The main result of this paper is a proof using real analysis of the monotonicity of the topological entropy for the family of quadratic maps, sometimes called Milnor's Monotonicity Conjecture. In contrast, the existing proofs rely in one way or another on complex analysis. Our proof is based on tools and algorithms previously developed by the authors and collaborators to compute the topological entropy of multimodal maps. Specifically, we use the number of transverse intersections of the map iterations with the so-called critical line. The approach is technically simple and geometrical. The same approach is also used to briefly revisit the superstable cycles of the quadratic maps, since both topics are closely related.Recent progress on skeleton-based action recognition has been substantial, benefiting mostly from the explosive development of Graph Convolutional Networks (GCN). However, prevailing GCN-based methods may not effectively capture the global co-occurrence features among joints and the local spatial structure features composed of adjacent bones. https://www.selleckchem.com/products/sw033291.html They also ignore the effect of channels unrelated to action recognition on model performance. Accordingly, to address these issues, we propose a Global Co-occurrence feature and Local Spatial feature learning model (GCLS) consisting of two branches. The first branch, based on the Vertex Attention Mechanism branch (VAM-branch), captures the global co-occurrence feature of actions effectively; the second, based on the Cross-kernel Feature Fusion branch (CFF-branch), extracts local spatial structure features composed of adjacent bones and restrains the channels unrelated to action recognition. Extensive experiments on two large-scale datasets, NTU-RGB+D and Kinetics, demonstrate that GCLS achieves the best performance when compared to the mainstream approaches.In this paper, a deep learning (DL)-based predictive analysis is proposed to analyze the security of a non-deterministic random number generator (NRNG) using white chaos. In particular, the temporal pattern attention (TPA)-based DL model is employed to learn and analyze the data from both stages of the NRNG the output data of a chaotic external-cavity semiconductor laser (ECL) and the final output data of the NRNG. For the ECL stage, the results show that the model successfully detects inherent correlations caused by the time-delay signature. After optical heterodyning of two chaotic ECLs and minimal post-processing are introduced, the model detects no patterns among corresponding data. It demonstrates that the NRNG has the strong resistance against the predictive model. Prior to these works, the powerful predictive capability of the model is investigated and demonstrated by applying it to a random number generator (RNG) using linear congruential algorithm. Our research shows that the DL-based predictive model is expected to provide an efficient supplement for evaluating the security and quality of RNGs.The hypothesis of an increase in free energy (exergy) by ecosystems during evolution is tested on direct measurements. As a measuring system of thermodynamic parameters (exergy, information, entropy), a series of measurements of reflected solar radiation in bands of Landsat multispectral imagery for 20 years is used. The thermodynamic parameters are compared for different types of ecosystems depending on the influx of solar radiation, weather conditions and the composition of communities. It is shown that maximization of free energy occurs only in a succession series (time scale of several hundred years), and on a short evolutionary time scale of several thousand years, various strategies of energy use are successfully implemented at the same time forests always maximize exergy and, accordingly, transpiration, meadows-disequilibrium and biological productivity in summer, and swamps, due to a prompt response to changes in temperature and moisture, maintaining disequilibrium and productivity throughout the year. On the basis of the obtained regularities, we conclude that on an evolutionary time scale, the thermodynamic system changes in the direction of increasing biological productivity and saving moisture, which contradicts the hypothesis of maximizing free energy in the course of evolution.With their constantly increasing peak performance and memory capacity, modern supercomputers offer new perspectives on numerical studies of open many-body quantum systems. These systems are often modeled by using Markovian quantum master equations describing the evolution of the system density operators. In this paper, we address master equations of the Lindblad form, which are a popular theoretical tools in quantum optics, cavity quantum electrodynamics, and optomechanics. By using the generalized Gell-Mann matrices as a basis, any Lindblad equation can be transformed into a system of ordinary differential equations with real coefficients. Recently, we presented an implementation of the transformation with the computational complexity, scaling as O(N5logN) for dense Lindbaldians and O(N3logN) for sparse ones. However, infeasible memory costs remains a serious obstacle on the way to large models. Here, we present a parallel cluster-based implementation of the algorithm and demonstrate that it allows us to integrate a sparse Lindbladian model of the dimension N=2000 and a dense random Lindbladian model of the dimension N=200 by using 25 nodes with 64 GB RAM per node.In this paper, data-transmission using the nonlinear Fourier transform for jointly modulated discrete and continuous spectra is investigated. A recent method for purely discrete eigenvalue removal at the detector is extended to signals with additional continuous spectral support. At first, the eigenvalues are sequentially detected and removed from the jointly modulated received signal. After each successful removal, the time-support of the resulting signal for the next iteration can be narrowed, until all eigenvalues are removed. The resulting truncated signal, ideally containing only continuous spectral components, is then recovered by a standard NFT algorithm. Numerical simulations without a fiber channel show that, for jointly modulated discrete and continuous spectra, the mean-squared error between transmitted and received eigenvalues can be reduced using the eigenvalue removal approach, when compared to state-of-the-art detection methods. Additionally, the computational complexity for detection of both spectral components can be decreased when, by the choice of the modulated eigenvalues, the time-support after each removal step can be reduced.