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• We develop a model of opinion formation that endows the heterogeneous HK dynamics with a time-varying communication topology. • Noise-induced synchronization of our model is rigorously investigated both mathematically and numerically. • We demonstrate that opinion formation is noise-synchronizable if and only if the switching communication topology is uniformly jointly connected. • Our model reveals that connected discourse topology in combination with noise can lead to a quasi-consensus that is inducible from any initial state or anyunderlying system size. • Our findings have profound implications for the design of future strategies for opinion control andoptimization. A fundamental question that arises in the analysis of the noise-based synchronization of opinion dynamics with bounded confidence (BC) is what opinion structures can be synchronized by noise. In the standard Hegselmann-Krause (HK) model, each agent examines the opinion values of all other agents and then selects neighbors who are appropriate for opinion updating in accordance with the BC scheme. In reality, however, people are more likely to exchange opinions with only a limited set of individuals, resulting in a predetermined local communication network as postulated in the DeGroot model. In this paper, we develop a new model of opinion formation that endows the heterogeneous HK dynamics with a time-varying communication topology, and we investigate its noise-induced synchronization both mathematically and numerically. We show that opinion dynamics in this model are noise-synchronizable if and only if the switching communication graph is uniformly jointly connected. Our rigorous mathematical analysis and simulation experiments demonstrate that connected discourse topology in combination with fair amounts of noise can lead to a quasi-consensus that is inducible from any initial state or any underlying system size. Our findings have profound implications for the design of future strategies of social control and global opinion optimization. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we derive a new class of flexible threshold asymmetric Generalized Autoregression Conditional Heteroskedasticity (GARCH) models. We use this tool for analysis and modeling of the properties that are apparent in many financial time series. In general, the transmission of volatility in the stock market is time-varying, nonlinear, and asymmetric with respect to both positive and negative results. Given this fact, we adopt the method of fuzzy logic systems to modify the threshold values for an asymmetric GARCH model. Our simulations use stock market data from the Taiwan weighted index (Taiwan), the Nikkei 225 index (Japan), and the Hang Seng index (Hong Kong) to illustrate the performance of our proposed method. From the simulation results, we have determined that the forecasting of volatility performance is significantly improved if the leverage effect of clustering is considered along with the use of expert knowledge enabled by the GARCH model. [Copyright &y& Elsevier]