Loop-corrected belief propagation for lattice spin models

Belief propagation (BP) is a message-passing method for solving probabilistic graphical models. It is very successful in treating disordered models (such as spin glasses) on random graphs. On the other hand, finite-dimensional lattice models have an abundant number of short loops, and the BP method is still far from being satisfactory in treating the complicated loop-induced correlations in these systems. Here we propose a loop-corrected BP method to take into account the effect of short loops in lattice spin models. We demonstrate, through an application to the square-lattice Ising model, that loop-corrected BP improves over the naive BP method significantly. We also implement loop-corrected BP at the coarse-grained region graph level to further boost its performance.Comment: 11 pages, minor changes with new references added. Final version as published in EPJ

Non-conforming Tender and Attempt at Cure: A Comparative Study of The Uniform Code and the United Nations Convention on Contracts for the International Sale of Goods

The seller’s right to cure in case of a breach is an area of significance in domestic as well as international sales. In resolving conflict between trading parties due to the breach, the seller’s cure of the non-conforming tenders is generally recognized as the most effective and economically sound measure to avoid litigation costs, minimize damages, and time waste, and most importantly, achieve respective contractual purposes of the parties. This thesis will attempt to illustrate significant differences between CISG and U.C.C. as to basic policies governing of contract, remedies available to the buyer in response to the seller’s breach, and the seller’s right to cure the nonconformity. The purpose is to compare strengths and weaknesses of U.C.C and CISG in providing opportunities for cure, and to provide practical considerations in the drafting of international sales contracts and in the choice of law