Related papers: Multiscale Methods
We introduce a diffusion-based generative model to describe the distribution of galaxies in our Universe directly as a collection of points in 3-D space (coordinates) optionally with associated attributes (e.g., velocities and masses),…
In this work we investigate the multivariate statistical description of the matter distribution in the nonlinear regime. We introduce the multivariate Edgeworth expansion of the lognormal distribution to model the cosmological matter field.…
We present a self-consistent framework to perform the wavelet analysis of two-dimensional statistical distributions. The analysis targets the 2D probability density function (p.d.f.) of an input sample, in which each object is characterized…
Generalized continuum models for describing one-dimensional shear deformations of a Cosserat lattice are considered and their application to describing of structural effects essential for interfaces are discussed. The two-field…
Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…
A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant…
In these lectures I give an overview of gravitational lensing, concentrating on theoretical aspects, including derivations of some of the important results. Topics covered include the determination of surface mass densities of intervening…
This letter presents a new approach using the cosmic peculiar velocity field to characterize the morphology and size of large scale structures in the local Universe. The algorithm developed uses the three-dimensional peculiar velocity field…
Two main strategies have been implemented in mapping the local universe: whole-sky 'shallow' surveys and 'deep' surveys over limited parts of the sky. The two approaches complement each other in studying cosmography and statistical…
The phases of the Fourier modes appearing in a plane-wave expansion of cosmological density fields play a vital role in determining the morphology of gravitationally-developed clustering. We demonstrate this qualitatively and quantitatively…
We discuss correlation properties of a general mass density field introducing a classification of structures based on their complexity. Standard cosmological models for primordial mass fluctuations are characterized by a sort of large-scale…
This paper develops a geometrical model of dislocations and disclinations in single crystals at the mesoscopic scale. In the continuation of previous work the distribution theory is used to represent concentrated effects in the defect lines…
The correlation between a galaxy's morphology and its observed optical spectrum is investigated. As an example, 4000 galaxies from the 2dF Galaxy Redshift Survey, which possess both good quality spectra and have visually determined…
Previous work developed a space-time metric with two cosmological scales; one that conveniently describes the classical evolution of the dynamics, and the other describing a scale associated with macroscopic quantum aspects like vacuum…
Many questions remain in turbulence research---and related fields---about the underlying physical processes that transfer scalar quantities, such as the kinetic energy, between different length scales. Measurement of an ensemble-averaged…
We propose a phenomenological generalization of the models of large-scale structure formation in the Universe by gravitational instability in two ways: we include pressure forces to model multi-streaming, and noise to model fluctuations due…
The statistical translation invariance of cosmological random fields is broken by a finite survey boundary, correlating the observable Fourier modes. Standard methods for generating Gaussian fields either neglect these correlations, or are…
We suggest a new method for estimating the fractal dimension of the spatial distribution of galaxies, the method of selected cylinders. We show the capabilities of this method by constructing a two-point conditional column density for…
Methods for compression and classification of galaxy spectra, which are useful for large galaxy redshift surveys (such as the SDSS, 2dF, 6dF and VIRMOS), are reviewed. In particular, we describe and contrast three methods: (i) Principal…
The COSMOS field has been the subject of a wide range of observations, with a number of studies focusing on reconstructing the 3D dark matter density field. Typically, these studies have focused on one given method or tracer. In this paper,…