Let the coronas C<sub>n</sub>⊙K<sub>1</sub> be the polygons with one additional end-point for eachvertex.Thom Grace conjectured that C<sub>n</sub>⊙K<sub>1</sub> are ha...Let the coronas C<sub>n</sub>⊙K<sub>1</sub> be the polygons with one additional end-point for eachvertex.Thom Grace conjectured that C<sub>n</sub>⊙K<sub>1</sub> are harmonious for n even.In this paper,aproof of his conjecture is given.展开更多
The problem of sequential fault diagnosis is to construct a diagnosis tree that can isolate the failure sources with minimal test cost. Pervious sequential fault diagnosis strategy generating algorithms only consider ...The problem of sequential fault diagnosis is to construct a diagnosis tree that can isolate the failure sources with minimal test cost. Pervious sequential fault diagnosis strategy generating algorithms only consider the execution cost at application stage, which may result in a solution with poor quality from the view of life cycle cost. Furthermore, due to the fact that uncertain information exists extensively in the real-world systems, the tests are always imperfect. In order to reduce the cost of fault diagnosis in the realistic systems, the sequential fault diagnosis problem with imperfect tests considering life cycle cost is presented and formulated in this work, which is an intractable NP-hard AND/OR decision tree construction problem. An algorithm based on AND/OR graph search is proposed to solve this problem. Heuristic search based on information theory is applied to generate the sub-tree in the algorithm. Some practical issues such as the method to improve the computational efficiency and the diagnosis strategy with multi-outcome tests are discussed. The algorithm is tested and compared with previous algorithms on the simulated systems with different scales and uncertainty. Application on a wheel momentum system of a spacecraft is studied in detail. Both the simulation and application results suggest that the cost of the diagnosis strategy can be reduced significantly by using the proposed algorithm, especially when the placement cost of the tests constitutes a large part of the total cost.展开更多
Recommendation algorithms regard user-item interaction as a sequence to capture the user’s short-term preferences,but conventional algorithms cannot capture information of constantly-changing user interest in complex...Recommendation algorithms regard user-item interaction as a sequence to capture the user’s short-term preferences,but conventional algorithms cannot capture information of constantly-changing user interest in complex contexts.In these years,combining the knowledge graphwith sequential recommendation has gained momentum.The advantages of knowledge graph-based recommendation systems are that more semantic associations can improve the accuracy of recommendations,rich association facts can increase the diversity of recommendations,and complex relational paths can hence the interpretability of recommendations.But the information in the knowledge graph,such as entities and relations,often fails to be fully utilized and high-order connectivity is unattainable in graph modelling in knowledge graph-based sequential recommender systems.To address the above problems,a knowledge graph-based sequential recommendation algorithm that combines the gated recurrent unit and the graph neural network(KGSRGG)is proposed in the present work.Specifically,entity disambiguation in the knowledge graph is performed on the preprocessing layer;on the embedding layer,the TransR embedding technique is employed to process the user information,item information and the entities and relations in the knowledge graph;on the aggregation layer,the information is aggregated by graph convolutional neural networks and residual connections;and at last,on the sequence layer,a bi-directional gated recurrent unit(Bi-GRU)is utilized to model the user’s sequential preferences.The research results showed that this newalgorithm performed better than existing sequential recommendation algorithms on the MovieLens-1M and Book-Crossing datasets,as measured by five evaluation indicators.展开更多
文摘Let the coronas C<sub>n</sub>⊙K<sub>1</sub> be the polygons with one additional end-point for eachvertex.Thom Grace conjectured that C<sub>n</sub>⊙K<sub>1</sub> are harmonious for n even.In this paper,aproof of his conjecture is given.
基金Project(C1320063131)supported by China Civil Space Foundation
文摘The problem of sequential fault diagnosis is to construct a diagnosis tree that can isolate the failure sources with minimal test cost. Pervious sequential fault diagnosis strategy generating algorithms only consider the execution cost at application stage, which may result in a solution with poor quality from the view of life cycle cost. Furthermore, due to the fact that uncertain information exists extensively in the real-world systems, the tests are always imperfect. In order to reduce the cost of fault diagnosis in the realistic systems, the sequential fault diagnosis problem with imperfect tests considering life cycle cost is presented and formulated in this work, which is an intractable NP-hard AND/OR decision tree construction problem. An algorithm based on AND/OR graph search is proposed to solve this problem. Heuristic search based on information theory is applied to generate the sub-tree in the algorithm. Some practical issues such as the method to improve the computational efficiency and the diagnosis strategy with multi-outcome tests are discussed. The algorithm is tested and compared with previous algorithms on the simulated systems with different scales and uncertainty. Application on a wheel momentum system of a spacecraft is studied in detail. Both the simulation and application results suggest that the cost of the diagnosis strategy can be reduced significantly by using the proposed algorithm, especially when the placement cost of the tests constitutes a large part of the total cost.
文摘Recommendation algorithms regard user-item interaction as a sequence to capture the user’s short-term preferences,but conventional algorithms cannot capture information of constantly-changing user interest in complex contexts.In these years,combining the knowledge graphwith sequential recommendation has gained momentum.The advantages of knowledge graph-based recommendation systems are that more semantic associations can improve the accuracy of recommendations,rich association facts can increase the diversity of recommendations,and complex relational paths can hence the interpretability of recommendations.But the information in the knowledge graph,such as entities and relations,often fails to be fully utilized and high-order connectivity is unattainable in graph modelling in knowledge graph-based sequential recommender systems.To address the above problems,a knowledge graph-based sequential recommendation algorithm that combines the gated recurrent unit and the graph neural network(KGSRGG)is proposed in the present work.Specifically,entity disambiguation in the knowledge graph is performed on the preprocessing layer;on the embedding layer,the TransR embedding technique is employed to process the user information,item information and the entities and relations in the knowledge graph;on the aggregation layer,the information is aggregated by graph convolutional neural networks and residual connections;and at last,on the sequence layer,a bi-directional gated recurrent unit(Bi-GRU)is utilized to model the user’s sequential preferences.The research results showed that this newalgorithm performed better than existing sequential recommendation algorithms on the MovieLens-1M and Book-Crossing datasets,as measured by five evaluation indicators.
