Doctor of Philosophy
Applied Mathematics, Illinois Institute of Technology (IIT), Graduation Date: May 2012
Advisor: Dr. Gregory E. Fasshauer Thesis Title: Analyzing reproducing kernel approximation methods via a Green function approach,
Thesis 2nd version (corrections of Section 6.2), Correction manual of original and library version Keywords: meshfree method, reproducing kernel, Green function, Green kernel, conditionally positive definite function, positive definite kernel,
reproducing kernel Hilbert space, reproducing kernel Banach space, generalized Sobolev space, kernel-based collocation method, stochastic field, Gaussian field, Gaussian process, partial differential equation, stochastic partial differential equation.
Master of Science (partial course work)
Mathematical Science, South China Normal University (SCNU), Sep. 2006 - Jul. 2007, partial courses work, completed 18 credits
Advisor: Dr. Liren Huang
Research Topic: Optimization Computation with Generalized Derivatives
Bachelor of Science
Mathematical Science, South China Normal University (SCNU), Graduation Date: Jul. 2006
Bachelor Thesis: Application of Generalized Gradients in Optimization Theory
GENEALOGY
RESEARCH INTERESTS
Kernel-based Methods, Meshfree Methods, Radial Basis Functions, High Dimensional Approximation
Statistical Learning, Support Vector Machines, Data Mining,
Numerical Solutions of Stochastic Partial Differential Equations, Random Dynamical System with L\'evy Process
Reproducing Kernels of Sobolev Spaces via a Green Kernel Approach with Differential Operators and Boundary Operators,
(with G. E. Fasshauer), Advances in Computational Mathematics, Volume 38, Issue 4, Pages 891-921, 2013,
DOI: 10.1007/s10444-011-9264-6 (The wrong reference number of Theorem 4.5 is fixed to Theorem 4.3.), arXiv:1109.5755v1.
Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Differential Operators,
Technical Report of Illinois Institute of Technology 2010,
arXiv:1109.0109v1.
Support Vector Machines:
Solving Support Vector Machines in Reproducing Kernel Banach Spaces with Positive Definite Functions,
(with G. E. Fasshauer and F. J. Hickernell), Applied and Computational Harmonic
Analysis, to appear, arXiv:1209.1171.
Solving support vector machines in reproducing kernel Hilbert versus Banach spaces,
Approximation Theory XIV, Springer, Pages 377-395, 2014.
Constructions of Reproducing Kernel Banach Spaces via Generalized Mercer's Kernels,
(with Y. Xu), submitted soon.
Stochastic Partial Differential Equations:
Approximation of Stochastic Partial Differential Equations by a Kernel-based Collocation Method,
(with I. Cialenco and G. E. Fasshauer), International Journal of Computer Mathematics, Volume 89, Issue 18, Pages 2543-2561, 2012,
DOI: 10.1080/00207160.2012.688111,
Updated the Journal Version (given the proof of the convergence analysis of the new stochastic estimator in Section 3.2): arXiv:1108.4213, PDF.
Kernel-based Collocation Methods versus Galerkin Finite Element Methods for Approximating Elliptic Stochastic Partial Differential Equations,
(with G. E. Fasshauer), Meshfree Methods for Partial Differential Equations VI, Springer, Pages 155-170, 2013,
PDF.
A Kernel-based Collocation Method for Elliptic Partial Differential Equations with Random Coefficients,
(with G. E. Fasshauer), Monte Carlo and Quasi-Monte Carlo Methods 2012, Springer, 2013, Springer, Pages 331-348, 2013.
Approximation of Nonlinear Stochastic Partial Differential Equations by A Kernel-based Collocation Method,
International Journal of Applied Nonlinear Science, 2013, Volume 1, Number 2, Pages 156-172, 2014.
Kernel-based Approximation Methods for Stochastic Partial Differential Equations,
submitted, arXiv:1303.5381.
Random Dynamical Systems:
Coming soon
Image Proessing:
Coming soon
Others:
Happy Travel on Tall Highway,
(with H. Cai, A. Xu and H. Wang), Journal of South China Normal University (Chinese), 2005.6.
Generalization of One Probability Example,
Teachers Training and Management (Journal of Shaoguan College, Chinese), 2005, No.2
PROJECTS:
1-Norm Support Vector Machines via Green Kernels, 2011.
Approximation of (Stochastic) Partial Differential Equations by Gaussian Processes via a Reproducing Kernel Approach, 2010-2011.
Approximation of Stable/Unstable Manifolds of Random Dynamical Systems by Support Vector Machine Methods, 2009.
PRESENTATIONS AND CONFERENCES
Kernel-based Approximation Methods for Stochastic Partial Differential Equations
Sigma Xi Award in recognition of the outstanding accomplishments in research and scholarship, 2012, Sigma Xi, news
Karl Menger Student Award, 2012, Illinois Institute of Technology, news
Award in recognition of outstanding efforts and accomplishments on behalf of the SIAM Student Chapter at 2011-2012, 2012, SIAM, news
Award for student research poster at Annual Karl Menger Lecture, 2009, Illinois Institute of Technology, news
Meritorious Winner of the Mathematical Contest in Modeling (MCM) administered by the Consortium for Mathematics and Its Applications (COMAP), 2005, SIAM
"Zhentai" scholarship for outstanding students, 2005, South China Normal University
Travel grant to the International Conference on Spectral and High Order Methods 2014, 2014, ICOSAHOM 2014 Organizing Committee
Travel grant to the 5th International Conference on Computational Harmonic Analysis, 2014, ICCHA5 Organizing Committee
Travel grant to the workshop of Low-dimensional Structure in High-dimensional Systems, 2013, SAMSI
Travel grant to the 14th International Conference Approximation Theory, 2013, AT14 Organizing Committee
Travel grant to the Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods, 2012, Stanford University
Graduate student travel grant to the Joint Mathematics Meetings, 2012, AMS
COMPUTER SKILLS
Fluent in C++ and Matlab/Maple/Mathematica
PAST TEACHING EXPERIENCES
Teaching Assistant of Probability and Statistics (Math 474 & 563), Applied Analysis (Math 500), Dynamical Systems (Math 515),
Computational Mathematics (Math 577), and etc. at Illinois Institute of Technology, 2007-2012
Internship at South China Institute of Software Engineering, Guangzhou University, 2006
