Related papers: Wavelet Analysis of One-Dimensional Cosmological D…
The study of the properties of cosmic structures in the universe is one of the most fascinating subject of the modern cosmology research. Far from being predicted, the large scale structure of the matter distribution is a very recent…
Weak gravitational lensing, resulting from the bending of light due to the presence of matter along the line of sight, is a potent tool for exploring large-scale structures, particularly in quantifying non-Gaussianities. It stands as a…
One of the new frontiers of astronomical research is the exploration of time variability on the sky at different wavelengths and flux levels. We have carried out a pilot project using DPOSS data to study strong variables and transients, and…
The lecture introduces a trous wavelet transforms, explains how to estimate the spatial density for galaxy distributions, and, finally, how to describe the morphology of cosmological density fields. An example application of these methods…
We propose a new method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces and data from economy. The results are compared with those…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
Using wavelet analysis approach, we can derive a measure of the disorder content of solar activity, following the temporal evolution of the so-called wavelet entropy. The interesting feature of this parameter is its ability to extract a…
Cosmic variance is the intrinsic scatter in the number density of galaxies due to fluctuations in the large-scale dark matter density field. In this work, we present a simple analytic model of cosmic variance in the high redshift Universe…
Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
We investigate the use of wavelet transforms in detecting and characterising non-Gaussian structure in maps of the cosmic microwave background (CMB). We apply the method to simulated maps of the Kaiser-Stebbins effect due to cosmic strings…
I review some results of estimation of the power spectrum of density fluctuations from galaxy redshift surveys and discuss advances that may be possible with the Sloan Digital Sky Survey. I then examine the realities of power spectrum…
Cosmological simulations are an important method for investigating the evolution of the Universe. In order to gain further insight into the processes of structure formation, it is necessary to identify isolated bound objects within the…
We propose a general approach to characterise fluctuations of measured cross sections of nuclear giant resonances. Simulated cross sections are obtained from a particular, yet representative self-energy which contains all information about…
Surveys of galaxy clusters provide a promising method of testing models of structure formation in the universe. Within the context of our standard structure formation scenario, surveys provide measurements of the geometry of the universe…
We address the problem of discretizing continuous cosmological signals such as a galaxy distribution for further processing with Fast Fourier techniques. Discretizing, in particular representing continuous signals by discrete sets of sample…
This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {\it needlets}. We establish a minimax result and prove its…
The COBE results, to be followed in the near future by other Cosmic Microwave Background measurements, are providing us with a new fundamental tool to probe the formation of large scale structure in the Universe, and in so doing to…
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the…
In many astrophysical systems, smoothly-varying large-scale variations coexist with small-scale fluctuations. For example, a large-scale velocity or density gradient can exist in molecular clouds that exhibit small-scale turbulence. In…