Related papers: Analysis of Large Scale Structure using Percolatio…
In an expanding universe, velocity field and gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolve in time and these can be scaled suitably so that the constant of proportionality…
We study large-scale structures from numerical simulations, paying particular attention to supercluster-like structures. A grid-density-contour based algorithm is adopted to locate connected groups. With the increase of the linking density…
Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…
We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…
In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the…
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological…
The Large Scale Structure in the galaxy distribution is investigated using The First Data Release of the Sloan Digital Sky Survey. Using the Minimal Spanning Tree technique we have extracted sets of filaments, of wall--like structures, of…
We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of…
In this study we use simulations of 128$^3$ particles to study the ellipticity and orientation of clusters of galaxies in N-body simulations of differing power-law initial spectra (P(k) \propto k^n ,n = +1, 0, -1, -2$), and density…
We investigate the clustering morphology of a swarm of freely rising deformable bubbles. A three-dimensional Vorono\"i analysis enables us to quantitatively distinguish between two typical clustering configurations: preferential clustering…
In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…
We study the links between star formation history and structure for a large mass-selected galaxy sample at 0.05 < z_phot < 0.30. The galaxies inhabit a very broad range of environments, from cluster cores to the field. Using HST images, we…
Clusters of galaxies are the largest gravitationally-bound objects in the Universe, having diameters on order of Mpc. Our work asked whether their shapes (morphologies) change over time as the Universe ages. We observed a sample of 165…
We present a novel approach to reconstruct gas and dark matter projected density maps of galaxy clusters using score-based generative modeling. Our diffusion model takes in mock SZ and X-ray images as conditional inputs, and generates…
The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been tackled recently by characterizing the properties of its representative graphs…
With the advent of galaxy surveys which provide large samples of galaxies or galaxy clusters over a volume comparable to the horizon size (SDSS-III, HETDEX, Euclid, JDEM, LSST, Pan-STARRS, CIP etc.) or mass-selected large cluster samples…
`Galaxy groups' have hardly been realised as a separate class of objects with specific characteristics in the structural hierarchy. The presumption that the self-similarity of dark matter structures is a valid prescription for the baryonic…
To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to…
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…
We estimate the distribution of intrinsic shapes of the APM galaxy clusters from their corresponding distribution of projected shapes. We smooth the discrete galaxy distribution and define the cluster shape by fitting the best ellipse to…