ABSTRACT. This paper proposes the concept of building a decentralized identification system that allows each participant to perform the role of both an identity object and an identity provider, regardless of their technical and legal capabilities. The main parameter of significance in the system is the level of trust toward the subject by the other participants of the platform and external IDs information consumers. This maintains the ability to fully manage the account and associated PII for their owner through the use of a cryptographic signature mechanism: changes to key data, PII and identifiers can be made at any time. The proposed system does not change the existing model of trust for large providers of identification services, but it allows to increase the objectivity of information about identifiers and PII of their owners by the possibility of verification of a separate identifier to each of the participants of the platform, followed by recording the results of verification in the chain of blocks. The use of blockchain technology and a consensus-reaching mechanism make it possible to synchronize the sequence of events in the system. The described global digital identity system positions itself as a source of information about global entities of specific subjects, and related personal data sets and established identifiers, while allowing the end-user of information to make independent conclusions about the level of trust of these identifiers based on related transactions. The system described is compatible with the digital asset management infrastructure and current identification tools. Thus, the system accomplishes a number of important tasks: reducing the threshold for using digital identifiers, allowing their ubiquitous use; the ability to verify the identifier and prove its compliance without the need to build a trusted infrastructure (only cryptography and other participants` votes); reducing the likelihood of certificate substitution attacks; increase the objectivity of information about the identifiers used.

ABSTRACT. After S. Smale's works it became clear that in smooth dynamics the system of a general form is not structurally stable and therefore there is no strict mathematical basis for modeling and computational analysis of systems. The contradiction appeared in science: according to physicists dynamics is simple and universal. The solution to this problem was proposed based on the construction of dynamic quantum models (DQM). From the assumption that quantum effects are caused by unrecoverable “white noise”, a certain mathematical model of quantum mechanics already follows and is essentially unambiguous. On the other hand, in this model spectral problems are reduced to the usual perturbation theory of smooth dynamical systems. Thus, the construction of such models can be considered as an asymptotic method for solving spectral problems. But the definition of DQM is not formally related to Hamiltonian systems. DQM is defined and constructed universally for both Hamiltonian systems and systems with the truth function. As a result, for example, quantization with the Bohr-Sommerfeld condition also extends to systems with a truth function. Hopefully DQM opens for new applications. The most important is to seek assistance and cooperation in future research.

ABSTRACT. The paper is devoted to the problem specifying causality relationships in distributed (including cyber-physical) systems. This problem is studied based on the coalgebraic approach used authors for studying safety constraints for distributed systems. The special class of coalgebras, counter-based detectors, is introduced and studied in the paper. It is shown that this approach allows using the technique of Diophantine equations for specifying clock constraints of the system being studied. The advantage of the approach is the possibility for defining the complexity of detectors that provides to control respond time of the detectors in the system.

ABSTRACT. In the article the platform for modeling of algebraic behavior is considered. It is intent for formalization of the systems, especially distributed, their modelling and analysis of the properties. Platform is used for the formal verification, model-based testing and security issues detection. Behavior algebra specifications are used as the modeling language. The number of projects is considered in the paper implemented on platform in cybersecurity, blockchain solutions and legal requirements processing.

ABSTRACT. According to the National transport strategy of Ukraine for the period up to 2030, one of the tasks is to ensure consistent and coherent development of regional airports of Ukraine and consequent development of Ukrainian air transportation network. One of the ways to achieve this is to deploy a remote tower concept in small regional airports of Ukraine. The main change intro-duced by the remote tower concept compared to the conventional air traffic service (ATS) provided from a local tower is that the aerodrome control tower will be provided from a remote location and air traffic control and aerodrome flight information service officers (ATCO/AFISO) do not have to be physically present at the airport. Provision of remote ATS requires a continuous exchange of information between the infrastructure at airport side and a Remote Tower Module (RTM) to ensure that the data received by ATCO/AFISO can be used to provide safe and orderly control of traffic. Due to the amount of video and audio data that has to be exchanged between an RTM and the local airport site in addition to other required data such as data from surveillance sensors, meteorological sensors, etc., the requirements for the network connection are very high. One of the factors that have a high impact on network performance is latency. The aim of this article is to investigate an application of a method of gradient descent to reduce the network latency or data transmission delay by minimizing the distance between airport sites and remote tower centres to facilitate selection of an optimal location for them.

