Prof. Stephen SMALE (史梅爾)

PhD – University of Michigan, USA

University Distinguished Professor (Office of the Provost)

Prof. Stephen SMALE

Contact Information

Office: B6513 Academic 1
Phone: +852 3442-5280
Fax: +852 3442-0250
Email: smale@cityu.edu.hk

Research Interests

  • Complexity and Computation

Biography

1930 Born July 15 at Flint, Michigan
1952 BS, University of Michigan
1953 MS, University of Michigan
1957 PhD, University of Michigan
1956–68 Instructor, University of Chicago
1958–60 Member, Institute for Advanced Study, Princeton
1960–62 Alfred P. Sloan Research Fellow
1960–61 Associate Professor of Mathematics, University of California, Berkeley
1961–64 Professor of Mathematics, Columbia University
1962 Visiting Professor, College de France, Paris (Spring)
1964–94 Professor of Mathematics, University of California, Berkeley
1966 Member, Institute for Advanced Study, Princeton (Fall)
1967–68 Research Professor, Miller Institute for Basic Research in Science, Berkeley
1969–70 Visiting Member, Institut des Hautes Etudes Scientifiques (Fall)
1972–73 Visiting Member, Institut des Hautes Etudes Scientifiques (Fall)
1972–73 Visiting Professor, University of Paris, Orsay (Fall)
1974 Visiting Professor, Yale University (Fall)
1976 Visiting Professor, Instituto de Matematica Pura e Aplicada, Rio de Janeiro
1976 Visiting Professor, Institut des Hautes Études Scientifiques (May, June)
1976– Professor without stipend, Department of Economics, University of California, Berkeley
1979–80 Research Professor, Miller Institute for Basic Research in Science, Berkeley
1987 Visiting Scientist, IBM Corporation, Yorktown Heights (Fall)
1987 Visiting Professor, Columbia University (Fall)
1988 Visiting Professor, Instituto de Matematica Pura e Aplicada, Rio de Janeiro
1994 Visiting Professor, Instituto de Matematica Pura e Aplicada, Rio de Janeiro
1994– Professor of Mathematics (and Economics) Emeritus, University of California, Berkeley
1995–2001 Distinguished University Professor, City University of Hong Kong
2002–2009 Professor, Toyota Technological Institute at Chicago
2009–Present University Distinguished Professor, City University of Hong Kong

Honours (Selected)

  • 1974 Honorary Degree, University of Warwick
  • 1987 Honorary Degree, Queen's University, Kingston, Ontario
  • 1994 Class of the Grand Cross of the Brasilian National Order of Scientific Merit
  • 1996 Honorary Doctor of Science, University of Michigan
  • 1996 National Medal of Science, Washington, D. C.
  • 1997 Doctor Honoris Causa, Université Pierre et Marie Curie, Paris
  • 1997 Honorary Doctor of Science, City University of Hong Kong
  • 1997 Honorary Member of the Moscow Mathematical Society
  • 1998 Honorary Member of the London Mathematical Society
  • 1999 Honorary Doctorate of Rostov State University
  • 2004 Honorary Doctorate of University of Genoa
  • 2005 Jurgen Moser Prize of SIAM, Dynamics Group
  • 2007 Wolf Prize

List of Publications (1994–2009)

The Godel Incompleteness Theorem and Decidability Over a Ring. (with Lenore Blum) In M. Hirsch, J. Marsden, and M. Shub (Eds.)

From Topology to Computation: Proceedings of the Smalefest, pp. 321–339. Springer-Verlag 1993.

Some Autobiographical Notes In M. Hirsch, J. Marsden, M. Shub, (Eds.), From Topology to Computation: Proceedings of the Smalefest, pp. 3–21. Springer-Verlag 1993.

Complexity of Bezout's Theorem V: Polynomial Time (with Mike Shub), /Theoretical Computer Science/, *133* (1994), pp. 141–164. [ ps | pdf ]

Separation of Complexity Classes in Koiran's Weak Model (with Felipe Cucker and Mike Shub), /Theoretical Computer Science/, *133* (1994), pp. 3–14. [ ps | pdf ]

On the Intractibility of Hilbert's Nullstellensatz and an Algebraic Version of "NP≠P?" (with Mike Shub), /Duke Math Jour/, *81* pp. 47–54 (1995). [ ps | pdf ]

Complexity of Bezout's Theorem IV: Probabability of success; Extensions (with Mike Shub), /SIAM Jour. of Numerical Analysis/, *33* (1996) pp. 128–148. [ ps | pdf ]

Complexity and Real Computation: A Manifesto (with L. Blum, F. Cucker and M. Shub) /International Journal of Bifurcation and Chaos/, *6* (1996) pp. 3–26.

Algebraic Settings for the Problem "P≠NP?" (with L. Blum, F. Cucker, M. Shub), Lectures in Applied Mathematics vol. 32, ed. J. Renegar, M. Shub and S. Smale, pp. 125–144, /Amer. Math. Soc./ 1996. [ ps | pdf ]

Complexity theory and numerical analysis, /Acta Numerica/, (1997) pp. 523–551. [ ps | pdf ]

Complexity and real computation (with L. Blum, F. Cucker, and M. Shub), Springer-Verlag 1998.

Finding a Horseshoe on Beaches of Rio,/Mathematrical Intelligencer/, Vol. 20, (1988) No. 1, 39-44.

