Related papers: Characterizing cluster morphology using vector-val…
Minkowski functionals (MFs) quantify the topological properties of a given field probing its departure from Gaussianity. We investigate their use on lensing convergence maps in order to see whether they can provide further insights on the…
We investigate the properties of globular clusters in a galaxy cluster, using the particle tagging method with a semi-analytical approach in a cosmological context. We assume globular clusters form from dark matter halo mergers and their…
This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…
Several methods are used to evaluate, from observational data, the dynamical state of galaxy clusters. Among them, the morphological analysis of cluster images is well suited for this purpose. We report a new approach to the morphology,…
Surveys of galaxy clusters provide a promising method of testing models of structure formation in the universe. Within the context of our standard structure formation scenario, surveys provide measurements of the geometry of the universe…
This is a concise introduction to Fomin-Zelevinsky's cluster algebras and their links with the representation theory of quivers in the acyclic case. We review the definition of cluster algebras (geometric, without coefficients), construct…
Minkowski functionals have recently been introduced into cosmology as novel tools for studying the large-scale distribution of matter in the Universe. We present a brief overview of the method, including its mathematical foundations as well…
The links between the internal structure of galaxy groups and clusters and cosmological parameters are reviewed here. The mass density profiles of clusters, inferred from both optical analyses of the galaxy surface number density profile…
X-ray observations of galaxy clusters reveal a large range of morphologies with various degrees of disturbance, showing that the assumptions of hydrostatic equilibrium and spherical shape which are used to determine the cluster mass from…
Minkowski valuations provide a systematic framework for quantifying different aspects of morphology. In this paper we apply vector- and tensor-valued Minkowski valuations to neuronal cells from the cat's retina in order to describe their…
We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster mutation at a tropical level and show that cluster algebras,…
In a follow-up study to a previous analysis of the IRAS 1.2Jy catalogue, we quantify the morphological fluctuations in the PSCz survey. We use a variety of measures, among them the family of scalar Minkowski functionals. We confirm the…
Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical…
We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of three-dimensional vectors, covectors, and matrices. The construction uses Kuperberg's calculus of webs on marked…
A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged…
We study the properties of superclusters detected in the Abell/ACO cluster catalogue. We identify the superclusters utilizing the `friend-of-friend' procedure, and then determine supercluster shapes by using the differential geometry…
Many observable properties of globular clusters (GCs) provide valuable insights for unveiling the hierarchical assembly of their host galaxy. For the Milky Way (MW) in particular, GCs from different accreted satellite galaxies show distinct…
We give a new proof of the generalized Minkowski identities relating the higher degree mean curvatures of orientable closed hypersurfaces immersed in a given constant sectional curvature manifold. Our methods rely on a fundamental…
The traditional method of morphological classification, by visual inspection of images of uniform quality and by reference to standards for each type, is critically examined. The rate of agreement among traditional morphologists on the…
We compute the Form Factors of the relevant scaling operators in a class of integrable models without internal symmetries by exploiting their cluster properties. Their identification is established by computing the corresponding anomalous…