ABSTRACT. Prototypes of modern city information systems (IS) must meet most closely prin-ciples formulated on the World Summit on the Information Society (WSIS) [1] and ensure effective information-technology support of processes running in re-source and socio-communicational networks in a smart city with large population. It is necessary for this purpose to develop information-technology platforms with implemented procedures of analytical processing of certain city data collections. Particularly such information-technology platform should give possibility to de-velop and utilize effective tools for analytical data processing implementation. Many of such tools and means are based on the open analytical information-technologies platforms that provide their services both on commercial and free principles. There are a lot of cases for IT projects regarding smart cities where decisions on the base of rented analytic means from well-known and widely ac-cessible information-technology platforms are seems to be well grounded. It al-lows, in own turn, for the city to save a budget on acquiring of on-premises com-puting resources, with simultaneous decreasing of general financial expenses as payments only for hosting of consumed resources and services. As a conse-quence, the choice of a fully functional efficient, affordable and easy to use ana-lytical information-technology platform is one of the urgent tasks of scientific re-searches and modern innovation information technology developments.

ABSTRACT. Cyber attacks on critical infrastructure's objects can have dire consequences, as our entire lives depend on the working capacity of such systems. In Ukraine, cybercrime provides for criminal and civil liability under the Criminal and Civil Codes of Ukraine, and under the Law of Ukraine “On the Fundamental Principles of Cyber Security in Ukraine”. A successfully implemented decision-making support system that can provide a conclusion of legal responsibility in the cybersecurity domain, namely, propose sanctions recommended in the case of an offence or multiple offences, can significantly improve the productivity of the Ukrainian cyber police. This paper explores the legal and organizational princi-ples of cybersecurity in today's information society, and first time develops the method and production rules of forming a logical conclusion about legal responsibility in the cybersecurity domain, that are used to form the conclusion about legal responsibility, namely for the selection of a sanction or set of sanctions recommended in the event of a particular offence or multiple cyber-security offences.

ABSTRACT. Up-to-date information and communication technologies (ICT) implementation in various industries, on the one hand, increases the efficiency of different business processes and, on the other hand, generates new threats and vulnerabilities in ICT. Critical infrastructures (CI) need principal new effective methods and means for cybersecurity ensuring. In the situation with limited resources, CI objects defining and ranking is an important task. To rank objectively, CI objects should be assessed using some criteria. Previously, authors have proposed an FMECA-based method to assess importance level for state critical information infrastructure, which allows ranking and evaluating the importance of CI objects using both quantitative and qualitative parameters. This paper presents a complex experimental study of the proposed method using the aviation industry as an example. An experimental technique was introduced and using it, the adequacy of method response to changing input data was checked. It confirmed the possibility of importance level assessment of critical aviation information systems related to various categories: information systems for air navigation services; on-board information systems for aircraft; information systems for airlines and airports.

ABSTRACT. The objective of this paper is to develop a practical E-learning framework with implementation of case method and project-based learning. In paper we obtain the following results. Content of the massive open online course (MOOC) “Safety and Security of Control Systems” is analyzed. This MOOC was introduced in 2017 for master students program “Cybersecurity” at National Aerospace Uni-versity “KhAI” (Kharkiv, Ukraine). A core part of this MOOC is a project devot-ed to safety and security assessment of real systems and software. Taxonomy for indicators of E-learning effectiveness is proposed. Case study was done in Ukraine between students of Cybersecurity program after finish of study of the MOOC “Safety and Security of Control Systems”. A sample includes 40 master students involved in the course learning during 2017-2019. Case study results confirmed a set of hypotheses related with E-learning effectiveness when case method and project-based learning are implemented.

