Related papers: Cluster algebras: Notes for the CDM-03 conference

We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task?…

In this contribution we review the algebraic cluster model (ACM) for $\alpha$-cluster nuclei with $A=4k$ nucleons and its extension to the cluster shell model (CSM) for $A=4k+x$ nuclei. Particular attention is paid to the question to what…

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 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…

In this note for the joint meeting of DMV and GDM we illustrate with examples the role of computer algebra in university mathematics education. We discuss its potential in teaching algebra, but also computer algebra as a subject in its own…

We introduce quasi-homomorphisms of cluster algebras, a flexible notion of a map between cluster algebras of the same type (but with different coefficients). The definition is given in terms of seed orbits, the smallest equivalence classes…

Let C be the category of finite-dimensional representations of a quantum affine algebra of simply-laced type. We introduce certain monoidal subcategories C_l (l integer) of C and we study their Grothendieck rings using cluster algebras.

This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.

We review some recent progress on applications of Cluster Expansions. We focus on a system of classical particles living in a continuous medium and interacting via a stable and tempered pair potential. We review the cluster expansion in…

The classification of Grassmannian cluster algebras resembles that of regular polygonal tilings. We conjecture that this resemblance may indicate a deeper connection between these seemingly unrelated structures.

Data clustering is an approach to seek for structure in sets of complex data, i.e., sets of "objects". The main objective is to identify groups of objects which are similar to each other, e.g., for classification. Here, an introduction to…

Some aspects of Computer Algebra (notably Computation Group Theory and Computational Number Theory) have some good databases of examples, typically of the form "all the X up to size n". But most of the others, especially on the polynomial…

Clusters of galaxies can be used for very different kinds of cosmological tests. I review a few of the methods: determination of cluster masses and dark matter content, metal enrichment and its connection to the origin of the intra-cluster…

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

These are the notes for some lectures given by this author at Harish-Chandra Research Institute, Allahabad in March 2014 for a workshop on Schur multipliers. The lectures aimed at giving an overview of the subject with emphasis on groups of…

We introduce admissible group actions on cluster algebras, cluster categories and quivers with potential and study the resulting orbit spaces. The orbit space of the cluster algebra has the structure of a generalized cluster algebra. This…

Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…

Time series, as one of the most fundamental representations of sequential data, has been extensively studied across diverse disciplines, including computer science, biology, geology, astronomy, and environmental sciences. The advent of…

The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have…

We propose a description of cluster states in nuclei in terms of representations of unitary algebras U(n+1), where n is the number of space degrees of freedom. Within this framework, a variety of situations including both vibrational and…