Gong Xinwei, Socolar Joshua E S
Center for Nonlinear and Complex Systems and Physics Department, Duke University, Durham, North Carolina, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066107. doi: 10.1103/PhysRevE.85.066107. Epub 2012 Jun 8.
We study two measures of the complexity of heterogeneous extended systems, taking random Boolean networks as prototypical cases. A measure defined by Shalizi et al. for cellular automata, based on a criterion for optimal statistical prediction [Shalizi et al., Phys. Rev. Lett. 93, 118701 (2004)], does not distinguish between the spatial inhomogeneity of the ordered phase and the dynamical inhomogeneity of the disordered phase. A modification in which complexities of individual nodes are calculated yields vanishing complexity values for networks in the ordered and critical regimes and for highly disordered networks, peaking somewhere in the disordered regime. Individual nodes with high complexity are the ones that pass the most information from the past to the future, a quantity that depends in a nontrivial way on both the Boolean function of a given node and its location within the network.
我们以随机布尔网络作为典型案例，研究了异构扩展系统复杂性的两种度量。沙利齐等人基于最优统计预测标准[沙利齐等人，《物理评论快报》93，118701(2004)]为细胞自动机定义的一种度量，无法区分有序相的空间不均匀性和无序相的动力学不均匀性。一种修改方法是计算单个节点的复杂性，对于处于有序和临界状态的网络以及高度无序的网络，该方法会得出趋近于零的复杂性值，而在无序状态的某个位置达到峰值。具有高复杂性的单个节点是那些将最多信息从过去传递到未来的节点，这个量以一种非平凡的方式取决于给定节点的布尔函数及其在网络中的位置。