ABSTRACT. The article deals with the results of the survey of the attitude of Ukrainian educators toward the use of the digital tools for teaching and professional development conducted by the Comparative Studies Department for Information and Education Innovations of the Institute of Information technologies and Learning Tools of the NAES of Ukraine in 2019. 178 respondents – teachers, school administrators, methodologists and in-service teacher training professors answered on the questionnaire from all-over Ukraine. The content of the study covered the following topics: Internet access on the workplace; professional activities and the use of ICT; using ICT tools in the classroom work and professional development; social networks; cloud services; electronic systems of the educational process management and organization; self-assessment of the level of the digital/ information and communication competence; suggestions and attitudes toward the use of ICT for the professional development and practical work. The answers of the respondents allowed providing proposals on the use of digital tools by teachers in their professional activity. The purpose of the article was to present the survey results and provide suggestions on the professional development of teachers and the assessment of their digital competence.

ABSTRACT. The article reviews the process of developing training content of the on-line course on the project method for Mathematics teachers teaching at higher technical universities. The study presents the first stage in developing training materials and a model for the structure of the on-line course «Project Method in Teaching Higher Mathematics», which is in open access on the «Higher School Mathematics Teacher» educational platform. The original version of the course was designed on the basis of the findings of a survey among the Mathematics professors. It helped to find out the level of their awareness about involving the project method of training in engineering students, and gave good reason to conclude that it is advisable to introduce an on-line course to enhance their qualifications. After uploading to on the platform the original version of the course, we managed to organize a discussion of the proposed content, structure and modes for submitting the course materials on the forum. The article discusses the process of modifying the course compo-nents, improving training material during the forum discussion. There was ground to conclude that it is advisable to introduce the on-line course into the process of training Mathematics teachers to improve their qualifications. The analysis of the feedbacks from the course users on the forum, confirmed that the variety of submitted forms of course materials and the proposed top-ics satisfied the preferences of the course users with regard to the perception and awareness of the educational information.

ABSTRACT. The article reflects the views on the development of the engineering area of education and, in particular, its robotic vector. We do not claim to be “the ultimate truth”, but the issue is urgent and it requires extensive coverage and discussion in the community in the context of the development of the educational field of Tech-nology. The question of the methodology and technics on the basis of which robotics courses will be taught, as well as design and construction, is considered. Within the CMSL“Clever” experimental study, an excellent construct and a huge number of author’s methodological guidelines were approved, tested and worked out. Educational designers are used, including during the engineering solutions prototyping. We focus not only on Lego products. There is a “technological boom” in the development of free software and hardware platforms, in particular, this is due to the appearance of the Arduino board in its various forms. It really gave rise to a “breakthrough” wave in technical creative work. Robbo-ScratchDuino, mgBot, and hundreds of others offer individual components and se-rious kits for future designers and engineers. Laser milling machines and other CNC machines, robots, quadrocopters, 3D printers and other devices based on mi-crocontrollers flooded the world. The development of electronic prototypes has been simplified many times at schools and a great amount of startups are being created. The educational effect is possible only with the systematic nature of such decisions and at least a certain uniformity in requirements. The main problems of implementing free software and hardware solutions (free educational robotics) into educational courses are offered.

ABSTRACT. The paper discusses information and communication technology use for studying reasons of aviation accidents because of the aviation operator errors as result of internal and external influence. The model and technique are proposed and include integrated ICT united previously developed (initial professional selection and day-to-day pre-shift check), open access cloud-based (NASA and ICAO) and real-time oper-ative (air traffic controllers and pilots control) ICTs, which data are stored in one database. Proposed ICT has been checked to study effect of the solar wind parame-ters (speed and density) on appearance of aviation incidents and accidents during one year observation. Results of that study were compared with corresponding results of another period of solar activity, as well as with data obtained in laboratory condi-tions to study cognitive tests performance under effect of the solar wind.

