Manipulating light at distance by a metasurface using momentum transformation

A momentum conservation approach is introduced to manipulate light at distance using metasurfaces. Given a specified field existing on one side of the metasurface and specified desired field transmitted from the opposite side, a general momentum boundary condition is established, which determines the amplitude, phase and polarization transformation to be induced by the metasurface. This approach, named momentum transformation, enables a systematic way to synthesize metasurfaces with complete control over the reflected and transmitted fields. Several synthesis illustrative examples are provided: a vortex hypergeometric-Gaussian beam and a "delayed-start" accelerated beam for Fresnel region manipulation, and a pencil beam radiator and a holographic repeater for Frauenhofer region manipulation

The expected area of the filled planar Brownian loop is Pi/5

Let B_t be a planar Brownian loop of time duration 1 (a Brownian motion conditioned so that B_0 = B_1). We consider the compact hull obtained by filling in all the holes, i.e. the complement of the unique unbounded component of R^2\B[0,1]. We show that the expected area of this hull is Pi/5. The proof uses, perhaps not surprisingly, the Schramm Loewner Evolution (SLE). Also, using the result of Yor about the law of the index of a Brownian loop, we show that the expected areas of the regions of non-zero index n equal 1/(2 Pi n^2). As a consequence, we find that the expected area of the region of index zero inside the loop is Pi/30; this value could not be obtained directly using Yor's index description.Comment: 15 pages, 3 figure

A Hybrid Micromachined High -Q Cavity Resonator at 5.8 GHz

A novel hybrid micromachined resonator with high quality factor and small size at 5.8GHz is presented. The design of the resonator is based on a micromachined cavity filled with a high dielectric constant material. Energy is coupled into the cavity from input and output microstrip lines via slots. It is shown experimentally that the limiting factor in achieving a higher Q with the given dielectric materials is the dielectric loss. This resonator provides a low cost, minimum size and compact solution for the fabrication of planar, narrow-band filters and diplexers in modern wireless communication systems.

Is HIV short-sighted? Insights from a multistrain nested model

An important component of pathogen evolution at the population level is evolution within hosts. Unless evolution within hosts is very slow compared to the duration of infection, the composition of pathogen genotypes within a host is likely to change during the course of an infection, thus altering the composition of genotypes available for transmission as infection progresses. We develop a nested modeling approach that allows us to follow the evolution of pathogens at the epidemiological level by explicitly considering within-host evolutionary dynamics of multiple competing strains and the timing of transmission. We use the framework to investigate the impact of short-sighted within-host evolution on the evolution of virulence of human immunodeficiency virus (HIV), and find that the topology of the within-host adaptive landscape determines how virulence evolves at the epidemiological level. If viral reproduction rates increase significantly during the course of infection, the viral population will evolve a high level of virulence even though this will reduce the transmission potential of the virus. However, if reproduction rates increase more modestly, as data suggest, our model predicts that HIV virulence will be only marginally higher than the level that maximizes the transmission potential of the virus

PyNeb: a new tool for analyzing emission lines. I. Code description and validation of results

Analysis of emission lines in gaseous nebulae yields direct measures of physical conditions and chemical abundances and is the cornerstone of nebular astrophysics. Although the physical problem is conceptually simple, its practical complexity can be overwhelming since the amount of data to be analyzed steadily increases; furthermore, results depend crucially on the input atomic data, whose determination also improves each year. To address these challenges we created PyNeb, an innovative code for analyzing emission lines. PyNeb computes physical conditions and ionic and elemental abundances, and produces both theoretical and observational diagnostic plots. It is designed to be portable, modular, and largely customizable in aspects such as the atomic data used, the format of the observational data to be analyzed, and the graphical output. It gives full access to the intermediate quantities of the calculation, making it possible to write scripts tailored to the specific type of analysis one wants to carry out. In the case of collisionally excited lines, PyNeb works by solving the equilibrium equations for an n-level atom; in the case of recombination lines, it works by interpolation in emissivity tables. The code offers a choice of extinction laws and ionization correction factors, which can be complemented by user-provided recipes. It is entirely written in the python programming language and uses standard python libraries. It is fully vectorized, making it apt for analyzing huge amounts of data. The code is stable and has been benchmarked against IRAF/NEBULAR. It is public, fully documented, and has already been satisfactorily used in a number of published papers.Comment: 17 pages, 12 figures. Accepted for publication in Astronomy & Astrophysics. Typos and reference list corrected in this versio

High breakdown estimators for principal components: the projection-pursuit approach revisited.

Li and Chen (J. Amer. Statist. Assoc. 80 (1985) 759) proposed a method for principal components using projection-pursuit techniques. In classical principal components one searches for directions with maximal variance, and their approach consists of replacing this variance by a robust scale measure. Li and Chen showed that this estimator is consistent, qualitative robust and inherits the breakdown point of the robust scale estimator. We complete their study by deriving the influence function of the estimators for the eigenvectors, eigenvalues and the associated dispersion matrix. Corresponding Gaussian efficiencies are presented as well. Asymptotic normality of the estimators has been treated in a paper of Cui et al. (Biometrika 90 (2003) 953), complementing the results of this paper. Furthermore, a simple explicit version of the projection-pursuit based estimator is proposed and shown to be fast to compute, orthogonally equivariant, and having the maximal finite-sample breakdown point property. We will illustrate the method with a real data example. (c) 2004 Elsevier Inc. All rights reserved.breakdown point; dispersion matrix; influence function; principal components analysis; projection-pursuit; robustness; dispersion matrices; s-estimators; robust; covariance; location; scale;

Non Gaussian extrema counts for CMB maps

In the context of the geometrical analysis of weakly non Gaussian CMB maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments expansion of the joint probability distribution of an isotropic random field, its gradient and invariants of the Hessian. Analytic expressions for these counts are given to second order in the non Gaussian correction, while a Monte Carlo method to compute them to arbitrary order is presented. Matching count statistics to these estimators is illustrated on fiducial non-Gaussian "Planck" data.Comment: 4 pages, 1 figur