The question of the existence of a spin liquid state in the half-filled Hubbard model on the honeycomb (also known as graphene) lattice is revisited. The variational cluster approximation, the cluster dynamical mean field theory, and the cluster dynamical impurity approximation are applied to various cluster systems. Assuming that the spin liquid phase coincides with the Mott insulating phase i...

The question of the existence of a spin liquid state in the half-filled Hubbard model on the honeycomb (aka graphene) lattice is revisited. The Variational Cluster Approximation (VCA), the Cluster Dynamical Mean Field Theory (CDMFT) and the Cluster Dynamical Impurity Approximation (CDIA) are applied to various cluster systems. Assuming that the spin liquid phase coincides with the Mott insulati...

We generalize the linked cluster expansion of Matsubara Green functions into nonequilibrium situations. This allows us to compute nonequilibrium correlation functions and, consequently, physical observables for interacting quantum systems with intermediate interaction strengths. As a specific example, we study nonlinear dc transport in a resonant tunneling system with electron-phonon interactio...

We consider the Ordered Cluster Traveling Salesman Problem (OCTSP). In this problem, a vehicle starting and ending at a given depot must visit a set of n points. The points are partitioned intoK,K n, prespeci ed clusters. The vehicle must rst visit the points in cluster 1, then the points in cluster 2, : : :, and nally the points in cluster K so that the distance traveled is minimized. We prese...

Cluster analysis is a technique used to group objects into clusters such that similar objects are grouped together in the same cluster. Early methods were derived from multivariate statistics. Some newer methods are based on rough sets, introduced by Pawlak [3], [4]. An extension of rough sets to rough clusters was introduced in [5]. The lower approximation (LA) of a rough cluster contains obje...

Recently, Huang and Lin suggested a combination of two successfull mean-field theories, the 2-cluster approximation and paradisical mean-field, for the Nagel-Schreckenberg cellular automaton model of traffic flow. We argue that this new approximation is inconsistent since it violates the Kolmogorov conditions. In a recent work [1] Huang and Lin have studied a combination of two mean-field theor...

A new approach supporting the possibility of cluster buckling during the main phase transition in the lipid bilayer is presented. The elastic energy is calculated via harmonic approximation which yields the potential minimum in the case of buckling cluster, if critical cluster size is achieved. The significance of this event for interbilayer interaction in multilamellar vesicles is discussed.

Clustering is a common problem in the analysis of large data sets. Streaming algorithms, which make a single pass over the data set using small working memory and produce a clustering comparable in cost to the optimal offline solution, are especially useful. We develop the first streaming algorithms achieving a constant-factor approximation to the cluster radius for two variations of the k-cent...

In this paper we present a fast and accurate procedure called clustered low rank matrix approximation for massive graphs. The procedure involves a fast clustering of the graph and then approximating each cluster separately using existing methods, e.g. the singular value decomposition, or stochastic algorithms. The cluster-wise approximations are then extended to approximate the entire graph. Th...

The quantum mechanical formula for Mayer's second cluster integral for the gas of relativistic particles with hard-core interaction is derived. The proper pion volume calculated with quantum mechanical formula is found to be an order of magnitude larger than its classical evaluation. The second cluster integral for the pion gas is calculated in quantum mechanical approach with account for both ...