Modern systems for assessing personnel competencies are highly labour-intensive and subjective. The paper aims to develop a methodology and a system for the automated formation of benchmark competency profiles based on the analysis of job vacancy data from the Russian labour market utilising natural language processing (NLP) methods and large language models (LLM). The study relies on an analysis of 78,882 job vacancies across 269 professional roles from the “hh.ru” platform. The research applies the locally deployed LLM model “gemma3:12b-it-qat” to extract competencies, “ai-forever/sbert_large_nlu_ru” embeddings for deduplication, and frequency analysis to identify relevant requirements. The author has developed a system for creating structured competency profiles. The combined approach (LLM, word embedding, and frequency ranking) identifies significant professional requirements in terms of specialties and qualification levels. The example of the profession “Data Scientist” demonstrates the differentiation of skills: from basic instrumental knowledge for junior positions to system design competencies for senior specialists. The profiles enable real- time tracking of trends in the development of required competencies. The results confirm the effectiveness of big data and LLM methods for the objective assessment of labour market requirements. The profiles are useful for performance appraisal systems, educational programme development, and HR analytics. The study may be of interest to specialists in the field of human resource management and to educational organisations. A promising direction is the integration of additional data sources for assessing the actual level of personnel competencies.

The formation of technological sovereignty and innovative development of industry covers all sectors of this sphere, including medium-tech industries. The article aims to identify factors contributing to the growth of innovative activity in the medium-tech sector of highlevel industrial production. The information base includes statistical data from the Federal State Statistics Service of the Russian Federation for 2019–2023. The paper uses statistical methods of analysis. Based on the theoretical analysis, the study identifies structural and systemic industry factors, as well as intra-industry economic factors for the development of innovation in the medium-tech sector of the high-level industry. Empirical analysis shows that external structural factors related to market type, level of competition, and market size have the greatest impact on the level of innovation activity in the high-level medium-tech sector in 2019–2023. The obtained results have great significance for the formation of a technological development model of the Russian economy.

The article deals with a comprehensive analysis of digital solutions used in the physical culture and sports industry in the Sverdlovsk Oblast. The study analyses the digital services involved in the implementation of digital transformation in this field. The paper considers the areas of their use and the goals of their integration into the current processes of organisations in the Sverdlovsk Oblast. The methods include synthesis, content analysis, secondary data analysis, and comparison. Additionally, we apply the method of participant observation, which allows us to identify the conditions for the implementation of new tools for the digitalisation of the industry. Content analysis of regulatory documents, development strategies and the results of empirical researches in the field of physical culture and sport allows us to identify the key directions of the digital interaction between the participants of this process. The results of the study may help to justify adjustments to the introduction procedures, and to review the current services related to digital tools used in the implementing digitalisation of the physical culture and sports industry in the Sverdlovsk Oblast. In turn, these aspects affect the realisation of government programmes for improving the conditions for the development of physical culture and sports in the region through the digital transformation of the industry.

The paper deals with a comparative analysis of three key machine learning (ML) paradigms: supervised learning, unsupervised learning, and reinforcement learning – along with an evaluation of popular ML frameworks such as TensorFlow, PyTorch, and Scikit learn. The author considers the main differences, advantages and limitations of ML approaches, focusing on factors such as: computational cost, scalability and ease of imple mentation. The study looks at the interpretability aspects of ML models and analyses the computational resources required for their operation, including the load on the central pro cessing unit and random access memory. The results provide the necessary information on how different ML methodologies and technologies shape real applications and influence practical decision-making in systems driven by artificial intelligence.

In the context of rapidly growing volumes of scientific information, there is a need for automated analysis methods capable of identifying the most promising research direc tions. The relevance of the study is due to the impossibility of manually processing huge data sets and the need for operational strategic planning of scientific activities. The article aims to develop and test a data processing pipeline for scientific publications, which will allow the systematisation of large amounts of information and provide decision support in scientific organisations. The implementation of the pipeline utilises the Lens.org platform, which provides access to extensive databases of scientific publications. Information col lection followed by preprocessing includes duplicate removal, tokenisation, lemmatisation and text vectorisation. The author applies the Latent Dirichlet Allocation (LDA) to identify hidden topics. Additionally, the paper conducts citation analysis and graph analysis of the relationships between publications, and also pays special attention to the development of a new metric – the “Priority Index”, which combines indicators of citation, thematic rel evance, and temporal trend of publications. Testing of the pipeline on a sample of more than 50 000 publications for 2014–2024 demonstrates high accuracy and efficiency of the proposed method. The research results enable the identification of key research directions, such as artificial intelligence, big data processing, and distributed energy systems, as well as tracing the dynamics of their development.

