Network systems are commonly encountered and investigated in various disciplines, and network dynamics that refer to collective node state changes over time are one area of particular interests of many researchers. Recently, dynamic structural equation model (DSEM) has been introduced into the field of network dynamics as a powerful statistical inference tool. In this study, in recognition that parameter identifiability is the prerequisite of reliable parameter inference, a general and efficient approach is proposed for the first time to address the structural parameter identifiability problem of linear DSEMs for cyclic networks. The key idea is to transform a DSEM to an equivalent frequency domain representation, then Masons gain is employed to deal with feedback loops in cyclic networks when generating identifiability equations. The identifiability result of every unknown parameter is obtained with the identifiability matrix method. The proposed approach is computationally efficient because no symbolic or expensive numerical computations are involved, and can be applicable to a broad range of linear DSEMs. Finally, selected benchmark examples of brain networks, social networks and molecular interaction networks are given to illustrate the potential application of the proposed method, and we compare the results from DSEMs, state-transition models and ordinary differential equation models.

中文翻译：

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有向循环图的动态结构方程模型：结构可识别性问题

网络系统在各个学科中经常遇到和研究，涉及集体节点状态随时间变化的网络动态是许多研究人员特别感兴趣的领域之一。最近，动态结构方程模型（DSEM）作为一种强大的统计推理工具被引入网络动力学领域。在这项研究中，认识到参数可识别性是可靠参数推断的先决条件，首次提出了一种通用且有效的方法来解决循环网络线性 DSEM 的结构参数可识别性问题。关键思想是将 DSEM 转换为等效的频域表示，然后在生成可识别方程时使用 Mason 增益来处理循环网络中的反馈回路。每个未知参数的可识别性结果是用可识别性矩阵方法获得的。所提出的方法在计算上是有效的，因为不涉及符号或昂贵的数值计算，并且可以适用于广泛的线性 DSEM。最后，给出了大脑网络、社交网络和分子交互网络的选定基准示例，以说明所提出方法的潜在应用，并比较了 DSEM、状态转移模型和常微分方程模型的结果。