Xingping Sun 901 S

Xingping Sun 901 S. National Avenue, Springﬁeld, MO 65897 (417) 836-6935 [email protected] http://math.missouristate.edu/xsun.aspx

RESEARCH INTERESTS

Approximation Theory, Machine Learning, Radial Basis Functions

EDUCATION

Ph.D. in Mathematics University of Texas at Austin 1990 M.S. in Mathematics Northwestern University (China) 1984 B.S. in Mathematics Henan Normal University (China) 1981

PROFESSIONAL EXPERIENCES

Professor Missouri State University 2000 - Present Visiting Professor Texas A & M University 2009 -2010 Visiting Professor Vanderbilt University Spring 2003 Visiting Professor University of Leicester (UK) Summer 2003 Associate Professor Missouri State University 1995 - 2000 Visiting Associate Prof. University of Texas at Austin 1996 Assistant Professor S.W. Missouri State University 1990 - 1995 Visiting Research Fellow University of Leicester (UK) 1993 Teaching Assistant University of Texas at Austin 1986 - 1990 Instructor Henan Normal University (China) 1985 - 1986

ADMINISTRATIVE EXPERIENCES • 2012 - 2015, Associate Dean, College of Natural and Applied Sciences, Missouri State University. • 2011 - 2012, Interim Associate Dean, College of Natural and Applied Sciences, Missouri State University.

AWARDS AND GRANTS 1. Visiting Fellowship Research Grant, $4,640 Science and Engineering Research Council of Great Britain, (1993). 2. Missouri State University Faculty Summer Research Fellowship Award, $4,000 (1994). 3. Visiting Fellowship Research Grant, The S˜aoPaulo Research Foundation, $5,500 (1994). 4. Visiting Fellowship Research Grant, $2,240 Engineering and Physical Sciences Research Council of Great Britain, (1995).

1 5. Missouri State University Foundation Excellence in Research Award, $2,400 (1996) 6. Missouri State University Faculty Summer Research Fellowship Award, $ 5,000 (1997). 7. Missouri State University Faculty Research Grant, $5,500 (1999). 8. Missouri State University Faculty Summer Research Fellowship Award, $5,000 (2000). 9. Visiting Fellowship Research Grant, $15,240 Engineering and Physical Sciences Research Council of Great Britain, (2003-2005). 10. Missouri State University Faculty Summer Research Fellowship Award, $5,000 (2004). 11. Missouri State University Faculty Research Grant, $3,575 (2004). 12. Missouri State University Excellence in Research Award, $2,400 (2004). 13. Excellence in Teaching Award, $1,200 College of Natural and Applied Sciences, Missouri State University, (2006). 14. Short-Term Visiting Professor Award, $4,928, Fudan University, Shanghai, China, (2007). 15. Visiting Fellowship Research Grant, $8,750 Engineering and Physical Sciences Research Council of Great Britain, (2009) (PI: Jeremy Levesley; Co-PI: Wolfgang Castell and Xingping Sun). 16. Short-Term Visiting Professor Award, $4,928, Fudan University, Shanghai, China, (2010). 17. Missouri State University Faculty Summer Research Fellowship Award, $6,000 (2011). 18. National Science Foundation: Research Experience for Undergraduate Students, $297,000 (2012-2014) (with Les Reid and Jorge Rebaza). 19. The S˜aoPaulo Research Foundation and ENAMA, $5,896, (2014). 20. Short-Term Visiting Professor Award, $4,928, Fudan University, Shanghai, China, (2015). 21. Short-Term Visiting Professor Award, $4,928, Fudan University, Shanghai, China, (2016). 22. National Science Foundation: Research Experience for Undergraduate Students, $297,000 (2016-2018) (with Les Reid, Jorge Rebaza, and Steven Senger).

