School of Sciences, Beijing University of Posts and Telecommunications, Beijing, China.
Faculty of Science, Ningbo University, Ningbo, China.
Sci Rep. 2017 Mar 21;7:44639. doi: 10.1038/srep44639.
Many practical systems can be described by dynamic networks, for which modern technique can measure their outputs, and accumulate extremely rich data. Nevertheless, the network structures producing these data are often deeply hidden in the data. The problem of inferring network structures by analyzing the available data, turns to be of great significance. On one hand, networks are often driven by various unknown facts, such as noises. On the other hand, network structures of practical systems are commonly nonlinear, and different nonlinearities can provide rich dynamic features and meaningful functions of realistic networks. Although many works have considered each fact in studying network reconstructions, much less papers have been found to systematically treat both difficulties together. Here we propose to use high-order correlation computations (HOCC) to treat nonlinear dynamics; use two-time correlations to decorrelate effects of network dynamics and noise driving; and use suitable basis and correlator vectors to unifiedly infer all dynamic nonlinearities, topological interaction links and noise statistical structures. All the above theoretical frameworks are constructed in a closed form and numerical simulations fully verify the validity of theoretical predictions.
许多实际系统可以用动态网络来描述，对于这些网络，现代技术可以测量其输出，并积累极其丰富的数据。然而，产生这些数据的网络结构通常隐藏在数据中。通过分析可用数据推断网络结构的问题变得非常重要。一方面，网络通常受到各种未知因素的驱动，例如噪声。另一方面，实际系统的网络结构通常是非线性的，不同的非线性可以提供丰富的动态特征和现实网络的有意义的功能。尽管许多研究工作在研究网络重建时都考虑了每个因素，但很少有论文系统地同时处理这两个困难。在这里，我们提出使用高阶相关计算（HOCC）来处理非线性动力学；使用两时间相关来去相关网络动力学和噪声驱动的影响；并使用合适的基向量和相关向量来统一推断所有动态非线性、拓扑相互作用链接和噪声统计结构。所有上述理论框架都是以封闭形式构建的，数值模拟完全验证了理论预测的有效性。
