Related papers: Proper Fourier decomposition formalism for cosmolo…
Since the late 1970's, redshift surveys have been vital for progress in understanding large-scale structure in the Universe. The original CfA redshift survey collected spectra of 20-30 galaxies per clear night on a 1.5 meter telescope; over…
Galaxies and the dark matter halos that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealised calculations and analysis of observational data. The assumption leads to an exact…
Finite Sample Smeariness (FSS) has been recently discovered. It means that the distribution of sample Fr\'echet means of underlying rather unsuspicious random variables can behave as if it were smeary for quite large regimes of finite…
Context. Gravitational lensing is one of the leading tools in understanding the dark side of the Universe. The need for accurate, efficient and effective methods which are able to extract this information along with other cosmological…
I discuss the classical cosmological tests-- angular size-redshift, flux-redshift, and galaxy number counts-- in the light of the cosmology prescribed by the intepretation of CMB anisotropies. The discussion is somewhat of a primer for…
Spin (spherical) random fields are very important in many physical applications, in particular they play a key role in Cosmology, especially in connection with the analysis of the Cosmic Microwave Background radiation. These objects can be…
The importance of Cepheids is well known in many fields of astronomy. Section 2 introduces the Fourier decomposition, a tool to describe quantitatively the light curves of pulsating stars. Sect. 3 shows how an observational result was…
We discuss the influence of the cosmological background density field on the spherical infall model. The spherical infall model has been used in the Press-Schechter formalism to evaluate the number abundance of clusters of galaxies, as well…
We present a novel local-based face verification system whose components are analogous to those of biological systems. In the proposed system, after global registration and normalization, three eye regions are converted from the spatial to…
I propose an analysis method, based on spin-spherical harmonics and spherical Bessel functions, for large-scale weak lensing surveys which have source distance information through photometric redshifts. I show that the distance information…
Considering the Friedmann--Lema\^{i}tre--Robertson--Walker (FLRW) metric and the Einstein scalar field system as an underlying gravitational model to construct fractional cosmological models has interesting implications in both classical…
The Old Quantum Mechanics actions discretization rules for periodic motions on the atomic scale (Bohr-Sommerfeld) have been suitably modified in order to account the gravitational field instead of the electrostatic one. The new rules are…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
Measurements of angular correlations between initial and final particles in $\beta$ decay remain one of the most promising ways of probing the Standard Model and looking for new physics. As experiments reach unprecedented precision well…
In this paper, we describe Fourier-based Wave Front Sensors (WFS) as linear integral operators, characterized by their Kernel. In a first part, we derive the dependency of this quantity with respect to the WFS's optical parameters: pupil…
In this article, we compare a set of Wave Front Sensors (WFS) based on Fourier filtering technique. In particular, this study explores the "class of pyramidal WFS" defined as the 4 faces pyramid WFS, all its recent variations (6, 8 faces,…
Geospatial object detection of remote sensing imagery has been attracting an increasing interest in recent years, due to the rapid development in spaceborne imaging. Most of previously proposed object detectors are very sensitive to object…
A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the…
These are advanced lecture notes covering recent developments in the methodology used to analyse galaxy surveys. The focus is particularly on direct measurements of the galaxy power spectrum although I also discuss its Fourier transform,…
We show that the lensing efficiency of cosmic shear generically has a simple shape, even in the case of a tomographic survey with badly behaved photometric redshifts. We argue that source distributions for cosmic shear can therefore be more…