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We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on…
Luminous elliptical galaxies generally display a rich star cluster system, whose properties provide strong constraints on the physics of galaxy formation and evolution. Star cluster system studies, however, concentrate on galaxies located…
An objective classification of 147 globular clusters in the inner region of the giant elliptical galaxy M87 is carried out with the help of two methods of multivariate analysis. First independent component analysis is used to determine a…
Cluster analysis is the distribution of objects into different groups or more precisely the partitioning of a data set into subsets (clusters) so that the data in subsets share some common trait according to some distance measure. Unlike…
Previous studies of the galaxy and galaxy cluster distribution in the local Universe found indications for a large extension of the Local Supercluster up to a radius of 190 h_70^-1 Mpc. We are using our large and highly complete CLASSIX…
Extensive surveys of galaxy clusters motivate us to assess the likelihood of cluster-cluster lensing (CCL), namely, gravitational-lensing of a background cluster by a foreground cluster. We briefly describe the characteristics of CCLs in…
We investigate the large-scale distribution of galaxy clusters taken from several X-ray catalogs. Different statistics of clustering like the conditional correlation function (CCF) and the minimal spanning tree (MST) as well as void…
Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of…
Stars are usually formed in clusters in the dense cores of molecular clouds. These embedded clusters show a wide variety of morphologies from hierarchical clusters with substructure to centrally condensed ones. Often they are elongated and…
We discuss an algebraic treatment of four-body clusters which includes both continuous and discrete symmetries. In particular, tetrahedral configurations with T(d) symmetry are analyzed with respect to the energy spectrum, transition form…
We propose an algorithm for clustering high dimensional data. If $P$ features for $N$ objects are represented in an $N\times P$ matrix ${\bf X}$, where $N\ll P$, the method is based on exploiting the cluster-dependent structure of the…
The channel size distribution in hard sphere systems, based on the local neighbor correlation of four particle positions, is investigated for all volume fractions up to jamming. For each particle, all three particle combinations of…
Clusters of galaxies have a huge mass which can act as gravitational lenses. Galaxies behind clusters can be distorted to form arcs in images by the lenses. Herein a search was done for giant lensed arcs by galaxy clusters using the SDSS…
Due to the recent evolution of sequencing techniques, the number of available genomes is rising steadily, leading to the possibility to make large scale genomic comparison between sets of close species. An interesting question to answer is:…
Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of…
Cluster structure of 16O,18O and 20O is investigated by the antisymmettrized molecular dynamics (AMD) plus generator coordinate method (GCM). We have found the K^{\pi}=0$_2^+$ and 0$_1^-$ rotational bands of 18O that have the prominent…
We introduce a new self-consistent structure finding algorithm that parses large scale cosmological structure into clusters, filaments and voids. This structure finding algorithm probes the cosmological structure at multiple scales and…
By virtue of their high galaxy space densities and their large spatial separations, clusters are efficient and accurate tracers of the large-scale density and velocity fields. Substantial progress has been made over the past decade in the…
Strong lensing galaxy clusters provide a unique and powerful way to test simulation-derived structure predictions that follow from $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmology. Specifically, the relative alignments of the dark matter…
Recent analysis of the distribution of clusters of galaxies is reviewed. Clusters of galaxies located in rich superclusters form a quasiregular lattice similar in structure to honeycombs. The power spectrum of clusters of galaxies has a…