AI 中文总结
研究布尔网络动力学分解，通过赋予可能动力学空间半环结构，实现对布尔网络动力学的系统分解，为网络模块化建立代数基础，引入新数学工具，推动代数方法在网络相关问题中的应用。
AI 中文摘要
理解布尔网络的动力学对于网络简化、设计、控制和逆向工程等问题至关重要。随着布尔网络模型规模和复杂性不断增加，以与其动力学兼容的方式将网络分解为模块变得越发重要。本文表明，赋予可能动力学空间一个半环结构，能依据其组成模块的动力学对任何布尔网络的动力学进行系统分解。此代数框架提供了一种系统方法来分析局部动力学行为如何组合产生全局动力学。我们的结果为网络模块化建立了具体代数基础，为研究复杂布尔网络引入了新数学工具，并为代数方法应用于网络分析、分解和控制问题打开了大门。
英文摘要
Understanding the dynamics of Boolean networks is central to problems such as network reduction, design, control, and reverse engineering. As Boolean network models continue to grow in size and complexity, it becomes increasingly important to decompose networks into modules in a manner that is compatible with their dynamics. In this paper, we show that endowing the space of possible dynamics with a semiring structure enables a systematic decomposition of the dynamics of any Boolean network in terms of the dynamics of its constituent modules. This algebraic framework provides a systematic way to analyze how local dynamical behaviors combine to produce global dynamics. Our results establish a concrete algebraic foundation for network modularity and introduce new mathematical tools for the study of complex Boolean networks, and opens the door to the application of algebraic methods to problems of network analysis, decomposition, and control.
