Related papers: Alpha Shape Topology of the Cosmic Web
We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology,…
We introduce a multiscale topological description of the Megaparsec weblike cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of…
We introduce a new descriptor of the weblike pattern in the distribution of galaxies and matter: the scale dependent Betti numbers which formalize the topological information content of the cosmic mass distribution. While the Betti numbers…
Using a set of $\Lambda$CDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We…
We trace the connectivity of the cosmic web as defined by haloes in the Planck-Millennium simulation using a persistence and Betti curve analysis. We normalise clustering up to the second-order correlation function, and use our systematic…
The spatial cosmic matter distribution on scales of a few up to more than a hundred Megaparsec displays a salient and pervasive foamlike pattern. Voronoi tessellations are a versatile and flexible mathematical model for such weblike spatial…
This study presents a numerical analysis of the topology of a set of cosmologically interesting three-dimensional Gaussian random fields in terms of their Betti numbers $\beta_0$, $\beta_1$ and $\beta_2$. We show that Betti numbers entail a…
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…
The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our…
We discuss the intimate relationship between the filamentary features and the rare dense compact cluster nodes in this network, via the large scale tidal field going along with them, following the cosmic web theory developed Bond et al. The…
This paper is an introductory and informal exposition on the topology of polygonal meshes. We begin with a broad overview of topological notions and discuss how homeomorphisms, homotopy, and homology can be used to characterise topology. We…
Suppose we have identified three clusters of galaxies as being topological copies of the same object. How does this information constrain the possible models for the shape of our Universe? It is shown here that, if the Universe has flat…
The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body…
Observations reveal that on large scales the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions -- voids. This thesis reports the construction of a sophisticated computational…
A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability…
Galaxy superclusters, the largest galaxy structures in the cosmic web, are formed due to the gravitational collapse (although they are not usually gravitationally bound). Their geometrical properties can shed light on the structure…
We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes…
We stress the importance of stochastic geometry as a branch of mathematical statistics particularly suited to model and investigate nontrivial spatial patterns. One of its key concepts, Voronoi tessellations, represents a versatile and…
The algebraic cluster model is is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the…
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level.…