Logical modeling is a powerful tool in biology, offering a system-level understanding of the complex interactions that govern biological processes. A gap that hinders the scalability of logical models is the need to specify the update function of every vertex in the network depending on the status of its predecessors. To address this, we introduce in this paper the concept of strong regulation, where a vertex is only updated to active/inactive if all its predecessors agree in their influences; otherwise, it is set to ambiguous. We explore the interplay between active, inactive, and ambiguous influences in a network. We discuss the existence of phenotype attractors in such networks, where the status of some of the variables is fixed to active/inactive, while the others can have an arbitrary status, including ambiguous.

翻译：逻辑建模是生物学中的一种有力工具，能够系统层面地理解控制生物过程的复杂相互作用。制约逻辑模型可扩展性的一个瓶颈在于，需要根据每个顶点前驱节点的状态来指定其更新函数。为解决这一问题，本文引入了强调控的概念：仅当某个顶点的所有前驱节点在影响上达成一致时，该顶点才被更新为活跃/非活跃状态；否则，其状态被设定为模糊。我们探讨了网络中活跃、非活跃与模糊影响之间的相互作用，并讨论了此类网络中表型吸引子的存在性——其中部分变量的状态固定为活跃/非活跃，而其他变量可处于任意状态（包括模糊状态）。