We study worst-case bounds on the quality of any fixed point assignment of the max-product algorithm for Markov Random Fields (MRF). We start providing a bound independent of the MRF structure and parameters. Afterwards, we show how this bound can be improved for MRFs with specific structures such as bipartite graphs or grids. Our results provide interesting insight into the behavior of max-pro...

We investigate dual decomposition for joint MAP inference of many strings. Given an arbitrary graphical model, we decompose it into small acyclic sub-models, whose MAP configurations can be found by finite-state composition and dynamic programming. We force the solutions of these subproblems to agree on overlapping variables, by tuning Lagrange multipliers for an adaptively expanding set of var...

This paper presents three new methodologies for the basic operations, which aim at finding new ways of computing union (maximum) and intersection (minimum) membership values by taking into effect the entire membership values in a fuzzy set. The new methodologies are conceptually simple and easy from the application point of view and are illustrated with a variety of problems such as Cartesian p...

Abstract. In this paper, lexicographic products of two fuzzy graphs namely, lexicographic min-product and lexicographic max-product which are analogous to the concept lexicographic product in crisp graph theory are defined. It is illustrated that the operations lexicographic products are not commutative. The connected, effective and complete properties of the operations lexicographic products a...

3-Methylindole (3 MI) is a selective pulmonary toxicant, and cytochrome P450 (P450) bioactivation of 3 MI, through hydroxylation, epoxidation, or dehydrogenation pathways, is a prerequisite for toxicity. CYP2F1 and CYP2F3 exclusively catalyze the dehydrogenation of 3 MI to 3-methyleneindolenine, without detectable formation of the hydroxylation or epoxidation products. It was not known whether ...