We propose a general error-driven algorithm to compute form factors in complex scenes equipped with a suitable cluster hierarchy. This opens the way for the efficient approximation of form factors in a controlled manner, with guaranteed error bounds at every stage of the calculation. In particular we discuss the issues of bounding the error in the form factor approximation using average cluster...

These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...

■ FA01 Marriott Chicago A Approximation Algorithms III Cluster: Approximation Algorithms Invited Session Chair: Cliff Stein, Columbia University, 326 S W Mudd Building, 500 W. 120th Street, New York, NY, 10027, [email protected] 1 Differentially Private Approximation Algorithms Kunal Talwar, Microsoft Research, Silicon Valley Campus, 1065 La Avenida, Mountain View, CA, 94043, United State...

The electronic energy loss of molecular clusters as a function of impact parameter is far less understood than atomic energy losses. For instance, there are no analytical expressions for the energy loss as a function of impact parameter for cluster ions. In this work, we describe two procedures to evaluate the combined energy loss of molecules: Ab initio calculations within the semiclassical ap...

We study the problem of minimizing the broadcast time for a set of processors in a cluster, where processor pi has transmission time ti, which is the time taken to send a message to any other processor in the cluster. Previously, it was shown that the Fastest Node First method (FNF) gives a 1.5 approximate solution. In this paper we show that there is a polynomial time approximation scheme for ...

We consider the problem of correlation clustering on graphs with constraints on both the cluster sizes and the positive and negative weights of edges. Our contributions are twofold: First, we introduce the problem of correlation clustering with bounded cluster sizes. Second, we extend the region of weight values for which the clustering may be performed with constant approximation guarantees in...

Abstract. The standard formulas for sample size and power calculation, as implemented in the command sampsi, make use of a normal approximation to the t-distribution. When the sample sizes are small, this approximation is poor, resulting in overestimating power (or underestimating sample size). One particular situation in which this is likely to be important is the field of cluster randomized t...

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the Euclidean cluster diameter is large. Therefore, it is preferred to assign smaller costs to the paths that stay close to the input points. In this paper, we c...

The ground state energy of ideal α-matter at T = 0 is analyzed within the framework of variational theory of Bose quantum liquids. Calculations are done for three local α−α potentials with positive volume integrals and twobody correlation functions obtained from the Pandharipande-Bethe equation. The energy per particle of α matter is evaluated in the cluster expansion formalism up to four-body ...