École Polytechnique

About: École Polytechnique is a education organization based out in Palaiseau, France. It is known for research contribution in the topics: Laser & Plasma. The organization has 18995 authors who have published 39265 publications receiving 1225163 citations. The organization is also known as: Ecole Polytechnique & Polytechnique.

Constructive and destructive facets of Weil descent on elliptic curves

Abstract: In this paper we look in detail at the curves which arise in the method of Galbraith and Smart for producing curves in the Weil restriction of an elliptic curve over a finite field of characteristic 2 of composite degree. We explain how this method can be used to construct hyperelliptic cryptosystems which could be as secure as cryptosystems based on the original elliptic curve. On the other hand, we show that the same technique may provide a way of attacking the original elliptic curve cryptosystem using recent advances in the study of the discrete logarithm problem on hyperelliptic curves. We examine the resulting higher genus curves in some detail and propose an additional check on elliptic curve systems defined over fields of characteristic 2 so as to make them immune from the methods in this paper.

Discovery of the Binary Pulsar PSR B1259-63 in Very-High-Energy Gamma Rays around Periastron with H.E.S.S

Abstract: We report the discovery of very-high-energy (VHE) γ-ray emission of the binary system PSR B1259−63/SS 2883 of a radio pulsar orbiting a massive, luminous Be star in a highly eccentric orbit. The observations around the 2004 periastron passage of the pulsar were performed with the four 13 m Cherenkov telescopes of the HESS experiment, recently installed in Namibia and in full operation since December 2003. Between February and June 2004, a γ-ray signal from the binary system was detected with a total significance above 13σ. The flux was found to vary significantly on timescales of days which makes PSR B1259−63 the first variable galactic source of VHE γ-rays observed so far. Strong emission signals were observed in pre- and post-periastron phases with a flux minimum around periastron, followed by a gradual flux decrease in the months after. The measured time-averaged energy spectrum above a mean threshold energy of 380 GeV can be fitted by a simple power law F0(E/ 1T eV) −Γ with a photon index Γ= 2.7 ± 0.2stat ± 0.2sys and flux normalisation F0 = (1.3 ± 0.1stat ± 0.3sys) × 10 −12 TeV −1 cm −2 s −1 .T his detection of VHE γ-rays provides unambiguous evidence for particle acceleration to multi-TeV energies in the binary system. In combination with coeval observations of the X-ray synchrotron emission by the RXTE and INTEGRAL instruments, and assuming the VHE γ-ray emission to be produced by the inverse Compton mechanism, the magnetic field strength can be directly estimated to be of the order of 1 G.

On the Convergence of the Iterates of the Fast Iterative Shrinkage/Thresholding Algorithm

Abstract: We discuss here the convergence of the iterates of the "Fast Iterative Shrinkage/Thresholding Algorithm," which is an algorithm proposed by Beck and Teboulle for minimizing the sum of two convex, lower-semicontinuous, and proper functions (defined in a Euclidean or Hilbert space), such that one is differentiable with Lipschitz gradient, and the proximity operator of the second is easy to compute. It builds a sequence of iterates for which the objective is controlled, up to a (nearly optimal) constant, by the inverse of the square of the iteration number. However, the convergence of the iterates themselves is not known. We show here that with a small modification, we can ensure the same upper bound for the decay of the energy, as well as the convergence of the iterates to a minimizer.

Photophysical and Photochemical Processes in Micellar Systems

Abstract: Reference LPI-ARTICLE-1980-008View record in Web of Science Record created on 2006-02-21, modified on 2017-05-12

Dual Norms and Image Decomposition Models

Abstract: Following a recent work by Y. Meyer, decomposition models into a geometrical component and a textured component have recently been proposed in image processing. In such approaches, negative Sobolev norms have seemed to be useful to modelize oscillating patterns. In this paper, we compare the properties of various norms that are dual of Sobolev or Besov norms. We then propose a decomposition model which splits an image into three components: a first one containing the structure of the image, a second one the texture of the image, and a third one the noise. Our decomposition model relies on the use of three different semi-norms: the total variation for the geometrical component, a negative Sobolev norm for the texture, and a negative Besov norm for the noise. We illustrate our study with numerical examples.