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https://www.selleckchem.com/products/byl719.html Stochastic separation theorems play important roles in high-dimensional data analysis and machine learning. It turns out that in high dimensional space, any point of a random set of points can be separated from other points by a hyperplane with high probability, even if the number of points is exponential in terms of dimensions. This and similar facts can be used for constructing correctors for artificial intelligent systems, for determining the intrinsic dimensionality of data and for explaining various natural intelligence phenomena. In this paper, we refine the estimations for the number of points and for the probability in stochastic separation theorems, thereby strengthening some results obtained earlier. We propose the boundaries for linear and Fisher separability, when the points are drawn randomly, independently and uniformly from a d-dimensional spherical layer and from the cube. These results allow us to better outline the applicability limits of the stochastic separation theorems in applications.In the present paper, we study a diauxic growth that can be generated by a class of model at the mesoscopic scale. Although the diauxic growth can be related to the macroscopic scale, similarly to the logistic scale, one may ask whether models on mesoscopic or microscopic scales may lead to such a behavior. The present paper is the first step towards the developing of the mesoscopic models that lead to a diauxic growth at the macroscopic scale. We propose various nonlinear mesoscopic models conservative or not that lead directly to some diauxic growths.In quantum computation, what contributes supremacy of quantum computation? One of the candidates is known to be a quantum coherence because it is a resource used in the various quantum algorithms. We reveal that quantum coherence contributes to the training of variational quantum perceptron proposed by Y. Du et al., arXiv1809.06056 (2018). In detail, we show that in t

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