This study focuses on the observability of the probabilistic Boolean multiplex network. Firstly, the dynamical model and structure of probabilistic Boolean multiplex network are proposed. Using the semi‐tensor product method, the logical dynamics of probabilistic Boolean multiplex network is converted into an equivalent algebraic representation. Then, the condition for the observability of probabilistic Boolean multiplex network is obtained. Finally, the proposed result is effectively illustrated by a numerical example.

Density peaks clustering has become a nova of clustering algorithm because of its simplicity and practicality. However, there is one main drawback: it is time-consuming due to its high computational complexity. Herein, a density peaks clustering algorithm with sparse search and K-d tree is developed to solve this problem. Firstly, a sparse distance matrix is calculated by using K-d tree to replace the original full rank distance matrix, so as to accelerate the calculation of local density. Secondly, a sparse search strategy is proposed to accelerate the computation of relative-separation with the intersection between the set of k nearest neighbors and the set consisting of the data points with larger local density for any data point. Furthermore, a second-order difference method for decision values is adopted to determine the cluster centers adaptively. Finally, experiments are carried out on datasets with different distribution characteristics, by comparing with other six state-of-the-art clustering algorithms. It is proved that the algorithm can effectively reduce the computational complexity of the original DPC from O(n 2 K) to O(n(n 1−1/K + k)). Especially for larger datasets, the efficiency is elevated more remarkably. Moreover, the clustering accuracy is also improved to a certain extent. Therefore, it can be concluded that the overall performance of the newly proposed algorithm is excellent.INDEX TERMS Density peaks clustering, sparse search strategy, K-d tree, computational complexity, second-order difference method.

This study focuses on the finite-time set reachability of probabilistic Boolean multiplex control networks (PBMCNs). Firstly, based on the state transfer graph (STG) reconstruction technique, the PBMCNs are extended to random logic dynamical systems. Then, a necessary and sufficient condition for the finite-time set reachability of PBMCNs is obtained. Finally, the obtained results are effectively illustrated by an example.

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