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We have used the Largest Cluster Statistics and the Average Filamentarity to quantify respectively the connectivity and the shapes of the patterns seen in the galaxy distribution in two volume limited subsamples extracted from the…
Simple analytic arguments are used to understand the predominantly filamentary web in the large-scale distribution of galaxies. Numerical simulations of superclusters are performed to assess the feasibility of directly mapping the…
Geometrical model of structure of the universe is examined to obtain analytical expression for the two points nonlinear correlation function. According to the model the objects (galaxies) are concentrated into two types of structure…
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…
Cellular systems are observed everywhere in nature, from crystal domains in metals, soap froth and cucumber cells to the network of cosmological voids. Surprisingly, despite their disparate scale and origin all cellular systems follow…
Galaxies evolve within the intricate geometry of the cosmic web, yet the distinct roles of its primary components - nodes and filaments remain incompletely understood. Using the EAGLE cosmological hydrodynamical simulation, we investigate…
Galaxies represent the visible fabric of the Universe and there has been considerable progress recently in both observational and theoretical studies. The underlying goal is to understand the present-day diversity of galaxy forms, masses…
The intersections between a spherical shell and the faces of Voronoi's polyhedrons are numerically evaluated. The nodes of these intersections are the points that share the same distances from three nuclei. The nodes are assumed to be the…
The theory of structure formation predicts that galaxies form within extended massive dark matter halos built from smaller pieces that collided and merged, resulting in the hierarchy of galaxies, groups, and clusters observed today. Here we…
After numerical simulations by E. Praton, we interprete the cocoon-like structure observed for the distribution of galaxies around us as an effect of infall velocities onto clusters. In this view structures like the Cocoon (or even like the…
The analysis of images (of obtained in various ranges of the lengths of waves) of luminous objects in the Universe by means of a method of multilevel dynamic contrasting led author to the conclusions: a) the structures of all observable…
We probe gravitational clustering in N-body simulations using geometrical descriptors sensitive to `connectedness': the genus curve, percolation and shape statistics. We find that both genus and percolation curves provide complementary…
Clusters of galaxies, the largest collapsed structures in the Universe, are located at the intersection of extended filaments of baryons and dark matter. Cosmological accretion onto clusters through large scale filaments adds material at…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
We present a numerical study of topological descriptors of initially Gaussian and scale-free density perturbations evolving via gravitational instability in an expanding universe. We carefully evaluate and avoid numerical contamination in…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
The main tools in cosmology for comparing theoretical models with the observations of the galaxy distribution are statistical. We will review the applications of spatial statistics to the description of the large-scale structure of the…
We report on two quantitative, morphological estimators of the filamentary structure of the Cosmic Web, the so-called global and local skeletons. The first, based on a global study of the matter density gradient flow, allows us to study the…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
Cosmic structures at large scales represent the earliest and most extended form of matter condensation. In this lecture we review the application of the methods and concepts of modern statistical physics to these structures. This leads to a…