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IntroductionBoolean networks are dynamic systems used to model complex biolog...

IntroductionBoolean networks are dynamic systems used to model complex biological networks. One important problem in Boolean network analysis is to find a control strategy that can stabilize these networks by flipping the states of certain nodes. However, the existing control strategies often lack robustness, as they are designed based on specific network structures and cannot adapt to different networks.In this paper, we propose a robust flipping stabilization approach for Boolean networks using Q-learning. Q-learning is a reinforcement learning technique that has been successfully applied to various control problems. By applying Q-learning to Boolean network stabilization, our approach can adapt to different network structures and achieve robust control performance.MethodologyThe goal of our approach is to find an optimal control policy that can stabilize Boolean networks by flipping the states of certain nodes. We represent the Boolean network as a directed graph, where the nodes represent the Boolean variables and the edges represent the regulatory relationships between variables.We use a Q-learning framework to learn the optimal control policy. Q-learning is a model-free reinforcement learning technique that uses a Q-function to estimate the expected utility of taking a particular action in a given state. In our case, each state corresponds to a certain network configuration, and each action corresponds to flipping the state of a specific node. The Q-function is updated iteratively using the Q-learning update rule.To ensure robustness, we introduce a mechanism to handle network perturbations. When the network structure or dynamics change, the learned Q-function might become outdated. To address this issue, we propose a two-step learning process. In the first step, we train a Q-function on an initial network and obtain an initial control policy. In the second step, we fine-tune the Q-function using a limited number of network perturbations. This allows the Q-function to adapt to different network structures and achieve robust control performance.Experimental ResultsWe conducted experiments on several benchmark Boolean networks to evaluate the performance of our approach. The results show that our Q-learning-based approach can effectively stabilize Boolean networks by flipping the states of certain nodes. Moreover, our approach achieves better robustness compared to existing control strategies, as it can adapt to different network structures and handle network perturbations.ConclusionIn this paper, we proposed a robust flipping stabilization approach for Boolean networks using Q-learning. Our approach can adapt to different network structures and achieve robust control performance. Experimental results demonstrate the effectiveness and robustness of our approach. In future work, we plan to further investigate the applicability of our approach to larger and more complex biological networks.