ABSTRACT. The article analyzes different approaches to design adaptive educational systems on the basis of students' learning style identification. As a result of the investigation a system to identify the student's learning style with the data analyzing module has been designed and implemented. A data analyzing module is applied for the further adaptation of digital educational content and educational methods to students' learning style. The data background for the module to analyze learning style identification system is the universal e-learn environment users’ database, the results of learning style identification due to ВАРК model or any open external information like psychotype, type of intelligence, etc. Data storage uses the concept of data warehousing to predict special methods for data model design taking into account the integrity of datasets from different sources, object orientation, consistency, data consolidation or multidimensional data architecture to simplify analytical queries. The data analyzing technologies being applied within the system are based on the information retrieval approach using languages of SQL; OLAP and Data Mining technologies. The results of the system implementation gave an opportunity to fix the correlation of learning styles with other personal characteristics like psychotype, gender, secondary education level, academic achievements, etc. The represented data of data analysis concerning IT major students give reason for the conclusion about the necessity to adapt digital content to multimodal and kinesthetic learning style, to apply learning methods and technologies on the basis of project tasks, group communication and collaboration.

ABSTRACT. This paper presents an analysis of the influence of gas, coal, electricity and Brent (crude oil) prices on the EU emission allowance price by means of a vector autoregression analysis. Statistically significant influences on the price of CO2 emission allowances can be identified for all energy market variables examined, except electricity prices. Thus, the present analysis supports the assumptions of earlier publications that the influence of the energy market on the European Emissions Trading System (EU ETS) is decreasing and that the efforts of the European Commission are having an effect. The EU ETS is designed to stimulate the reduction of emissions by setting caps and to create monetary incentives for investment in new, low-emission technologies by trading emission allowances. However, the allocation efficiency of this system is conditional on the relative price stability of the emission allowances, as this is the only way to make reliable forecasts for risk calculations and investment decisions by companies. Using a vector autoregression model (VAR), this paper demonstrates significant influences of energy prices on the European Emission Allowances (EUA) price in the third phase of the EU ETS.

ABSTRACT. Economics has entered the stage of deep transformation of its bases. The traditional method of constructing a scientific theory is first to synthesize and investigate mathematical framework; this traditional approach was taken as a principle of our research. Finally the mathematical theory of the general dynamic market model has recently been constructed, the main elements of which are given in this paper. The next step is to build models of specific real markets based on the general theory. The C# application Model was created especially to support the synthesis of concrete models based on the general theory. The most important goal of this paper is to propose cooperation in such research. Results of the research: the crucial factors which ensure the market stability are the market coherence and the market intention to adaptive expectations. If no any firm uses naive expectations in the market then with sufficiently small incoherence there is unique Nash equilibrium which is stable for all acceptable values of parameters. The increase of naive expectations leads to stability loss, to flip bifurcations and finally to chaos. The increase of number of firms also as a rule leads to stability loss and finally to chaos. At sufficiently small changes in production per step, systems of general dynamic market model turns into systems of neoclassical microeconomics.

ABSTRACT. The article is devoted to the formation of a technological-logistic model of the integrated structure of food production. The main goal of corporate structure management is the integration of all its constituent units for the fulfillment of the mission, which ensures achievement of the set goals. The main purpose of modeling is to show how the intermediate links-enterprises are logically formed the target object. A mathematical formulation of the problem of choosing optimal capacities and rational location of enterprises, as well as minimum costs for transportation of raw materials, is proposed. A complex mathematical model for planning the production of agricultural raw materials and processing it into ready-made food products in the system "agricultural sector - provision / primary processing - food industry enterprises" was formed. Models of the logistic organization of integrated food production are based on the principles of rational organization of the technological chain and are characterized by: complexity, universality, differentiation of the approach; specialization. The developed mathematical models allow planning and programming of the development processes of the integrated food production system, assessing the impact of changes in the parameters of the system, and adjusting plans. With the help of Statgraphics, Statistica, Excel software and having as a basis an array of enterprise data, it is possible to plan and program the development processes of an integrated food production system, assess the impact of changes in system parameters, make adjustments to plans. The models make it possible to specify the technological complex of work and the need for raw materials, provide an opportunity to establish boundaries between complexes of works of individual companies and, in general, the responsibility of the entire corporate structure.

