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The categorization of sleep stages helps to diagnose different sleep-related ailments. In this paper, an entropy-based information-theoretic approach is introduced for the automated categorization of sleep stages using multi-channel electroencephalogram (EEG) signals. This approach comprises of three stages. First, the decomposition of multi-channel EEG signals into sub-band signals or modes is performed using a novel multivariate projection-based fixed boundary empirical wavelet transform (MPFBEWT) filter bank. Second, entropy features such as bubble and dispersion entropies are computed from the modes of multi-channel EEG signals. Third, a hybrid learning classifier based on class-specific residuals using sparse representation and distances from nearest neighbors is used to categorize sleep stages automatically using entropy-based features computed from MPFBEWT domain modes of multi-channel EEG signals. The proposed approach is evaluated using the multi-channel EEG signals obtained from the cyclic alternating pattern (CAP) sleep database. Our results reveal that the proposed sleep staging approach has obtained accuracies of 91.77%, 88.14%, 80.13%, and 73.88% for the automated categorization of wake vs. sleep, wake vs. rapid eye movement (REM) vs. Non-REM, wake vs. light sleep vs. deep sleep vs. REM sleep, and wake vs. S1-sleep vs. S2-sleep vs. S3-sleep vs. REM sleep schemes, respectively. The developed method has obtained the highest overall accuracy compared to the state-of-art approaches and is ready to be tested with more subjects before clinical application.Image-to-image steganography is hiding one image in another image. However, hiding two secret images into one carrier image is a challenge today. The application of image steganography based on deep learning in real-life is relatively rare. In this paper, a new Steganography Convolution Neural Network (SteganoCNN) model is proposed, which solves the problem of two images embedded in a carrier image and can effectively reconstruct two secret images. SteganoCNN has two modules, an encoding network, and a decoding network, whereas the decoding network includes two extraction networks. First, the entire network is trained end-to-end, the encoding network automatically embeds the secret image into the carrier image, and the decoding network is used to reconstruct two different secret images. The experimental results show that the proposed steganography scheme has a maximum image payload capacity of 47.92 bits per pixel, and at the same time, it can effectively avoid the detection of steganalysis tools while keeping the stego-image undistorted. Meanwhile, StegaoCNN has good generalization capabilities and can realize the steganography of different data types, such as remote sensing images and aerial images.In financial markets, information constitutes a crucial factor contributing to the evolution of the system, while the presence of heterogeneous investors ensures its flow among financial products. When nonlinear trading strategies prevail, the diffusion mechanism reacts accordingly. Under these conditions, information englobes behavioral traces of traders' decisions and represents their actions. The resulting effect of information endogenization leads to the revision of traders' positions and affects connectivity among assets. In an effort to investigate the computational dimensions of this effect, we first simulate multivariate systems including several scenarios of noise terms, and then we apply direct causality tests to analyze the information flow among their variables. Finally, empirical evidence is provided in real financial data.Financial time series have a fractal nature that poses challenges for their dynamical characterization. The Dow Jones Industrial Average (DJIA) is one of the most influential financial indices, and due to its importance, it is adopted as a test bed for this study. The paper explores an alternative strategy to the standard time analysis, by joining the multidimensional scaling (MDS) computational tool and the concepts of distance, entropy, fractal dimension, and fractional calculus. First, several distances are considered to measure the similarities between objects under study and to yield proper input information to the MDS. Then, the MDS constructs a representation based on the similarity of the objects, where time can be viewed as a parametric variable. The resulting plots show a complex structure that is further analyzed with the Shannon entropy and fractal dimension. In a final step, a deeper and more detailed assessment is achieved by associating the concepts of fractional calculus and entropy. selleck products Indeed, the fractional-order entropy highlights the results obtained by the other tools, namely that the DJIA fractal nature is visible at different time scales with a fractional order memory that permeates the time series.A set of core features is set forth as the essence of a thermodynamic description, which derive from large-deviation properties in systems with hierarchies of timescales, but which are not dependent upon conservation laws or microscopic reversibility in the substrate hosting the process. The most fundamental elements are the concept of a macrostate in relation to the large-deviation entropy, and the decomposition of contributions to irreversibility among interacting subsystems, which is the origin of the dependence on a concept of heat in both classical and stochastic thermodynamics. A natural decomposition that is known to exist, into a relative entropy and a housekeeping entropy rate, is taken here to define respectively the intensive thermodynamics of a system and an extensive thermodynamic vector embedding the system in its context. Both intensive and extensive components are functions of Hartley information of the momentary system stationary state, which is information about the joint effect of system processes on its contribution to irreversibility. Results are derived for stochastic chemical reaction networks, including a Legendre duality for the housekeeping entropy rate to thermodynamically characterize fully-irreversible processes on an equal footing with those at the opposite limit of detailed-balance. The work is meant to encourage development of inherent thermodynamic descriptions for rule-based systems and the living state, which are not conceived as reductive explanations to heat flows.