INVITED TALKS (SELECTED) 1. The solvability of radial basis function interpolation, in “The Sixth Texas International Sym- posium on Approximation Theory”, College Station, TX, 1989. 2. Ridge functions and their application in multivariate interpolation, in “UT and Texas A&M Joint Conference on Approximation Theory”, Center for Approximation Theory, Texas A&M University, 1989. 3. Interpolation by sums of ridge functions, Seminar, Center for Approximation Theory, Texas A&M University, 1989. 4. Multivariate interpolation using linear combinations of radial basis functions, in “The Sixth Conference of Southeast Approximators”, Memphis State University, 1991. 5. Ridge function spaces and their interpolation property, in “The Seventh Texas International Symposium on Approximation Theory”, Austin, Texas, 1992.

2 6. Analytic monotone extensions, in “The 873rd Regional Conference of American Mathematical Society”, Springfield, MO, 1992. 7. Scattered Hermite interpolation by positive definite functions, Seminar, Department of Math- ematics and Computer Science, University of Leicester, Leicester, England, 1993. 8. Strictly positive definite functions on spheres, in “The International Conference on Constructive Approximation”, Tel Aviv University, Tel Aviv, Israel, 1994. 9. Distance matrices and their applications, in “The International Conference on Differential Equations”, University of Sao Paulo, Brazil, 1994. 10. Some newly developed interpolation methods, Colloquium, University of Strathclyde, Glasgow, Scotland, 1995. 11. Scattered Cardinal Hermite interpolation by positive definite functions, in “The 919th Meeting of American Mathematical Society”, Memphis, Tennessee, 1997. 12. Strictly positive definite functions on the complex Hilbert sphere, in “The Ninth International Conference on Approximation Theory”, Nashville, TN, 1998. 13. Strictly positive definite functions on spheres, in “The International Conference on Partial Differential Equations and Numerical Analysis”, Beijing, China, 1998. 14. Positive definite functions and cubature formulas on spheres, in “The Fourth International Conference on Curves and Surfaces”, Saint-Malo, France, July 1-7, 1999. 15. Positive definite functions on the circle, in “The First International Conference on Analysis and Combinatorics”, Dalian, China, 2000. 16. Strictly positive definite functions on spheres of dimension greater than one, in “The Tenth International Conference on Approximation Theory”, St. Louis, MO, 2001. 17. The structure of native spaces and their approximation property, in “The International Conference on Advances in Constructive Approximation”, Nashville, TN, 2003. 18. Approximation between native spaces, Colloquium, University of Leicester, Leicester, England, 2003. 19. Minimal Riesz energy on spheres, Colloquium, University of Missouri-St. Louis, St. Louis, MO, 2004. 20. Approximation in native spaces, in “The Tenth International Conference on Approximation Theory”, Gatlinburg, TN, 2004. 21. Minimal separation of the Riesz energy points, in “The Fourth International Workshop on Special Functions and Their Applications”, Klobster, Irsee, Germany, 2004. 22. On the separation of the minimal energy points, Seminar, Texas A&M University, College Station, TX, 2005. 23. The discrepancy and minimum separation of the minimal energy points, Colloquium, The University of Texas at Austin, Austin, TX, 2005. 24. Native space approximation and its applications to uniform distributions on spheres, Collo- quium, Catholic University of Lueven, Lueven, Belgium, 2005. 25. Rough native space approximation and the estimates of discrepancy on spheres, Colloquium, University of Dundee, Dundee, Scotland, 2005.

3 26. Direct and inverse theorems of approximation in Sobolev spaces, Seminar, City University of Hong Kong, Hong Kong, China, 2006. 27. Radial basis function approximation and applications, in “The First International Summer School on Numerical Linear Algebra”, The Chinese University of Hong Kong, Hong Kong, China, 2006. 28. Approximation of equilibrium measures via radial basis functions, Colloquium, Georgia South- ern University, March 2008. 29. Approximation of probability measures by normalized counting measures, in “Algorithms for Approximation VI”, UK, August, 2009.

