Some technical aspects of Cluster Perturbation Theory (CPT) are presented. CPT is an approximation scheme for calculating the oneparticle Green function of the Hubbard model of interacting electrons on a lattice. It proceeds by (i) dividing the lattice into identical clusters and calculating the Green function by exact diagonalization on a given cluster (ii) extending this Green function to the...

We start by clarifying the terms which appear in the title. For a given theory of selfinteracting quantum fields, by Gaussian approximation we mean the Gaussian part of the interacting measure. By mean field approximation we understand the leading term of the expansion given in [1, 2] and by variational approximation we understand the old variational technique performed with some particular tri...

We propose a new abstraction technique for verifying topology properties of dynamic communicating systems (DCS), a special class of infinite-state systems. DCS are characterized by unbounded creation and destruction of objects along with an evolving communication connectivity or topology. We employ a lightweight graph transformation system to specify DCS. Hierarchical Abstraction computes a bou...

Multiple Sequence Alignment is one of the most fundamental problems in computational molecular biology. The running time of the best known scheme for finding an optimal alignment, based on dynamic programming, increases exponentially with large number of input sequences. Hence, many approximation algorithms are suggested for the problem. Most of the bounded error approximation multiple sequence...

We present and analyze a new framework for graph clustering based on a specially weighted version of correlation clustering, that unifies several existing objectives and satisfies a number of attractive theoretical properties. Our framework, which we call LambdaCC, relies on a single resolution parameter λ, which implicitly controls both the edge density and sparsest cut of all output clusters....

Quorum systems are a mechanism for obtaining fault-tolerance and efficient distributed systems. We consider geographic quorum systems; a geographic quorum system is a partitioning of a set X of points in the plane (representing servers) into quorums (i.e. clusters) of size k. The distance between a point p and a cluster C is the Euclidean distance between p and the farthest point in C. We prese...

Local Principal Component Analysis (LPCA) is one of the popular techniques for dimensionality reduction and data compression of large data sets encountered in computer graphics. The LPCA algorithm is a variant of kmeans clustering where the repetitive classification of high dimensional data points to their nearest cluster leads to long execution times. The focus of this paper is on improving th...

The Fréchet distance is a popular distance measure for curves. We study the problem of clustering time series under the Fréchet distance. In particular, we give (1 + ε)-approximation algorithms for variations of the following problem with parameters k and `. Given n univariate time series P , each of complexity at most m, we find k time series, not necessarily from P , which we call cluster cen...

The cluster variation method (CVM) is a hierarchy of approximate variational techniques for discrete (Ising–like) models in equilibrium statistical mechanics, improving on the mean–field approximation and the Bethe–Peierls approximation, which can be regarded as the lowest level of the CVM. In recent years it has been applied both in statistical physics and to inference and optimization problem...

We propose a new abstraction technique for verifying topology properties of dynamic communicating systems (DCS), a special class of infinite-state systems. DCS are characterized by unbounded creation and destruction of objects along with an evolving communication connectivity or topology. We employ a lightweight graph transformation system to specify DCS. Hierarchical Abstraction computes a bou...