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...

We consider the problem of inference in a graphical model with binary variables. While in theory it is arguably preferable to compute marginal probabilities, in practice researchers often use MAP inference due to the availability of efficient discrete optimization algorithms. We bridge the gap between the two approaches by introducing the Discrete Marginals technique in which approximate margin...

We propose a new approach to the analysis of Loopy Belief Propagation (LBP) byestablishing a formula that connects the Hessian of the Bethe free energy with theedge zeta function. The formula has a number of theoretical implications on LBP.It is applied to give a sufficient condition that the Hessian of the Bethe free energyis positive definite, which shows non-convexity for...

The wave functions for two dimensional Bloch electrons in a uniform magnetic field at the mid-band points are studied with the help of the algebraic structure of the quantum group Uq(sl2). A linear combination of its generators gives the Hamiltonian. We obtain analytical and numerical solutions for the wave functions by solving the Bethe Ansatz equations, proposed by Wiegmann and Zabrodin on th...

We develop and illustrate a very simple eikonal technique in the framework of one-particle quantum mechanics for calculating radiation during scattering and apply it to derive the celebrated result of Bethe and Maximon for bremsstrahlung from a point coulomb target with a large charge Ze . This approach is a modification of that developed in a previous paper for calculating radiation during the...

We give the exact solution to the problem of a random walk on the Bethe lattice through a mapping on an asymmetric random walk on the half-line. We also study the continuous limit of this model, and discuss in detail the relation between the random walk on the Bethe lattice and Brownian motion on a space of constant negative curvature. PACS : 05.40.+j ; 05.50.+q Electronic addresses : monthus@a...

We present a new derivation of the spectral gap of the totally asymmetric exclusion process on a half-filled ring of size L by using the Bethe Ansatz. We show that, in the large L limit, the Bethe equations reduce to a simple transcendental equation involving the polylogarithm, a classical special function. By solving that equation, the gap and the dynamical exponent are readily obtained. Our m...

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hami...

The Bariev model with open boundary conditions is introduced and analysed in detail in the framework of the Quantum Inverse Scattering Method. Two classes of independent boundary reflecting K-matrices leading to four different types of boundary fields are obtained by solving the reflection equations. The models are exactly solved by means of the algebraic nested Bethe ansatz method and the four...

We investigate the generalized supersymmetric t− J model with boundary impurities in different gradings. All three different gradings: fermion, fermion, boson (FFB), boson, fermion, fermion (BFF) and fermion, boson, fermion (FBF), are studied for the generalized supersymmetric t − J model. Boundary K-matrix operators are found for the different gradings. By using the graded algebraic Bethe ansa...