This paper explores the asymptotic synchronization of drive-response Markovian jump Boolean networks (MJBNs) using an algebraic state space representation. For two switching signals, an augmented variable is introduced, recasting the synchronization problem into an asymptotic set stability challenge. Initially, a criterion is developed to identify all nonnegative solutions of a related equation via stochastic processes. Then, an alternative criterion based on invariant subsets and the largest singular value is proposed, where the equivalence of the proposed two criteria is demonstrated. Contrasting with deterministic BNs, where synchronization methods depend on finite power of state transition matrices, the criteria for MJBNs involve a more intricate approach. Numerical examples are included to validate the effectiveness of the proposed theoretical concepts.

The storage and transmission of large-scale data are recognized as significant challenges that incur substantial costs due to the massive volume of information involved. Lossless compression offers a potential solution to this problem. In this work, we explore the online lossless state compression (LSC) in finite-valued networks by effectively combining the methods of finite state automata and reinforcement learning. To achieve online lossless compression, the concept ofk-step compressed walks (state sequences) is introduced. By constructing a finite state automaton to identify all insertable walks, the recoverability conditions of online lossless compression are presented. For any given compressed walkw’c, one algorithm is proposed to find a minimal recoverablekmin-step compressed walk, thereby improving the compression ratio. Furthermore, it can be found that if a compressed walk keeps recoverability, adding more states to it would not break this property. Additionally, a model-free reinforcement learning framework based on Q-learning is developed to obtain globally minimal recoverable compressed walks. Finally, a numerical example is given to demonstrate the efficiency of the proposed online lossless compression scheme, achieving a compression ratio of 44.4%.

In this article, set stabilization in switched Boolean networks is investigated through link augmentations. Link augmentation is introduced as a selective process for adding specific edges between nodes in the wiring digraph of the network. For the implementation of link augmentation, various variables are integrated into the dynamics governing networks, utilizing basic logical operators. A key aspect of this article is the incorporation of additional functions introduced by the link augmentations into the original dynamics of the system using constrained logical operators. Further, several criteria for set stabilization are formulated, and the link augmentation control strategy is innovatively designed, utilizing theQ-learning Algorithm. Finally, a biological example is presented to demonstrate the effectiveness of the proposed methods.

Stability maintenance in systems refers to the capacity to preserve inherent stability characteristics. In this article, stability maintenance of large boolean networks (BNs) subjected to perturbations is investigated using a distributed pinning control (PC) strategy. The concept of edge removal as a form of perturbation is introduced, and several criteria for achieving global stability are established. Two forms of distributed PCs, one implemented before perturbation occurs and the other after, are introduced. It is noteworthy that the designs of the controllers are solely dependent on the system’s in-neighbors. The proposed method significantly decreases the computational complexity, reducing it from$O(2^{2|\texttt {V}|})$to$O(|\texttt {V}|+ |\texttt {E}| + \kappa \cdot 2^{K})$, where$|\texttt {V}|, |\texttt {E}|$denotes the cardinality of vertices and arcs of the adjacent graph of BN,$\kappa $is the number of the pinning nodes, and K represents the maximum in-degree of the network. In the worst-case scenario, the computational complexity is bounded by$O(|\texttt {V}|+ |\texttt {E}| + \kappa \cdot 2^{|\texttt {V}|})$. To validate the effectiveness of the proposed methods, results from multiple gene networks are presented, including a model representing the human rheumatoid arthritis synovial fibroblast, among which only 12 of the 359 nodes are deemed essential.

This brief devotes to investigating the long-run behavior estimation of temporal Boolean networks (TBNs) with multiple data losses, especially the asymptotical stability. The information transmission is modeled by Bernoulli variables, based on which an augmented system is constructed to facilitate the analysis. A theorem guarantees that the asymptotical stability of the original system can be converted to that of the augmented system. Subsequently, one necessary and sufficient condition is obtained for asymptotical stability. Furthermore, an auxiliary system is derived to study the synchronization issue of the ideal TBNs with normal data transmission and TBNs with multiple data losses, as well as an effective criterion for verifying synchronization. Finally, numerical examples are given to illustrate the validity of the theoretical results.

In this article, minimal pinning control for oscillatority (i.e., instability) of Boolean networks (BNs) under algebraic state space representations method is studied. First, two criteria for oscillatority of BNs are obtained from the aspects of state transition matrix (STM) and network structure (NS) of BNs, respectively. A distributed pinning control (DPC) from these two aspects is proposed: one is called STM-based DPC and the other one is called NS-based DPC, both of which are only dependent on local in-neighbors. As for STM-based DPC, one arbitrary node can be chosen to be controlled, based on certain solvability of several equations, meanwhile a hybrid pinning control (HPC) combining DPC and conventional pinning control (CPC) is also proposed. In addition, as for NS-based DPC, pinning control nodes (PCNs) can be found using the information of NS, which efficiently reduces the high computational complexity. The proposed STM-based DPC and NS-based DPC in this article are shown to be simple and concise, which provide a new direction to dramatically reduce control costs and computational complexity. Finally, gene networks are simulated to discuss the effectiveness of theoretical results.