Related papers: Block Thresholding on the Sphere
A new gridding technique for the solution of partial differential equations in cubical geometry is presented. The method is based on volume penalization, allowing for the imposition of a cubical geometry inside of its circumscribing sphere.…
This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially…
Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients…
This paper constructs a semi-discrete tight frame of tensor needlets associated with a quadrature rule for tangent vector fields on the unit sphere $\mathbb{S}^2$ of $\mathbb{R}^3$ --- tensor needlets. The proposed tight tensor needlets…
We adress the problem of spherical deconvolution in a non parametric statistical framework, where both the signal and the operator kernel are subject to error measurements. After a preliminary treatment of the kernel, we apply a…
We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds…
We consider the regression model with (known) random design. We investigate the minimax performances of an adaptive wavelet block thresholding estimator under the $\mathbb{L}^p$ risk with $p\ge 2$ over Besov balls. We prove that it is near…
A method is presented for the fast evaluation of the transient acoustic field generated outside a spherical surface using surface data on the sphere. The method employs Lebedev quadratures, which are optimal integration on the sphere, and…
We propose a computationally feasible estimator for the needlet trispectrum, which develops earlier work on the bispectrum by Donzelli et al. (2012). Our proposal seems to enjoy a number of useful properties, in particular a) the…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
The problem of (non)random distribution of points on the sphere is investigated. Published procedures for obtaining preferred direction and preferred plane for points on the sphere (in the sky) are discussed. It is shown that the published…
In this work, we have studied the possibility of setting up Bell's inequality violating experiment in the context of cosmology, based on the basic principles of quantum mechanics. First we start with the physical motivation of implementing…
Observations of the Cosmic Microwave Background (CMB) provide increasingly accurate information about the structure of the Universe at the recombination epoch. Most of this information is encoded in the angular power spectrum of the CMB.…
We discuss Spherical Needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover…
For many decades, ultrahigh energy charged particles of unknown origin that can be observed from the ground have been a puzzle for particle physicists and astrophysicists. As an attempt to discriminate among several possible production…
This work considers the problem of calculating an interval-valued state estimate for a nonlinear system subject to bounded inputs and measurement errors. Such state estimators are often called interval observers. Interval observers can be…
We simulate numerically Boussinesq convection in non-rotating spherical shells for a fluid with a unity Prandtl number and Rayleigh numbers up to $10^9$. In this geometry, curvature and radial variations of the gravitationnal acceleration…
A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…
The angular power spectrum of a stationary random field on the sphere is estimated from the needlet coefficients of a single realization, observed with increasingly fine resolution. The estimator we consider is similar to the one recently…