After analysis of scientific literature, we defined that concept of “augmented reality” has following synonyms: “advanced reality”, “improved reality”, “enriched reality”, “mixed reality” and “hybrid reality”. Analysis of scientific literature and own practical experience of the use of augmented reality technologies application in educational practices allowed to state next: augmented reality technologies have a great potential for application in education; there are some cases of augmented reality use for school education; positive aspects of augmented reality technologies application in higher education institutions are confirmed by experiments (isolated cases); only few universities in Ukraine apply augmented reality technologies to educate students; only few universities in Ukraine have special subjects or modules in schedule to teach students to develop augmented reality technologies; various scientific events, mass events, competitions are held in Ukraine, and specialized training on the augmentation of augmented reality technologies is carried out, but this is non-systematic and does not have special state orientation and support. Features of introduction of virtual and augmented reality technologies at Sumy State University (Ukraine) are identified: “e-learning ecosystems” was created; in 2019, augmented and virtual reality research laboratory was established. Advantages and disadvantages of project activity in education are described: project activity is one of the most important components of educational process; it promotes creative self-development and self-realization of project implementers and forms various life competencies. It is determined that augmented reality application for implementation of educational projects will help: to increase students’ interest for educational material; formation of new competences; increase of students’ motivation for independent educational and cognitive activity; activation of educational activities; formation of positive motivation for personal and professional growth; conditions creation for development of personal qualities (creativity, teamwork, etc.). Current trends in implementation of educational projects were identified: most of the winner projects were implemented using augmented reality technology; augmented reality technologies were used in projects to teach different disciplines in higher education institutions. Augmented reality technology application for project activity has positive impact on learning outcomes and competitiveness of the national workforce; it will enhance the country’s position in the global economic space.

After analysis of scientific literature, we defined that concept of “augmented reality” has following synonyms: “advanced reality”, “improved reality”, “enriched reality”, “mixed reality” and “hybrid reality”. Analysis of scientific literature and own practical experience of the use of augmented reality technologies application in educational practices allowed to state next: augmented reality technologies have a great potential for application in education; there are some cases of augmented reality use for school education; positive aspects of augmented reality technologies application in higher education institutions are confirmed by experiments (isolated cases); only few universities in Ukraine apply augmented reality technologies to educate students; only few universities in Ukraine have special subjects or modules in schedule to teach students to develop augmented reality technologies; various scientific events, mass events, competitions are held in Ukraine, and specialized training on the augmentation of augmented reality technologies is carried out, but this is non-systematic and does not have special state orientation and support. Features of introduction of virtual and augmented reality technologies at Sumy State University (Ukraine) are identified: “e-learning ecosystems” was created; in 2019, augmented and virtual reality research laboratory was established. Advantages and disadvantages of project activity in education are described: project activity is one of the most important components of educational process; it promotes creative self-development and self-realization of project implementers and forms various life competencies. It is determined that augmented reality application for implementation of educational projects will help: to increase students’ interest for educational material; formation of new competences; increase of students’ motivation for independent educational and cognitive activity; activation of educational activities; formation of positive motivation for personal and professional growth; conditions creation for development of personal qualities (creativity, teamwork, etc.). Current trends in implementation of educational projects were identified: most of the winner projects were implemented using augmented reality technology; augmented reality technologies were used in projects to teach different disciplines in higher education institutions. Augmented reality technology application for project activity has positive impact on learning outcomes and competitiveness of the national workforce; it will enhance the country’s position in the global economic space.

The article considers the problem of using immersive learning in the educational and scientific activities of the university. Literature survey revealed that there is a need for an integrated approach for introduction of immersive learning at the university. It involves the creation of a specialized laboratory of virtual and augmented reality with appropriate technical equipment, introduction of immersive learning methodology in university educational programs, development of software and hardware solutions for immersive learning, and research on the immersive learning effectiveness. We present the description of a specialized university department acting as a developer of software products for immersive learning. We show original developments in the field of immersive education for exact sciences and arts and humanities students. The article describes products that are designed to fulfill the third university mission: to ensure the citizens well-being. We propose "immersive institute" model which can be implemented both at the level of the university in general and at the level of its educational and scientific departments.

