Let b be aBMO-function. It is well-known that the linear commutator [b, T ] of a Calderón-Zygmund operator T does not, in general, map continuously H(R) into L(R). However, Pérez showed that if H(R) is replaced by a suitable atomic subspace H b(R ) then the commutator is continuous from H b(R ) into L(R). In this paper, we find the largest subspace H b (R ) such that all commutators of Calderón...

Bilinear maps, or pairings, initially proposed in a cryptologic context for cryptanalytic purposes, proved afterward to be an amazingly flexible and useful tool for the construction of cryptosystems with unique features. Yet, they are notoriously hard to implement efficiently, so that their effective deployment requires a careful choice of parameters and algorithms. In this paper we review the ...

We study a version of Whitney’s embedding problem in projective geometry: What is the smallest dimension of an affine space that can contain an n-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points? This problem is related to the generalized vector field problem, existence of non-singular bilinear maps, and the immersion problem for real projec...

We construct a fully collusion resistant tracing traitors system with sublinear size ciphertexts and constant size private keys. More precisely, let N be the total number of users. Our system generates ciphertexts of size O( √ N) and private keys of size O(1). We first introduce a simpler primitive we call private linear broadcast encryption (PLBE) and show that any PLBE gives a tracing traitor...

We consider the composition of random i.i.d. aane maps of a Hilbert space to itself. We show convergence of the n'th composition in the Wasserstein metric via a contraction argument. The contraction condition involves the operator norm of the expectation of a bilinear form. This is contrasted with the usual contraction condition of a negative Lyapunov exponent. Our condition is stronger but eas...

We present a novel closed-form solution for the joint self-calibration of video and range sensors. The approach single assumption is the availability of synchronous time of flight (i.e., range distances) measurements and visual position of the target on images acquired by a set of cameras. In such case, we make explicit a rank constraint that is valid for both image and range data. This rank pr...

In this paper, we propose an efficient authenticated key establishment scheme for self-organizing sensor networks. The proposed scheme has low communication cost and eliminates expensive operations required by most ID-based schemes, such as sensor nodes calculating bilinear maps. Additionally, the proposed scheme provides perfect forward secrecy.

We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...

This paper presents a new voice conversion method called Weighted Frequency Warping (WFW), which combines the well known GMM approach and the frequency warping approach. The harmonic plus stochastic model has been used to analyze, modify and synthesize the speech signal. Special phase manipulation procedures have been designed to allow the system to work in pitch-asynchronous mode. The experime...

A warping operator consists of an invertible axisdeformation applied either in the signal domain or in thecorresponding Fourier domain. Additionally, a warping trans-formation is usually required to preserve the signal energy, thuspreserving orthogonality and being invertible by its adjoint.Initially, the design of such operators has been motivated bythe idea of suitably...