Double-thresholded estimator of extreme value index

The purpose of this Note is to propose an estimator of the extreme value index constructed by using only the number of points exceeding random thresholds. We prove the weak consistency and the asymptotic normality of this estimator. We deduce from this last result that the rate of convergence of our estimator is in a power of the sample size. To our knowledge, this rate of convergence is not reached by any other estimate of the extreme value index. Through a simulation, we compare our estimator to the moment estimator (Dekkers et al., Ann. Statist. 17 (1989) 1833–1855). To cite this article: L. Gardes, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Wavelength division (de)multiplexing based on dispersive self-imaging

We proposed and experimentally demonstrated wavelength division (de)multiplexers (WDMs) utilizing the wavelength dispersive nature of self-imaging multimode interferometers. Proof-of-principle devices fabricated on the silicon-on-insulator platform operated as 4-channel WDMs with a free spectral range of >90 nm, an averaging cross talk of <-20 dB for a 1 nm band, and an insertion loss of <2.0 dB. The potential for higher channel counts and smaller channel wavelength spacing was also predicted. This type of WDM is easy to design and fabricate. The underlying concept is applicable to all planar waveguide platforms.     

Fusion-fission of heavy systems

The influence of the entrance channel on fission processes was studied by forming the same composite system by two different target-projectile combinations (⁴⁰Ar+²⁰⁹Bi and⁵⁶Fe+¹⁸⁷Re, respectively). Compound nucleus fission and quasi fission were observed and the analysis was performed in the framework of the extra-extra-push model, which provides a qualitative interpretation of the results; limits for the extra-extra-push threshold are given, but problems with quantitative predictions for the extra-push are noted.     

Liquid chromatographic/electrospray ionization mass spectrometric identification of the oxidation end‐products of trans‐resveratrol in aqueous solutions

trans‐Resveratrol (3,5,4′‐trihydroxystilbene) is a natural polyphenolic compound that exhibits antioxidant properties. Our study aimed at studying the HO ^. ‐induced oxidation of resveratrol (100 µmol.L^?1) in aerated aqueous solutions. Gamma radiolysis of water was used to generate HO ^. /O free radicals (I = 10 Gy.min^?1, dose = 400 Gy). Oxidation products were identified by direct infusion mass spectrometry and high‐performance liquid chromatography/mass spectrometry. For each product, structural elucidation was based on simple mass spectra, fragmentation spectra and deuterium/hydrogen exchange spectra; the comparison with mass spectra of synthetic products provided valuable information allowing the complete identification of the oxidation products. Four products resulting from the direct attack of HO ^. radicals towards resveratrol were identified respectively as piceatannol (trans‐3,5,3′,4′‐tetrahydroxystilbene), 3,5‐dihydroxybenzoic acid, 3,5‐dihydroxybenzaldehyde and 4‐hydroxybenzaldehyde. Copyright © 2010 John Wiley & Sons, Ltd.     

Estimation of the conditional tail index using a smoothed local Hill estimator

For heavy-tailed distributions, the so-called tail index is an important parameter that controls the behavior of the tail distribution and is thus of primary interest to estimate extreme quantiles. In this paper, the estimation of the tail index is considered in the presence of a finite-dimensional random covariate. Uniform weak consistency and asymptotic normality of the proposed estimator are established and some illustrations on simulations are provided.     

Correlations between fission fragments and light charged-particles in the reaction20Ne+197Au at 13 MeV/nucleon

rgy of light charged-particles has been measured in coincidence with one or two fission fragments in the reaction²⁰Ne+¹⁹⁷Au at a bombarding energy of 13 MeV/u. The fission cross section was found equal to 1,340±260 mb. Assuming that it represents the totality of the fusion cross section, the critical valuel _c is deduced equal to 93±9?, higher thanl _Bf=0=74 in the rotating liquid drop model. The main emission source for protons and alpha particles seems to be a thermally equilibrated composite system. The competition between fission and charged particle emission is unexpected in the frame of the statistical treatment. A high energy component is observed in the forward direction. These results correspond to the first step of a study programme on the evolution of nucleus-nucleus collisions between 10 and 100 MeV per nucleon.     

High-contrast 40 Gb/s operation of a 500 μm long silicon carrier-depletion slow wave modulator

In this Letter, we demonstrate a highly efficient, compact, high-contrast and low-loss silicon slow wave modulator based on a traveling-wave Mach-Zehnder interferometer with two 500?μm long slow wave phase shifters. 40 Gb/s operation with 6.6?dB extinction ratio at quadrature and with an on-chip insertion loss of only 6?dB is shown. These results confirm the benefits of slow light as a means to enhance the performance of silicon modulators based on the plasma dispersion effect.     

Silicon slow-light-based photonic mixer for microwave-frequency conversion applications

We describe and demonstrate experimentally a method for photonic mixing of microwave signals by using a silicon electro-optical Mach-Zehnder modulator enhanced via slow-light propagation. Slow light with a group index of ~11, achieved in a one-dimensional periodic structure, is exploited to improve the upconversion performance of an input frequency signal from 1 to 10.25 GHz. A minimum transmission point is used to successfully demonstrate the upconversion with very low conversion losses of ~7 dB and excellent quality of the received I/Q modulated QPSK signal with an optimum EVM of ~8%.     

Asymptotic distribution of a Pickands-type estimator of the extreme-value index

One of the main goals of extreme-value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme-value index ξ. The aim of this Note is to establish the asymptotic distribution of the estimator of $\xi \in \mathbb{R}$ introduced in Gardes and Girard [A Pickands-type estimator of the extreme-value index, Technical Report LMC-IMAG, RR-1063, 2004]. We also give its rate of convergence in some typical situations. To cite this article: L. Gardes, S. Girard, C. R. Acad. Sci. Paris, Ser. I 341 (2005).