Related papers: Cluster algebras associated with open Richardson v…
We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians ${\rm Gr}(k,n)$. A finite cluster algebra provides a natural triangulation for the…
Categories of partitions are combinatorial structures arising from the representation theory of certain compact quantum groups and are linked to classical diagram algebras such as the Temperley-Lieb algebra. In this paper, we present…
We express cluster variables of type $B_n$ and $C_n$ in terms of cluster variables of type $A_n$. Then we associate a cluster tilted bound symmetric quiver $Q$ of type $A_{2n-1}$ to any seed of a cluster algebra of type $B_n$ and $C_n$.…
We introduce a cluster evaluation technique called Tree Index. Our Tree Index algorithm aims at describing the structural information of the clustering rather than the quantitative format of cluster-quality indexes (where the representation…
This paper proposes a simple, automatic and efficient clustering algorithm, namely, Automatic Merging for Optimal Clusters (AMOC) which aims to generate nearly optimal clusters for the given datasets automatically. The AMOC is an extension…
Let $F(z)$ be an arbitrary complex polynomial. We introduce the local root clustering problem, to compute a set of natural $\varepsilon$-clusters of roots of $F(z)$ in some box region $B_0$ in the complex plane. This may be viewed as an…
We give algorithms for the computation of the algebraic de Rham cohomology of open and closed algebraic sets inside projective space or other smooth complex toric varieties. The methods, which are based on Gr\"obner basis computations in…
Time series data, spanning applications ranging from climatology to finance to healthcare, presents significant challenges in data mining due to its size and complexity. One open issue lies in time series clustering, which is crucial for…
We classify mutation-finite cluster algebras with arbitrary coefficients of geometric type.
In this paper, we address the problem of classifying clutter returns in order to partition them into statistically homogeneous subsets. The classification procedure relies on a model for the observables including latent variables that is…
Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and explain how discrete integrable systems can appear in the…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
Numerous methods for finding clusters at moderate to high redshifts have been proposed in recent years, at wavelengths ranging from radio to X-rays. In this paper we describe a new method for detecting clusters in two-band optical/near-IR…
Clustering algorithms are fundamental tools across many fields, with density-based methods offering particular advantages in identifying arbitrarily shaped clusters and handling noise. However, their effectiveness is often limited by the…
The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…
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…
We have been represented the collective information of estimation procedures of parameters of the open clusters and put them together for showing the importance of clusters to understand their role in stellar evolution phenomenon. Moreover,…