Related papers: Voronoi chords in flat cosmology
3D Voronoi's tessellation method was first applied to identify groups of galaxies in the structure of a supercluster. The sample under consideration consists of more than 7000 galaxies of the Local Supercluster (LS) with radial velocities…
Swarm robotics, or very large-scale robotics (VLSR), has many meaningful applications for complicated tasks. However, the complexity of motion control and energy costs stack up quickly as the number of robots increases. In addressing this…
Recent work on distinct multicellular organisms has revealed a hitherto unknown type of biological noise; rather than a regular arrangement, cellular neighborhood volumes, obtained by Voronoi tessellations of the cell locations, are broadly…
In view of the result of Kontsevich, now often called ``the fundamental theorem of Vassiliev theory'', identifying the graded dual of the associated graded vector space to the space of Vassiliev invariants filtered by degree with the linear…
We compare the reduced void probability function (VPF) inside and outside of cosmic voids in the TNG300-1 simulation, both in real and simulated redshift space. The VPF is a special case of the counts-in-cells approach for extracting…
Voids are the most prominent feature of the LSS of the universe. Still, they have been generally ignored in quantitative analysis of it, essentially due to the lack of an objective tool to identify and quantify the voids. To overcome this,…
In this paper, we consider a Riemannian manifold $M$ and the Poisson-Voronoi tessellation generated by the union of a fixed point $x_0$ and a Poisson point process of intensity $\lambda$ on $M$. We obtain asymptotic expansions up to the…
Voronoi tessellations are used to partition the Euclidean space into polyhedral regions, which are called Voronoi cells. Labeling the Voronoi cells with the class information, we can map any classification problem into a Voronoi…
As a hypothetical topological defect in the geometry of spacetime, vortex strings play a crucial role in shaping the clusters of galaxies that exist today, and their distinct features can provide observable clues about the early universe's…
Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…
The 3D network originated by the faces of irregular Poissonian Voronoi Polyhedrons may represent the backbone on which the galaxies are originated. As a consequence the spatial appearance of the catalogs of galaxies can be reproduced. The…
We present here a new method using interferometric measurements of quasars, that allows the determination of direct geometrical distances on cosmic scales. Quasar Broad Emission Line Regions sizes provide a "meter rule" with which to…
We discover new Voronoi formulae for automorphic forms on GL($n$) for $n\geq 4$. There are $[n/2]$ different Voronoi formulae on GL($n$), which are Poisson summation formulae weighted by Fourier coefficients of the automorphic form with…
We present a class of general prolate and oblate spheroidal spacetimes for the description of cosmic structures in the Universe. They are exact geometries which represent, in an appropriated way, the imbedding of spheroidal matter-energy…
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…
In this paper, we construct a new family of random series defined on $\R^D$, indexed by one scaling parameter and two Hurst-like exponents. The model is close to Takagi-Knopp functions, save for the fact that the underlying partitions of…
We present the preliminary result of our project, consisting in studying the properties of a large sample of galaxy clusters. The M\"{u}nster Red Sky Survey, which is a large galaxy catalogue covering an area of about 5000 square degrees on…
We investigate the evolution of cosmic voids in the Schrodinger Poisson formalism, finding wave mechanical solutions for the dynamics in a standard cosmological background with appropriate boundary conditions. We compare the results in this…
We calculate the void probability function (VPF) in simulations of Lyman-$\alpha$ emitters (LAEs) across a wide redshift range ($z=3.1,\ 4.5,\ 5.7,\ 6.6$). The VPF measures the zero-point correlation function (i.e. places devoid of…
We study the statistics of the Voronoi cell perimeter in large bi-pointed planar quadrangulations. Such maps have two marked vertices at a fixed given distance $2s$ and their Voronoi cell perimeter is simply the length of the frontier which…