinear Theory of Confined Supersonic Instability Modes |
James Riley |
| Steven Siems |
A Numerical Investigation of Cloud-Top Entrainment Instability and Related Experiements |
Chris Bretherton |
| Ciyou Zhu |
Methods for Large-Scale Extended Linear-Quadratic Programming |
Terry Rockafellar |
1990
|
| Scott Coble |
Automatic Control of Extracorporeal Blood Oxygenation |
Juris Vagners |
| Mark Pernarowski |
The Mathematical Analysis of Bursting Electrical Activity in Pancreatic Beta Cells |
Jirair Kevorkian |
| Ruoxin Zhang |
Problems of Hierarchical Optimization: Nonsmoothness and Analysis of Solutions |
Terry Rockafellar |
1989
|
| Richard Beyer |
A Computational Model of the Cochlea using the Immersed Boundary Method |
Randall LeVeque |
| David Bosley |
Transient and Sustained Resonance in Very Slowly Varying Oscillatory Hamiltonian systems with Application to Free-Election Lasers |
Jirair Kevorkian |
| Marie Lelong |
Weakly-nonlinear Internal Wave/Vortical Mode Interactions in Stably-Stratified Flows |
James Riley |
| Joseph Manke |
A Tensor Product B-spline Method for Numerical Grid Generation |
Loyce Adams |
| Maria Ong |
Hierarchical Basis Preconditioners for Second-Order Elliptic Problems in Three Dimensions |
Loyce Adams |
| Radhakrishnan Srinivasan |
Asymptotic Solutions of Weakly Nonlinear, Dispersive Wave Propagation Problems by Fourier Analysis |
Jirair Kevorkian |
| Kraig Winters |
Intensification and Instability of Internal Gravity Waves at Caustics and Critical Levels |
James Riley |
1988
|
| Philip Harrison |
A New Algorithm for Parsing Generalized Phrase Structure Grammar |
Juris Vagners |
| Angel Muleshkov |
Analytical and Numerical Determination of Steady Seepage Towards Vertical Cuts |
Chris Bretherton |
| Jun Yu |
Passage Through the Critical Froude Number for Shallow Water Waves over a Variable Bottom |
Jirair Kevorkian |
1987
|
| Pierre Mourad |
A Nonlinear Wave-Wave Interaction Theory for the Generation of Multiscale Large Eddies in a Neutral Atmospheric Boundary Layer |
|
| Donald Owen |
A Numerical Streamline Approach to Steady Internal Flows |
Carl Pearson |
1986
|
| Jeffrey Cordova |
Numerical Streamline Methods for Solving Steady Flow Problems (Methods, Compressible, Free Surface, Finite Difference.) |
|
| Jie Sun |
On Monotropic Piecewise Quadratic Programming (Network, Algorithm, Convex Programming, Decomposition Method.) |
|