From the Managing Editors

E. D. Konstantinova, A. P. Sergeev

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DATA VISUALIZATION METHODS IN BIOMEDICAL RESEARCH

S. Y. Ogorodnikova, E. D. Konstantinova

The article presents the results of applying multidimensional data visualization methods to solving an applied problem from the field of medicine. We used retrospective data of 586 patients with bladder cancer who underwent radical cystectomy from December 2001 to May 2021 in the urological oncology department of the Sverdlovsk Regional Oncology Center. Such approaches as survival curves (according to the Kaplan – Meier method), heat maps and classification trees are implemented as methods for visualizing multidimensional data. The Statistica for Windows 10 version and MatLAB2021b packages were used for data analysis. On the basis of three approaches, the possibility of identifying relationships between numerical data based on a visual analysis of the resulting set of graphic images is shown.
Examples of constructing visual, intuitive decision rules for each of the methods in solving the problem of assessing the 5- and 10-year survival of Sverdlovsk Regional Oncology Center patients who underwent radical cystectomy with three different methods of uroderivation are demonstrated. The features, advantages and disadvantages of each of the approaches in relation to working with data in biomedical research are considered. It is shown that the methods of visualization of multidimensional data and approaches based on them are promising for the analysis and visual presentation of experimental numerical results from the field of medicine.

LINEAR AND NONLINEAR REGRESSION IN BIOLOGY AND MEDICINE: A MOVING AVERAGE APPROACH

A. N. Varaksin, Yu. V. Shalaumova, T. A. Maslakova

Testing of assumptions of linear and non-linear (logistic) regressions are discussed in this method paper. We propose a moving average approach as one of the methods for checking the linearity of the relationship between predictor X and response Y in linear regression and the linearity of the relationship between predictor X and the logit of response Y in logistic regression. Specific examples show the advantages of a moving average over the common data stratification approach. The importance of graphical representation of moving average results in linear and (especially) logistic regression is emphasized.

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DEVELOPMENT OF A METHOD FOR CONTROLLING AN ACTIVE EXOSKELETON FOR THE REHABILITATION OF MOTOR ACTIVITY OF THE HUMAN UPPER LIMBS

V. M. Antipov, A. A. Badarin, A. V. Andreev, V. V. Grubov, E. N. Pitsik, S. A. Lobov, V. A. Maksimenko, V. B. Kazantsev, A. E. Hramov

We present the results of the development of methods for controlling an active exoskeleton for the rehabilitation of motor activity of the human upper limbs. We describe an experimental setup, a software implementation of a real-time control system, and a developed
software environment for stimulating a subject during a neurophysiological experiment. The object of study of the described system is the processes of activation of human brain regions from the point of view of the analysis of recorded bioelectrical electroencephalographic
signals during motor activity, suitable for use in the tasks of rehabilitation of motor activity. The purpose of the work is to develop the software and hardware part of the experiment to study real-time algorithms for controlling the exoskeleton of the upper limbs for rehabilitation and training tasks using brain-computer interfaces.

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DETECTION OF THE BEGINNING OF THE IMAGINARY MOVEMENT

V. S. Khorev, N. V. Smirnov, S. A. Kurkin, A. P. Sergeev, S. Y. Gordleeva, A. E. Hramov

This work is devoted to the development of a method for determining the moment of the beginning of the imaginary motion act by recording electroencephalogram signals from the data obtained in the course of an experimental study of the imaginary motion acts. In the course of the experiment, electrical signals of the brain activity were recorded. The signals that were pre-processed and filtered then were used to test the method of determining the beginning of movement. To demonstrate the operation of the method, the dependences of the averaged power in the alpha-band and the topograms were plotted. The resulting algorithms were used to detect and identify the patterns of neural activity that emerge during imagery movements, as well as their features, in comparison with real motor activity and observation of movements.

