A method for solving a boundary-value problem of penetration of plane monochromatic electromagnetic fields through the plane screen made of permalloy is developed. Setting the boundary-value problem is based on the use of differential Maxwell equations and complementary nonlinear differential equation for the field of magnetization, characterizing permalloy. The classical boundary conditions of continuity of the tangential components of the fields and complementary boundary conditions for the field of magnetization on the front surfaces of the screen are used. To simplify the solution of the boundary-value problem as a result of exclusion of the values of the second infinitesimal order, included in nonlinear equation, the nonlinear task is transformed into linear one. The roots (wave numbers) of dispersion algebraic equation of a fourth-order, characterizing the electromagnetic fields in the layer made of permalloy, are constructed. A complete system of four forward and four backward counter-propagating electromagnetic waves in the permalloy layer is formed. The two-sided boundary conditions connecting electromagnetic fields on both sides of the screen are obtained. An analytical solution of the boundary-value problem with two-sided boundary conditions is performed. The amplitudes of reflected and transmitted through the screen electromagnetic fields are analytically calculated.

The definition of rating is given and mathematical model of finding the values of object quantity by means of rating is specified. With the help of the rating it is possible to consider both objective and subjective measurements from a single point of view. If, as example, some sequence of objects is sorted by a varying uniformly magnitude an object number in the sequence could be considered as the rating.

The axiomatic definition of the rating is based on a mathematical model of measurement. The formalization of the process of measuring an arbitrary value begins with a clarification of the concept of measurement. During the measurement, the sizes of objects are compared, the matrix of paired comparisons is axiomatically determined, on the basis of this matrix the rating is located. Knowing the rating you can find the value. Then by means of a rating the laws of Fechner and Stevens are analyzed. The equivalence of Fechner and Stevens laws is a confirmation of the algorithm for determining the values of the measured value based on the rating.

The subjective method of finding the rating requires a special method of checking the reliability of the information received. Verification of the reliability of the subjective measurement is proposed to perform the method of alternatives. In the alternatives method, each object is compared twice, and different objects are selected as the object for comparison. The criterion of reliability of subjective measurement is the statistical coincidence of rating values obtained by alternative methods of comparison.

Considered problem of model based verification of control systems is the checking whether the system behavior satisfies the requirements fixed in the design specification The testing includes the experiments consisting in simulation of investigated system to see input-output correspondence to the model. The test sequence is generated on the basis of the model that describes the desired behavior of the system. The method to construct a test sequence for verification of hardware (or software) implementation of a control system with behavior parallelism is suggested that is based on traversal of the graph of the states that are reachable in system functioning. A method for constructing the set of reachable global states for a parallel algorithm of the control system behavior and a method to obtain the test sets are described. The description of the system functioning, which is given by the design specification, is assumed to be correct. The hardware (or software) implementation that must conform to this specification is to be verified.

A synthesis of logical circuits, comprising functional combination blocks of very large scale integration circuits, is one of the most important tasks of computer-aided design. As the data size of design tasks increases, the execution time of synthesis of logic circuits also increases. The global technological independent optimization as the first stage of synthesis of logical circuit is especially labor-consuming. The second stage is technological mapping of optimized logical representations of functions to the logical elements of technological library. The main features of logical circuit, such as area, performance, power consumption, depend on the efficiency of the first stage – global logical optimization. The evolution of methods of global logical optimization has revealed the efficiency of Shannon expansion in case of optimization of multi-level representations of the systems of fully defined Boolean function. A number of methods and programs were developed using graphical representations of Shannon expansions – BDD representations. Most of the developed methods of optimization of BDD-representations use the initial representations of functions systems in the form of disjunctive normal form (DNF).

In the article an algorithm of minimization of nodes number of Boolean net, which is a multi-level representation of the system of fully defined Boolean function, is proposed. Minimization is based on Shannon expansion and a search of equal (with accuracy up to inversion) nodes in Boolean net. Such algorithm of logical optimization was implemented as application. The experiments have shown that this algorithm and the application is reasonable to use in cases when the initial multi-level representation of functions is impossible to define as DNF system, or when DNF system contains a large number of elementary conjunctions.

