论文标题
时间，结构和功能异质性在随机布尔网络中扩展了临界和抗侵蚀性
Temporal, structural, and functional heterogeneities extend criticality and antifragility in random Boolean networks
论文作者
论文摘要
大多数复杂系统模型都是均匀的，即所有元素具有相同的属性（空间，时间，结构，功能）。但是，大多数天然系统都是异质的：很少有要素比其他元素更重要，更大，更强大或更快。在同质系统中，通常在参数空间中非常狭窄的区域发现临界性 - 变化与稳定性之间的平衡，接近相变。使用随机的布尔网络 - 一个离散动力学系统的一般模型 - 我们表明，在时间，结构和功能上 - 可以扩展发现关键性的参数区域。此外，发现抗差异的参数区域也随着异质性而增加。但是，对于均质网络中的特定参数发现了最大的抗差异。我们的工作表明，同质性和异质性之间的“最佳”平衡是非平底，上下文依赖性的，在某些情况下是动态的。
Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality -- a balance between change and stability, order and chaos -- is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks -- a general model of discrete dynamical systems -- we show that heterogeneity -- in time, structure, and function -- can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the "optimal" balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic.
