Departamento de Electromagnetismo y Fisica de la Materia and Instituto Carlos I de Fisica Teórica y Computacional, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain.
Nat Commun. 2013;4:2521. doi: 10.1038/ncomms3521.
Hallmarks of criticality, such as power-laws and scale invariance, have been empirically found in cortical-network dynamics and it has been conjectured that operating at criticality entails functional advantages, such as optimal computational capabilities, memory and large dynamical ranges. As critical behaviour requires a high degree of fine tuning to emerge, some type of self-tuning mechanism needs to be invoked. Here we show that, taking into account the complex hierarchical-modular architecture of cortical networks, the singular critical point is replaced by an extended critical-like region that corresponds--in the jargon of statistical mechanics--to a Griffiths phase. Using computational and analytical approaches, we find Griffiths phases in synthetic hierarchical networks and also in empirical brain networks such as the human connectome and that of Caenorhabditis elegans. Stretched critical regions, stemming from structural disorder, yield enhanced functionality in a generic way, facilitating the task of self-organizing, adaptive and evolutionary mechanisms selecting for criticality.
临界特征，如幂律和标度不变性，已在皮质网络动力学中得到实证发现，有人推测，在临界状态下具有功能优势，例如最佳计算能力、记忆和大动态范围。由于临界行为需要高度的微调才能出现，因此需要调用某种自调谐机制。在这里，我们表明，考虑到皮质网络复杂的层次模块结构，奇异临界点被扩展的类似临界区域所取代，这在统计力学的行话中对应于格里菲斯相。通过计算和分析方法，我们在合成层次网络中发现了格里菲斯相，也在人类连接组和秀丽隐杆线虫等经验大脑网络中发现了格里菲斯相。源于结构无序的拉伸临界区域以通用的方式产生增强的功能，为自组织、自适应和进化机制选择临界状态提供便利。
