École normale supérieure de Cachan

About: École normale supérieure de Cachan is a education organization based out in Cachan, Île-de-France, France. It is known for research contribution in the topics: Decidability & Nonlinear system. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

Lattice Signatures and Bimodal Gaussians

Abstract: Our main result is a construction of a lattice-based digital signature scheme that represents an improvement, both in theory and in practice, over today’s most efficient lattice schemes. The novel scheme is obtained as a result of a modification of the rejection sampling algorithm that is at the heart of Lyubashevsky’s signature scheme (Eurocrypt, 2012) and several other lattice primitives. Our new rejection sampling algorithm which samples from a bimodal Gaussian distribution, combined with a modified scheme instantiation, ends up reducing the standard deviation of the resulting signatures by a factor that is asymptotically square root in the security parameter. The implementations of our signature scheme for security levels of 128, 160, and 192 bits compare very favorably to existing schemes such as RSA and ECDSA in terms of efficiency. In addition, the new scheme has shorter signature and public key sizes than all previously proposed lattice signature schemes.

Diamonds with a high density of nitrogen-vacancy centers for magnetometry applications

Abstract: Nitrogen-vacancy (NV) centers in millimeter-scale diamond samples were produced by irradiation and subsequent annealing under varied conditions. The optical and spin-relaxation properties of these samples were characterized using confocal microscopy, visible and infrared absorption, and optically detected magnetic resonance. The sample with the highest ${\text{NV}}^{\ensuremath{-}}$ concentration, approximately 16 ppm $(2.8\ifmmode\times\else\texttimes\fi{}{10}^{18}\text{ }{\text{cm}}^{\ensuremath{-}3})$, was prepared with no observable traces of neutrally charged vacancy defects. The effective transverse spin-relaxation time for this sample was ${T}_{2}^{\ensuremath{\ast}}=118(48)\text{ }\text{ns}$, predominately limited by residual paramagnetic nitrogen which was determined to have a concentration of 49(7) ppm. Under ideal conditions, the shot-noise limited sensitivity is projected to be $\ensuremath{\sim}150\text{ }\text{fT}/\sqrt{\text{Hz}}$ for a $100\text{ }\ensuremath{\mu}\text{m}$-scale magnetometer based on this sample. Other samples with ${\text{NV}}^{\ensuremath{-}}$ concentrations from 0.007 to 12 ppm and effective relaxation times ranging from 27 to over 291 ns were prepared and characterized.

An algebraic framework for linear identification

Abstract: A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.

Image Denoising Methods. A New Nonlocal Principle

Abstract: The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding performance when the image model corresponds to the algorithm assumptions but fail in general and create artifacts or remove fine structures in images. The main focus of this paper is, first, to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms and, second, to propose a nonlocal means (NL-means) algorithm addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the “method noise,” defined as the difference between a digital image and its denoised version. The NL-means algorithm is proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods is compared in four ways; mathematical: asymptotic order of magnitude of the method noise under regularity assumptions; perceptual-mathematical: the algorithms artifacts and their explanation as a violation of the image model; quantitative experimental: by tables of $L^2$ distances of the denoised version to the original image. The fourth and perhaps most powerful evaluation method is, however, the visualization of the method noise on natural images. The more this method noise looks like a real white noise, the better the method.