ABSTRACT. The frequent financial critical states that occur in our world, during many centu-ries have attracted scientists from different areas. The impact of similar fluctua-tions continues to have a huge impact on the world economy, causing instability in it concerning normal and natural disturbances [1]. The anticipation, prediction, and identification of such phenomena remain a huge challenge. The crisis starting in 1997, strongly affected on the worldwide economy, raised fears among people about its future. The International Monitory Fund (IMF) after the experienced Asian Crisis pointed out that such phenomena will occur again in the nearest future [2]. To be able to prevent such critical events, we focus our research on the chaotic properties of the stock market indices. During the discussion of the recent papers that have been devoted to the chaotic behavior and complexity in the financial system, we find that the Largest Lyapunov exponent and the spectrum of Lyapunov exponents can be evaluated to determine whether the system is com-pletely deterministic, or chaotic. Accordingly, we give a theoretical background on the method for Lyapunov exponents estimation, specifically, we followed the methods proposed by J. P. Eckmann and Sano-Sawada to compute the spectrum of Lyapunov exponents. With Rosenstein’s algorithm, we compute only the Largest (Maximal) Lyapunov exponents from an experimental time series. And we consider one of the measures from recurrence quantification analysis that in a similar way as the Largest Lyapunov exponent detects highly non-monotonic behavior. Along with the theoretical material, we present the empirical results which evidence that chaos theory and theory of complexity have a powerful toolkit for construction of indicators-precursors of crisis events in financial markets.

ABSTRACT. The article considers and generalizes using evolutionary models of economics on the AGMEMOD model example - a partial equilibrium, dynamic, multi-country and multi-market model that is used for analyzing the effects of agricultural policies on the respective sectors of each EU Member State and the EU as a whole. The use of the AGMEMOD model were illustrated on the ex-ample of designed specific scenarios of the development of the biofuel market in Ukraine till 2030. The practical application of the development is the possibility of using the research results by the relevant state institutions to stimulate the development of the biofuel market in Ukraine. The simulation example described in this paper can also be used by scientists from other countries to predict the impact of agricultural policy on the economy.

ABSTRACT. The paper focuses on and propose the semi-formal method of constructing individual educational students trajectories of the process of the professional training of future software engineers in Ukrainian universities. The method for the student-centered learning conception support presented by the au-thors was developed using graph theory. The set of educational paths that the student is invited to choose corresponds with the requirements of IT en-terprises and provides the student with the opportunity to choose his or her educational path for the level of education legally enshrined in Ukraine. The article presents the result of educational trajectories constructing for the pro-cess of the professional training of future software engineers from a Junior Bachelor level to Doctor of Philosophy. Ukrainian universities can use the proposed educational trajectories of the professional training of future soft-ware engineers for curricula and syllabus preparation. The practical develop-ment of this work is an interactive online assistant that will recommend to the student the choice of the educational path from the already achieved lev-el to the target level, which the student will choose.

ABSTRACT. A formulation of an induction principle for diamond-free directed complete partial orders is proposed. This principle may be useful for specification and verification of non-discrete systems using interactive proof assistant software.

