Related papers: Fast and Exact Spin-s Spherical Harmonic Transform…
This is a direct computation of the spectral representation of homogeneous spin-weighted spherical random fields with arbitrary integer spin. It generalises known results from Cosmology for the spin-2 Cosmic Microwave Background…
Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must…
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…
We describe a accurate and fast pixel-based statistical method to interpolate fields of arbitrary spin on the sphere. We call this method Fast and Lean Interpolation on the Sphere (FLINTS). The method predicts the optimal interpolated…
Recently it has been shown that the quantum spin-1/2 spin operators can be exactly transformed not only in spinless, but also in spinful canonical Fermi operators in 1D [\cite{JW1}], and 2D [\cite{JW2}] as well. In this paper, using the…
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 introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
Interventional C-arm systems allow flexible 2-D imaging of a 3-D scene while being capable of cone beam computed tomography. Due to the flexible structure of the C-arm, the rotation speed is limited, increasing the acquisition time compared…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…
Algorithms for the fast and exact computation of Wigner matrices are described and their application to a fast and massively parallel 4pi convolution code between a beam and a sky is also presented.
The main ideas and some of the most important results of the spherically symmetric self-consistent approach and a number of related theoretical algorithms are presented. These methods make it possible to study low-dimensional…
Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2--D classical spin systems and 1--D quantum spin systems. The method is scalable and has a controlled error. We illustrate…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
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…
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.…
We present a fast algorithm for generating full sky, high resolution ($\sim 5'$) simulations of the CMB anisotropy pattern. We also discuss the inverse problem, that of evaluating from such a map the full set of $a_{\ell m}$'s and the…
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…