The study aims to increase the functional efficiency of a machine learning cyber attack detection system. An information-extreme machine learning method of the cyberattack detection system with optimization of control tolerances for recognition features that reflect the traffic properties of the info-communication system has been developed. The method is developed within the framework of the functional approach to modeling of cognitive processes of natural intelligence at the formation and acceptance of classification decisions. This approach, in contrast to known methods of data mining, including neuron-like structures, allows giving the recognition system adaptability to arbitrary initial conditions of the learning matrix and flexibility in retraining the system by expanding the recognition classes alphabet. The method idea is to maximize the information capacity of the attack detection system in the machine learning process. A modified Kullback information measure is used as a criterion for optimizing machine learning parameters. According to the proposed categorical functional model, algorithmic software for attack detection system in the mode of machine learning with the depth of the second level has been developed and implemented. However, the depth level is determined by the number of machine learning parameters, which were optimized. The geometric parameters of the recognition hyperspherical containers classes and the control tolerances on the recognition features were considered as optimization parameters, which played the role of input data quantization levels in the transformation of the input Euclidean learning matrix of the type "object-property" into a working binary learning matrix given in the Hamming space. Admissible transformations of the working training matrix of the offered method allow adapting the input mathematical description of the attacks detection system to the maximum full probability of the correct classification decisions acceptance. Based on the results of information-extreme machine learning within the geometric approach, decisive rules are constructed as practically invariant to the multidimensionality of the recognition features space. The computer simulation results of information-extreme machine learning of the attack detection system to recognize four host traffic of different profiles confirm the developed method's efficiency.

The aim: To determine the pathogenetic expediency, efficiency and the place of therapeutic plasmapheresis in a complex treatment of patients with chronic hepatitis. Materials and methods: It was carried out the analysis of case histories of 77 patients. In the course of treatment, the patients were diagnosed with chronic toxic hepatitis (K.71). Diagnosis was exposed in accordance with the official documentation introduced by the Gastroenterological department of Sumy Regional Clinical Hospital CH”SRCH”, Sumy Regional Infectious Diseases Clinical Hospital named after Krasovytsky ZY and Sumy Regional Center of Blood Service. Results: It was found that total protein indicator is the normal range and albumin after plasmapheresis and during conservative treatment. Markers of cytolysis and cholestasis are have great value may. The most significant changes were observed in rates indicating lesion of the hepatic parenchyma, including ALT, AsAT and alkaline phosphatase. In conservative treatment, the percentage of the alkaline phosphatase level improved by 31%, after the course of plasmapheresis – by 58%. The obtained figures of cholestasis indexes indicate the effectiveness of both methods of treatment, but treatment with plasmapheresis has a more expressed effect on the decrease of alkaline phosphatase level. The level of bilirubin improve on 38,8% after plasmapheresis and 65% in the comparison group. Conclusion: Inclusion in the complex therapy of chronic hepatitis plasmapheresis reduces the severity of cytolysis and cholestasis, increases remission and significantly improves clinical manifestations.

E-learning students are generally heterogeneous and have different capabilities knowledge base and needs. The aim of the Sumy State University (SSU) e-learning system project is to cater to these individual needs by assembling individual learning path. This paper shows current situation with e-learning in Ukraine, state-of-art of development of the adaptive e-learning systems and shows results of SSU research in this area. Nowadays the received solutions are different from the known analogues considering an expanded set of information about the features of a particular student's learning activities (19 indicators are analysed, including indicators of progress such as the level of knowledge and student individual features). The corresponding software solutions are being tested in the SSU e-learning environment.

The problems of qualitative training of a specialist in the specialty 125 "Cybersecurity" are considered in the work. The importance of the aspect of mathematical training is emphasized. Factors that ensure proper professional training of students and the formation of their defined MES integrated competence. The international experience of training cybersecurity specialists is reviewed. It is noted that in most US universities, the course of discrete mathematics, the course of algorithms and their mathematical implementation at the bachelor's level is a mandatory part of obtaining a degree in computer science.

The study of aspects of the digital economy and indicators of the assessment of the state of the economy and society is relevant for the development of transformation policies in accordance with the goals of sustainable development. The progress of technologies and new possibilities of digitalization of the economy give impetus to the improvement of evaluation methods and the system of indicators. In Ukraine, at the state level, considerable attention is paid to the development of the digital economy and society. Digitization is defined as a mechanism of economic growth due to the ability of technologies to positively influence the efficiency, effectiveness, cost and quality of economic, public and personal activities. The concept of the development of the digital economy and society of Ukraine for 2018-2020 was adopted, and in 2021 the law “On stimulating the development of the digital economy in Ukraine” was adopted by the Verkhovna Rada. Further development tasks are defined in the Digitalization Strategy of Ukraine until 2030. The purpose of this work is to develop a complex of formal mathematical models that provide a description of the task of determining the level of digital development of the country (a description of the task of determining the indicators of the progress of digital transformation in achieving the goals of sustainable development) from the standpoint of system analysis. The scientific studies and recommendations presented in the work are sufficiently substantiated and reliable. They are based on the analysis of the methods and systems of influential international institutions, on the review of the works of domestic and foreign specialists. To achieve the goal of the research, general scientific methods were used: content analysis, grouping and systematization, systems theory and system approach, abstract-logical methods – for theoretical generalizations and conclusions. A literature review was conducted and a nomenclature of indicators of the progress of digital transformation in achieving the goals of sustainable development was determined. On its basis, the structure of a complex of models of system analysis of the subject area of digital transformation progress indicators was formed. For the first time, the structures of component models were developed, which describe the necessary elements of the subject area of ​​the task of determining indicators of the progress of digital transformation.