1] Department of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany [2] Faculty of Information Studies in Novo mesto, 8000 Novo mesto, Slovenia.
Department of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.
Sci Rep. 2014 May 22;4:5030. doi: 10.1038/srep05030.
Inferring the internal interaction patterns of a complex dynamical system is a challenging problem. Traditional methods often rely on examining the correlations among the dynamical units. However, in systems such as transcription networks, one unit's variable is also correlated with the rate of change of another unit's variable. Inspired by this, we introduce the concept of derivative-variable correlation, and use it to design a new method of reconstructing complex systems (networks) from dynamical time series. Using a tunable observable as a parameter, the reconstruction of any system with known interaction functions is formulated via a simple matrix equation. We suggest a procedure aimed at optimizing the reconstruction from the time series of length comparable to the characteristic dynamical time scale. Our method also provides a reliable precision estimate. We illustrate the method's implementation via elementary dynamical models, and demonstrate its robustness to both model error and observation error.
推断复杂动力系统的内部相互作用模式是一个具有挑战性的问题。传统方法通常依赖于检查动力单元之间的相关性。然而，在转录网络等系统中，一个单元的变量也与另一个单元变量的变化率相关。受此启发，我们引入了导数变量相关性的概念，并将其用于设计一种从动力时间序列重建复杂系统（网络）的新方法。使用可调可观测变量作为参数，通过一个简单的矩阵方程来构建具有已知相互作用函数的任何系统的重建。我们提出了一种旨在从与特征动力时间尺度相当的时间序列中优化重建的方法。我们的方法还提供了可靠的精度估计。我们通过基本动力模型说明了该方法的实现，并证明了它对模型误差和观测误差的鲁棒性。
