Related papers: Robust Morphological Measures for Large-Scale Stru…
In the language of random counting measures many structural properties of the Poisson process can be studied in arbitrary measurable spaces. We provide a similarly general treatise of Gibbs processes. With the GNZ equations as a definition…
We introduce a new methodology to robustly determine the mass profile, as well as the overall distribution, of Local Group satellite galaxies. Specifically we employ a statistical multilevel modelling technique, Bayesian hierarchical…
The Minkowski functionals are useful statistics to quantify the morphology of various random fields. They have been applied to numerous analyses of geometrical patterns, including various types of cosmic fields, morphological image…
We present a new method for embedding a causal set into Minkowski spacetime. The method is similar to a previously presented method, but is simpler and provides better embedding results. The method uses spacetime volumes to define causal…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
Measuring the morphological parameters of galaxies is a key requirement for studying their formation and evolution. Surveys such as the Sloan Digital Sky Survey (SDSS) have resulted in the availability of very large collections of images,…
With the booming development of data science, many clustering methods have been proposed. All clustering methods have inherent merits and deficiencies. Therefore, they are only capable of clustering some specific types of data robustly. In…
Modeling the mass distribution of galaxy-scale strong gravitational lenses is a task of increasing difficulty. The high-resolution and depth of imaging data now available render simple analytical forms ineffective at capturing lens…
A Poisson system is a Poisson point process and a group action, together forming a measure-preserving dynamical system. Ornstein and Weiss proved Poisson systems over many amenable groups were isomorphic in their 1987 paper. We consider…
We describe application of the `shapelet' linear decomposition of galaxy images to morphological classification using images of $\sim$ 3000 galaxies from the Sloan Digital Sky Survey. After decomposing the galaxies we perform a principal…
The universe is composed of galaxies that have diverse shapes. Once the structure of a galaxy is determined, it is possible to obtain important information about its formation and evolution. Morphologically classifying galaxies means…
In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two…
A new approach to the study of the large-scale stellar cluster distribution in the Galaxy based on two-point correlation techniques is presented. The basic formalism for this method is outlined and its applications are then investigated by…
We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods,…
We focus on the analysis of planar shapes and solid objects having thin features and propose a new mathematical model to characterize them. Based on our model, that we call an epsilon-shape, we show how thin parts can be effectively and…
The mass measurement of galaxy clusters is an important tool for the determination of cosmological parameters describing the matter and energy content of the Universe. However, the standard methods rely on various assumptions about the…
We present a novel approach to measuring the expansion rate and the geometry of the Universe, which combine time-delay cosmography in lens galaxy clusters with pure samples of 'cosmic chronometers' (CCs) by probing the member galaxies. The…
We study nonequilibrium dynamics of SU(2) lattice gauge theory in Minkowski space-time in a classical-statistical regime, where characteristic gluon occupancies are much larger than unity. In this strongly correlated system far from…
We propose a real-space formalism of the topological Euler class, which characterizes the fragile topology of two-dimensional systems with real wave functions. This real-space description is characterized by local Euler markers whose…
The Minkowski problem in convex geometry concerns showing that a given Borel measure on the unit sphere is, up to perhaps a constant, some type of surface area measure of a convex body. Two types of Minkowski problems in particular are an…