This paper discussed how to handle the fairness conditions in partial Kripke structures. The partial Kripke structures were used for partial state spaces model checking, which is a new technique to solve problems of s...This paper discussed how to handle the fairness conditions in partial Kripke structures. The partial Kripke structures were used for partial state spaces model checking, which is a new technique to solve problems of state explosion. This paper extended the partial Kripke structure with fairness conditions by defining a partial fair Kripke structure, and a 3 valued fair CTL(Computation Tree Logic) semantics correspondingly. It defines a fair preorder between partial Kripke structures that preserves fairness and is akin to fair bisimulation. In addition, a pertinent theorem is also given, which indicates the relationship between the partial state spaces and the more complete one by illustrating the characterizations of states in the partial fair structure in terms of CTL formulae.展开更多
In social network analysis, logistic regression models have been widely used to establish the relationship between the response variable and covariates. However, such models often require the network relationships to ...In social network analysis, logistic regression models have been widely used to establish the relationship between the response variable and covariates. However, such models often require the network relationships to be mutually independent, after controlling for a set of covariates. To assess the validity of this assumption,we propose test statistics, under the logistic regression setting, for three important social network drivers. They are, respectively, reciprocity, centrality, and transitivity. The asymptotic distributions of those test statistics are obtained. Extensive simulation studies are also presented to demonstrate their finite sample performance and usefulness.展开更多
基金National Natural Science Foundation of China( No.60 173 10 3 )
文摘This paper discussed how to handle the fairness conditions in partial Kripke structures. The partial Kripke structures were used for partial state spaces model checking, which is a new technique to solve problems of state explosion. This paper extended the partial Kripke structure with fairness conditions by defining a partial fair Kripke structure, and a 3 valued fair CTL(Computation Tree Logic) semantics correspondingly. It defines a fair preorder between partial Kripke structures that preserves fairness and is akin to fair bisimulation. In addition, a pertinent theorem is also given, which indicates the relationship between the partial state spaces and the more complete one by illustrating the characterizations of states in the partial fair structure in terms of CTL formulae.
文摘In social network analysis, logistic regression models have been widely used to establish the relationship between the response variable and covariates. However, such models often require the network relationships to be mutually independent, after controlling for a set of covariates. To assess the validity of this assumption,we propose test statistics, under the logistic regression setting, for three important social network drivers. They are, respectively, reciprocity, centrality, and transitivity. The asymptotic distributions of those test statistics are obtained. Extensive simulation studies are also presented to demonstrate their finite sample performance and usefulness.
