相关论文: Fast spin +-2 spherical harmonics transforms and a…
Interferometric observation of the CMB polarization can be expressed as a linear sum of spherical harmonic coefficients $a_{\pm 2,lm}$ of the CMB polarization. The linear weight for $a_{\pm 2,lm}$ depends on the observational configuration…
We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…
We propose an efficient way to test rotational invariance in the cosmological perturbations by use of galaxy correlation functions. In symmetry-breaking cases, the galaxy power spectrum can have extra angular dependence in addition to the…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
I present an exact and explicit solution to the scalar (Stokes flux intensity) radio interferometer imaging equation on a spherical surface which is valid also for non-coplanar interferometer configurations. This imaging equation is…
In the previous paper [arXiv:2210.10435], the nonlinear perturbation theory of cosmological density field is generalized to include the tensor-valued bias of astronomical objects, such as spins and shapes of galaxies and any other tensors…
3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity.…
The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) scheme is used extensively in astrophysics for data collection and analysis on the sphere. The scheme was originally designed for studying the Cosmic Microwave Background (CMB)…
We provide a fast algorithm to diagnose any directional dependence in the cosmological parameters by calculating maps of local cosmological parameter estimates and their joint errors. The technique implements a fast quadratic estimator…
We present Wavemoth, an experimental open source code for computing scalar spherical harmonic transforms (SHTs). Such transforms are ubiquitous in astronomical data analysis. Our code performs substantially better than existing publicly…
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from…
We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…
We investigate various pixelizations of the sky which allow for fast spherical transforms, for implementation in full sky CMB experiments such as Planck and MAP. We study the effect of varying pixel shape and area on the extraction of the…
We give a detailed derivation of the spherical harmonics which correspond to the spectrum in the tables of the 1985 paper by Kim, Romans and the author on the Kaluza-Klein dimensional reduction of IIB supergravity on $S_5$ to 5-dimensional…
Existing methods for rotation estimation between two spherical ($\mathbb{S}^2$) patterns typically rely on spherical cross-correlation maximization between two spherical function. However, these approaches exhibit computational complexities…
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we…
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…
In this article, we improve the partial regularity theory for minimizing $1/2$-harmonic maps in the case where the target manifold is the $(m-1)$-dimensional sphere. For $m\geq 3$, we show that minimizing $1/2$-harmonic maps are smooth in…
We investigate asymptotic symmetries in flat backgrounds of dimension higher than or equal to four. For spin two we provide the counterpart of the extended BMS transformations found by Campiglia and Laddha in four-dimensional Minkowski…
A nonlinear model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature is exactly solved. This model depends of a parameter $\la$ that is related with the curvature of the space. Firstly the relation with other…