On the morning of September 14th, the research group held the 15th session of “Li Nan Research Group’s Academic Lecture Series" online. The event was presided over by Dr. Li Nan, who invited Dr. Gao Jianxi, an assistant professor of the Computer Science Department of Rensselaer Polytechnic Institute (RPI), to deliver a keynote report on the “resilience and tipping points of complex systems”, based on more than a dozen influential papers he had published in journals such as Nature, Nature Physics and PNAS. The report was attended by nearly 30 teachers and students from universities such as Tsinghua University, Northeastern University of the US, Beijing Jiaotong University, Nanjing Tech University, Tianjin Chengjian University.
Fig. 1 The theme of the lecture delivered by Dr. Gao
Dr. Gao delivered the report on how to use network science theories to understand, predict, and control complex systems. The report was divided into three parts, covering the definition and understanding of system resilience, the resilience study of a single high-dimensional complex system, and the study of cascading failures of interdependent complex systems.
In the first part, Dr. Gao introduced the concept of resilience of complex systems, starting with the vulnerability of complex systems. He believed that the resilience of complex systems is the ability of a system to adjust its activities to retain its basic functions in case of errors, failures, and environmental changes, and is an inherent attribute of many complex systems. On this basis, Dr. Gao Jianxi believed that the current research mainly focuses on low-dimensional systems, while complex systems in reality comprise many individuals and complex interactions between individuals. There are certain challenges for studying the resilience of high-dimensional complex systems.
Fig.2 Definition of a system’s resilience
In the second part, around the single high-dimensional complex systems, Dr. Gao mainly introduced the dimensionality reduction method of high-dimensional complex systems, the state prediction method of complex systems with incomplete information, and the recovery method of complex systems after disturbance. First, Dr. Gao introduced the dimensionality reduction method of high-dimensional complex systems, which can represent the resilience as a variable to accurately predict the resilience of the system. By applying the above method in ecosystems, biological networks and power networks, the results verified that the method was effective. Then, Dr. Gao introduced the state prediction method of complex systems with incomplete information, which can accurately predict the state of the system based on limited data and information. Applying the above method in the biological network and the disease transmission network, the results showed a good prediction effect. Further, Dr. Gao introduced the recovery of complex systems, mainly considering the impact of system size, external noise, connection strength, disturbance strategy and disaster scenarios on system recovery and resilience, and introduced the research results on grid networks, complex social systems and transportation systems.
Fig. 3 The dimensionality reduction method of high-dimension complex systems
In the third part, Dr. Gao mainly introduced the research results on the cascade failure analysis of associated complex systems, focusing on the tipping point prediction method of associated systems. The method can determine the distance of cross-system tipping points based on limited data. On this basis, Dr. Gao further introduced the research results of applying the above method in complex systems such as symbiotic ecosystems, disease transmission networks and crowd movement network, and the results verified the effectiveness of the method.
Fig. 4 Cascading failure analysis process of interdependent networks
In the exchange session that followed the report, Dr. Gao further discussed with the attendees on the data types and acquisition methods used in the research, how to protect the system before a disaster, and how to improve the cross-field cooperation skills. The whole report lasted nearly 90 minutes.
Fig. 5. Group photo of attendees of the lecture online
