Search

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 + + + 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 this paper, we propose an approach to solving the problem of recognizing skin lesions, namely melanoma, based on the analysis of dermoscopic images using deep learning methods. For this purpose, the architecture of a deep convolutional neural network was developed, which was applied to the processing of dermoscopic images of various skin lesions contained in the HAM10000 data set. The data under study were preprocessed to eliminate noise, contamination, and change the size and format of images. In addition, since the disease classes are unbalanced, a number of transformations were performed to balance them. The data obtained in this way were divided into two classes: Melanoma and Benign. Computer experiments using the built deep neural network based on the data obtained in this way have shown that the proposed approach provides 94% accuracy on the test sample, which exceeds similar results obtained by other algorithms.

Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer algebra system. In this case, the extensibility of the system should be taken into account. In this paper, we consider a technology for extending the SymPy computer algebra system with a low-level module that implements a random number generator., Comment: in English; in Russian

The paper investigates the problem of recognizing human emotions by voice using deep learning methods. Deep convolutional neural networks and recurrent neural networks with bidirectional LSTM memory cell were used as models of deep neural networks. On their basis, an ensemble of neural networks is proposed. We carried out computer experiments on using the constructed neural networks and popular machine learning algorithms for recognizing emotions in human speech contained in the RAVDESS audio record database. The computational results showed a higher efficiency of neural network models compared to machine learning algorithms. Accuracy estimates for individual emotions obtained using neural networks were 80%. The directions of further research in the field of recognition of human emotions are proposed.

This paper examines the problem of detecting skin malignancies, in particular, melanoma, from the analysis of dermoscopic images using deep learning methods. For this purpose, a deep convolutional neural network architecture was developed, which was used to process dermoscopic images of various skin lesions contained in the HAM10000 data set. The studied images were previously cleared of noise and other contaminants for processing by neural networks. In addition, since the disease classes are unbalanced, a number of transformations have been made to balance them. At the first stage, the images were divided into two classes: melanoma and benign tumor. At the second stage, all images of skin injuries were grouped into seven classes. Computer experiments on the use of the constructed deep neural network on the data obtained in this way have shown that the proposed approach provides 91%.

Self-oscillating modes in control systems of computer networks quite negatively affect the characteristics of these networks so the investigation of parameters of self-oscillations as well as self-oscillations areas is actual. But due to the non-linear nature of usually constructed mathematical models the study of self-oscillations areas and parameters are extremely labor-intensive. It is of interest to obtain a so-called parametric portrait describing the zones of occurrence of self-oscillations depending on the value of the parameters: one parameter (two-dimensional graph), two parameters (three-dimensional graph), and so on. Such a parametric portrait allows us to purposefully manage the characteristics of the investigated control system. The paper describes a parametric study technique based on the method of harmonic linearization because in the standard mathematical model based on ordinary linearization by Taylor expansion a self-oscillation regime disappears (due to Taylor expansion linearization). To verify the theoretical results obtained, simulation is used. In addition, it is proposed to use the computer algebra system for analytical calculations. For this, the criteria for choosing software were formulated. Based on these criteria, a set of software for analytical and numerical calculations was proposed.

To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number of simple stereotyped operations, which are adequately supported by computer algebra systems. In this paper, we distinguish between two stages of working with a mathematical model: model development and model usage. Each of these stages implies its own computer algebra system. As a model problem, we consider the problem of geometrization of Maxwell's equations. Two computer algebra systems---Cadabra and FORM---are selected for use at different stages of investigation., in Russian; in English

Background. Spinors are more special objects than tensors. Therefore spinors possess more properties than the more generic objects such as tensors. The group of Lorentz two-spinors is the covering group of the Lorentz group. Purpose. Since the Lorentz group is the symmetry group of Maxwell equations, it is reasonable to use Lorentz two-spinors and not tensors when writing the Maxwell equations. Method. We write the Maxwell equations using Lorentz two-spinors. Also a convenient representation of Lorentz two-spinors in terms of the Riemann-Silberstein complex vectors is used. Results. In the spinor formalism (in the representation of the Lorentz spinors and Riemann-Silberstein vectors) we have constructed the Hamiltonian of Maxwellian optics. With the use of spinors, the Maxwell equations take a form similar to the Dirac equation. Conclusions. For Maxwell equations in the Dirac-like form we can expand research methods by means of quantum field theory. In this form, the connection between the Hamiltonians of geometric, beam and Maxwellian optics is clearly visible.

SymPy computer algebra library is used for automatic generation of ordinary and stochastic systems of differential equations from the schemes of kinetic interaction. Schemes of this type are used not only in chemical kinetics but also in biological, ecological and technical models. This paper describes the automatic generation algorithm with an emphasis on application details.

Background. This paper study statistical data gathered from wind turbines located on the territory of the Republic of Poland. The research is aimed to construct the stochastic model that predicts the change of wind speed with time. Purpose. The purpose of this work is to find the optimal distribution for the approximation of available statistical data on wind speed. Methods. We consider four distributions of a random variable: Log-Normal, Weibull, Gamma and Beta. In order to evaluate the parameters of distributions we use method of maximum likelihood. To assess the the results of approximation we use a quantile-quantile plot. Results. All the considered distributions properly approximate the available data. The Weibull distribution shows the best results for the extreme values of the wind speed. Conclusions. The results of the analysis are consistent with the common practice of using the Weibull distribution for wind speed modeling. In the future we plan to compare the results obtained with a much larger data set as well as to build a stochastic model of the evolution of the wind speed depending on time., in English; in Russian