Superefficient drift estimation on the Wiener space

In the framework of a nonparametric functional estimation for the drift of a Brownian motion $X_t$ we construct Stein type estimators of the form $X_t+D_t\log F$ which are superefficient when $\sqrt{F}$ is a superharmonic functional on the Wiener space for the Malliavin derivative D. To cite this article: N. Privault, A. Réveillac, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Hydrothermal preparation and photoluminescence of bundle-like structure of ZnWO4 nanorods

ZnWO₄ nanorods with a bundle-like structure were synthesized at 180°C for 12 h by a hydrothermal technology from Na₂WO₄⋅2H₂O and ZnSO₄⋅7H₂O in the presence of sodium dodecyl sulfate (SDS). The as-synthesized bundle-like structure of ZnWO₄ nanorods was characterized by various techniques: TEM, XRD and EDS. The luminescence properties of the bundle-like structure of the ZnWO₄ nanorods were investigated by photoluminescence (PL) spectroscopy.     

Development of new apertures for coherent X‐ray experiments

When one performs a coherent small‐angle X‐ray scattering experiment, the incident beam must be spatially filtered by slits on a length scale smaller than the transverse coherence length of the source which is typically around 10 µm. The Fraunhofer diffraction pattern of the slit is one of the important sources of background in these experiments. New slits which minimize this parasitic background have been designed and tested. The slit configuration apodizes the beam by the use of partially transmitting inclined slit jaws. A model is presented which predicts that the high wavevector tails of the diffraction pattern fall as the inverse fourth power of the wavevector instead of the inverse second power that is observed for standard slits. Using cleaved GaAs single‐crystal edges, Fraunhofer diffraction patterns from 3 and 5.5 keV X‐rays were measured, in agreement with the theoretical model proposed. A novel phase‐peak diffraction pattern associated with phase variations of the transmitted electric field was also observed. The model proposed adequately accounts for this phenomenon.     

Universality properties of Gelfand–Tsetlin patterns

A standard Gelfand–Tsetlin pattern of depth n is a configuration of particles in ${\{1,\ldots,n\} \times \mathbb{R}}$ . For each ${r \in \{1, \ldots, n\}, \{r\} \times \mathbb{R}}$ is referred to as the rth level of the pattern. A standard Gelfand–Tsetlin pattern has exactly r particles on each level r, and particles on adjacent levels satisfy an interlacing constraint. Probability distributions on the set of Gelfand–Tsetlin patterns of depth n arise naturally as distributions of eigenvalue minor processes of random Hermitian matrices of size n. We consider such probability spaces when the distribution of the matrix is unitarily invariant, prove a determinantal structure for a broad subclass, and calculate the correlation kernel. In particular we consider the case where the eigenvalues of the random matrix are fixed. This corresponds to choosing uniformly from the set of Gelfand–Tsetlin patterns whose nth level is fixed at the eigenvalues of the matrix. Fixing ${q_n \in \{1,\ldots,n\}}$ , and letting n → ∞ under the assumption that ${\frac{q_n}n \to \alpha \in (0, 1)}$ and the empirical distribution of the particles on the nth level converges weakly, the asymptotic behaviour of particles on level q _n is relevant to free probability theory. Saddle point analysis is used to identify the set in which these particles behave asymptotically like a determinantal random point field with the Sine kernel.     

Origin of the 330 nm absorption band and effect of doping Yb in LiYF4 crystals

The electronic structures of LiYF₄ (YLF) crystals containing F color center (YLF-F) and Yb doped YLF crystals (Yb³⁺:YLF, Yb²⁺:YLF) are systematically studied within the framework of the density functional theory. The calculated results indicate that the 330 nm absorption band originates from the F center in YLF crystals. Thus the doping of Yb³⁺ can weaken the 330 nm absorption band by competing with F vacancies in capturing free electrons arising after γ-irradiation and change to Yb². By analyzing the lattice relaxation and the electronic structure of YLF containing Yb²⁺, we can reasonably believe that once Yb²⁺ is formed in YLF crystal, its compensating hole will turn out to be shared by two F⁻ nearest to Yb²⁺ forming a diatomic fluoride molecular ion () perturbed by Yb²⁺, or to say V_F color center. According to the molecular-orbital linear combination of atomic orbital (MO-LCAOs) theory, compared to the alkali halides, e.g. LiF, the in V_F center in LiYF₄ peaks at about 340 nm, which is in agreement with the experimental results.     

Efficient 1047 nm CW laser emission of Nd:YLF under direct pumping into the emitting level

We demonstrate a 1047 nm Nd:LiYF₄ (Nd:YLF) laser by directly pumping into the upper lasing level with a tunable Ti:Sapphire laser. The results obtained for direct upper laser level pumping at 863, 872 and 880 nm of Nd:YLF were compared with traditional 806 nm pump band excitation. Highly efficient 1047 nm continuous-wave (CW) laser emission under direct pumping at 880 nm in an 8 mm thick, 1.0 at.% Nd:YLF crystal is obtained. The slope efficiency is improved from 55.6% for traditional pumping at 806 nm to 76.3% for direct pumping at 880 nm.     

Burstiness and fractional diffusion on complex networks

Many dynamical processes on real world networks display complex temporal patterns as, forinstance, a fat-tailed distribution of inter-events times, leading to heterogeneouswaiting times between events. In this work, we focus on distributions whose averageinter-event time diverges, and study its impact on the dynamics of random walkers onnetworks. The process can naturally be described, in the long time limit, in terms ofRiemann-Liouville fractional derivatives. We show that all the dynamical modes possess, inthe asymptotic regime, the same power law relaxation, which implies that the dynamics doesnot exhibit time-scale separation between modes, and that no mode can be neglected versusanother one, even for long times. Our results are then confirmed by numericalsimulations.     

Existence and attractivity of time periodic solutions for Nicholson's blowflies model with nonlinear diffusion

This paper is concerned with the existence and attractivity of time periodic solutions for one‐dimensional Nicholson's blowflies model with nonlinear diffusion. By constructing some suitable Lyapunov functionals and combining with Leray–Schauder fixed point theorem, we establish the existence of nonnegative time periodic solutions. Using the method of upper and lower solutions and its associated monotone iterations, we obtain the existence of the attractor for this model. Copyright © 2013 John Wiley & Sons, Ltd.     

An alternating direction algorithm for matrix completion with nonnegative factors

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are partially known (to a certain accuracy). This problem aggregates two existing problems: (i) nonnegative matrix factorization where all entries of M are given, and (ii) low-rank matrix completion where nonnegativity is not required. By taking the advantages of both nonnegativity and low-rankness, one can generally obtain superior results than those of just using one of the two properties. We propose to solve the non-convex constrained least-squares problem using an algorithm based on the classical alternating direction augmented Lagrangian method. Preliminary convergence properties of the algorithm and numerical simulation results are presented. Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm produces factorizations of similar quality using only about half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspectral images, the proposed algorithm yields overall better qualities than those produced by two recent matrix-completion algorithms that do not exploit nonnegativity.     

Surface plasmonic resonance sensor by metal strip pair arrays

We present a surface plasmonic resonance sensor composed of Ag strip pairs array embedded in the background material. The calculated results demonstrate that one of the transmission dips of the structure is very sensitive to the background materials. Meanwhile, the structure could achieve the sensitivity (nm/RIU) about 700 nm/RIU, when the slits width of Ag strip pairs is 10 nm.