Related papers: Introduction to Cluster Algebras. Chapters 4-5

We define a class of associative algebras generalizing 'clannish algebras', as introduced by the second author, but also incorporating semilinear structure, like a skew polynomial ring. Clannish algebras generalize the well known 'string…

We take some initial steps to explore physical applications of the cluster superalgebras recently defined by Ovsienko and Shapiro. Our primary example is a fermionic extension of the $A_2$ cluster algebra, having fifteen cluster…

This book introduces the concept of neutrosophic bilinear algebras and their generalizations to n-linear algebras, n>2. This book has five chapters. The first chapter is introductory in nature and gives a few essential definitions and…

Cluster analysis plays an indispensable role in machine learning and data mining. Learning a good data representation is crucial for clustering algorithms. Recently, deep clustering, which can learn clustering-friendly representations using…

We consider triangulated orbit categories, with the motivating example of cluster categories, in their usual context of algebraic triangulated categories, then present them from another perspective in the framework of topological…

This contribution gives a short review of recent theoretical advances in most topics of nuclear cluster physics concentrating, however, around {$\alpha$} particle clustering. Along the route, the point of view will be critical mentioning…

The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type $A_n$, by counting the mutation class of any quiver with underlying graph $A_n$. It will also follow that if $T$ and…

We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…

Clustering is a fundamental learning task widely used as a first step in data analysis. For example, biologists use cluster assignments to analyze genome sequences, medical records, or images. Since downstream analysis is typically…

We recall several results in Auslander-Reiten theory for finite-dimensional algebras over fields and orders over complete local rings. Then we introduce $n$-cluster tilting subcategories and higher theory of almost split sequences and…

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…

In this paper, we will describe a network architecture that demonstrates high performance on various sizes of datasets. To do this, we will perform an architecture search by dividing the fully connected layer into three levels in the…

We give an overview of some recent developments in semigroup C*-algebras.

In this paper we present a complete classification (isomorphism classes with some isomorphism invariants) of complex associative algebras up to dimension five (including both cases: unitary and non-unitary). In some symbolic computations we…

Clustering is a well-known unsupervised machine learning approach capable of automatically grouping discrete sets of instances with similar characteristics. Constrained clustering is a semi-supervised extension to this process that can be…

This is a brief and informal introduction to cluster algebras. It roughly follows the historical path of their discovery, made jointly with A.Zelevinsky. Total positivity serves as the main motivation.

This paper tries to present a more unified view of clustering, by identifying the relationships between five different clustering algorithms. Some of the results are not new, but they are presented in a cleaner, simpler and more concise…

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…

Let $G=SL(2,5)$ be the special linear group of $2 \times 2$-matrices with coefficients in the field with $5$ elements. We show that the principal block over a splitting field $K$ of characteristic two of the group algebra $KG$ has a…

Matrix mutation appears in the definition of cluster algebras of Fomin and Zelevinsky. We give a representation theoretic interpretation of matrix mutation, using tilting theory in cluster categories of hereditary algebras. Using this, we…