Flapping-wing flight control is a multi-input and multi-output nonlinear system with uncertainties, which is affected by modeling errors, parameter variations, external disturbances, and unmodeled dynamics. Parameter uncertainty has a great impact on the stability control of flapping-wing flight, and gain adjustment is a common means to deal with parameter uncertainty, but it is complex and time-consuming. Based on the mechanism of flapping-wing flight, a nonlinear dynamic model for flapping-wing dynamic flight is established by analyzing the forces, moments, and attitude changes of the fuselage and wing in detail. Based on the constructed dynamic model, a fast robust adaptive flapping-wing flight control method is proposed. The state predictor is designed to estimate and monitor the uncertain parameters in the flapping-wing attitude control model, and the adaptive law adjusts the parameter estimation to ensure that the output error between the state predictor and the controlled object is stable in the Lyapunov sense, and finally the adaptive control law is obtained. At the same time, the Monte Carlo-support vector machine method is used to optimize the boundary of the control parameters in the flight control to obtain the control parameters that can meet the control expectations, and the obtained parameters are classified and judged according to the stable level flight conditions. Based on the adjusted parameters and the predetermined control signal, the control amount is adjusted according to the control law. When the adaptive gain is large enough, the simulation results show that the system has good transient response characteristics.

Proper description of the return distribution is crucial for investment practitioners. The underestimation of the tail risk may lead to severe consequences, even for assets with moderate fluctuations. However, many empirical studies found that the distribution tails of many financial assets drop off more slowly than the Gaussian distributions. Therefore, we intend to model and calibrate the heavy tails observed in financial fluctuations in this study. By maximizing the Varma entropy with value-at-risk and expected shortfall constraints, we obtain the probability distribution of stock return and observe that the tail of stock return distribution is a power law. Since the variance of the real stock portfolio may be a random variable, using the mean-VaR-ES constraints to maximize the Varma entropy effectively avoids the problem of assuming that the variance is a constant value under the traditional mean-variance constraint. Therefore, the deduced theoretical model would be more consistent with the real market. Using high-frequency data from China’s stock markets, we calibrate our theoretical model and give the concrete form of probability density distribution p(x) for different time intervals. The calibration results show that the tail of the stock return distribution is a power law with most of the power-law orders between −2 and −7. We prove the robustness of our results by calibrating the Varma entropy for S&P 500 of the USA stock market and different stock market indices in China’s A-share market. Our research’s findings not only offer a theoretical perspective for researchers but also give investing professionals a theoretical foundation on which to base their decisions.

The topological structure of the world air transportation network has been the subject of much research. However, to better understand the reality of air networks, one can consider the traffic, the number of passengers, or the distance between flights. This paper studies the weighted world air transportation network through the component structure, recently introduced in the network literature, by using the number of flights. The component structure is based on the community or multiple core-periphery structures and splits the network into local and global components. The local components capture the regional flights of these two mesoscopic structures (dense parts). The global components capture the inter-regional flights (links between the dense parts). We perform a comparative analysis of the world air transportation network and its components with their weighted counterparts. Moreover, we explore the strength and the s-core of these networks. Results display fewer local components well delimited and more global components covering the world than the unweighted world air transportation network. Centrality analysis reveals the difference between the top airports with high traffic and the top airports with high degrees. This difference is more pronounced in the global air network and the largest global component. Core analysis shows similitude between the s-core and the k-core for the local and global components, even though the latter includes more airports. For the world air network, the North and Central America-Caribbean airports dominate the s-core, whereas the European airports dominate the k-core.