Related papers: Quantifying galactic clustering and departures fro…
Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of…
The cloud-scale density, velocity dispersion, and gravitational boundedness of the interstellar medium (ISM) vary within and among galaxies. In turbulent models, these properties play key roles in the ability of gas to form stars. New high…
We study statistical properties of galaxy structures in several samples extracted from the 2dF Galaxy Redshift Survey. In particular, we measured conditional fluctuations by means of the scale-length method and determined their probability…
We follow the evolution of the galaxy population in a Lambda-CDM cosmology by means of high-resolution N-body simulations in which the formation of galaxies and their observable properties are calculated using a semi-analytic model. We…
We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…
This paper presents new geometric aspects of the behaviors of solutions to the porous medium equation (PME) and its associated equation. First we discuss the Legendre structure with information geometry on the manifold of generalized…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for…
The galaxy pairwise velocity dispersion (PVD) can provide important tests of non-standard gravity and galaxy formation models. We describe measurements of the PVD of galaxies in the Galaxy and Mass Assembly (GAMA) survey as a function of…
Studies of the distribution and evolution of galaxies are of fundamental importance to modern cosmology; these studies, however, are hampered by the complexity of the competing effects of spectral and density evolution. Constructing a…
Using cosmological $N$-body simulations and the void probability function (VPF), we investigate the statistical properties of voids within a wide range of initially Gaussian models for the origin of large-scale structure. We pay particular…
Galaxy clusters are connected at their peripheries to the large scale structures by cosmic filaments that funnel accreting material. These filamentary structures are studied to investigate both environment-driven galaxy evolution and…
Recent developments in extreme value statistics have established the so-called geometric approach as a powerful modelling tool for multivariate extremes. We tailor these methods to the case of spatial modelling and examine their efficacy at…
We present a novel non-parametric method for inferring smooth models of the mean velocity field and velocity dispersion tensor of the Milky Way from astrometric data. Our approach is based on Stochastic Variational Gaussian Process…
We investigate the extremal process of four-dimensional membrane models as the size of the lattice $N$ tends to infinity. We prove the cluster-like geometry of the extreme points and the existence as well as the uniqueness of the extremal…
We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…
Current observational evidence suggests that all large galaxies contain globular clusters (GCs), while the smallest galaxies do not. Over what galaxy mass range does the transition from GCs to no GCs occur? We investigate this question…
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes.…
We have developed a method based on wavelets to obtain the true underlying smooth density from a point distribution. The goal has been to reconstruct the density field in an optimal way ensuring that the morphology of the reconstructed…
The gravitational evolution of the cosmic one-point probability distribution function (PDF) has been estimated using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion around a Gaussian…