基于噪声时间序列的时滞相互作用复杂动力网络逆向工程
Reverse engineering of complex dynamical networks in the presence of time-delayed interactions based on noisy time series
摘要：
复杂动态网络的逆向工程对于许多领域都很重要，在这些领域中，揭示未知网络的完整拓扑结构并估计表征网络结构和动态过程的参数是很有意义的。我们考虑复杂的振荡器网络的时间延迟的相互作用在噪声环境中，并开发了一种有效的方法来推断网络的完整拓扑结构和评估的时间延迟量仅基于噪声污染的时间序列。特别是，我们开发了一个分析理论，建立动态相关矩阵，它可以构建纯粹的时间序列，可以操纵产生的网络拓扑结构和时间延迟量的同时。广泛的数值支持，以验证该方法。虽然我们的方法提供了一个可行的解决方案，网络逆问题，重大的困难，局限性和挑战仍然存在，这些都进行了彻底的讨论。
英文摘要：
Reverse engineering of complex dynamical networks is important for a variety of fields where uncovering the full topology of unknown networks and estimating parameters characterizing the network structure and dynamical processes are of interest. We consider complex oscillator networks with time-delayed interactions in a noisy environment, and develop an effective method to infer the full topology of the network and evaluate the amount of time delay based solely on noise- contaminated time series. In particular, we develop an analytic theory establishing that the dynamical correlation matrix, which can be constructed purely from time series, can be manipulated to yield both the network topology and the amount of time delay simultaneously. Extensive numerical support is provided to validate the method. While our method provides a viable solution to the network inverse problem, significant difficulties, limitations, and challenges still remain, and these are discussed thoroughly.
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