Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator

The minimum covariance determinant (MCD) scatter estimator is a highly robust estimator for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is relatively fast to compute and intuitively appealing. In this note we derive its influence function and compute the asymptotic variances of its elements. A comparison with the one step reweighted MCD and with S-estimators is made. Also finite-sample results are reported.     

Une variante à la Coxeter du groupe de Steinberg

LetG _n ()be the semi-direct product of the symmetric groupS _n by the Steinberg groupSt _n ()of a ringWe first prove thatG _n ()has a Coxeter-type presentation. The canonical morphism St _n () GL _n ()extends to a group homo G_n() GL _n ()We next determine the kernel of for n = We also give an expression for the generator of the algebraic K group K ₂(Z)of the integers in terms of permutation matrices.     

Fiber grating couplers for silicon nanophotonic circuits: Design modeling methodology and fabrication tolerances

Silicon nanophotonic circuits can exhibit a very high level of functional integration due to the very small cross sections of the silicon waveguides. However, to be implemented in data transmission networks, such circuits still must be interfaced with optical fibers having much larger dimensions. Due to this mismatch in size, a coupling structure is required in order to minimize the coupling loss. Diffraction grating coupler structures are one of the best candidates to perform this mode size conversion with good performances. However, they are also very sensitive to fabrication tolerances that may require an adaptation of the coupling conditions. In this paper, we present an iterative numerical method to optimize the design of a grating coupler by analyzing the out coupled beam from the waveguide towards the fiber. Using this method we show in details the sensitivity of the grating couplers to the principal fabrication variabilities in order to maximize the robustness of the design. A grating with 53% fiber to waveguide coupling efficiency is designed. Considering the dispersion of the modern CMOS fabrication processing, it appears that the optimal fiber coupling ratio remains rather constant but the optimal coupling angle at a given wavelength may vary by as much as ±10°.     

Turbulent transport of material particles: an experimental study of finite size effects

We present experimental Lagrangian statistics of finite sized, neutrally bouyant, particles transported in an isotropic turbulent flow. The particle's diameter is varied over turbulent inertial scales. Finite size effects are shown not to be trivially related to velocity intermittency. The global shape of the particle's acceleration probability density functions is not found to depend significantly on its size while the particle's acceleration variance decreases as it becomes larger in quantitative agreement with the classical k(-7/3) scaling for the spectrum of Eulerian pressure fluctuations in the carrier flow.     

Synthesis and structural characterization of a highly substituted triazine ring comprising a sterically flexible methylene linker and coordinating substituents

The efficient multi-step, large-scale synthesis, spectroscopic characterization and solid-state molecular structure of a new type of three-fold functionalized, sterically demanding triazine is reported. The aromatic heterocycle 6,6′,6′'-((1,3,5-triazine-2,4,6-triyl)tris(methylene))tris(2,4-di-tert-butylphenol) possesses three 2,4-di-tert-butylphenol synthons bound to the 1,3,5-triazine ring via synthetically challenging methylene linkages in the 2,4,6 positions. The key to success was found in the generation of a highly reactive imidate hydrochloride salt, namely ethyl 2-(3,5-di-tert-butyl-2-methoxyphenyl)acetimidate hydrochloride, that readily undergoes cyclotrimerization. The reported preparation opens new perspectives in the design and synthesis of novel triazine molecules bearing flexible and sterically demanding functionalized groups for various applications.     

Adaptation of PTB’s analytical modelling for TDCR–Cherenkov activity measurements at LNHB

Designed for triple to double coincidence ratio measurements based on liquid scintillation, the three-photomultipliers detection system can also be applied for Cherenkov counting using aqueous solutions. For activity determination, a specific modelling of Cherenkov light emission has to be constructed. For that purpose, the analytical modelling first developed at PTB was adapted to account for the physical features of the detection system used at LNHB. The first results are presented in the case of activity measurements of two high-energy β^?-emitters (⁹⁰Y and ⁸⁹Sr). The analytical modelling was also tested for the standardization of ⁶⁸Ge in a solution of ⁶⁸Ge/⁶⁸Ga in equilibrium in the framework of a BIPM international comparison in 2014.     

Electronic Structure and Magnetic Anisotropy of an Unsaturated Cyclopentadienyl Iron(I) Complex with 15 Valence Electrons

The 15 valence-electron iron(I) complex [Cp^ArFe(IiPr₂Me₂)] ( 1 , Cp^Ar=C₅(C₆H₄-4-Et)₅; IiPr₂Me₂=1,3-diisopropyl-4,5-dimethylimidazolin-2-ylidene) was synthesized in high yield from the Fe^II precursor [Cp^ArFe(μ-Br)]₂. ⁵⁷Fe Mössbauer and EPR spectroscopic data, magnetic measurements, and ab initio ligand-field calculations indicate an S= 3/2 ground state with a large negative zero-field splitting. As a consequence, 1 features magnetic anisotropy with an effective spin-reversal barrier of U_eff=64 cm⁻¹. Moreover, 1 catalyzes the dehydrogenation of N,N-dimethylamine–borane, affording tetramethyl-1,3-diaza-2,4-diboretane under mild conditions.     

Assembly of the Entire Carbon Backbone of a Stereoisomer of the Antitumor Marine Natural Product Hemicalide

A strategy for the assembly of the entire carbon backbone of a stereoisomer of the antitumor marine natural product hemicalide has been investigated. The devised convergent approach relies on Horner–Wadsworth–Emmons and Julia–Kocienski olefination reactions for the construction of the C6=C7 and C34=C35 double bonds, respectively, an aldol reaction to create the C27−C28 bond, and a Suzuki–Miyaura cross-coupling as the endgame to form the C15−C16 bond.     

Resampling strategies to improve surrogate model‐based uncertainty quantification: Application to LES of LS89

Uncertainty quantification (UQ) is receiving more and more attention for engineering applications particularly from robust optimization. Indeed, running a computer experiment only provides a limited knowledge in terms of uncertainty and variability of the input parameters. These experiments are often computationally expensive, and surrogate models can be constructed to address this issue. The outcome of an uncertainty quantification study is, in this case, directly correlated to the surrogate's quality. Thus, attention must be devoted to the design of experiments to retrieve as much information as possible. This work presents 2 new strategies for parameter space resampling to improve a Gaussian process surrogate model. These techniques indeed show an improvement of the predictive quality of the model with high‐dimensional analytical input functions. Finally, the methods are successfully applied to a turbine blade large‐eddy simulation application: the aerothermal flow around the LS89 blade cascade.