Related papers: Utilizing Voronoi Tessellations to Determine Radia…
For a group of pedestrians without any spatial boundaries, the methods of density estimation is a wide area of research. Besides, there is a specific difficulty when the density along one given pedestrian trajectory is needed in order to…
Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a…
A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in {\it ab-initio} electronic-structure calculations. We combine a weighted Voronoi tessellation with…
Gersho's conjecture in 3D asserts the asymptotic periodicity and structure of the optimal centroidal Voronoi tessellation. This relatively simple crystallization problem remains to date open. We prove bounds on the geometric complexity of…
We present a new non-parametric method for determining mean 3D density and mass profiles from weak lensing measurements around stacked samples of galaxies or clusters, that is, from measurement of the galaxy-shear or cluster-shear…
The lecture notes describe the Delaunay Tessellation Field Estimator for Cosmic Web analysis. The high sensitivity of Voronoi/Delaunay tessellations to the local point distribution is used to obtain estimates of density and related…
We compare the environmental and star formation properties of far-infrared detected and non--far-infrared detected galaxies out to $z \sim0.5$. Using optical spectroscopy and photometry from the Galaxy And Mass Assembly (GAMA) and Sloan…
We study the Voronoi volume function (VVF) -- the distribution of cell volumes (or inverse local number density) in the Voronoi tessellation of any set of cosmological tracers (galaxies/haloes). We show that the shape of the VVF of biased…
Navarro, Frenk, \& White have recently found numerically that the density profile of dark-matter halos can be described by a universal two-parameter function over a broad range of halo masses. The profile is singular, approaching the halo…
The Voronoi Entropy (VE) and the continuous measure of symmetry (CSM) characterize the orderliness of a set of points on a 2D plane. The Voronoi entropy is the Shannon entropy of the Voronoi tessellation of the plane into polygons,…
Weak lensing is one of the best available diagnostic tools to measure the total density profiles of distant clusters of galaxies. Unfortunately, it suffers from the well-known mass-sheet degeneracy, so that weak lensing analyses cannot lead…
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 Charting Cluster Construction with VUDS and ORELSE (C3VO) survey is an ongoing imaging and spectroscopic campaign aiming to map out the growth of structure up to $z\sim5$ and was born from the combination of the Visible Multi-Object…
Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…
We address the question of how well the density profile of galaxy clusters can be determined by combining strong lensing and velocity dispersion data. We use cosmological dark matter simulations of clusters to test the reliability of the…
Connecting the collective behavior of disordered systems with local structure on the particle scale is an important challenge, for example in granular and glassy systems. Compounding complexity, in many scientific and industrial…
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the…
We present an experimental study of the preferential concentration of sub-Kolmogorov inertial particles in active-grid-generated homogeneous and isotropic turbulence, characterized via Vorono\"i tessellations. We show that the detection and…
We investigate the application of volume statistics to probe the distribution of underdense regions in the large-scale structure of the Universe. This statistic measures the distortion of Eulerian volume elements relative to Lagrangian ones…
The Voronoi tessellation is the partition of space for a given seeds pattern and the result of the partition depends completely on the type of given pattern "random", Poisson-Voronoi tessellations (PVT), or "non-random", Non Poisson-Voronoi…