Related papers: Multiscale Methods
The deflection of ultra-high energy cosmic rays depends on the shape of the injection spectrum of the source and the pervasive cosmic magnetic fields. In this work it is applied the wavelet transform on the sphere to search for energy…
The multiscale dynamics of glow discharge plasma is analysed through wavelet transform, whose scale dependent variable window size aptly captures both transients and non-stationary periodic behavior. The optimal time-frequency localization…
One of the main problems of observational cosmology is to determine the range in which a reliable measurement of galaxy correlations is possible. This corresponds to determine the shape of the correlation function, its possible evolution…
Gravitational lensing of distant objects caused by gravitational tidal forces from inhomogeneities in the universe is weak in most cases, but it is noticed that it gives a great deal of information about the universe, especially regarding…
The question of the nature of galaxy clustering and the possible homogeneity of galaxy distribution is one of the fundamental problem of cosmology. It is well established that galaxy structures are characterized, up to a certain scale, by…
New type of tomographic probability distribution, which contains complete information on the density matrix (wave function) related to the Fresnel transform of the complex wave function, is introduced. Relation to symplectic tomographic…
Due to our vantage point in the disk of the Galaxy, its 3D structure is not directly accessible. However, knowing the spatial distribution, e.g. of atomic and molecular hydrogen gas is of great importance for interpreting and modelling…
Methods for the statistical characterization of the large-scale structure in the Universe will be the main topic of the present text. The focus is on geometrical methods, mainly Minkowski functionals and the J-function. Their relations to…
We propose a novel technique to refine the modelling of galaxy clusters mass distribution using gravitational lensing. The idea is to combine the strengths of both "parametric" and "non-parametric" methods to improve the quality of the fit.…
We study statistical properties of galaxy structures in several samples extracted from the 2dF Galaxy Redshift Survey. In particular, we measured conditional fluctuations by means of the scale-length method and determined their probability…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
These lectures cover the basics of inflationary models for the early universe, concentrating particularly on the generation of density fluctuations from scalar-field dynamics. The subsequent gravitational dynamics of these fluctuations in…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
We review the analysis of the Cosmic Web by means of an extensive toolset based on the use of Delaunay and Voronoi tessellations. The Cosmic Web is the salient and pervasive foamlike pattern in which matter has organized itself on scales of…
This work presents a formalism for deriving likelihoods of the cosmological density field directly from first principles within Perturbation Theory (PT). By assuming a perturbative expansion around the Gaussian initial density field and…
A flexible model is developed for multivariate generalized spherical distributions, i.e. ones with level sets that are star shaped. To work in dimension above 2 requires tools from computational geometry and multivariate numerical…
We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional…
We introduce a new 2-D hexagon technique to probe the topological structure of the universe, in which we map regions of the sky with high and low galaxy densities onto a 2-D lattice of hexagon unit cells, We define filled cells as…
Here I present results from individual galaxy studies and galaxy surveys in the Local Universe with particular emphasis on the spatially resolved properties of neutral hydrogen gas. The 3D nature of the data allows detailed studies of the…
A wavelet space-scale decomposition (SSD) analysis of large scale structures in the universe has been developed. The SSD method of identifying and measuring structures in the spatial distribution of objects has been demonstrated. The…