Related papers: Characterizing cluster morphology using vector-val…
Observations reveal that on large scales the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions -- voids. This thesis reports the construction of a sophisticated computational…
Dynamically relaxed galaxy clusters have long played a role in galaxy cluster studies because it is thought their properties can be reconstructed more precisely and with less systematics. As relaxed clusters are desirable, there exist a…
Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented…
Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…
Correlations among the independently measured physical properties of globular clusters (GCs) can provide powerful tests for theoretical models and new insights into their dynamics, formation, and evolution. We review briefly some of the…
X-ray observations have played a key role in the study of substructure and merging in galaxy clusters. I review the evidence for cluster substructure and mergers obtained from X-ray observations with satellites that operated before Chandra…
Many statistical methods have been proposed in the last years for analyzing the spatial distribution of galaxies. Very few of them, however, can handle properly the border effects of complex observational sample volumes. In this paper, we…
We review several aspects of clusters of galaxies and their application to cosmology. We present first results of numerical simulations of the dynamics of the intra-cluster gas and of different interaction processes between cluster galaxies…
Various cosmological applications of galaxy clusters are presented. Clusters are used to determine the baryon fraction, dark matter distribution and the matter density of the universe. They also contain a wealth of information about…
In recent years multi-wavelength observations have shown the presence of substructures related to merging events in a high fraction of galaxy clusters. Clusters can be roughly grouped into two categories -- relaxed and non-relaxed -- and a…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
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…
Galaxy morphologies play an essential role in the study of the evolution of galaxies. The determination of morphologies is laborious for a large amount of data giving rise to machine learning-based approaches. Unfortunately, most of these…
We measure the geometry, topology and morphology of the superclusters in mock SDSS catalogues prepared by Cole et al.(1998). The mock catalogues refer to $\tau$CDM and $\L$CDM {\em flat} cosmological models and are populated by galaxies so…
This work explores the morphology and dynamical properties of cores within rich superclusters, highlighting their role as transitional structures in the large-scale structure of the Universe. Using projected and radial velocity…
We present a morphological study of the two richest superclusters from the 2dF Galaxy Redshift Survey (SCL126, the Sloan Great Wall, and SCL9, the Sculptor supercluster). We use Minkowski functionals, shapefinders, and galaxy group…
This is a survey of results on positivity of vector bundles, inspired by the Brunn-Minkowski and Pr\'ekopa theorems. Applications to complex analysis, K\"ahler geometry and algebraic geometry are also discussed.
The study of shapes of the images of objects is an important issue not only because it reveals its dynamical state but also it helps to understand the object's evolutionary history. We discuss a new technique in cosmological image analysis…
The K-means algorithm is among the most commonly used data clustering methods. However, the regular K-means can only be applied in the input space and it is applicable when clusters are linearly separable. The kernel K-means, which extends…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…