30. Approximation on the Voronoi cells of the Ad lattices, Colloquium, Institute of Software, Chinese Academy of Sciences, Beijing, China, August, 2010. 31. Minimal energy configurations on spheres, Colloquium, Department of Physics, Astronomy and Materials Science, Missouri State University, 2010. 32. Approximation Theory: Reproducing Kernel View Point, a Series of Three Seminars, Institute of Mathematical Sciences, China Jiliang University, 2011. 33. Sampling scattered data with Bernstein polynomials, in “The 14th International Conference on Approximation theory, San Antonio, 2013. 34. Approximation of equilibrium measures via multiplier embedding in native spaces, Approxi- mation Day, University of Sao Paulo, ICMC, Sao Carlos, Brazil, October, 2014. 35. Theories and Applications of Conditionally Positive Definite Functions, a Short Course Con- sisting of Three Lectures in the 8th Brazilian National Conference on Analysis and Its Ap- plications, November 5 - 7, 2014, Recife, Brazil. 36. Minimal energy point sets and sphere packing, Colloquium, China Jiliang University, Hangzhou, China, 2015. 37. Chebyshev type inequality for stochastic Bernstein polynomials, 30 mins Talk, Discrete and Continuous Dynamic Systems 2016, Orlando. 38. Minimal energy point set configurations and equilibrium measures on manifolds, Colloquium, Tianjin Polytechnic University, 2016. 39. Order statistics and stochastic Bernstein polynomials, Colloquium, Henan Normal University, 2017. 40. Monte Carlo approximation by Bernstein polynomials, invited talk in the Sixth International Conference on Computational Harmonic Analysis, Fudan University, Shanghai, China, 2017. 41. Sphere packing in higher dimensional spaces and minimal energy point set configurations, Colloquium, Henan University of Science and Technology, 2017.

PUBLICATIONS 1. On a problem in monotone approximation, Journal of Approximation Theory 57 (1989), 239- 244. 2. On the solvability of radial function interpolation, in “Approximation Theory VI”, C. Chui, L. Schumaker and J. Ward (eds), Academic Press, New York, 1989, 643-646.

4 3. (with K. Guo) Scattered data interpolation by linear combinations of translates of conditionally positive definite functions, Numerical Functional Analysis and Optimization 12 (1991), 137- 152. 4. Norm estimates for inverses of Euclidean distance matrices, Journal of Approximation Theory 70 (1992), 339-347. 5. (with E.W. Cheney) The fundamentality of the set of ridge functions, Aequationes Mathemat- icae 44 (1992), 226-235. 6. Cardinal and scattered-cardinal interpolation by functions having non-compact support, Com- puters and Mathematics with Application 24 (1992), 195-200. 7. Solvability of multivariate interpolation by radial or related functions, Journal of Approximation Theory 72 (1993), 252-267. 8. Ridge function spaces and their interpolation property, Journal of Mathematical Analysis and Applications 179 (1993), 28-40. 9. (with K. Guo and S. Hu) Conditionally positive definite functions and Laplace-Stieltjes integrals, Journal of Approximation Theory 74 (1993), 249-265. 10. (with K. Guo and S. Hu) Cardinal interpolation by linear combinations of translates of conditionally positive definite functions, Numerical Functional Analysis and Optimization 14 (1993), 371-381. 11. Conditionally positive definite functions and their application to multivariate interpolation, Journal of Approximation Theory 74 (1993), 159-180. 12. (with Les Reid) Distance matrices and ridge function interpolation, Canadian Journal of Mathematics 45 (1993), 1313-1323. 13. (with X. Yu) Analytic monotone extension of boundary data, Journal of Approximation Theory 77 (1994), 314-330. 14. Scattered Hermite interpolation using radial basis functions, J. Linear Algebra and Its Appli- cations 207 (1994), 135-146. 15. Cardinal Hermite interpolation using positive definite functions, Numerical Algorithms 7 (1994), 253-268. 16. (with S. Kilmer and X. Yu) A problem of analytic monotone extensions in three dimensions, in “Approximation, Probability, and Related Fields” G. Anastassiou (ed.), (303-315), Plenum Press, New York and London, 1994. 17. The fundamentality of translates of a continuous functions on spheres, Numerical Algorithms 8 (1994), 131-134. 18. (with Jeremy Levesley) Scattered Hermite interpolation by ridge functions, Numerical Func- tional Analysis and Optimization 16 (1995), 989-1002. 19. Conditional positive definiteness and complete monotonicity, in “Approximation Theory VIII, Vol. 1: Approximation and Interpolation”, C.K. Chui and L.L. Schumaker (eds), pp. 537- 540. World Publishing Co., Inc. 1995. 20. (with S. Kilmer, W. Light, and X. Yu) Approximation by translates of a positive definite function, J. Mathematical Analysis and Applications 201 (1996), 631-641.

