Related papers: Multiscale Methods
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive…
The changes of main paradigms on the structure and evolution of the Universe are reviewed. Two puzzles of the modern cosmology, the mean density of matter and the regularity of the Universe on large scales, as well as the possibility to…
The treatment of 1 + 3 covariant perturbation in a multifluid cosmology with the consideration of f (G) gravity, G being the Gauss-Bonnet term, is done in the present paper. We define a set of covariant and gauge-invariant variables to…
We present a class of general prolate and oblate spheroidal spacetimes for the description of cosmic structures in the Universe. They are exact geometries which represent, in an appropriated way, the imbedding of spheroidal matter-energy…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…
Luminous tracers have been used extensively to map the large-scale matter distribution in the Universe. Similarly the dynamics of stars or galaxies can be used to estimate masses of galaxies and clusters of galaxies. However, assumptions…
Lecture 1. Algebraic properties of correlators in 2D topological field theory. Moduli of a 2D TFT and WDVV equations of associativity. Lecture 2. Equations of associativity and Frobenius manifolds. Deformed flat connection and its monodromy…
Any multivariate distribution can be uniquely decomposed into marginal (1-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an…
We extend the mimetic cosmology to models containing gauge invariant $p$-forms. The $0$-form case reproduces the well-known results of the mimetic dark matter, the $1$-form corresponds to the gauge field mimetic model while the $2$-form…
Following novel development and adaptation of the Metric Space Technique (MST), a multi-scale morphological analysis of the Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5) was performed. The technique was adapted to perform a…
Weak gravitational lensing provides a unique method to map directly the distribution of dark matter in the universe and to measure cosmological parameters. This cosmic-shear technique is based on the measurement of the weak distortions that…
We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear…
A novel method allowing to compute density, velocity and other fields in cosmological N--body simulations with unprecedentedly high spatial resolution is described. It is based on the tessellation of the three-dimensional manifold…
It is common practice in cosmology to model large-scale structure observables as lognormal random fields, and this approach has been successfully applied in the past to the matter density and weak lensing convergence fields separately. We…
Cosmic voids and their corresponding redshift-projected mass densities, known as troughs, play an important role in our attempt to model the large-scale structure of the Universe. Understanding these structures enables us to compare the…
These lecture notes delve into field-level inference, a framework offering a robust way to extract more information and avoid biases compared to traditional methods for cosmological data analysis. The core idea is to analyse uncompressed…
Astrophysical processes such as feedback from supernovae and active galactic nuclei modify the properties and spatial distribution of dark matter, gas, and galaxies in a poorly understood way. This uncertainty is one of the main theoretical…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
We extend a recently developed galaxy morphology classification method, Quantitative Multiwavelength Morphology (QMM), to connect galaxy morphologies to their underlying physical properties. The traditional classification of galaxies…