Li Ming, Lü Linyuan, Deng Youjin, Hu Mao-Bin, Wang Hao, Medo Matúš, Stanley H Eugene
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230026, China.
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China.
Natl Sci Rev. 2020 Aug;7(8):1296-1305. doi: 10.1093/nsr/nwaa029. Epub 2020 Feb 20.
The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, study of the connections between different percolation transitions is still lacking. Here we propose a unified framework to study the origins of the discontinuous transitions of the percolation process on interacting networks. The model evolves in generations with the result of the present percolation depending on the previous state, and thus is history-dependent. Both theoretical analysis and Monte Carlo simulations reveal that the nature of the transition remains the same at finite generations but exhibits an abrupt change for the infinite generation. We use brain functional correlation and morphological similarity data to show that our model also provides a general method to explore the network structure and can contribute to many practical applications, such as detecting the abnormal structures of human brain networks.
相互连接系统的结构及其对系统动力学的影响是一个经过大量研究的跨学科主题。尽管在不同模型中发现了各种临界现象，但对不同渗流转变之间联系的研究仍然不足。在此，我们提出一个统一框架来研究相互作用网络上渗流过程不连续转变的起源。该模型逐代演化，当前渗流的结果取决于先前状态，因此具有历史依赖性。理论分析和蒙特卡罗模拟均表明，在有限代时转变的性质保持不变，但在无限代时会出现突变。我们利用脑功能相关性和形态相似性数据表明，我们的模型还提供了一种探索网络结构的通用方法，可应用于许多实际场景，比如检测人类脑网络的异常结构。
