decomposition property
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Author(s):  
Huiping Guo ◽  
Hongru Li

AbstractDecomposition 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.


10.37236/9621 ◽  
2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Margaret Bayer ◽  
Bennet Goeckner ◽  
Su Ji Hong ◽  
Tyrrell McAllister ◽  
McCabe Olsen ◽  
...  

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.


2021 ◽  
Vol 15 (4) ◽  
Author(s):  
Volodymyr Dilnyi

AbstractWe 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.


2021 ◽  
Vol 31 (0) ◽  
pp. 47-54
Author(s):  
Shingo HIRAO ◽  
Hitomi HASEGAWA ◽  
Kenji MORI ◽  
Hidetomo YAMAMORI

2020 ◽  
Vol 22 (2) ◽  
pp. 181-198
Author(s):  
Rajwan Hmood ◽  
◽  
Iraq T. Abbas ◽  
H. A. AlSattar ◽  
◽  
...  

2020 ◽  
Vol 69 (4) ◽  
pp. 765-778 ◽  
Author(s):  
Takayuki Hibi ◽  
Hidefumi Ohsugi ◽  
Akiyoshi Tsuchiya

2020 ◽  
Vol 33 (4) ◽  
pp. 433-437
Author(s):  
Masashi Yamamoto ◽  
Koki Akita ◽  
Shiro Nagaoka ◽  
Hironobu Umemoto ◽  
Hideo Horibe

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 863 ◽  
Author(s):  
Luisa Di Piazza ◽  
Kazimierz Musiał

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.


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