Related papers: Utilizing Voronoi Tessellations to Determine Radia…
In the present work we focus on future experiments using cluster abundance observations to constraint the Dark Energy equation of state parameter, w. To obtain tight constraints from this kind of experiment, a reliable sample of galaxy…
We introduce a new class of spatial-temporal point processes based on Voronoi tessellations. At each step of such a process, a point is chosen at random according to a distribution determined by the associated Voronoi cells. The point is…
A longstanding open question in the field of dense disordered matter is how precisely structure and dynamics are related to each other. With the advent of machine learning, it has become possible to agnostically predict the dynamic…
We measure the Voronoi density probability distribution function (PDF) for both dark matter and halos in N-body simulations. For the dark matter, Voronoi densities represent the matter density field smoothed on a uniform mass scale, which…
We present the results of methodological works on automated analysis of the large scale distribution of galaxies. Selecting candidates for clusters and groups of galaxies was carried out using two complementary methods of determining the…
The purpose of this note is to clarify the effect of the finite size of spherical particles upon the characteristics of their spatial distribution through a random Poisson process (RPP). This information is of special interest when using…
Voronoi Tessellations form an attractive and versatile geometrical asymptotic model for the foamlike cosmic distribution of matter and galaxies. In the Voronoi model the vertices are identified with clusters of galaxies. For a substantial…
We introduce a framework for the generation of grid-shell structures that is based on Voronoi diagrams and allows us to design tessellations that achieve excellent static performances. We start from an analysis of stress on the input…
In this paper we present a novel method to identify and characterize stellar clusters deeply embedded in a dark molecular cloud. The method is based on measuring stellar surface density in wide-field infrared images using star counting…
Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…
Several systems involve spatial arrangements of elements such as molecules or cells, the characterization of which bears important implications to biological and physical investigations. Traditional approaches to quantify spatial order and…
We present new techniques to perform adaptive spatial binning of two-dimensional (2D) data to reach a chosen constant signal-to-noise ratio per bin. These methods are required particularly for the proper analysis of Integral Field…
Optimally resolved one-dimensional density and velocity profiles through cosmological N-body simulations are constructed by means of the Voronoi-Delaunay tessellation reconstruction technique. In a fully self-adaptive fashion a strikingly…
We propose a new smoothing method for obtaining surface densities from discrete particle positions from numerical simulations. This is an essential step for many applications in gravitational lensing. This method is based on the ``scatter''…
We have developed a geometrical method based on 3D Voronoi polyhedra and Delaunay tessellation for identifying and reconstructing clusters of galaxies in the next generation of deep, flux-limited redshift surveys. We here describe this…
Purpose: The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role when the raw data and image data are related through the Fourier…
We present a flexible, annulus-by-annulus method to constrain the 2-D thermal structure of a protoplanetary disk from optically thick spectral line emission. Using synthetic disk models with a known temperature and density structure, we…
We have searched for extended X-ray sources in the ROSAT PSPC archive using the Voronoi Tesslation and Percolation algorithm (VTP). This algorithm detects all significant sources regardless of shape or size, and is particularly suited to…
We introduce an algorithm to estimate the redshift distribution of a sample of galaxies selected photometrically given a subsample with measured spectroscopic redshifts. The approach uses a non-parametric Voronoi tessellation density…
Voronoi intensity estimators, which are non-parametric estimators for intensity functions of point processes, are both parameter-free and adaptive; the intensity estimate at a given location is given by the reciprocal size of the…