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VERTICAL DISTRIBUTION OF DUST CHARACTERISTICS OF THE ATMOSPHERIC SURFACE LAYER IN EKATERINBURG

I. E. Subbotina, M. S. Remezova, A. G. Buevich, A. P. Sergeev, E. M. Baglaeva, A. V. Shichkin, A. S. Butorova, M. V. Sergeeva

Pollution of the surface layer of the atmosphere with particulate matter in urban areas is a danger to public health. Air quality information is the basis for health policy making. The paper investigates the vertical distribution of the concentration of dust particles, their elemental and dispersion composition in the surface layer of atmospheric air in Yekaterinburg at a height of 0,5 m to 10 m during 8 days of April 2021. The mass concentration of dust is represented by heterogeneous data with a variation coefficient of more than 30 %, it has a weak tendency to decrease with height. In quantitative terms, dust particles PM2.5 make up about 45 % of the total number of particles. X-ray fluorescence analysis revealed 12 elements contained in dust particles, the most significant content being sulfur, calcium and ferrum. The proportion of the most metals and calcium in particulate matter decreases with height, while the content of sulfur and arsenicum increases. The content of cuprum, zincum and stibium in particulate matter is constant at all measured heights.

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COMPARATIVE ANALYSIS OF DATA SPLITTING ALGORITHMS FOR TRAINING ARTIFICIAL NEURAL NETWORKS IN MODELING THE SPATIAL DISTRIBUTION OF HEAVY METALS IN THE TOPSOIL

E. M. Baglaeva, A. P. Sergeev, A. V. Shichkin, A. G. Buevich, I. E. Subbotina, A. S. Butorova

A comparison of five algorithms for selecting a training subset for artificial neural networks to interpolate the spatial distribution of a feature according to environmental components screenings is presented. The initial data were the contents of chromium in the
topsoil in the residential areas of the city of Noyabrsk (YNAO, Russia). The spatial distributions of the element content in the topsoil were interpolated by a multilayer perceptron (MLP). Root mean squared error (RMSE) statistics were calculated as accuracy metrics for each
algorithm. A smaller error is shown by the Space&quartile quote algorithm based on the spatial-probabilistic quoting of the initial data. Taking into account the information about the error statistics of the algorithms for splitting the original set, it is possible to improve the
accuracy of the artificial neural network model in solving environmental problems.

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JOINT ACTION OF BINARY FACTORS AND RISKS’ EQUALITY

J. V. Nagrebeskaya, A. I. Fatkullina

In this paper we study the models of interaction of two and three independent binary factors in the case of binary response, which are widely used in medical and biological sciences. The main attention is paid to the formalization of the concept of “interaction” and
its connection with the risks’ difference equality. It is shown that this equality can be obtained from equating all interaction terms to zero in their representation used in the analysis of variance. The system of risks’ differences equations for two and three factors is obtained
and solved, and its invariance with respect to the action of a symmetry group of experiment is shown. The interpretation of the solution for the system of risks’ differences equations is presented: in the case of two factors the effect of their impact is equal to the sum of effects
of isolated action of each factor separately; in the case of three factors (a) the effect of all these factors is equal to the sum of effects of isolated action of each factor separately; (b) the effect of any two factors is equal to the sum of effects of isolated action of each factor
separately in the absence of the third one. In addition, a study of the solution of equality of risks for two and three factors within the framework of the deterministic model, leading to a Boolean formalization of this model, was carried out. It is proved that for the values of the Boolean function representing a given response, the system of risks’ differences equations for both two and three factors is satisfied if and only if this Boolean function significantly depends on no more than one variable.
It is shown that within the framework of the deterministic model, the concept of “joint action” of binary factors, introduced and studied in the works of the first author, more accurately describes the interaction of these factors than violation of risks’ differences equations.

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ANALYSIS OF DISCRETE DATA. BASIC NOTIONS

V. G. Panov

The review article is devoted to methods of discrete data analysis. The main attention is paid to exact methods based on the representation of discrete probability distributions as power series distributions. The examples presented in the article relate to medicine and biology.

Environmental issues – a systemic approach (from Archives of IIE UB RAS)

V. N. Chukanov