This paper uses the AR (1)-GJR (1, 1)-SKT model to describe the marginal distribution of 15 stock index returns. A hybrid R-Vine Copula model is constructed to analyze the risk contagion effect of international stock markets under the four crisis events, which include the subprime mortgage crisis, the European debt crisis, the abnormal fluctuations of the Chinese stock market in 2015 and the Sino-US trade friction in 2018. The empirical results show that the international stock markets maintain symmetrical top-to-bottom dependence characteristics in the long term. The risk contagion will cause the Kendall rank correlation coefficient and tail correlation coefficient among stock markets to rise suddenly. The subprime crisis has a strong contagious effect and a long duration, and the European debt crisis is relatively mild. In 2015, the abnormal fluctuations in the Chinese stock market had a strong contagious effect on international stock markets, but the duration was short. In 2018, the Sino-US trade friction held a weaker contagious effect on the international stock markets. China's Shanghai and Shenzhen stock markets are more integrated with Hong Kong stock market in China.

The enhancement of the robustness of complex networks has been a hotspot in the field of network science in recent years. It is both of great scientific significance and theoretical value to explore the strategy of enhancing the robustness for network structure design and function improvement. On the basis of extensive collation and systematic analysis of domestic and foreign literature, this paper summarizes comprehensively the key point and main ideasof the current research on the enhancement strategies of complex networks robustness from three aspects: pre-defense, in-process recovery and post-optimization. The advantages, disadvantages and applicability of different strategies are compared and analyzed. Then we look forward to future research direction in this field.

To improve the ability to predict the evolution trend of public opinion, a public opinion evolution trend prediction model based on an improved wolf pack algorithm and optimized long-short term memory neural network is proposed. Use Halton Sequence to initialization to improve population diversity. Design step factor to perform Gauss-Sine perturbation transformation to improve wolf group exploration and development capabilities. Combine with the spiral in the whale optimization algorithm to improve the siege mechanism to enhance the local search ability of wolves. The bidirectional memory population is used to increase the cooperative ability of the wolf pack. The improved wolf pack algorithm (IWPA) is applied to the hyperparameter prediction of the LSTM neural network. Using keywords such as “COVID-19” and “Food Safety”, the experiment proves that the IWPA-LSTM neural network public opinion evolution prediction model has good accuracy and generality. The model is suitable for the prediction of various public opinion evolution trends.

Reviews and prospects the existing academic literature in terms of research paradigms, research methods and research tools on the complexity of international capital flow network. Studies show that the research paradigm ofcomplexity science based on discrete spatial network is pretty suitablefor the research on the complexity of international capital flow network. And the procedure, consisting of "construction of complex discrete network—system evolution—relationship analysis on input and output—proposals fordecision making ", can work quite well while doing this research. Besides, the construction and topological structure analysis of international trade capital flow network, which also belongs to international fund interactive network, could be applied to the research on the complexity of international capital flow network in the context of increasing data availability. And after the expansion on network node and neighbor mode, the newly defined generalized cellular automaton model could be used as a powerful tool for evolution and parameter calculation of international capital flow network.

With requirements of continuous improvements to customers’ service, Vehicle Routing Problems with Time Windows (VRPTW) attracted more and more attention. Aiming to minimize the total cost and to maximize customers’ satisfaction, a bi-objective integer programming model is established. A Hybrid Ant Colony Optimization (HACO) is designed to solve it. An elitist-ant strategy is set up to explore the bi-objective functions respectively and to get better non-dominant solutions. The evaporation factors are redefined to balance local and global search capabilities of the algorithm and to avoid premature convergence. NSGA-Ⅱ is used to guide the bi-objective optimizing process, a variable neighborhood search algorithm is used to expand the search space, in order to obtain the better Pareto solution set. The optimal parameter combination was determined by an orthogonal experiment, and the Solomon standard instances are used to test the performance of the algorithm. The simulation results show that the HACO can effectively solve the vehicle routing problem with time windows, and the performance of HACO has a significant improvement.

As a form of public opinion, view and attitude, opinion widely exists in people′s life. It is important to clarify the evolution mechanism of opinion, explicit the existing research progress, and promote the rational governance of public opinion. In view of the lack of relevant introduction of binary opinion dynamics and the separation of the relationship between binary and group opinion dynamics, this paper summarized the research status of opinion dynamics at home and abroad. Firstly, it introduces the binary opinion dynamics model from the perspective of research method and interaction characteristic; Secondly, it combed the research results of group opinion dynamics from the perspective of individual characteristic, behavior characteristic, opinion characteristic, external environment and perspective dynamics. Finally, based on the existing research, it clarifies the problems, the mechanism of opinion evolution from the empirical perspective, the strengthening of opinions and the reduction of disputes, and the relationship between the evolution of views and group decision-making, that need to be solved in the future.

The conditions for the spontaneous emergence of cooperation under the complex human behavior model have become the focus of many disciplines. Exploring the conditions for cooperation has both important scientific significance and theoretical value for understanding the institutional arrangements in human society. The social dilemma games provide a theoretical prototype for studying cooperation issues between multiple individuals. As a dynamic analysis method that can describe individuals′ learning and strategy adjustment processes, evolutionary game theory has been one of the most effective frameworks for studying the evolution of cooperation. This review article systematically summarizes the research progress of using the evolutionary game method to study the issues of group cooperation in social dilemma games. Specifically, the following topics are included: research progress of (1) social dilemma game models, evolutionary game theory and equilibrium analysis methods, (2) social dilemma games and the evolution of cooperation under reward/punishment mechanism and reputation mechanism, (3) social dilemma games and the evolution of cooperation with separation strategy and extortion strategy, and (4) social dilemma games and the evolution of cooperation under the network reciprocity. Finally, prospects for further research issues in this area are presented.

As a type of collective behavior in social systems, opinion polarization may greatly influence social stability. Thus, this paper systematically sorts out and summarizes the research status of opinion polarization. Based on reviews of the concept and modeling of opinion polarization in social and political fields, the two interaction mechanisms of opinions that lead to opinion polarization are extracted. From the perspective of individuals, the paper focuses on discussion two kinds of social psychological effects that may lead to opinion polarization, viz., biased assimilation and hostile media effect. The key to integration of polarization research in different fields lies in the internal change mechanism of individual opinion. One of the emphasis in future research should focus on the mutual corroboration of models and real data.

Mission of this research is to better capture the complexity of large-scale financial systems and overcome the insufficiency of equilibrium based neoclassical finance and behavioral finance in revealing the mechanism of financial crisis and the emergence of order. This study started from the dilemma of existing theories and the motivation of introducting complexity science. Then advances of multi-agent simulation and complex network analysis are summarized and discussed as two fundimental instruments of complexity science. Research trends of complexity science in financial research, are proposed as the result of the discussions. This study provides methodology reference and analytical tools for the theoretical research and practical applications of complex financial systems in the new era.

In order to provide effective decision-making basis for improvement of complex network invulnerability and protection of important nodes, this paper establishes a complex network invulnerability and node importance evaluation model based on redundancy. Firstly, the redundancy of complex networks is defined. At the same time, based on the redundancy, the invulnerability of the network is quantified. Then, this paper uses the global attribute of redundancy to evaluate the importance of each node in the network by means of node deletion. Finally, this paper uses actual networks for simulation experiments. The results show that the model and algorithm can provide a solution to the problem of high invulnerability network construction under some cost constraints, and at the same time they are effective and superior for evaluating the importance of nodes in larger networks.