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Документ Analysis of efficiency of the bioinspired method for decoding algebraic convolutional codes(Технологический центр, 2019) Panchenko, Sergii; Prykhodko, Sergii; Kozelkov, Sergii; Shtompel, Mykola; Kosenko, Viktor; Shefer, Oleksandr; Dunaievska, О. I.It has been shown that convolutional codes are widely used, along with various decoding methods, to improve the reliability of information transmission in wireless telecommunication systems. The general principles of synthesis and the parameters and algebraic non-systematic convolutional codes with arbitrary coding rate and maximum achievable code distance have been shown. The basic stages of the bioinspired method for decoding algebraic convolutional codes using a random shift mechanism have been presented. It has been shown that the essence of the presented decoding method implies applying the procedure of differential evolution with the heuristically determined parameters. In addition, this method uses information about the reliability of the adopted symbols to find the most reliable basis for the generalized generator matrix. The mechanism of random shift for the modification of the accepted sequence is additionally applied for the bioinspired search based on various most reliable bases of a generalized generator matrix. The research results established that the bioinspired method for decoding algebraic convolutional codes ensures greater efficiency compared with the algebraic decoding method in the communication channel with additive white Gaussian noise. Depending on the parameters of the algebraic convolutional code and the necessary error coefficient, the energy gain from encoding ranges from 1.6 dB to 3 dB. It was shown that the presented bioinspired decoding method can be used for convolutional codes with a large code constraint length. In doing so, the presented method for decoding algebraic convolutional codes is less efficient than the Viterbi decoding method and turbo codes at a sufficient number of decoding iterations.Документ On eigenvalues of banded matrices(Інститут математики НАН України, 2019) Akhiiezer, O. B.; Dunaievska, О. I.In the paper, asymptotics for eigenvalues of Hermitian, compact operators, generated by infinite, banded matrices is obtained in terms of the asymptotics of their matrix entries. Analogues for banded matrices of Gershgorin’s disks theory are discussed.Документ Simulation of the formation of innovative engineering industry cluster(Publishing House "Education and Science", 2015) Akhiezer, Elena; Dunaievska, О. I.; Mekhovich, Sergey; Heliarovska, OksanaДокумент Probabilistic estimation of stability of solutions of optimization problems(Research and Scientific Group, Poland, 2018) Dunaievska, О. I.The issues of stability of solution of optimization problems are considered on the example of transportation problem of linear programming, in which the transportation costs are random variables with a known distribution density. The complexity of solving such optimization problems by classical methods is substantiated. It is proved that the problem of estimating stability admits an analytic solution if the optimal solution of the problem is sought using the matrix minimum method. This solution is based on the search for the probability that characterizes the level of stability of solving the optimization problem. The corresponding computational procedure is described. An example is considered that illustrates it graphically.Документ Use of triangular models of non-stationary processes in modeling variability of heart rhythm(Харківський національний університет радіоелектроніки, 2019) Akhiiezer, O. B.; Dunaievska, О. I.; Shyshkin, Mykhailo; Butova, Olha; Rohovyi, AntonThe subject matter is a mathematical model describing the process of heart rhythm variability, which is based on the use of triangular models of non-stationary random processes in the Hilbert space. The goal of the research is to develop a mathematical model of nonstationary processes of cardiac activity based on a triangular model. This research was the basis for the development of a Matlab model that implements the proposed method for analyzing heart rate variability. Tasks are: to give a description of the variability heart rate as a non-stationary process in Hilbert space in terms of correlation functions; to research the possibility of constructing a correlation and spectral theory of a non-stationary process using triangular models; to synthesize the mathematical model of nonstationary process on the basis of correlation theory for solving mathematical processing and forecasting tasks on the basis of ECG data. Using the proposed mathematical method, we implemented the Matlab model of a heart signal generator, which allowed us to synthesize an ECG with different variability parameters in noisy conditions. Methods of mathematical statistics, simulation modeling, theory of random processes and control theory are used in this work. Results of this research are as follows: 1) It has been shown that the new approach to the description of the HRV as a random process in the application of the triangular model in the Hilbert space made it possible to obtain expressions for the correlation function. 2) The imitation simulation showed the sensitivity of the method within the 5% error rate under the conditions of different types of influence on HRV. The qualitative assessment of the possibilities of the proposed models to generate artificial ECG provided the possibility of visual analysis by the cardiologist of the identity of the interpretation of real ECG records. The identities of modeling results were checked on time samples of electrocardiographs of 7 patients from open PhysioNet cardiographic libraries on samples with the duration T = 10 s. 3) The standard low-frequency oscillations and "white noise" barrier are clearly differentiated on the applied correlation function by the distribution of spectral density power within the frequency range of 0,15-0,3 Hz. Conclusion. The simulation results confirmed the correctness of the theoretical conclusions about the possibility of using models based on the representation of non-stationary processes in a triangular Hilbert space.Документ Machine learning methods application for solving the problem of biological data analysis(Національний технічний університет "Харківський політехнічний інститут", 2018) Akhiiezer, O. B.; Dunaievska, О. I.; Serdiuk, I. V.; Spivak, S. V.According to statistics, every fifth married couple is faced with the inability to conceive a child. Male germ cells are very vulnerable, and the growing number of cases of male infertility confirms that in today's world there are many factors that affect the activity of spermatozoa and their number. But the important thing is not so much their quantity, but quality. The spermogram is an objective method of laboratory diagnosis, which allows to accurately assess the man’s ability to fertilize by analyzing ejaculate for a number of key parameters. Only a spermogram can answer the question of a possible male infertility and the presence of urological diseases. When constructing spermograms, it is important to determine not only the number of good spermatozoa, but also their morphology and mobility. Therefore, research and improvement of some stages of spermogramm is the purpose of the study. This article addresses the problem of classification of spermatozoa in good and bad ones, taking into account their mobility and morphology, using methods of machine learning. In order to implement the first stage of machine learning (with a teacher) in the graphic editor, educational specimens (training sample) were created. The training was implemented by three methods: the method of support vector machine, the logistic regression and the method of K - the nearest neighbors. As a result of testing, the method K - the nearest neighbors is chosen. At the testing stage, a sample of 15 different spermatozoa was used in different variations of rotation around their axis. The test sample did not contain specimens from the training sample and was formed taking into account the morphological characteristics of the spermatozoa, but did not copy them from the training sample. At the final stage of study, the program's functioningwas tested on real data.