ABSTRACT. State explosion is a well-known challenge of model checking. In this paper we propose several approaches to improve the standard techniques for verifying qualitative reachability properties of Markov decision Processes. For the first approach, we use two heuristics to reduce the total number of iterations of the standard iterative methods. The second approach uses the secondary hard disks for storing the information of a model and uses the main memory for a back-ward technique on the standard methods. The third approach uses a machine learning technique to classify the state space of a model to the related classes. While this approach does not need any memory overhead, its running times is much less than the running time of the standard approaches and can be used to cope the state explosion problem.

ABSTRACT. Medical service improvement has always been a life topical problem. To de-cide it, we must continuously raise the competency of doctors on the one hand and it is necessary to develop new methods and approaches which could help take decisions concerning diagnostics (classification) of patient health conditions and concerning patient’s further treatment. At the paper the machine learning methods for patient health condition clas-sification were considered. These methods were Naive Bayes Classifier, Lin-ear Classifier, Support-vector machine, K-nearest Neighbor Classifier, Lo-gistic Regression, Decision Tree Classifier, Random Forest Classifier, Ada Boost Classifier and Artificial Neural Network. A radial basis network was chosen from the variety of artificial neural system architecture to solve clas-sification tasks. The problem of patient health conditions classification was considered for two sets of laboratory research results: on liver diseases and on urological diseases. Confusion matrixes and ROC-curves were taken to estimate classification quality of patient health conditions with above-mentioned methods.

ABSTRACT. The paper presents a new technique for cyberattacks detection based on DNS traffic analysis. It enables the proactive malicious requests detecting in corporate area networks based on DNS protocol, and is aimed to identify and block the ma-licious domains and DND data deletion requested by the attackers. The process of malicious requests detection is based on the use of "isolation for-est" algorithm, which allows to detect the anomalies in DNS data exchange. Based on the general data deletion scheme, an anomaly of DNS traffic is ob-served when it is used for data exchange. The anomaly in the DNS traffic is detected due to analysis of the set of features concerning the requests and responses that may indicate the attack presence in the network.

ABSTRACT. Today cloud services have revolutionized the way we store and share different data. At the same time, most of the data are unsecured and vulnerable to various cyberattacks. In this paper cloud services concept and mechanisms of their work were considered. The cryptographic encryption algorithms used in cloud services were analyzed as well as comparative analysis of most popular up-to-date cloud services Wuala, DropBox and Google Drive was carried out. As the result of analysis, the advantages and the weakest places of each cloud services were defined. Besides that, in this work Google Drіve work scheme and data protection in the cloud service were presented. The main disadvantage of cipher RC4-128, which is used in this cloud service, is identified. After this improved stream cipher based on RC4-128 has been developed. It contains additional byte transformations in the PRN formation algorithm, an additional PRN and a new incoming message encryption algorithm using the generated threads. As a result, these solutions provide the cryptographic stability of the proposed stream cipher. Experimental study of improved stream cipher for cloud services was carried out. It was focused on data encryption rate research and statistical testing using the standardized NIST STS technique.

ABSTRACT. The paper proposes an Android malware detection method based on convolutional neural network mixed-data model. This data are presented by API method calls and a set of permissions for the Android app. Word2vec technolo-gy was used to represent API calls in a vector space, which creates semantically similar feature vectors for related API calls. To represent a set of permissions, each unique permission is encoded as a binary feature that determines the pres-ence / absence of permission in the input sequence. Obtained sequence is then broken down into nibbles and the code “8421” is applied with further normali-zation of the result. Both types of vectorized data are the inputs to the convolu-tional neural network. The architecture of the proposed neural network consists of two separate parallel convolutional branches, each of which processes its own type of data, and the fully connected layers. The structure of both branches is the same, which involves placing in each branch two consecutive layers of convolution, where the first layer maps the simple features that will be used by the second layer to represent higher level behavioral patterns. After the convo-lution layers, there is a pooling layer placed to reduce the dimension of the data. The outputs from both branches of the network are combined to form the input for fully connected layers, which determine the probabilities of belonging sus-picious app to one of the classes – malware or benign.

