Related papers: An introduction to higher cluster categories
This is Addendum to ``Structure of seeds in generalized cluster algebras'', Pacific J. Math. {277} (2015), 201--218. We extend the class of generalized cluster algebras studied therein to embrace examples in some applications.
We introduce the study of parametrized higher category theory and parametrized higher algebra, and we describe the main theorems of the series of Expos\'es that make up the monograph.
We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions.
Let C be a fusion category which is an extension of a fusion category D by a finite group G. We classify module categories over C in terms of module categories over D and the extension data (c,M,a) of C. We also describe functor categories…
The domain of cluster analysis is a meeting point for a very rich multidisciplinary encounter, with cluster-analytic methods being studied and developed in discrete mathematics, numerical analysis, statistics, data analysis, data science,…
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
The mixture models have become widely used in clustering, given its probabilistic framework in which its based, however, for modern databases that are characterized by their large size, these models behave disappointingly in setting out the…
Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii)…
This paper continues the study of cluster algebras initiated in math.RT/0104151. Its main result is the complete classification of the cluster algebras of finite type, i.e., those with finitely many clusters. This classification turns out…
We introduce some classes of genuine higher categories in homotopy type theory, defined as well-behaved subcategories of the category of types. We give several examples, and some techniques for showing other things are not examples. While…
In this article, we study higher Nil $K$-groups via binary complexes. More particularly, we exhibit an explicit form of generators of higher Nil $K$-groups in terms of binary complexes.
Some key issues in robust clustering are discussed with focus on Gaussian mixture model based clustering, namely the formal definition of outliers, ambiguity between groups of outliers and clusters, the interaction between robust clustering…
This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…
Cluster analysis methods are used to identify homogeneous subgroups in a data set. In biomedical applications, one frequently applies cluster analysis in order to identify biologically interesting subgroups. In particular, one may wish to…
This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…
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…
A short exposition with complete proofs of the theory of cluster expansions for an abstract polymer system is presented.
This is a survey of old and new problems and results in additive number theory.
Recommender systems are one of the most applied methods in machine learning and find applications in many areas, ranging from economics to the Internet of things. This article provides a general overview of modern approaches to recommender…