5 21. (with Amos Ron) Strictly positive definite functions on spheres, Mathematics of Computation 65 (1996), 1513-1530. 22. (with E. W. Cheney) Fundamental sets of continuous functions on spheres, Constructive Approximation 13 (1997), 245-250. 23. (with S. Kilmer and X.M. Yu) Analytic monotone extension in two and three dimensions, Numerical Functional Analysis and Optimization 18 (1&2) (1997), 131-141. 24. (with E. W. Cheney) Interpolation on sphere by positive definite functions, in “Approximation Theory”, N. K. Govil, R. N. Mohapatra, Z. Nashed, A. Sharma, J. Szabados eds. PP. 141-156, Marcel Dekker, Inc. New York, Basel, Hong Kong, 1998. 25. (with J. Levesley, W.A. Light, and D. Ragozin) A simple approach to variational theory for interpolation on spheres, International Series of Numerical Analysis, Vol. 132 (1999), Birkhauser Verlag Basel/Switzerland. 26. (with J. Levesley and Z. Luo) Norm estimates of interpolation matrices and their inverses associated with strictly positive definite functions on spheres, Proceedings of American Mathematical Society 127 (1999), 2127-2134. 27. (with V. Menegatto) Strictly positive definite functions on the complex Hilbert sphere, Ad- vances in Computational Mathematics 11 (1999), 105-119 . 28. Scattered cardinal Hermite interpolation by positive definite functions, Computers and Math- ematics with Applications 40 (2000), 165-169. 29. (with D. Chen and V. Menegatto) A necessary and sufficient condition for strictly positive definite functions on spheres, The Proceedings of American Mathematical Society 131 (2003), 2733-2740. 30. Strictly positive definite functions on the unit circle, Mathematics of Computation 74 (2005), 709-721. 31. (with J. Levesley) Approximation in rough native spaces by shifts of smooth kernels on spheres, J. Approximation Theory 133 (2005), 269-283. 32. (with J. Levesley) Corrigendum to and two open questions arising from “Approximation in rough native spaces by shifts of smooth kernels on spheres”, Journal of Approximation Theory 138 (2006), 124-127. 33. (with J. Levesley) Perturbation of operators associated with interpolations on manifolds, J. Computational and Applied Mathematics 199 (2007), no. 1, 159–171. 34. (with F. Narcowich and J. D. Ward ) Approximation in Sobolev spaces on spherical domains, Advances in Computational Mathematics 27 (2007), no. 1, 107–124. 35. (with A.B.J. Kuijlaars and E. B. Saff) Minimal discrete energy and discrepancy on spheres, J. Computational and Applied Mathematics 199 (2007), no. 1, 172–180. 36. (with F. Narcowich, J. D. Ward, and H. Wendland) Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions, Foundation of Computational Mathematics 7 (2007), no. 3, 369–390. 37. (with S. Damelin and J. Levesley) Energy estimates and the Weyl Criterion on compact homogeneous manifolds, in “Algorithms for Approximation V”, A. Iske and J. Levesley, (eds.), Springer-Verlag, Heidelberg, 359–367, 2007.

6 38. (with Z. Chen) Spherical basis functions and uniform distribution of points on spheres, Journal of Approximation Theory 151 (2008), 186-207. 39. (with S. Damelin, J. Levesley, and D. Ragozin) Energy estimates and invariant groups on compact homogeneous manifolds, Journal of Complexity 25 (2009), 152-162.

