2 Kernels 1 2.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Positive Definiteness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 General Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Inner Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Dualit...

We study the error performances of p -norm Support Vector Machine classifiers based on reproducing kernel Hilbert spaces. We focus on two category problem and choose the data-dependent polynomial kernels as the Mercer kernel to improve the approximation error. We also provide the standard estimation of the sample error, and derive the explicit learning rate.

Theodore M. Bartoletti,* Skyler L. Jackman,* Norbert Babai, Aaron J. Mercer, Richard H. Kramer, and Wallace B. Thoreson Department of Ophthalmology and Visual Sciences and Department of Pharmacology and Experimental Neuroscience, University of Nebraska Medical Center, Omaha, Nebraska; Department of Neurobiology, Harvard Medical School, Boston, Massachusetts; and Department of Molecular and Cell...

This paper presents an overview of design and manufacturing curriculum in effect at Mercer School of Engineering for the undergraduate students in Industrial Engineering. There is a need to incorporate changes in the design and manufacturing curriculum to meet the ABET requirements of EC 2000 (“a” through “k”). The work in progress, the future plan for changes, a sample lab experiment in roboti...

Discriminants are often used in pattern recognition to separate clusters of points in some multidimensional “feature” space. This paper provides two fast and simple techniques for improving on the classification performance provided by Fisher’s linear discriminant for two classes. Both of these methods are also extended to nonlinear decision surfaces through the use of Mercer kernels.

The definition of the orbital angular momentum established for coherent beams is extended to partially coherent beams, expressed in terms of two elements of the beam matrix. This extension is justified by use of the Mercer expansion of partially coherent fields. General Gauss-Schell-model fields are considered, and the relation between the twist parameter and the orbital angular momentum is ana...

∗ Instituto de Ciencias Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain, on leave from Old Dominion University, Norfolk, VA 23529 USA (e-mail: [email protected]) ∗∗ School of Engineering, Mercer University, Macon, GA 31207 USA (e-mail: thitsa [email protected]) ∗∗∗ School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA (e-mail: erik.ve...

In spite of increasing interest in the use of haemodialysis, there have been few reports of its use in infancy and childhood (Mateer, Greenman and Danowski, 1955; Carter, Aoyama, Mercer and Kolff, 1957; Keleman and Kolff, 1959; Breakey, Woodruff and Reus, 1961). We present here our experience of this problem in three children who were suffering from acute renal failure with signs of overhydration.