Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics

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ISSN / EISSN : 1812-5409 / 2218-2055
Total articles ≅ 184
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I. Bieda
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics pp 57-62; https://doi.org/10.17721/1812-5409.2021/1.6

Abstract:
Millions of videos are uploaded each day to Youtube and similar platforms. One of the many issues that these services face is the extraction of useful metadata. There are a lot of tasks that arise with the processing of videos. For example, putting an ad is better in the middle of a video, and as an advertiser, one would probably prefer to show the ad in between scene cuts, where it would be less intrusive. Another example is when one would like to watch only through the most interesting or important pieces of video recording. In many cases, it is better to have an automatic scene cut detection approach instead of manually labeling thousands of videos. The scene change detection can help to analyze video-stream automatically: which characters appear in which scenes, how they interact and for how long, their relations and importance, and also to track many other issues. The potential solution can rely on different facts: objects appearance, contrast or intensity changed, other colorization, background chang, and also sound changes. In this work, we propose the method for effective scene change detection, which is based on thresholding, and also fade-in/fade-out scene analysis. It uses computer vision and image analysis approaches to identify the scene cuts. Experiments demonstrate the effectiveness of the proposed scene change detection approach.
E. V. Ivohin, P. R. Vavryk, N. V. Rudoman
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics pp 69-73; https://doi.org/10.17721/1812-5409.2021/1.8

Abstract:
In this paper we provided the definition of the Audience overlap network, as well as proposed a simple algorithm to compute overlap between two users on social media based on public data about their followers. There was proposed an alternative approach for computing overlaps based only on public data about users. This approach allows to include content overlap and activity patterns signals to be incorporated into more general statistical models featuring other covariates such as influencers’ direct engagement in shared conversations; relative influencer sizes and histories and links to similar third-party content to recover otherwise censored network structures and properties. For validate results there was designed a calibration process which utilizes Evolution Strategies algorithm to find a set of conditions which will make Audience overlap network built using similarity measures structurally equivalent to the Audience overlap network build on full information about followers.
T. V. Kolianova
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics pp 81-84; https://doi.org/10.17721/1812-5409.2021/1.10

Abstract:
The article considers the isolated population described by the logistic equation and studies the influence of management on the change of its number. Depending on the value of the control parameter, there are three different cases of behavior of an isolated population. In the first case, when the quota is equal to the corresponding value, depending on the initial value, the population either goes to a stationary value, or dies out. In the second case, when the quota does not exceed the established value, depending on the initial population size, the population either goes to the largest stationary point, or dies out. And in the third case, when the quota exceeds the established value, regardless of the initial population size, the population dies out. Stationary points for stability in all three cases are studied and graphs of population behavior depending on different initial conditions are presented.
, I. I. Lovytska
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics pp 11-19; https://doi.org/10.17721/1812-5409.2021/1.1

Abstract:
In the paper, we consider the problem of simulation of a strictly φ-sub-Gaussian generalized fractional Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are widely used in financial and actuarial mathematics, queueing theory etc. We study some specific class of processes of generalized fractional Brownian motion and derive conditions, under which the model based on a series representation approximates a strictly φ-sub-Gaussian generalized fractional Brownian motion with given reliability and accuracy in the space C([0; 1]) in the case, when φ(x) = (|x|^p)/p, |x| ≥ 1, p > 1. In order to obtain these results, we use some results from the theory of φ-sub-Gaussian random processes. Necessary simulation parameters are calculated and models of sample pathes of corresponding processes are constructed for various values of the Hurst parameter H and for given reliability and accuracy using the R programming environment.
A. G. Rudnitskii, M. A. Rudnytska, L. V. Tkachenko, E. D. Pechuk
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics pp 43-54; https://doi.org/10.17721/1812-5409.2021/1.5

Abstract:
Denoising is an important step in the early stage of signal preprocessing in optoacoustic applications. The efficiency of such modern noise removal methods as wavelet or curvlet filtering depends significantly on the numerical combinations and forms of wavelet transform parameters, and the multidimensional extension of such filters is rather non-trivial. These issues are serious obstacle for using of these highly effective filters in the tasks of optoacoustic reconstruction, especially in real laboratorial or medical practice. The objective of our study was to find the optimal filter, convenient for use in laboratorian and medical practice, when the types of noise are a priori unknown, and the filter settings should not take much time. In the offered work spatial filters which have only one parameter of adjustment - the size of a window are considered. Three-dimensional extensions of such well-established denoising techniques, as mean filter, median filter, their adaptive variants (Wiener spatial filter and modified median filter), as well as iterative truncated arithmetic mean filter were analyzed. The proposed filters were tested on a test set that contains versions of Shepp-Logan's three-dimensional phantom with mixtures of Gaussian and alpha-stable noise, as well as speckle noise. The identification of the best filter for simultaneous suppression of these types of interference was carried out using the theory of fuzzy sets. In our tests, a modified median filter and an iterative truncated arithmetic mean filter were rated as the best choice when the goal is to minimize aberrations when noise is not known a priory.
A. S. Dzhoha
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics pp 20-26; https://doi.org/10.17721/1812-5409.2021/1.2

