相关论文: Cluster scattering coefficients in rank 2
The statement in the title was proved in \cite{Cao23} by introducing dominant sets of seeds, which are analogs of torsion classes in representation theory. In this note, we observe a short proof by the existence of consistent cluster…
We briefly review results on two-dimensional supersymmetric quantum field theories that exhibit factorizable particle scattering. Our particular focus is on a series of $N\!=\!1$ supersymmetric theories, for which exact $S$-matrices have…
The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic, and electromagnetic media. In view of their promising applications in inverse problems related to…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
We develop a recursive formula for the probability of a k-cluster in bootstrap percolation.
We have examined the spatial distribution of substructure in clusters of galaxies using Einstein X-ray observations. Subclusters are found to have a markedly anisotropic distribution that reflects the surrounding matter distribution on…
Working over various graded Lie algebras and in arbitrary dimension, we express scattering diagrams and theta functions in terms of counts of tropical curves/disks, weighted by multiplicities given in terms of iterated Lie brackets. Over…
Directed networks are broadly used to represent asymmetric relationships among units. Co-clustering aims to cluster the senders and receivers of directed networks simultaneously. In particular, the well-known spectral clustering algorithm…
We consider a scattering map that arises in the $\bar \partial $-approach to the scattering theory for the Davey-Stewartson II equation and show that the map is an invertible map between certain weighted $L^2$ Sobolev spaces.
Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. There has been a few work studying the community detection…
We consider a two-level system coupled to a mesoscopic two-terminal conductor that acts as measuring device. As a convenient description of the conductor we introduce its scattering matrix. We show how its elements can be used to calculate…
Modern network analysis often involves multi-layer network data in which the nodes are aligned, and the edges on each layer represent one of the multiple relations among the nodes. Current literature on multi-layer network data is mostly…
The article concerns the existence and uniqueness of quantisations of cluster algebras. We prove that cluster algebras with an initial exchange matrix of full rank admit a quantisation in the sense of Berenstein-Zelevinsky and give an…
We review the number counts to second order concentrating on the terms which dominate on sub horizon scales. We re-derive the result for these terms and compare it with the different versions found in the literature. We generalize our…
While not obvious from its initial motivation in linear algebra, there are many context where iterated traces can be defined. In this paper we prove a very general theorem about iterated 2-categorical traces. We show that many…
A formal relationship between scattering amplitudes in critical bosonic string theory and correlation functions of operators in topological string theory is found.
We present a computer program for the simulation of Mie scattering in case of arbitrarily large size parameters. The elements of the scattering matrix, efficiency factors as well as the corresponding cross sections, the albedo and the…
Motivated by the cluster structure of two-loop scattering amplitudes in N=4 Yang-Mills theory we define "cluster polylogarithm functions". We find that all such functions of weight 4 are made up of a single simple building block associated…
A Haag-Ruelle scattering theory for particles with braid group statistics is developed, and the arising structure of the Hilbert space of multiparticle states is analyzed.
We study Laurent expansions of cluster variables in a cluster algebra of rank 2 associated to a generalized Kronecker quiver. In the case of the ordinary Kronecker quiver, we obtain explicit expressions for Laurent expansions of the…