The Bethe theory of electron diffraction is used to calculate reflection electron diffraction intensities for mediiim and high energy electrons. A generalized Hill's determinant method is used for •he numencal calculations instead of the more common but slower matrix-eigenvalue technique. Results of a "systematics" calculation of the specular intensity as a function of incident angle are compar...

Abstract. The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called “Loop Series Expansion”, which is an expansion of the partition function. The main term of the series is the Bethe approximation while other terms are labelled by subgraphs called gen...

A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of replicas. In the scheme, survey propagation (SP), which is an efficient algorithm developed recently for analyzing the microscopic properties of glassy states for...

We present the exact Bethe lattice solution for a lattice gas Potts model defined in the generalized ensemble which was previously studied in elucidating the anomalous thermodynamic properties of water. For this model the locus of density maxima (TMD), the locus of isothermal compressibility extrema, (TEC), the spinodal curve, and the percolation curve for four hydrogen bonded molecules are cal...

We investigate different ways of generating approximate solutions to the inverse Ising problem (IIP). Our approach consists in to take as a starting point for further perturbation procedures, a Bethe mean-field solution obtained with a maximum spanning tree (MST) of pairwise mutual information which we refer to as the Bethe reference point. We consider three different ways of following this ide...

We study the Bethe ansatz equations for a generalized XXZ model on a one-dimensional lattice. Assuming the string conjecture we propose an integer version for vacancy numbers and prove a combinatorial completeness of Bethe's states for a generalized XXZ model. We nd an exact form for inverse matrix related with vacancy numbers and compute its determinant. This inverse matrix has a tridiagonal f...

we study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by devroye et. al (2011). in a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor ix_i floor$ where $x_0$, $ldots$ , $x_n$ is a sequence of i.i.d. random variables, with support in [0,...