Related papers: Cluster Theories and Cluster Structures of Type A
Two distinct structures of aggregates of atoms connected by anisotropic bonds with a network configuration are discussed from the viewpoint of a point set topology. A specific topological space connects the two types of topological…
Category Theory provides us with a clear notion of what is an internal structure. This will allow us to focus our attention on a certain type of relationship between context and structure.
We present here two detailed examples of additive categorifications of the cluster algebra structure of a coordinate ring of a maximal unipotent subgroup of a simple Lie group. The first one is of simply-laced type ($A_3$) and relies on an…
The proposal is to use clusters, graphs and networks as models in order to analyse the Web structure. Clusters, graphs and networks provide knowledge representation and organization. Clusters were generated by co-site analysis. The sample…
This is a survey paper of the theory of crystal bases, global bases and the cluster algebra structure on the quantum coordinate rings.
In this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of type $\widetilde{A}$. We are particularly interested…
Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. To a cluster algebra of simply laced Dynkin type one can associate the cluster category. Any cluster of the cluster algebra corresponds…
We introduce some new Frobenius subcategories of the module category of a preprojective algebra of Dynkin type, and we show that they have a cluster structure in the sense of Buan-Iyama-Reiten-Scott. These categorical cluster structures…
The cluster soft point is an attempt to introduce a novel generalization of the soft closure point and the soft limit point. A cluster soft set is defined to be the system of all cluster soft points of a soft set. Then the fundamental…
In the present paper we discuss the clustering procedure in the case where instead of a single metric we have a family of metrics. In this case we can obtain a partially ordered graph of clusters which is not necessarily a tree. We discuss…
The paper is motivated by an analogy between cluster algebras and Kac-Moody algebras: both theories share the same classification of finite type objects by familiar Cartan-Killing types. However the underlying combinatorics beyond the two…
The aggregated journal-journal citation matrix derived from the Journal Citation Reports 2001 can be decomposed into a unique subject classification by using the graph-analytical algorithm of bi-connected components. This technique was…
In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
We clarify the natural cluster algebra of type A that exists in a residual and tropical form in the kinematical space as suggested in 1711.09102 by the use of triangulations, mutations and associahedron on the definition of scattering…
In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…
We classify mutation-finite cluster algebras with arbitrary coefficients of geometric type.
We introduce the notion of a lower bound cluster algebra generated by projective cluster variables as a polynomial ring over the initial cluster variables and the so-called projective cluster variables. We show that under an acyclicity…
We investigate the internal structure of clusters of galaxies in high-resolution N-body simulations of 4 different cosmologies. There is a higher proportion of disordered clusters in critical-density than in low-density universes, although…
We use two high resolution CDM simulations to show that (i) when clusters of galaxies form the infall pattern of matter is not random but shows clear features which are correlated in time; (ii) in addition, the infall patterns are…