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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]

A generalized partial linear regression model is proposed to estimate population size at a specific time from multiple lists of a time-varying and heterogeneous population. The challenge is that we have millions of records and hundreds of parameters for a long period of time. This presents a challenge for data analysis, mainly due to the limitation of computer memory, computational convergence and infeasibility. In the paper, an analytical methodology is proposed for modeling a large data set with a large number of parameters. The basic idea is to apply the maximum likelihood estimator to data observed at each time separately, and then combine these results via weighted averages so that the final estimator becomes the maximum likelihood estimator of the whole data set (full MLE). The asymptotic distribution and inference of the proposed estimators is derived. Simulation studies show that the proposed procedure gives exactly the same performance as the full MLE, but the proposed method is computationally feasible while the full MLE is not, and has much lower computational cost than the full MLE if both methods work. The proposed method is applied to estimate the number of drug-abusers in Hong Kong over the period 1977–2014. • A generalized partial linear model is proposed for time-varying populations. • We propose an analytical methodology suitable for modeling large data set. • Our method is more computationally feasible for which the full MLE is not capable. • The proposed method is applied Hong Kong drug abusers populations estimation. • We developed an efficient and user-friendly R package called COWA. [ABSTRACT FROM AUTHOR]

• We propose a new complexity measure of time series called modified discrete generalized past entropy based on grain exponent. • We validate the method with logistic map and Hénon map, it can characterize the feature of both map effectively, distinguish the periodic and chaotic state of system accurately and sensitively. • We compare the method with the discrete generalized past entropy based on oscillation-based grain exponent (O-DGPE), our method can characterize the complexity of a system more accurately. • Stock markets of different area are distinguished well by our method, and it can get the result that the US market and Hong Kong market are more mature than the Chinese mainland market, which is consistent with the reality. In this paper, we propose the modified discrete generalized past entropy based on grain exponent (GE-MDGPE), to analyze complex dynamical systems. Gao et al. proposed discrete generalized past entropy based on oscillation-based grain exponent (O-DGPE) method in 2019, which has been proved to be a good measure of uncertainty of time series. Whereas, it still has some drawbacks, such as the effectiveness of O-DGPE is not good when characterizing some special systems. In order to solve these drawbacks, we therefore generalize O-DGPE method to put forward GE-MDGPE which can better characterize complex systems. While using two artificial model (logistic map, Hénon map) to qualify the proposed method, we find that the method can characterize the system more accurately than O-DPGE, and can distinguish the periodic system and chaotic system effectively and sensitively. Moreover, we discuss the influence of parameters β and j on the proposed method. At last, we apply the proposed method to analyze the financial series which are extracting from six indices: three U.S. stock indices and three Chinese stock indices. The results show that the method can clearly distinguish the stock markets of different levels of development, and the U.S. market and the Hong Kong market are more mature than the Chinese mainland market. [ABSTRACT FROM AUTHOR]

• We propose a new complexity measure of time series called discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph. • We use amplitude difference distribution instead of degree distribution to be the distribution probability extracted from horizontal visibility graph. • We validate the method with logistic map and Hénon map, and find it has higher accuracy and sensitivity than the traditional method in characterizing dynamical systems. • Stock markets of different area are distinguished well by our method, and it can get the result that the US market and the Hong Kong market are more developed than the Chinese mainland market, which is consistent with the reality. In this paper, we propose discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph as a new complexity measure of nonlinear time series. We use amplitude difference distribution instead of degree distribution to extract information from the network constructed from the horizontal visibility graph, and combine amplitude difference distribution with discrete generalized past entropy to propose the new method. By analyzing the logistic map and Hénon map with the proposed method, we find the proposed method not only can assess systems well, but also has higher accuracy and sensitivity than the traditional method in characterizing dynamical systems. Furthermore, we apply the proposed method to the financial data: the six indices from Chinese mainland, Hong Kong and US. The result shows that the US market and the Hong Kong market are more developed than the Chinese mainland market, which is consistent with the reality. [ABSTRACT FROM AUTHOR]

A novel hybrid learning process based on the "decompose-ensemble" principle is proposed in this paper, integrating the NSRX learning structure with extreme learning machine (ELM) as an efficient predictor. While training the proposed model, the self-adaptive decomposition method of empirical mode decomposition (EMD) is first used to divide a training set of tourist arrival series into several relatively regular sub-series. Then, these decomposed sub-series are reconstructed into three components of high, moderate, and low frequency based on the balance of reconstructed components' relative stationarity and the fluctuation patterns between components and the original data series. Next, extracted features and forecasting results for the three components, obtained via ELM, are combined with d -lags historical data from the undecomposed training set; this set serves as the training sample input to train the hybrid model for enhanced tourist arrival prediction. For illustration and verification purposes, the proposed learning paradigm is applied to predict Hong Kong's monthly inbound tourist arrivals from 14 source markets from January 2007 to December 2018. Empirical results demonstrate that the proposed novel ensemble-learning paradigm outperforms all benchmark models, including five popular single models and five ensemble models, in terms of prediction accuracy. These findings suggest that the proposed model shows promise in forecasting complicated time series demonstrating high volatility and irregularity. [ABSTRACT FROM AUTHOR]

Bayesian quasi-likelihoods constructed from estimating functions extend the scope of Bayesian inference to a wide range of semi-parametric problems. Nonetheless, when the estimating functions possess complex structure, like containing highly irregular weighting matrices, the quasi-likelihoods constructed from those estimating functions may deform with multiple modes, and thus lose their nice statistical properties. This makes incorporating the information from complex estimating functions, such as composite score functions, into Bayesian inference infeasible. This paper makes two contributions. First, we demonstrate and explain theoretically why the quasi-likelihoods constructed from complex estimating functions deform. Second, we introduce a method of quasi-likelihood regularization which effectively handles the deformation and restores the nice statistical properties of the quasi-likelihoods. The regularization can be easily implemented and asymptotically preserves all information from the original estimating functions, ensuring good estimation accuracy. Numerical studies are conducted to verify the effectiveness of the quasi-likelihood regularization on GARCH(1,1) model and Gaussian random field examples. Direct incorporation of the information from composite likelihoods into the regularized quasi-likelihoods is a highlighted application demonstrated in the numerical studies. We further apply the regularized quasi-likelihood to the spatio-temporal modeling of the ground-level ozone concentration in Hong Kong, and illustrate how our regularized quasi-likelihoods facilitate the simultaneous inference from multiple sources of complex semi-parametric information. [ABSTRACT FROM AUTHOR]