A decomposition structure learning algorithm in Bayesian network based on a two-stage combination method

Decomposition hybrid algorithms with the recursive framework which recursively decompose the structural task into structural subtasks to reduce computational complexity are employed to learn Bayesian network (BN) structure. Merging rules are commonly adopted as the combination method in the combination step. The direction determination rule of merging rules has problems in using the idea of keeping v-structures unchanged before and after combination to determine directions of edges in the whole structure. It breaks down in one case due to appearances of wrong v-structures, and is hard to operate in practice. Therefore, we adopt a novel approach for direction determination and propose a two-stage combination method. In the first-stage combination method, we determine nodes, links of edges by merging rules and adopt the idea of permutation and combination to determine directions of contradictory edges. In the second-stage combination method, we restrict edges between nodes that do not satisfy the decomposition property and their parent nodes by determining the target domain according to the decomposition property. Simulation experiments on four networks show that the proposed algorithm can obtain BN structure with higher accuracy compared with other algorithms. Finally, the proposed algorithm is applied to the thickening process of gold hydrometallurgy to solve the practical problem.

Lattice Polytopes from Schur and Symmetric Grothendieck Polynomials

Given a family of lattice polytopes, two common questions in Ehrhart Theory are determining when a polytope has the integer decomposition property and determining when a polytope is reflexive. While these properties are of independent interest, the confluence of these properties is a source of active investigation due to conjectures regarding the unimodality of the $h^\ast$-polynomial. In this paper, we consider the Newton polytopes arising from two families of polynomials in algebraic combinatorics: Schur polynomials and inflated symmetric Grothendieck polynomials. In both cases, we prove that these polytopes have the integer decomposition property by using the fact that both families of polynomials have saturated Newton polytope. Furthermore, in both cases, we provide a complete characterization of when these polytopes are reflexive. We conclude with some explicit formulas and unimodality implications of the $h^\ast$-vector in the case of Schur polynomials.

Solvability Criterion for Convolution Equations on a Half-Strip

We obtain the criterion of solvability of homogeneous convolution equation in a half-strip. Proof is based on a new decomposition property of the weighted Hardy space. This result has relations to the spectral analysis-synthesis problem, cyclicity problem, information theory. All data generated or analysed during this study are included in this published article.

Decompositions of Weakly Compact Valued Integrable Multifunctions

We give a short overview on the decomposition property for integrable multifunctions, i.e., when an “integrable in a certain sense” multifunction can be represented as a sum of one of its integrable selections and a multifunction integrable in a narrower sense. The decomposition theorems are important tools of the theory of multivalued integration since they allow us to see an integrable multifunction as a translation of a multifunction with better properties. Consequently, they provide better characterization of integrable multifunctions under consideration. There is a large literature on it starting from the seminal paper of the authors in 2006, where the property was proved for Henstock integrable multifunctions taking compact convex values in a separable Banach space X. In this paper, we summarize the earlier results, we prove further results and present tables which show the state of art in this topic.