The paper is devoted to the research of the two-criteria estimation method for linear regressions. The first criterion corresponds to the least absolute deviations, the second – to the non-strict ordinary least squares. The implementation of the method requires solving a two-criteria linear programming problem, the solution of which involves the formation of a Pareto set. The main goal of the article was to research how the normalization of the initial variables affects the formation of the Pareto set. For this, two samples were used. The first was created artificially and contains an outlier. The second was formed on the basis of real economic data. In both cases, when normalizing the variables, the Pareto set turned out to be more representative than when working with non-normalized indicators. The example with an outlier illustrates the robustness of the least absolute deviations and the anti-robust ness of the ordinary least squares. It is shown how, based on the predicted values of the explained variable, it is possible to choose the optimal Pareto vertex.

The absence or long lag of publication of official statistics on the level of so cio-economic development of territories forces researchers to turn to alternative data sourc es arising because of the rapid development of digital technologies. Programming language R is required to work with these datasets. The purpose of the paper is to acquaint readers with the capabilities of the R software environment when forming a municipal database for socio-economic research from various sources. The following data sources are considered here Rosstat database “Indicators of Municipalities”; 5-NDFL tax report form, web sources of the Federal Tax Service, website of the Central Electoral Commission of the Russian Federation, TurgetHunter service. As part of the preparatory stage of database creation, it is shown which parameters must be taken into account when creating an auxiliary key table. Using the example of working with data, the functions left_join(), pivot_longer(), fill(), group_by(), arrange(), summarize(), separate() are analyzed. The presented material can be used to develop educational tasks within the framework of the disciplines “Basics of Statis tics” or “Data Analysis”, as well as to prepare a statistical base for research into socio-eco nomic processes at the municipal level.

The research is devoted to the estimation the structural complexity of programs. The algorithm of finding cyclomatic routes for program executions is described. By now, two directions of obtaining estimates for the complexity estimates in software modules have been defined: structural and statistical. Both directions connect the value of program complexity with the labor intensity related to their development. The structural complexity of program modules is determined by the number of interacting components, the number and complexity of links between them. The complexity of a program's behavior depends to a large extent on the set of routes through which it is executed. The complexity metric obtained from these positions allows us to determine estimates of the cost of designing the program as a whole, as well as to identify the modules that are likely to contain the most errors, especially the logical ones.

In this paper, two approaches are used to construct the dynamic semantics of computer programs: the first is the representation of mathematical models of computational processes generated by a computer program in the form of a discrete transformer; the second is the representation of the mathematical model of a computer program in terms of functional grammars. The study focuses on the computational process generated by a computer program. Application of the discrete transducers concept to describe computational processes allows us to obtain a mathematical model or dynamic semantics of a program, which is a composition of two discrete systems B and C. In this case, component A is a control component (a model of the program block diagram), and component B is a model of the program memory. The decomposition of a program into two components B and B is convenient when studying the process of modelling a computational process. This is due to the fact that the prospects of searching for invariants in critical nodes of a programme for mathematical proof of correctness of a computer programme are opened. The comparative analysis of the two approaches leads to the theorem on the regularity of the representation of a function generated by a programme within the framework of functional grammar.

In developed economies the opportunities of the stock market are widely used to solve practical issues of financial security of the economy. The advantage of financial provision of the economy at the expense of the possibilities of the stock market in com parison with the so-called bank financing is obvious. This topic takes a special urgency for rather young market economy of Russia. Household savings occupy a special place in the implementation of investment activities. In the most developed countries, the population is traditionally regarded as the leading provider of financial resources for the national economy. What indicators and factors are need to be managed to achieve sustainable development of the domestic stock market in the era of digitalization? How are consumption and the stock market related? This paper will build an econometric model to help answer these two questions.