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© 2022 by the authors.The nature of dependence between random variables has always been the subject of many statistical problems for over a century. Yet today, there is a great deal of research on this topic, especially focusing on the analysis of nonlinearity. Shannon mutual information has been considered to be the most comprehensive measure of dependence for evaluating total dependence, and several methods have been suggested for discerning the linear and nonlinear components of dependence between two variables. We, in this study, propose employing the Rényi and Tsallis mutual information measures for measuring total dependence because of their parametric nature. We first use a residual analysis in order to remove linear dependence between the variables, and then we compare the Rényi and Tsallis mutual information measures of the original data with that the lacking linear component to determine the degree of nonlinearity. A comparison against the values of the Shannon mutual information measure is also provided. Finally, we apply our method to the environmental Kuznets curve (EKC) and demonstrate the validity of the EKC hypothesis for Eastern Asian and Asia-Pacific countries.

This study proposed a control method, a data-driven predictive control (DDPC), for the hand exoskeleton used for active, passive, and resistive rehabilitation. DDPC is a model-free approach based on past system data. One of the strengths of DDPC is that constraints of states can be added to the controller while performing the controller design. These features of the control algorithm eliminate an essential problem for rehabilitation robots in terms of easy customization and safe repetitive rehabilitation tasks that can be planned within certain constraints. Experiments were carried out with a designed hand rehabilitation system under repetitive and various therapy tasks. Real-time experiment results demonstrate the feasibility and efficiency of the proposed control approach to rehabilitation systems.

Statistical relationships among the variables of a complex system reveal a lot about its physical behavior. Therefore, identification of the relevant variables and characterization of their interactions are crucial for a better understanding of a complex system. Linear methods, such as correlation, are widely used to identify these relationships. However, information-theoretic quantities, such as mutual information and transfer entropy, have been proven to be superior in the case of nonlinear dependencies. Mutual information quantifies the amount of information obtained about one random variable through the other random variable, and it is symmetric. As an asymmetrical measure, transfer entropy quantifies the amount of directed (time-asymmetric) transfer of information between random processes and, thus, it is related to concepts, such as the Granger causality. This Special Issue includes 16 papers elucidating the state of the art of data-based transfer entropy estimation techniques and applications, in areas such as finance, biomedicine, fluid dynamics and cellular automata. Analytical derivations in special cases, improvements on the estimation methods and comparisons between certain techniques are some of the other contributions of this Special Issue. The diversity of approaches and applications makes this book unique as a single source of invaluable contributions from experts in the field. No sponsor