论文标题
单调布尔功能的联合可实现性
Joint Realizability of Monotone Boolean functions
论文作者
论文摘要
单调布尔功能（MBF）的研究历史悠久。我们探讨了基因调节的MBF与普通微分方程（ODE）模型之间的连接，特别是在实现MBF作为描述ODE状态过渡图的函数的问题。我们通过建立一类ODES的参数化动力学和MBF集合之间的联系来提出MBF有限收集的联合可实现性问题。我们提出了一个问题，即通过属于其右侧代数复杂性的增加的嵌套类别的ODE可以实现哪些MBF。随着我们逐步限制了ODE的代数形式，我们通过理论和明确的例子的结合表明，共同实现的函数类别严格降低。我们的结果影响了监管网络动力学以及MBF的经典领域的研究。我们以一系列潜在的扩展和猜想结束。
The study of monotone Boolean functions (MBFs) has a long history. We explore a connection between MBFs and ordinary differential equation (ODE) models of gene regulation, and, in particular, a problem of the realization of an MBF as a function describing the state transition graph of an ODE. We formulate a problem of joint realizability of finite collections of MBFs by establishing a connection between the parameterized dynamics of a class of ODEs and a collection of MBFs. We pose a question of what collections of MBFs can be realized by ODEs that belong to nested classes defined by increased algebraic complexity of their right-hand sides. As we progressively restrict the algebraic form of the ODE, we show by a combination of theory and explicit examples that the class of jointly realizable functions strictly decreases. Our results impact the study of regulatory network dynamics, as well as the classical area of MBFs. We conclude with a series of potential extensions and conjectures.
