Measuring the predictability and complexity of time series using entropy is essential tool designing and controlling a nonlinear system. However, the existing methods have some drawbacks related to the strong dependence of entropy on the parameters of the methods. To overcome these difficulties, this study proposes a new method for estimating the entropy of a time series using the LogNNet neural network model. The LogNNet reservoir matrix is filled with time series elements according to our algorithm. The accuracy of the classification of images from the MNIST-10 database is considered as the entropy measure and denoted by NNetEn. The novelty of entropy calculation is that the time series is involved in mixing the input information in the reservoir. Greater complexity in the time series leads to a higher classification accuracy and higher NNetEn values. We introduce a new time series characteristic called time series learning inertia that determines the learning rate of the neural network. The robustness and efficiency of the method is verified on chaotic, periodic, random, binary, and constant time series. The comparison of NNetEn with other methods of entropy estimation demonstrates that our method is more robust and accurate and can be widely used in practice.

Bitcoin is currently the leading global provider of cryptocurrency. Cryptocurrency allows users to safely and anonymously use the Internet to perform digital currency transfers and storage. In recent years, the Bitcoin network has attracted investors, businesses, and corporations while facilitating services and product deals. Moreover, Bitcoin has made itself the dominant source of decentralized cryptocurrency. While considerable research has been done concerning Bitcoin network analysis, limited research has been conducted on predicting the Bitcoin price. The purpose of this study is to predict the price of Bitcoin and changes therein using the grey system theory. The first order grey model (GM (1,1)) is used for this purpose. It uses a firstorder differential equation to model the trend of time series. The results show that the GM (1,1) model predicts Bitcoin's price accurately and that one can earn a maximum profit confidence level of approximately 98% by choosing the appropriate time frame and by managing investment assets.

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Analysis of nonlocal axial vibration in a nanorod is a crucial subject in science and engineering because of its wide applications in nanoelectromechanical systems. The aim of this paper is to show how these vibrations can be modelled within the framework of port-Hamiltonian systems. It turns out that two port-Hamiltonian descriptions in physical variables are possible. The first one is in descriptor form, whereas the second one has a non-local Hamiltonian density. In addition, it is shown that under appropriate boundary conditions these models possess a unique solution which is non-increasing in the corresponding 'energy', i.e., the associated infinitesimal generator generates a contraction semigroup on a Hilbert space, whose norm is directly linked to the Hamiltonian.

The aim of this paper is investigating the forced convection heat transfer in a channel with transverse rectangular cavities using the lattice Boltzmann method (LBM) which is not available in the literature yet. The effects of the Reynolds number (100–400), cavity aspect ratio ([Formula: see text], 0.5, 1.0), distance of cavities from each other ([Formula: see text]) in fixed depth of cavity ([Formula: see text]) on the velocity and temperature profiles are studied. Moreover, the flow patterns such as deflection and re-circulation zone inside the cavities are obtained. The local and averaged Nusselt numbers on the channel walls are achieved. The results show that the channel with cavities achieves heat transfer enhancements relative to the smooth channel. For the constant cavity aspect ratio, the maximum value of averaged Nusselt number in the channel is obtained in the case of [Formula: see text]. Heat transfer to the working fluids increases significantly by increasing the aspect ratio. The existed results are used to ascertain the validity of the numerical code and excellent agreement between results was found.