Related papers: An introduction to higher cluster categories
In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: 1. Some…
In recent years, much of the research on clustering algorithms has primarily focused on enhancing their accuracy and efficiency, frequently at the expense of interpretability. However, as these methods are increasingly being applied in…
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…
Cluster categories have been introduced by Buan, Marsh, Reineke, Reiten and Todorov in order to categorify Fomin-Zelevinsky cluster algebras. This survey motivates and outlines the construction of a generalization of cluster categories, and…
There are many clustering methods, such as hierarchical clustering method. Most of the approaches to the clustering of variables encountered in the literature are of hierarchical type. The great majority of hierarchical approaches to the…
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…
A key issue in cluster analysis is the choice of an appropriate clustering method and the determination of the best number of clusters. Different clusterings are optimal on the same data set according to different criteria, and the choice…
Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different…
We present a technique for clustering categorical data by generating many dissimilarity matrices and averaging over them. We begin by demonstrating our technique on low dimensional categorical data and comparing it to several other…
We consider a subclass of the class of group-theoretical fusion categories: To every finite group $G$ and subgroup $H$ one can associate the category of $G$-graded vector spaces with a two-sided $H$-action compatible with the grading. We…
In this note, we consider the $d$-cluster-tilted algebras, the endomorphism algebras of $d$-cluster-tilting objects in $d$-cluster categories. We show that a tilting module over such an algebra lifts to a $d$-cluster-tilting object in this…
A few, simple and qualitative examples of the potential of galaxy clusters as diagnostics of cosmology are presented. In relation to these we discuss briefly three ongoing or forthcoming cluster surveys in the optical/NIR, X-rays and the…
We construct an iterative method for factorising small strict n-categories into a unique (up to isomorphism) collection of small 1- categories. Following this we develop the theory to include a large class of $\infty$-categories. We use…
Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian. Based on this insight, we propose a…
There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the…
In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.
In this note we give a generalization for the higher order Hochschild cohomology and show that the secondary Hochschild cohomology is a particular case of this new construction.
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
Clusters of galaxies are large gravitationally bound systems which consist of several observable components: hundreds of galaxies, hot gas between the galaxies and sometimes relativistic particles. These components are emitting in different…