相关论文: Cluster Model of Decagonal Tilings

We present a set of cluster models that link the present-day properties of clusters to the processes that govern galaxy formation. These models treat the entropy distribution of the intracluster medium as its most fundamental property.…

The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are…

We investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation…

We describe random generation algorithms for a large class of random combinatorial objects called Schur processes, which are sequences of random (integer) partitions subject to certain interlacing conditions. This class contains several…

We introduce a new transfer matrix method for calculating the thermodynamic properties of random-tiling models of quasicrystals in any number of dimensions, and describe how it may be used to calculate the phason elastic properties of these…

The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…

Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…

Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…

This paper explores the cluster algebra structure of the moduli space $\mathscr{A}_{\mathrm{SL}_{n+1},\mathbb{S}}$ of twisted $\mathrm{SL}_{n+1}$-local systems on a surface. We derive general recurrence relations for cluster variables…

This paper gives new, efficient algorithms for approximate uniform sampling of contingency tables and integer partitions. The algorithms use the Burnside process, a general algorithm for sampling a uniform orbit of a finite group acting on…

Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…

Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…

We consider real symmetric and complex Hermitian random matrices with the additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble…

Deep clustering methods improve the performance of clustering tasks by jointly optimizing deep representation learning and clustering. While numerous deep clustering algorithms have been proposed, most of them rely on artificially…

Divergences that occur in density matrices of decay and scattering processes are shown to be regularized by tracing and unitarity or the optical theorem. These divergences are regularized by the lifetime of the decaying particle or the…

We analyze the cluster formation in a non-ergodic stochastic system as a result of counter-flow, with the aid of an exactly solvable model. To illustrate the clustering, a two species asymmetric simple exclusion process with impurities on a…

Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a…

The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…

We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…

Understanding how living organisms spontaneously develop complex functional structures inspires innovative approaches in engineering design. Here, we introduce a decentralized generative model based on morphogenesis to autonomously grow…