Detecting Asymptotic Non-regular Values by Polar Curves

Learning Curves: Asymptotic Values and Rate of Convergence

Training classifiers on large databases is computationally demanding. It is desirable to develop efficient procedures for a reliable prediction of a classifier's suitability for implementing a given task, so that resources can be assigned to the most promising candidates or freed for exploring new classifier candidates. We propose such a practical and principled predictive method. Practical bec...

Asymptotic Approximation by Quadratic Spline Curves

For a planar curve C with positive affine curvature, we derive an asymptotic formula for the area approximation by quadratic spline curves with n knots lying on C. The order of approximation is 1/n4 and the formula depends on an integral over the affine curvature. 1991 AMS subject classification: 52A10, 53A04, 53A15, 41A15, 41A50

Non-asymptotic theory of random matrices: extreme singular values

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to information theory operate with random matrices in fixed dimensions. This survey addresses the non-asymptotic theory of extreme singular values of random matrices w...

Asymptotic Hölder Absolute Values

Infinitesimal Adjunction and Polar Curves

The polar curves of foliations F having a curve C of separatrices generalize the classical polar curves associated to hamiltonian foliations of C. As in the classical theory, the equisingularity type ℘(F) of a generic polar curve depends on the analytical type of F , and hence of C. In this paper we find the equisingularity types ǫ(C) of C, that we call kind singularities, such that ℘(F) is com...