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Based on information theory, the single neuron adaptive control problem for stochastic systems with non-Gaussian noises is investigated in this paper. Here, the statistic information of the output within a receding window rather than the output value is used for the tracking problem. Firstly, the single neuron controller structure, which has the ability of self-learning and self-adaptation, is established. Then, an improved performance criterion is given to train the weights of the single neuron. Furthermore, the mean-square convergent condition of the proposed control algorithm is formulated. Finally, comparative simulation results are presented to show that the proposed algorithm is superior to the PID controller. The contributions of this work are twofold: (1) the optimal control algorithm is formulated in the data-driven framework, which needn't the precise system model that is usually difficult to obtain; (2) the control problem of non-Gaussian systems can be effectively dealt with by the simple single neuron controller under improved minimum entropy criterion. [ABSTRACT FROM AUTHOR]

We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned. [ABSTRACT FROM AUTHOR]