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Professor Louise Arakelian Raphael, Ph.D.

Education:
Ph. D. (1967) Catholic University

Research Interests: WAVELETS, APPROXIMATION THEORY, NEURAL NETS, ILL-POSED PROBLEMS

In recent collaborations with Mark Kon of Boston University and Dan Williams of Howard University, we have developed a theory for function approximation motivated by concepts of statistical learning theory. Currently we are applying our techniques to micorarray classification and gene transcription binding problems. In particular, based on seminal work of Frederico Girosi in the mid nineties, we have extended and applied his estimates method to reproducing kernel settings and designed a classification scheme that we are testing on DNA transciption factor binding sites data.

Selected Publications:[Five selected from 44 research publications]

• With Mark Kon. Approximating Functions in Reproducing Kernel Hilbert Spaces via Statistical Learning Theory, in Wavelets and Splines, G. Chen and M. J. Lai eds., Nashboro Press, Nashville, TN, May 2006, 271-286.
• With Mark Kon and Daniel Williams. Extending Girosi's Approximation Estimates for Functions in Sobolev Spaces via Statistical Learning Theory, J. of Analysis and Applications 3, No. 2, 2005, 67-90.
• With Mark Kon. A Characterization of Wavelet Convergence in Sobolev Spaces, Journal of Applicable Analysis, Vol. 78, 2001, pp. 271-324.
• With Susan Kelly and Mark Kon. Pointwise Convergence of Wavelet Expansions, Bulletin of AMS, Vol. 30 (1), Jan. 1994, pp. 87-94.
• With Robert Carroll. Some Inverse Problems with Spectral Limitations on Data, SIAM Journal of Applied Mathematical Analysis, Vol. 48, No. 5, 1988, pp. 1194-1205.

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