Related papers: An introduction to higher cluster categories
We give a more coherent definition of upward planar order.
The two most extended density-based approaches to clustering are surely mixture model clustering and modal clustering. In the mixture model approach, the density is represented as a mixture and clusters are associated to the different…
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…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
This paper develops techniques for producing presentations of upper cluster algebras. These techniques are suited to computer implementation, and will always succeed when the upper cluster algebra is totally coprime and finitely generated.…
In cluster analysis, it can be useful to interpret the partition built from the data in the light of external categorical variables which were not directly involved to cluster the data. An approach is proposed in the model-based clustering…
This survey article is intended as an introduction to the recent categorical classification theorems of the three authors, restricting to the special case of the category of modules for a finite group.
In this paper we give a graph theoretic combinatorial interpretation for the cluster variables that arise in most cluster algebras of finite type. In particular, we provide a family of graphs such that a weighted enumeration of their…
We continue the work started in parts (I) and (II). In this part we classify which continuous type A quivers are derived equivalent and introduce the new continuous cluster category with E-clusters, which are a generalization of clusters.…
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…
In this talk we summarize some recent developments in perturbative QCD and their application to particle physics phenomenology.
In this paper we introduce the notion of a relative volutive (higher) category, specializing to the notion of a lax volutive (higher) category. Our primary motivation to study these objects is the following: while any rigid symmetric…
We present an optical and near-infrared survey of galaxies in nearby clusters aimed at determining fundamental quantities of galaxies, such as multivariate luminosity function and color distribution for each Hubble type. The main…
This chapter combines an introduction and research survey about Schubert varieties. The theme is to combinatorially classify their singularities using a family of polynomial ideals generated by determinants.
In \cite{JKS} we gave an (additive) categorification of Grassmannian cluster algebras, using the category $\CM(A)$ of Cohen-Macaulay modules for a certain Gorenstein order $A$. In this paper, using a cluster tilting object in the same…
This survey note describes a brief systemic view to approaches for evaluation of hierarchical composite (modular) systems. The list of considered issues involves the following: (i) basic assessment scales (quantitative scale, ordinal scale,…
The paper focuses on a new class of combinatorial problems which consists in restructuring of solutions (as sets/structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
We classify the module categories over the double (possibly twisted) of a finite group.
We show that on an arbitrary collection of objects there is a wide variety of higher order architectures governed by hyperstructures. Higher order gluing, local to global processes, fusion of collections, bridges and higher order types are…