Related papers: Cluster type varieties
We report results of the observations of 15 regions in several molecular lines for a statistical study of massive cluster-forming clumps. We identified 24 clumps based on the C18O (J=1-0) data obtained by the NRO 45 m telescope, and found…
Clustering analysis identifies samples as groups based on either their mutual closeness or homogeneity. In order to detect clusters in arbitrary shapes, a novel and generic solution based on boundary erosion is proposed. The clusters are…
We calculate the mixed Hodge numbers of smooth 3-dimensional cluster varieties and show that they are of mixed Tate type. We also study the mixed Hodge structures of the cohomology and intersection cohomology groups of some singular cluster…
The deep locus of a cluster variety is defined to be the set of its points that do not belong to any cluster torus. We show that, if the cluster variety has a seed whose mutable part is a tree without multiple edges, then the deep locus can…
We propose a description of cluster states in nuclei in terms of representations of unitary algebras U(n+1), where n is the number of space degrees of freedom. Within this framework, a variety of situations including both vibrational and…
We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task?…
Classification of cluster variables in cluster algebras (in particular, Grassmannian cluster algebras) is an important problem, which has direct application to computations of scattering amplitudes in physics. In this paper, we apply the…
In this paper, we will place clusters in type $\tilde{\mathbb{A}}$ (equivalently triangluations of an annulus) into infinite families parametrized by winding numbers of certain arcs in the corresponding triangulation. We will count how many…
Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the process of grouping similar…
The analysis of the presence of substructures in 16 well-sampled clusters of galaxies suggests a stimulating hypothesis: Clusters could be classified as unimodal or bimodal, on the basis of to the sub-clump distribution in the {\em 3-D}…
Cluster integrable systems are a broad class of integrable systems modelled on bipartite dimer models on the torus. Many discrete integrable dynamics arise by applying sequences of local transformations, which form the cluster modular group…
Cluster analysis methods seek to partition a data set into homogeneous subgroups. It is useful in a wide variety of applications, including document processing and modern genetics. Conventional clustering methods are unsupervised, meaning…
We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a…
Globular clusters are large and dense agglomerate of stars. At variance with smaller clusters of stars, they exhibit signs of some chemical evolution. At least for this reason, they are intermediate between open clusters and massive objects…
We provide a systematic derivation of cluster alphabets of finite types. The construction is based on a geometric realization of the generalized worldsheets by gluing and folding a pair of polygons. The cross ratios of the worldsheet z…
A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…
The classification of Grassmannian cluster algebras resembles that of regular polygonal tilings. We conjecture that this resemblance may indicate a deeper connection between these seemingly unrelated structures.
We present a novel approach for finding and evaluating structural models of small metallic nanoparticles. Rather than fitting a single model with many degrees of freedom, the approach algorithmically builds libraries of nanoparticle…
We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.
Using cluster tilting theory, we investigate tilting objects in the stable category of vector bundles on a weighted projective line of weight type $(2, 2, 2, 2)$. More precisely, a tilting object consisting of rank-two bundles is…