Gaussian semiparametric estimates on the unit sphere

We study the weak convergence (in the high-frequency limit) of the parameter estimators of power spectrum coefficients associated with Gaussian, spherical and isotropic random fields. In particular, we introduce a Whittle-type approximate maximum likelihood estimator and we investigate its asympotic weak consistency and Gaussianity, in both parametric and semiparametric cases.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ475 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Needlet-Whittle Estimates on the Unit Sphere

We study the asymptotic behaviour of needlets-based approximate maximum likelihood estimators for the spectral parameters of Gaussian and isotropic spherical random fields. We prove consistency and asymptotic Gaussianity, in the high-frequency limit, thus generalizing earlier results by Durastanti et al. (2011) based upon standard Fourier analysis on the sphere. The asymptotic results are then illustrated by an extensive Monte Carlo study.Comment: 48 pages, 2 figure

Adaptive Nonparametric Regression on Spin Fiber Bundles

The construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric regression on sections of spin fiber bundles defined on the sphere. This can be viewed as a regression problem where the function to be estimated takes as its values algebraic curves (for instance, ellipses) rather than scalars, as usual. The problem is motivated by many important astrophysical applications, concerning for instance the analysis of the weak gravitational lensing effect, i.e. the distortion effect of gravity on the images of distant galaxies. We propose a thresholding procedure based upon the (mixed) spin needlets construction recently advocated by Geller and Marinucci (2008,2010) and Geller et al. (2008,2009), and we investigate their rates of convergence and their adaptive properties over spin Besov balls.Comment: 40 page

Normal Approximations for Wavelet Coefficients on Spherical Poisson Fields

We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelets/needlets coefficients based on a homogeneous spherical Poisson field. In particular, we develop some results from Peccati and Zheng (2011), based on Malliavin calculus and Stein's methods, to assess the rate of convergence to Gaussianity for a triangular array of needlet coefficients with growing dimensions. Our results are motivated by astrophysical and cosmological applications, in particular related to the search for point sources in Cosmic Rays data.Comment: 28 page

Flexible-bandwidth Needlets

We investigate here a generalized construction of spherical wavelets/needlets which admits extra-flexibility in the harmonic space, i.e., it allows the corresponding support in multipole (frequency) space to vary in more general forms than in the standard constructions. We study the analytic properties of this system and we investigate its behaviour when applied to isotropic random fields: more precisely, we establish asymptotic localization and uncorrelation properties (in the high-frequency sense) under broader assumptions than typically considered in the literature

Vitamin E Supplementation Reduces Plasma Vascular Cell Adhesion Molecule-1 and von Willebrand Factor Levels and Increases Nitric Oxide Concentrations in Hypercholesterolemic Patients

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Effects of oregano (Origanum vulgareL.) and rosemary (Rosmarinus officinalis L.) aqueous extracts on broiler performance, immune function and intestinal microbial population

ABSTRACT A 57-day study was performedto determine the effects of two aqueous extracts (AEs) on broiler performance, immune function and intestinal microflora. Four groups of 75 one-day-old female broilers (Ross308) received one of the following treatments: (1) a standard commercial feed (C); (2) C supplemented with 2 g/kg rosemary AE (R); (3) C supplemented with 2 g/kg oregano AE (O); (4) C supplemented with 1 g/kg oregano AE + 1 g/kg rosemary AE (OR). Individual body weight, average daily gain, average daily feed intake and feed conversion efficiency were determined at 1, 11, 22, 36 and 57 days. Sample collections for IgG titration and intestinal microflora examination were performed at 22 and 57 days. The addition of oregano AE alone or in combination with rosemary AEs improved body weight up to 36 days of age (P < .01). A time effect was recorded for total serum IgG in all groups (P < .001) and the percentage increase of the value was positively (P < .05) influenced by the AE supplementation. Lactobacilli raised (P < .001) in ileum and cecum of all groups supplemented with AEs. Staphylococcus spp. population was constantly lower in both intestinal tracts of the AE supplemented groups. On the basis of our results, AEs could improve broiler performance and immune function and contribute to a balanced gut microflora, essential for the digestion process and protection against enteropathogenic organisms