When measuring low-power optical signals, the receiving modules of systems should ensure a sufficiently high accuracy of the received data. In this regard, it is advisable to use photon counters. They are highly sensitive, but are characterized by data recording errors. The aim of this work is to determine the influence of average pulse count rate of photons as the output of the counter on the fidelity of received information taking into account also the dead time of the counter. The formula is obtained for calculating the reliability of data received over an asynchronous binary asymmetric homogeneous communication channel without memory with erasure, when photon counter with a dead time of prolonging type was used as a receiving module. According to the results of mathematical modeling, it was established that with an increase in the average count rate of signal pulses at the output of the photon counter in symbols 1 (n_s1), the reliability of the received data D grows up to saturation. Moreover, when other parameters being equal, with an increase of the average duration of the dead time of a prolonged type (τ_d), the saturation of the D(n_s1) dependence is fixed for large values of the average counting rate of signal pulses. For example, with n_s1 ≥ 35,0×104 s ^–1 for τd = 0; with n_s1 ≥ 38,9×104 s ^–1 for τd = 5 µs; with n_s1 ≥ 43,7×104 s ^–1 for τd = 10 µs; with n_s1 ≥ 50,0×104 s ^–1 for τd = 15 µs.

Physical cryptography is one of the current trends among the existing methods of protecting digital devices from illegal access. Circuit design solutions in physical cryptography are called digital physically unclonable functions (PUFs), which to be implemented ensure the uniqueness, non-reproducibility (non-cloning) of the protected digital device. In addition, PUFs should be efficient as hardware resources. The existing implementations of the arbiter PUF are based on the synthesis of configurable symmetric paths, when each link is a pair of two-input multiplexers providing two configurations of test signal translation: direct and cross. In order to build a single link on FPGA, it is necessary to use two built-in LUT-blocks, providing the implementation of two multiplexers, meanwhile the hardware resources of LUT-blocks are not fully utilized. The article presents a new architecture of symmetric paths of the arbiter PUF, allowing efficient use of hardware resources of LUT-blocks for various FPGA families.

Coding and non-coding nucleotide sequences of the human reference genome have been investigated. Seven models of vectorization of nucleotide sequences based on mono-, bi-, trigram nucleotide frequencies, parameters of the category-position-frequency model, the lengths of sequences, nucleotide correlation factors, statistical features of coding and non-coding regions of DNA molecules were developed. The most informative features of vectorization models were determined using feature selection and classification algorithms based on the random forests and support vector machine methods. The difference between coding and non-coding fragments of nucleotide sequences was established. An error of the coding and non-coding sequences classification using the random forests method on a set of the 23 most informative features is 2,93 %.

Two periods of scientific activity of Professor Alexander Alexandrovich Petrovsky, who was a member of the editorial board of the journal "Informatics" for 15 years (2004–2019), are presented. The main scientific results, his contribution to the development of the theory and to the hardware and software of the problem-oriented real-time systems and the processing of audio, speech and graphic information are shown, a list of the most significant works of the scientist is given.

The methods of geometric informative features selection of nuclei on fluorescent images of cancer cells are considered. During the survey, a review of existing geometric features was carried out, including both the signs of rotation resisted shape and displacement of the image, as well as signs of location in space. For the selection of characteristics, the methods were used: median, correlation with calculation of the Pearson correlation coefficient, correlation with calculation of the Spearman correlation coefficient, logistic regression model, random forest with CART trees and Gini criterion, random forest with CART trees and error minimization criterion. As a result of the investigation 11 characteristics were selected from 59 features, the quality of classification and time costs were calculated depending on the number of features for describing the objects. The use of 11 features is sufficient for the accuracy of classification as it allows to reduce time costs in 2,3 times.

The paper addresses the problem of segmentation of malignant tumors in large whole-slide histology images in the context of computer-assisted diagnosis of breast cancer. The method presented in this study is based on image classification procedure of norm/tumor type. The procedure calculates probability of belonging of each particular elementary image region of 256×256 pixels to the "tumor" class, which are isolated by corresponding sliding-window technique. The procedure capitalizes on convolutional neural networks and Deep Learning methods. The neural networks being employed were trained on a representative dataset of 600 000 fragments sampled from whole slide images and representing the morphological and colorimetric variability of two classes. The resultant probability maps were post-processed using conventional image processing algorithms to obtain the final binary masks of pathological regions. The proposed algorithm of segmentation of whole slide histological images can be used in computerized diagnosis of cancer for detection and segmentation of malignant tumors.

The methodical and hardware-software on the basis of processing and analysis of speech signals for operative and objective diagnostics of neurological pathologies accompanied by speech function disorders are offered. The testing of developed methodological and software tools was carried out on the basis of the Republican Scientific and Practical Center of Neurology and Neurosurgery of the Ministry of Healthcare of Belarus and the Belarusian State University of Informatics and Radioelectronics. The results of testing revealed qualitative (based on the obtained spectrogram, kepstrogram, histogram) and quantitative (based on calculated parameters) differences between the parameters of speech signals in normal and bulbar syndrome. Preliminary results of the research confirmed the feasibility of using the methodological and hardware-software for registration and processing speech signals for diagnosis of neurological diseases.