相关论文: Minkowski Functionals in Cosmology
Minkowski functionals have recently been introduced into cosmology as novel tools for studying the large-scale distribution of matter in the Universe. We present a brief overview of the method, including its mathematical foundations as well…
The Minkowski functionals are a mathematical tool to quantify morphological features of patterns. Some applications to the matter distribution in galaxy catalogues and N-body simulations are reviewed, with an emphasis on the effects of…
A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the…
Many statistical methods have been proposed in the last years for analyzing the spatial distribution of galaxies. Very few of them, however, can handle properly the border effects of complex observational sample volumes. In this paper, we…
We discuss the application of Minkowski functionals to galaxy catalogues with emphasis on the boundary corrections and point out the relevance for other statistical methods. The analysis of a cubic subsample of the CfA--1 data serves as an…
The morphological properties of large scale structure of the Universe can be fully described by four Minkowski functionals (MFs), which provide important complementary information to other statistical observables such as the widely used…
In order to quantify higher-order correlations of the galaxy cluster distribution we use a complete family of additive measures which give scale-dependent morphological information. Minkowski functionals can be expressed analytically in…
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…
In this study, we explore the potential of utilizing the four Minkowski functionals, which can fully describe the morphological properties of the large-scale structures, as a robust tool for investigating the modified gravity, particularly…
The Minkowski functionals are useful statistics to quantify the morphology of various random fields. They have been applied to numerous analyses of geometrical patterns, including various types of cosmic fields, morphological image…
We suggest novel statistics for the CMB maps that are sensitive to non-Gaussian features. These statistics are natural generalizations of the geometrical and topological methods that have been already used in cosmology such as the…
The study of shapes of the images of objects is an important issue not only because it reveals its dynamical state but also it helps to understand the object's evolutionary history. We discuss a new technique in cosmological image analysis…
Modern redshift surveys such as the 2 degree field Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky Survey (SDSS) reveal the fully 3 dimensional distribution of a million or so galaxies over a large cosmological volume. Visually…
We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which…
A complete family of statistical descriptors for the morphology of large--scale structure based on Minkowski--Functionals is presented. These robust and significant measures can be used to characterize the local and global morphology of…
We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to…
The morphology of galaxy clusters is quantified using Minkowski functionals, especially the vector-valued ones, which contain directional information and are related to curvature centroids. The asymmetry of clusters and the amount of their…
Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for…
To study the global morphology of the galaxy distribution in our local neighbourhood we calculate the Minkowski functionals for a sequence of volume limited samples within a sphere of 8 Mpc centred on our galaxy. The well known strong…
Minkowski functionals (MFs) quantify the topological properties of a given field probing its departure from Gaussianity. We investigate their use on lensing convergence maps in order to see whether they can provide further insights on the…