Mathematical Problems for the Next Century, /Mathematical Intelligencer/, Vol. 20, (1998) No. 2, 7–15. [ ps | pdf ]

Some Lower Bounds for the Complexity of Continuation Methods (with J-P Dedieu), /Jour of Complexity/, Vol. 14 (1998) 454–465. [ ps | pdf ]

The Work of Curtis T. McMullen, in Proceedings of the International Congress of Mathematicians Berlin 1998 Vol. 1 Documenta Mathematica Bielefeld, Germany, 1998 pp. 127–132. [ ps | pdf ]

A Polynomial Time Algorithm for Diophantine Equations in One Variable (with F. Cucker and P. Koiran), /Jour. Symbolic Computation/, Vol. 27 (1999) 21–29. [ ps | pdf ]

Cucker, Felipe; Smale, Steve
Complexity estimates depending on condition and round-off error. J. ACM 46 (1999), no. 1, 113–184.

Batterson, Steve Stephen Smale
The Mathematician Who Broke the Dimension Barrier. American Mathematical Society, Providence, RI, 2000. xviii+306 pp.

Smale, Steve
Mathematical Problems for the Next Century. Mathematics: Frontiers and Perspectives, 271–294, Amer. Math. Soc., Providence, 2000.

Smale, Stephen
The Collected Papers of Stephen Smale. Vol. 1–3. Edited by F. Cucker and R. Wong. Singapore University Press, Singapore; World Scientific Publishing Co., Inc., River Edge, NJ, 2000. Vol. 1: xxxiv+488 pp.; Vol. 2: pp. i–xii and 489–1031; Vol. 3: pp. i–xii and 1033–1677.

Cucker, Felipe; Smale, Steve
On the Mathematical Foundations of Learning. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 1–49.

Cucker, Felipe; Smale, Steve
Best Choices for Regularization Parameters in Learning Theory: On the Bias-Variance Problem. Found. Comput. Math. 2 (2002), no. 4, 413–428.

Smale, Steve; Zhou, Ding-Xuan
Estimating the Approximation Error in Learning Theory. Anal. Appl. (Singap.) 1 (2003), no. 1, 17–41.

Poggio, Tomaso; Smale, Steve
The Mathematics of Learning: Dealing with Data. Notices Amer. Math. Soc. 50 (2003), no. 5, 537–544.

Smale, Steve; Zhou, Ding-Xuan
Shannon Sampling and Function Reconstruction from Point Values. Bull. Amer. Math. Soc. (N.S.) 41 (2004), no. 3, 279–305.

Cucker, Felipe; Smale, Steve; Zhou, Ding-Xuan
Modeling Language Evolution. Found. Comput. Math. 4 (2004), no. 3, 315–343.

Hirsch, Morris W.; Smale, Stephen; Devaney, Robert L.
Differential Equations, Dynamical Systems, and an Introduction to Chaos. Second edition. Pure and Applied Mathematics (Amsterdam), 60. Elsevier/Academic Press, Amsterdam, 2004.

With F. Cucker, "On the mathematics of emergence", Japanese Jour of Mathematics (The first Takagi Lectures) Vol. 2, No. 1, March 2007. 197–227.

With A. Caponnetto, "Risk Bounds for Random Regression Graphs", Jour Foundations of computational mathematics (2007), vol 7, #4, 495–528.

With F. Cucker, "Emergent behavior in Flocks", IEEE Transactions on automatic control, Vol 52, issue 5 (May, 2007) 852–862.

With P. Niyogi and S. Weinberger, "Finding the homology of submanifolds with high confidence from random samples", Discrete and Computational geometry (2008) 39: 419–441.

With Y. Yao "Online learning algorithms", Foundations of computational mathematics vol. 6 no. 2 145–170 (2006).

With D.-X. Zhou, "Learning theory estimates via integral operators and their approximations", Constructive Approximations (2007) 26: 153–172.

with D.-X. Zhou, "Shannon 2: Connections to learning theory", Applied and Computational harmonic analysis 19 (2005) 285–302.

Recent Publications 

With Ding-Xuan Zhou, "Online Learning with Markov Sampling",1 "Analysis and Applications"., Vol. 7, Jan, 2009

With Ding-Xuan Zhou, "Geometry on Probability Spaces" 1"Constructive Application"., (2009) 30. 311-323.

With Partha Niyogi and Shmuel Weinberger, "A Topological View of Unsupervised Learning from Noisy Data", SIAM Journal on Computing 2011 40 (3) 646-663.

With L. Rosasco, J. Bouvrie, A. Caponnetto and T. Poggio, Mathematics of the Neural Response, 2010, Foundations of Computational Mathematics 10, 67-91.

with L. Bartholdi, T. Schich, N. Smale Hodge theory on Metric Spaces, 2012, 12, 1-48.
Journal Foundations of Computational Mathematics

with Nathan Smale, Abstract and Classical Hodge-DeRham theory 2010, Analysis and applications, 18 pp

with W. Shen, H. S. Wong, Q.-W Xiao, X. Guo, Introduction to the Peptide Binding Problem of Computational Immunology; New Results1 Journal Foundations of Computational Mathematics 2013, 34 pp

with M. Andreatta, S. Liaplagne, S. C. Li, 1Prediction of Residue-residue contacts from Protein famulies using similarity Rerrels and least squares regularization1 Bioinformatics, 2013 submitted.

MHC Binding Prediction with Kernel RLS pan and its variations with W. Shen, Y. T. Wei, X. Guo, H.-S. Wong and S. C. Li, submitted.