QI YE

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Department of Applied Mathematics
Illinois Institute of Technology

Room 258, Engineering 1 Building 10 West 32nd Street, Chicago, IL 60616
Tel 312.567.5867, Fax 312.567.3135
Email: qye3 at hawk.iit.edu and yeqi.iit at gmail.com


POSTDOC POSITION

Philip T. Church Postdoc
Department of Mathematics, Syracuse University, 2012 - current,
Joint work with Dr. Yuesheng Xu and Dr. Lixin Shen


EDUCATION

Doctor of Philosophy
Applied Mathematics, Illinois Institute of Technology (IIT), Aug. 2007 - 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 approximation 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, 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

Radial Basis Functions, Kernel-based Methods, Meshfree Approximation Methods,
Statistical Learning, Data Mining, Support Vector Machines,
Numerical Analysis, Stochastic Analysis, Numerical Methods for (Stochastic) Partial Differential Equations


RESEARCH ACTIVITIES

PAPERS: 

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators,
(with G. E. Fasshauer), Numerische Mathematik, Volume 119, Number 3, Pages 585-611, 2011, DOI:10.1007/s00211-011-0391-2, 
Updated the Journal Version, arXiv:1204.6448.

Reproducing Kernels of Sobolev Spaces via a Green Kernel Approach with Differential Operators and Boundary Operators, 
(with G. E. Fasshauer), Advances in Computational Mathematics, 2011, DOI: 10.1007/s10444-011-9264-6, 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, PDF (Revised Version). 

Solving Support Vector Machines in Reproducing Kernel Banach Spaces with Positive Definite Functions, 
(with G. E. Fasshauer and F. J. Hickernell), in preparation.

Approximation of Stochastic Partial Differential Equations by a Kernel-based Collocation Method, 
(with I. Cialenco and G. E. Fasshauer), International Journal of Computer Mathematics, 
Special Issue: Recent Advances on the Numerical Solutions of Stochastic Partial Differential Equations (SPDEs), 2012, 
DOI: 10.1080/00207160.2012.688111, arXiv:1108.4213v1. 

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 series: Lecture Notes in Computational Science and Engineering, to appear, 2012, PDF.

A Kernel-based Collocation Method for Elliptic Partial Differential Equations with Random Coefficients,
(with G. E. Fasshauer), submitted.

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

Midwest Numerical Analysis Day (NWNA Day) 2012, May 12-13 2012, Notre Dame, IN, Attended.

Approximation of stochastic partial differential equations by a kernel-based collocation method 
   the Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods, Feb 13-17, 2012, Sydney, Australia.

Approximation of stochastic partial differential equations by a kernel-based collocation method 
   2012 Joint Mathematics Meeting: AMS-SIAM Special Session on the Mathematics of Computation, Jan 4-7, 2012, Boston MA.

Approximation of stochastic partial differential equations by a kernel-based collocation method 
   Sixth International Workshop of Meshfree Methods for Partial Differential Equations, Oct 4-6, 2011, Bonn, Germany.

Approximation of Nonlinear Partial Differential Equations by Gaussian Processes via Mat¨Śrn Functions
   7th International Congress on Industrial and Applied Mathematics (ICIAM2011), July 18-22 2011, Vancouver, BC Canada.

Midwest Numerical Analysis Day (NWNA Day) 2011, May 7-8 2011, West Lafayette, IN, Attended.

Approximation of Linear Stochaitic Partial Differential Equations by Gaussian Processes via Mat¨Śrn Functions (Poster)
   Recent Advances in the Numerical Approximation of Stochastic Partial Differential Equations, August 9-13 2010, Chicago, IL.

Approximation of Linear Partial Differential Equations by Gaussian Processes via Mat¨Śrn Functions
   2010 SIAM Annual Meeting, July 12-16 2010, Pittsburgh, PA.

Approximating Stable and Unstable Manifolds of 2D Stochastic Dynamical Systems via Reproducing Kernels
   Midwest Numerical Analysis Day (NWNA Day) 2010, April 24-25 2010, Ames, IA.

A Green Function Approach to (Conditionally) Positive Definite Functions and Reproducing Kernels of Generalized Sobolev spaces
  13th International Conference Approximation Theory, March 7-10 2010, San Antonio, TX.

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach
  2009 Joint Midwest Numerical Analysis Day and SIAM Great Lakes Numerical PDEs Spring Conference, April 17-18 2009, Detroit, MI.

Midwest Numerical Analysis Day (NWNA Day) 2008, May 3 2008, St. Paul, MN, Attended.

CONFERENCES ORGANIZATION

IIT SIAM 2011: Recent Advances in Computational Science and Statistics, October 29-30 2011, Chicago IL, USA


TRAVEL

Visit to Huazhong University of Science and Technology on December 29-31 2010 (Thanks for the invitation Dr. Xu Sun.)
  Talk: Tutorial of Meshfree Approximation Method, PDF
Visit to Department of Mathematics, University of Iowa on June 21-25 2010 (dicussing with Dr. Kendall E. Atkinson)

AWARDS

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, SIAM, news

NSF travel award from Stanford University to the Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods (MCQMC 2012)

Graduate student travel grant to the Joint Mathematics Meetings 2012

Award for 2009 student research poster at Annual Karl Menger Lecture, 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

COMPUTER SKILLS

Fluent in C++ and Matlab/Maple/Mathematica


TEACHING EXPERIENCES

Teaching Assistant of Probability and Statistics (Math 474 & 563), Applied Analysis (Math 500), Dynamical Systems (Math 515), 
Computational Mathematics (Math 577)

ANOTHER PROFESSIONAL COURSES

Computer Sciences: Machine Learning CS 584, Advanced Scientific Computing (Parallel Computing) CS 595

Engineering: Statistical Signal Processing ECE 567


LEADERSHIP

President of Illinois Institute of Technology Chapter of SIAM in 2011


MEMBERSHIP

Society for Industrial and Applied Mathematics (SIAM)

Sigma Xi, The Scientific Research Society


ACTIVITY PHOTO

SIAM Annual 2012 Student Days Power Point Presentation

Facebook of IIT SIAM

Monte Carlo's Gallery, 2012


OTHER WEB SITES

Numerical Analysis in the Midwest

Society for Industrial and Applied Mathematics (SIAM)

Sigma Xi, The Scientific Research Society

Mathematical Association of America (MAA)

American Mathematical Society (AMS)

International Council for Industrial and Applied Mathematics (ICIAM)

Numerische Mathematik, Springer

The New York Review of Books