This study is concerned with probabilistic Boolean control networks (PBCNs) with state feedback control. A novel definition of bisimilar PBCNs is proposed

Given a distributed coordination algorithm (DCA) for agents coupled by a network, which can be characterized by a stochastic matrix, we say that the DCA can be asynchronously implemented if the consensus property is preserved when the agents are activated to update their states according to their own clocks. This paper focuses on two central problems in asynchronous implementation of DCA: which class of DCA can be asynchronously implemented, and which other cannot. We identify two types of stochastic matrices, called partially scrambling and essentially cyclic matrices, for which we prove that DCA associated with a partially scrambling matrix can be asynchronously implemented, and there exists at least one asynchronous implementation sequence, which fails to realize consensus for DCA associated with an essentially cyclic matrix.

Cooperative operations in which a UAV advances ahead of a UGV to conduct forward reconnaissance are critical in disaster relief and urban inspection missions. Prevalent air–ground coordination methods operate under the assumption of ideal communication or treat connectivity as a secondary objective. However, obstacle occlusion, such as high-rise buildings in urban areas and mountainous terrain, results in Non-Line-of-Sight (NLOS) conditions, disrupting communication between the two platforms. To address these challenges, this paper introduces a cooperative control framework based on dynamically varying modulation matrices for both the UAV and the UGV. By evaluating and mapping occlusion risks in real time, the cooperative motions of the UAV and UGV are adaptively adjusted to maintain Line-of-Sight (LOS). An LOS assessment function is designed and mapped to the eigenvalues of the modulation matrices, enabling smooth and adaptive coordination under changing environmental conditions while avoiding the limitations of traditional discrete mode-switching strategies. Theoretical analysis and simulation results confirm that the proposed approach not only ensures stable LOS connectivity but also enhances trajectory smoothness, adaptability, and computational efficiency.

The asymmetric semantic information within directionality makes directed network embedding essentially different from undirected network embedding. Existing directed network embedding methods, explicitly or implicitly, are established by preserving pairwise interactions yet distinguishing in-direction and out-direction. Noticing that the inherent semantic connotation of edge directions is still seldom leveraged to enhance directed network embedding, in this work, we propose a novel random walk embedding framework named RW4CF to encode hierarchical collaborative filtering features within directed networks. In detail, we interpret the directed link as a type of user-item interaction and formulate the concept of hierarchical collaborative filtering matrices as a heuristic structural feature for directed network embedding. Specifically, we incorporate a collaborative filtering window in the random walk scheme to encode collaborative filtering information. Theoretical analysis is given to prove that the obtained embedding by RW4CF is indeed a factorization of the hierarchical collaborative filtering matrices of the directed network. Moreover, to validate the efficiency of RW4CF, we conduct extensive experiments on directed network datasets and demonstrate the superior performances of RW4CF than the state-of-the-arts.