Related papers: Voronoi chords in flat cosmology
Topological analysis of galaxy distributions has gathered increasing attention in cosmology, as they are able to capture non-Gaussian features of large-scale structures (LSS) that are overlooked by conventional two-point clustering…
A Voronoi diagram is a basic geometric structure that partitions the space into regions associated with a given set of sites, such that all points in a region are closer to the corresponding site than to all other sites. While being…
Modelling cosmic voids as spheres in Euclidean space, the notion of a de-Sitter configuration space is introduced. It is shown that a uniform distribution over this configuration space yields a power-law approximating the void size…
These lecture notes introduce analytical tools, methods and results describing the growth of cosmological structure beyond the linear regime. The presentation is focused on the single flow regime of the Vlasov-Poisson equation describing…
The survey volume of a proper motion-limited sample is typically much smaller than a magnitude-limited sample. This is because of the noisy astrometric measurements from detectors that are not dedicated for astrometric missions. In order to…
The pair correlation function (PCF) has proven an effective tool for analyzing many physical systems due to its simplicity and its applicability to simulated and experimental data. However, as an averaged quantity, the PCF can fail to…
Consider the distances $\tilde{R}_o$ and $R_o$ from the nucleus to a uniformly random point in the 0-cell and the typical cell, respectively, of the $d$-dimensional Poisson-Voronoi (PV) tessellation. The main objective of this paper is to…
Several aspects of the internal structure of pseudoscalar mesons, accessible through generalized parton distributions in their zero-skewness limit, are examined. These include electromagnetic and gravitational form factors related to charge…
One of the most powerful techniques to study the dark sector of the Universe is weak gravitational lensing. In practice, to infer the reduced shear, weak lensing measures galaxy shapes, which are the consequence of both the intrinsic…
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small…
I present a regression algorithm that provides a continuous, piecewise-smooth function approximating scattered data. It is based on composing and blending linear functions over Voronoi cells, and it scales to high dimensions. The algorithm…
In this paper we discuss how to define a chord index via smoothing a real crossing point of a virtual knot diagram. Several polynomial invariants of virtual knots and links can be recovered from this general construction. We also explain…
In this work, a cut high-dimensional model representation (cut-HDMR) expansion based on multiple anchors is constructed via the clustering method. Specifically, a set of random input realizations is drawn from the parameter space and…
The general method for calculation of valence quark distributions in hadrons at intermediate $x$ is presented. The imaginary part of virtual photon forward scattering amplitude on quark current with hadron quantum number is considered in…
Quantized vortices in a complex wave field described by a defocusing nonlinear Schr\"odinger equation with a space-varying dispersion coefficient are studied theoretically and compared to vortices in the Gross-Pitaevskii model with external…
Voids are a prominent feature of fractal point distributions but there is no precise definition of what is a void (except in one dimension). Here we propose a definition of voids that uses methods of discrete stochastic geometry, in…
The concepts of Generalized Parton Distributions (GPD) are reviewed in an introductory and phenomenological fashion. These distributions provide a rich and unifying picture of the nucleon structure. Their physical meaning is discussed. The…
The spin-independent part of the virtual Compton scattering (VCS) amplitude from the nucleon is calculated within the framework of heavy baryon chiral perturbation theory (HBChPT). The calculation is performed to third order in external…
Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to…
In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological…