Vol 28, No 2 (2020)

The history of using machine learning algorithms to analyze statistical models is quite long. The development of computer technology has given these algorithms a new breath. Nowadays deep learning is mainstream and most popular area in machine learning. However, the authors believe that many researchers are trying to use deep learning methods beyond their applicability. This happens because of the widespread availability of software systems that implement deep learning algorithms, and the apparent simplicity of research. All this motivate the authors to compare deep learning algorithms and classical machine learning algorithms. The Large Hadron Collider experiment is chosen for this task, because the authors are familiar with this scientific field, and also because the experiment data is open source. The article compares various machine learning algorithms in relation to the problem of recognizing the decay reaction  τ^– →μ^– + μ^– + μ⁺ at the Large Hadron Collider. The authors use open source implementations of machine learning algorithms. We compare algorithms with each other based on calculated metrics. As a result of the research, we can conclude that all the considered machine learning methods are quite comparable with each other (taking into account the selected metrics), while different methods have different areas of applicability.

In the recent years thanks to the modern and sophisticated technologies the astronomers and astrophysicists were able to look deep into the Universe. This vast data poses some new problem to the cosmologists. One of the problems is to develop an adequate theory. Another one is to fit the theoretical results with the observational one. In this report within the scope of the isotropic and homogeneous Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological model we study the evolution of the Universe filled with dust or cosmological constant. The reason to consider this model is the present universe surprisingly homogeneous and isotropic in large scale. We also compare our results with the data from the SAI Supernovae Catalog. Since the observational data are given in terms of Hubble constant (????) and redshift (????) we rewrite the corresponding equations as a functions of ????. The task is to find the set of parameters for the mathematical model of an isotropic and homogeneous Universe that fits best with the astronomical data obtained from the study of supernovae: magnitude (????), redshift (????).

The article discusses the kinematic support, which allows reducing the horizontal dynamic effects on the building during earthquakes. The model of a seismic isolation support is considered from the point of view of classical mechanics, that is, we assume that the support is absolutely solid, oscillating in a vertical plane above a fixed horizontal solid plate. This approach allows a more adequate description of the interaction of the support with the soil and the base plate of the building. The paper describes the procedure for reducing the complete system of equations of motion of a massive rigid body on a fixed horizontal perfectly smooth plane to a form suitable for applying the finite difference method and its implementation in the Sage computer algebra system. The numerical calculations by the Euler method for grids with different number of elements are carried out and a mathematical model of the support as a perfectly rigid body in the Sage computer algebra system is implemented. The article presents the intermediate results of numerical experiments performed in Sage and gives a brief analysis (description) of the results.