CDI-Type I: Modeling and Predicting State-Topology Coevolution of Complex Adaptive Networks

快速发展的复杂网络科学为复杂系统建模提供了新颖的方法，即使在十年前也无法完全预见。它解决了复杂网络结构的自组织及其对系统行为的影响，这与自然科学和社会科学的许多领域具有重要的跨学科相关性，特别是在当今高度网络化的社会/政治/经济环境中。有趣的是，到目前为止，复杂网络科学几乎分别研究了“网络动力学”（具有固定拓扑结构的网络上的状态转换）或“网络动力学”（没有动态状态变化的网络的拓扑转换）。然而，在许多现实世界复杂的生物和社会网络中，这两种动态相互作用，并在相同的时间尺度上共同进化。状态拓扑协同进化的建模和预测是当前复杂网络科学中最重要的挑战之一。在本项目中，研究人员将建立一个通用的建模框架，可以有效地描述复杂自适应网络的状态-拓扑协同进化，并开发自动发现动态规则的计算方法，以最好地捕获经验数据中的状态转换和拓扑转换。为了实现这一目标，将使用图重写系统作为状态转换和拓扑转换的统一表示手段。网络演进将分为子网提取和子网替换两部分。对于每个部分，将探索和开发用于自动规则发现的算法。它们的有效性将通过应用于现实世界的网络数据来评估。这个项目将产生一个新的理论框架和一个计算工具包，将改变研究复杂网络动力学的方式。该项目的成果将通过各种渠道传播，并整合到宾厄姆顿大学和其他机构的多个教育项目中。开发的算法和软件工具将免费提供给研究人员和其他专业人员使用。开发的框架还将作为一种广义的概念/数学“语言”，用于建模、分析和讨论各种复杂系统的动态，这将激发跨许多不同应用领域的跨学科讨论和协作。将资助两名研究生研究助理。在征聘过程中将特别鼓励代表性不足的群体（妇女、少数民族个人）的成员。

The rapidly growing complex network science has presented novel approaches to complex systems modeling that were not fully foreseen even in a decade ago. It addresses the self-organization of complex network structure and its implications for system behavior, which holds significant cross-disciplinary relevance to many fields of natural and social sciences, particularly in today's highly networked social/political/economical circumstances. Interestingly, complex network science has so far addressed either "dynamics on networks" (state transition on a network with a fixed topology) or "dynamics of networks" (topological transformation of a network with no dynamic state changes) almost separately. In many real-world complex biological and social networks, however, these two dynamics interact with each other and coevolve over the same time scales. Modeling and predicting state-topology coevolution is now recognized as one of the most significant challenges in complex network science. In this project, the researchers will establish a generalized modeling framework that can effectively describe state-topology coevolution of complex adaptive networks and develop computational methods for automatic discovery of dynamical rules that best capture both state transition and topological transformation in the empirical data. To achieve this goal, graph rewriting systems will be used as a means of unified representation of state transition and topological transformation. Network evolution will be formulated in two parts, extraction and replacement of subnetworks. For each part, algorithms for automatic rule discovery will be explored and developed. Their effectiveness will be evaluated through application to real-world network data. This project will produce a novel theoretical framework and a computational toolkit that will transform the ways of studying the dynamics on and of complex networks. The outcomes of this project will be disseminated via various channels and integrated in multiple educational programs at Binghamton University and other institutions. The developed algorithms and software tools will be made freely available to researchers and other professionals for their own use. The developed framework will also serve as a generalized conceptual/mathematical "language" for modeling, analyzing and discussing the dynamics of various complex systems, which will galvanize interdisciplinary discussion and collaboration across many different areas of applications. Two graduate research assistants will be supported. Members of underrepresented groups (women, minority individuals) will be particularly encouraged in the recruitment process.