Let DKv denote the symmetric complete directed graph with v vertices, the covering number C(v,m) is a minimum number of covering DKv by m-circuits. In this paper, C(v,m) is determined for any fixed odd positive intege...Let DKv denote the symmetric complete directed graph with v vertices, the covering number C(v,m) is a minimum number of covering DKv by m-circuits. In this paper, C(v,m) is determined for any fixed odd positive integer m and positive integer v, m ≤ v ≤ m + 6.展开更多
A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs...A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v≥m. In this paper, the problem is reduced to the case m+6≤v≤2m- 4m-3+12 , for any fixed even integer m≥4 . In particular, the values of P(v,m) are completely determined for m=12 , 14 and 16.展开更多
In recent years,the development of machine learning has introduced new analytical methods to theoretical research,one of which is Bayesian network—a probabilistic graphical model well-suited for modelling complex non...In recent years,the development of machine learning has introduced new analytical methods to theoretical research,one of which is Bayesian network—a probabilistic graphical model well-suited for modelling complex non-deterministic systems.A recent study has revealed that the order in which variables are read from data can impact the structure of a Bayesian network(Kitson and Constantinou in The impact of variable ordering on Bayesian Network Structure Learning,2022.arXiv preprint arXiv:2206.08952).However,in empirical studies,the variable order in a dataset is often arbitrary,leading to unreliable results.To address this issue,this study proposed a hybrid method that combined theory-driven and data-driven approaches to mitigate the impact of variable ordering on the learning of Bayesian network structures.The proposed method was illustrated using an empirical study predicting depression and aggressive behavior in high school students.The results demonstrated that the obtained Bayesian network structure is robust to variable orders and theoretically interpretable.The commonalities and specificities in the network structure of depression and aggressive behavior are both in line with theorical expectations,providing empirical evidence for the validity of the hybrid method.展开更多
文摘Let DKv denote the symmetric complete directed graph with v vertices, the covering number C(v,m) is a minimum number of covering DKv by m-circuits. In this paper, C(v,m) is determined for any fixed odd positive integer m and positive integer v, m ≤ v ≤ m + 6.
文摘A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v≥m. In this paper, the problem is reduced to the case m+6≤v≤2m- 4m-3+12 , for any fixed even integer m≥4 . In particular, the values of P(v,m) are completely determined for m=12 , 14 and 16.
基金supported by National Natural Science Foundation of China(Grant No.32171089)Research Fund from Hangzhou Mingshitang Education Technology Development Co.,Ltd.(Project No.1222000035).
文摘In recent years,the development of machine learning has introduced new analytical methods to theoretical research,one of which is Bayesian network—a probabilistic graphical model well-suited for modelling complex non-deterministic systems.A recent study has revealed that the order in which variables are read from data can impact the structure of a Bayesian network(Kitson and Constantinou in The impact of variable ordering on Bayesian Network Structure Learning,2022.arXiv preprint arXiv:2206.08952).However,in empirical studies,the variable order in a dataset is often arbitrary,leading to unreliable results.To address this issue,this study proposed a hybrid method that combined theory-driven and data-driven approaches to mitigate the impact of variable ordering on the learning of Bayesian network structures.The proposed method was illustrated using an empirical study predicting depression and aggressive behavior in high school students.The results demonstrated that the obtained Bayesian network structure is robust to variable orders and theoretically interpretable.The commonalities and specificities in the network structure of depression and aggressive behavior are both in line with theorical expectations,providing empirical evidence for the validity of the hybrid method.