Abstract:
Online learning under delayed feedback has been recently gaining increasing attention. Learning with delays is more natural in most practical applications since the feedback from the environment is not immediate. For example, the response to a drug in clinical trials could take a while. In this paper, we study the multi-armed bandit problem with Bernoulli distribution in the environment with delays by evaluating the Explore-First algorithm. We obtain the upper bounds of the algorithm, the theoretical results are applied to develop the software framework for conducting numerical experiments.
O. F. Kashpur
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics pp 74-80; https://doi.org/10.17721/1812-5409.2021/1.9

Abstract:
The solution of many applied problems is to find a solution of nonlinear equations systems in finite- dimensional Euclidean spaces. The problem of finding the solution of a nonlinear system is divided into two problems: 1. The existence of a solution of a nonlinear equations system; in the case of nonunique of the solution, it is necessary to find the number of these solutions and their surroundings. 2. Finding the solution of a system of nonlinear equations with a given accuracy. Many publications are devoted to solving problem 2, namely the construction of iterative methods, their convergence and estimates of the solution accuracy. In contrast to problem 2, for problem 1 there is no general algorithm for solving this task, there are no constructive conditions for the existence of a solution of a nonlinear equations system in Euclidean spaces. In this article, in finite-dimensional Euclidean spaces, the constructive conditions for the existence of a solution of nonlinear systems of polynomial form are found. The connection of these conditions with the linear polynomial interpolant of the minimum norm, generated by a scalar product with Gaussian measure and the conditions of its existence, is given.
V. R. Kulian, O. O. Yunkova
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics pp 85-88; https://doi.org/10.17721/1812-5409.2021/1.11

Abstract:
In article we consider a problem of optimal investment strategy by a commercial bank building. This task is actual and the development of a procedure to solve it can help in making investment banking decisions. The general formulation of the problem consists of two criteria. The first one is to maximize the expected return, and the second is to minimize the risk of the investment transaction. Mathematical formulation of the problem is considered as a problem of nonlinear programming under constraints. The procedure for solving such a two-criteria optimization problem allows to obtain many solutions, which requires further steps to make a single optimal solution. According to the algorithm proposed in the work, the problem is divided into two separate problems of single-criteria optimization. Each of these tasks allows to obtain the optimal values of the investment vector both in terms of its expected return and in terms of investment risk. Additional constraints in the mathematical formulation of the problem, make it possible to take into account factors that, from the point of view of the investor, may influence decision-making. The procedures presented in this work allow to obtain analytical representations of formulas that describe the optimal values of the investment distribution vector for both mathematical formulations of the problem.
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics pp 89-101; https://doi.org/10.17721/1812-5409.2021/1.12

Abstract:
The article presents an analysis of the educational and professional program "Informatics" of the first (bachelor's) level of higher education in the sphere of knowledge 12 "Information Technology", specialty 122 "Computer Science", implemented at the Faculty of Computer Science and Cybernetics, Taras National University of Kyiv Shevchenko with educational and professional programs of the same level and specialty of other institutions of higher education of Ukraine in terms of program results. During the analysis, they were compared with the approved standard of the first (bachelor's) level of higher education in the specialty 122 "Computer Science". In order to analyze the authors developed a database of educational programs. The ratio of program results in different programs by common specialty is analyzed.
E. V. Іvоhіn, M. F. Makhno, V. O. Shklyar
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics pp 63-68; https://doi.org/10.17721/1812-5409.2021/1.7

Abstract:
The article proposes an algorithm for solving the problem of optimal distribution of the capacity of data transmission channels between providers and Internet users. A mathematical model of the problem of distribution of a limited homogeneous resource with transport-type constraints is formulated. A solution method based on Orlin's stream algorithm is considered. A practical application of the algorithm for solving a real distribution problem is proposed. The results of the capacity of the channels of the computer network are obtained with a perspective increase in the capacity of the connections represented by the intervals of the planned changes. An analysis of the solutions obtained with different number of switching servers was made, conclusions about the choice of the provider to meet the optimal information needs of users were made.
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