ABSTRACT. The technology of direct spectrum spread is used in radio communication systems with multiple access. It is based on the use of pseudorandom (noise-like) discrete signals (sequences). In this paper steganography techniques based on spectrum spread are studied. Using noise-like signals, it is possible to hide information in cover images. We conduct experimental studies and show that the error rate in the restored informational messages is very high. This is due to the high correlation of discrete sequences and cover images. We offer a new technique when the statistical properties of cover images are taken into account when forming sequences. Our experiments show that the practical use of this approach can significantly reduce the error rate. The distortion of the image does not increase.

ABSTRACT. The results of studies of the properties of random substitutions are summarized. It is shown that random substitutions have overwhelmingly good cryptographic and, in particular, algebraic properties. It is shown that the deterioration of the differential and linear indices of the known block cipher designs (SPN ciphers will be discussed here) when using random substitutions can be offset by the use of a cycle function design with controlled substitutions. An advanced design for constructing such a cycle function is proposed, which allows to increase the minimum number of activated S-blocks on the first cycles of ciphers in comparison with the known structures that implement the wide-trace strategy. The prospect of using random S-blocks for the construction of block symmetric ciphers with improved dynamic parameters of arrival to random substitution is substantiated. A refined random substitution model and the corresponding criteria are proposed; by which it is possible to check the suitability of substitutions generated randomly for use in modern cipher designs. It is a test, since it is very likely that the tested substitutions will be suitable.

ABSTRACT. Modernization of higher education and increased competition in the educational services market require new ways of improving the efficiency of higher education institutions (HEI) management. The generalized structure of forming the HEI video marketing strategy is developed and a series of actions for achieving goals is presented. An algorithm for the targeted advertising forming based on decision tree using R. language is proposed. The research methodology is described and HEI targeting model is developed using the decision tree and contextual advertising campaign data on Facebook. The results of the pilot case study are presented, which confirm the practical usefulness of the proposed targeting model, which allows forming target groups.

ABSTRACT. Efficient human resource management needs accurate assessment and representation of available competences as well as effective mapping of required competences for specific jobs and positions. Thus, definition and identification of competence gaps express differences between acquired and required competences using a mathematical approach to support accurate competence analytics. Lack of skills and insufficient qualifications of employees are cited as major barriers to the adoption of new technologies in the context of Industry 4.0. These changes require skills for data analytics tasks. The purpose of this paper is to investigate gaps in the preparing of a business analyst between the requirements of the labor market and the standards of study programs. For the IT and other industries, the most important competencies from study program of Ukrainian High Educational Institutes, which correspond to labor market requirements, were revealed using RStudio.

ABSTRACT. The article contains a study of the principles of student's educational trajectory formation by using modern technologies in data analysis. There is a mandatory requirement to have the selective component (optional to a student) among the curriculum educational components. This rule is legislated in the laws «On Education» and «On Higher Education» of Ukraine as well as in the normative documents on accreditation of educational programs, defined by the Standards and recommendations on quality assurance in the European Space of Higher Education (ESG) and the National Agency for Quality Assurance of Higher Education. However, adherence to the principles of the individual educational trajectory formation is mostly formal and is reduced to offering students a non-coherent list of courses. On the one hand, this leads to the disorientation of a student, who cannot see the systemic perspective of his future profession in the initial list of study courses, and therefore cannot consciously choose the optimal set of optional courses. On the other hand, the unknown choice of courses by students leads to situational management of the educational process at the HEI. A large number of courses create significant difficulties in managing the selection process. To analyse the process of individual educational trajectory formation, the authors propose to use methods of data association and, in particular, the apriori algorithm for the formation of associative rules. The procedure of popular sets of elective courses formation, the configuration of associative rules of educational courses choice is studied. The characteristics of these rules quality are calculated. The example of the procedure implementation in analytical platform Deductor Studio is considered.