Related papers: Clustering logarithms up to six loops

We extend the class of factorization theorems for non-global observables from fixed angular constraints to cross sections defined in terms of sequential jet clustering. The associated hard and soft functions depend not only on the…

Globular Clusters (GCs) have historically been subdivided in either two (disk/halo) or three (disk/inner-halo/outer-halo) groups based on their orbital, chemical and internal physical properties. The qualitative nature of this subdivision…

An outstanding problem in QCD and jet physics is the factorization and resummation of logarithms that arise due to phase space constraints, so-called non-global logarithms (NGLs). In this paper, we show that NGLs can be factorized and…

The invention of the transformer architecture has revolutionized Artificial Intelligence (AI), yielding unprecedented success in areas such as natural language processing, computer vision, and multimodal reasoning. Despite these advances,…

We consider the possibility of extracting the bottom quark mass from LEP data. The inclusive decay rate for $\zbb +\cdots$ is obtained at order $\as$ by summing up the one-loop two-parton decay rate to the tree-level three-parton rate. We…

We briefly summarize theoretical methods for carrying out QCD calculations to next-to-leading order in perturbation theory. In particular, we describe a new general algorithm that can be used for computing arbitrary jet cross sections in…

This paper deals with the clustering of univariate observations: given a set of observations coming from $K$ possible clusters, one has to estimate the cluster means. We propose an algorithm based on the minimization of the "KP" criterion…

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes…

As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…

We compute the next-to-next-to-leading order (NNLO) contributions to the three splitting functions governing the evolution of unpolarized non-singlet combinations of quark densities in perturbative QCD. Our results agree with all partial…

Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with non convex or nested structures. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a…

Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in…

In this paper, we propose a general model for plane-based clustering. The general model contains many existing plane-based clustering methods, e.g., k-plane clustering (kPC), proximal plane clustering (PPC), twin support vector clustering…

We explore the flow of quantum correlations in cluster states defined on ladder type graphs as measurements are done on qubits located on the nodes of the cluster. We focus on three qubits at the end of the ladder and compute the…

We construct a cross-entropy clustering (CEC) theory which finds the optimal number of clusters by automatically removing groups which carry no information. Moreover, our theory gives simple and efficient criterion to verify cluster…

We propose k^2-means, a new clustering method which efficiently copes with large numbers of clusters and achieves low energy solutions. k^2-means builds upon the standard k-means (Lloyd's algorithm) and combines a new strategy to accelerate…

In a previous paper we reported the discovery of super-leading logarithmic terms in a non-global QCD observable. In this short update we recalculate the first super-leading logarithmic contribution to the 'gaps between jets' cross-section…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

The k_t and Cambridge/Aachen inclusive jet finding algorithms for hadron-hadron collisions can be seen as belonging to a broader class of sequential recombination jet algorithms, parametrised by the power of the energy scale in the distance…

Clustering is a key task in machine learning, with $k$-means being widely used for its simplicity and effectiveness. While 1D clustering is common, existing methods often fail to exploit the structure of 1D data, leading to inefficiencies.…