We first analyze the limits of learning in high dimension. Hence, we stress the difference between high dimensional ambient space and intrinsic geometry associated to the marginal distribution. We observe that, in the semi-supervised setting, unlabeled data could be used to exploit low dimensionality of the intrinsic geometry. In order to formalize these intuitions we briefly introduce the mani...

in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.

for all x ∈ X, whereX denotes the dual space ofX and ⟨⋅, ⋅⟩ the generalized duality pairing between X and X. If X = H is a Hilbert space, then J becomes the identitymapping onH. A point x ∈ C is a fixed point of T : C ⊂ X → X provided Tx = x. Denote by F(T) the set of fixed points of T; that is, F(T) = {x ∈ C : Tx = x}. Let X be a normed linear space with dim X ≥ 2. The modulus of smoothness of...

Let f 2 C 1 ?1; 1] change its convexity nitely many times in the interval, say s times, at Y s : ?1 < y s < < y 1 < 1. We estimate the degree of simultaneous approximation of f and its derivative by polynomials of degree n, which change convexity exactly at the points Y s , and their derivatives. We show that provided n is suuciently large, depending on the location of the points Y s , the rate...

A cryptanalytic attack on the use of short RSA secret exponents is described. This attack makes use of an algorithm based on continued fractions which finds the numerator and denominator of a fraction in polynomial time when a close enough estimate of the fraction is known. The public exponent e and the modulus pq can be used to create an estimate of a fraction which involves the secret exponen...

This is a survey on best polynomial approximation on the unit sphere and the unit ball. The central problem is to describe the approximation behavior of a function by polynomials via smoothness of the function. A major effort is to identify a correct gadget that characterizes smoothness of functions, either a modulus of smoothness or a Kfunctional, the two of which are often equivalent. We will...

In this study four statistical grapheme-to-phoneme (G2P) conversion methods for canonical German are compared. The G2P models differ in terms of usage of morphologic information and of phoneme history (left context) information. In order to evaluate our models we introduce two measures, namely mean normalized Levenshtein distance for classification accuracy and conditional relative entropy for ...

Let F be a class of functions deened on a d-dimensional domain. Our task is to compute H m-norm "-approximations to solutions of 2mth-order elliptic boundary-value problems Lu = f for a xed L and for f 2 F. We assume that the only information we can compute about f 2 F is the value of a nite number of continuous linear functionals of f, each evaluation having cost c(d). Previous work has assume...

Abstract We define a Skorohod type anticipative stochastic integral that extends the Itô integral not only with respect to the Wiener process, but also with respect to a wide class of stochastic processes satisfying certain homogeneity and smoothness conditions, without requirements relative to filtrations such as adaptedness. Using this integral, a change of variable formula that extends the c...

The present paper addresses the issue of flexibility in expressive unit selection speech synthesis by using different style selection techniques. We select units from a mixed-style unit selection database, using either forced style switching, no control, symbolic target cost, or acoustic target cost as a style selection criterion. We assess the effect of selection technique, feature weight and ...