40. Approximation on the Voronoi cells of the Ad lattice, Constructive Approximation 32 (2010), 543–567. 41. (with F. Narcowich, J. D. Ward, and Z. Wu) LeVeque type inequalities and discrepancy estimates for minimal energy configurations on spheres, Journal of Approximation Theory 162 (2010), no. 6, 1256–1278. 42. (with J. Levesley) Approximating probability measures on manifolds via radial basis functions, Book Chapter, in “Approximation Algorithms for Complex Systems”, E. Georgoulis, A. Iske and J. Levesley, (eds.), Springer-Verlag, Berlin, Heidelberg, 151-180, 2011. 43. (with T. Hangelbroek, F. Narcowich, and J. Ward) Kernel Approximation on Manifolds II: The L∞-norm of the L2-projector, SIAM Journal on Mathematical Analysis 43 (2011), No. 2, 662-684. 44. (with Z. Wu and L. Ma) Sampling scattered data with Bernstein polynomials: stochastic and deterministic error estimates, Advances in Computational Mathematics 38 (2013), no. 1, 187-205. 45. (with S. Lin, Y. Rong, and Z. Xu) Learning capability of relaxed greedy algorithms, IEEE Transactions on Neural Networks and Learning Systems 24 (2013), 1598-1608. 46. (with S. Lin and Z. Xu) Discretizing Spherical Integrals and Its Applications, in “Dynamical Systems, Differential Equations and Applications, Discrete and Continuous Dynamic Systems- Proceedings 2013, 499 - 514, D. Costa, W. Feng, Z. Feng, X. Lu, X. Sun, M. Taniguchi, and A. Vitola (eds), AIMS Publication. 47. (with T. Jordãoand V. Menegatto) Eigenvalue sequences of positive integral operators and moduli of smoothness, in “Approximation Theory XIV: San Antonio 2013”, 239-254, G. E. Fasshauer and L.L. Schumaker (eds), Springer Proceedings in Mathematics & Statistics, Volume 83. 48. (with T. Jordão) A general type of spherical mean operators and K-functionals of fractional orders, Communication in Pure and Applied Analysis 14, No. 3 (2015), 743-757. 49. (with E. Hintikka) Convergence of Sequences of Polygons, Involve 9 (2016), no. 5, 751 - 764. 50. (with J. Millett) The existence of limits and continuity, College Math. J. 48 (2017), no. 1, 3135. 51. (with A. Kushpel and J. Levesley) Interpolation of functions of exponential type by shifts of a basis function, submitted. 52. (with S. Senger and Z. Wu) Optimal order Jackson type error estimate for scaled Shepard approximation, submitted. 53. (with Z. Wu) Chebyshev type inequality for stochastic Bernstein polynomials, submitted. 54. (with S. Lin, Z. Xu, and J. Zeng) Model selection of polynomial kernel regression, preprint.

7 SELECTED PROFESSIONAL SERVICES 1. Organizer of the Special Session on Approximation Theory in the 873rd Regional Conference of American Mathematical Society. 2. Organizer of the Special Session dedicated to Will Light in the International Conference on Advances in Constructive Approximation. 3. Referee of the following mathematical journals: SIAM Mathematical Journal (Numerical Anal- ysis), Mathematics of Computation, Journal of Mathematical Analysis and Applications, Journal D’Analyse Math´ematique,Applied and Computational Harmonic Analysis, Journal of Approximation Theory, Numerical Functional Analysis and Optimization, Applicable Anal- ysis, Journal of Approximation Theory and Applications, Taiwanese Journal of Mathematics, Advances in Computational Mathematics, Methods and Applications of Analysis, Bulletin of Institute of Mathematics, Academia Sinica. 4. Organizer of the Special Session on Complexity of Algorithms in the International Conference on Algorithms on Approximation. 5. Co-editor of the AIMS Orlando International Conference Proceedings.

SELECTED UNIVERSITY, COLLEGE, AND DEPARTMENT SERVICES 1. Member of the Faculty Concerns Committee, Southwest Missouri State University, two year term, 1994-1996. 2. Member of the Scholastic Committee, College of Natural and Applied Sciences, Southwest Missouri State University, 1996. 3. Faculty Senator representing the Mathematics Department, Missouri State University, two year term, 2002-2004. 4. Chair, Search Committee, Department of Mathematics, Missouri State University, 2007. 5. Chair, Personnel Committee, Department of Mathematics, Missouri State University, 2008. 6. Chair, Tenure and Promotion Committee, Department of Mathematics, Missouri State Uni- versity, 2008.