In the conditions of the development of modern economy, human capital is one of the main factors of economic growth. The formation of human capital begins with the birth of a person and continues throughout life, so the value of human capital is inseparable from its carriers, which in turn makes it difficult to account for this factor. This has led to the fact that currently there are no generally accepted methods of calculating the value of human capital. There are only a few approaches to the measurement of human capital: the cost approach (by income or investment) and the index approach, of which the most well-known approach developed under the auspices of the UN. This paper presents the assigned task in conjunction with the task of demographic dynamics solved in the time-age plane, which allows to more fully take into account the temporary changes in the demographic structure on the dynamics of human capital. The task of demographic dynamics is posed within the framework of the Mac-Kendrick-von Foerster model on the basis of the equation of age structure dynamics. The form of distribution functions for births, deaths and migration of the population is determined on the basis of the available statistical information. The numerical solution of the problem is given. The analysis and forecast of demographic indicators are presented. The economic and mathematical model of human capital dynamics is formulated on the basis of the demographic dynamics problem. The problem of modeling the human capital dynamics considers three components of capital: educational, health and cultural (spiritual). Description of the evolution of human capital components uses an equation of the transfer equation type. Investments in human capital components are determined on the basis of budget expenditures and private expenditures, taking into account the characteristic time life cycle of demographic elements. A one-dimensional kinetic equation is used to predict the dynamics of the total human capital. The method of calculating the dynamics of this factor is given as a time function. The calculated data on the human capital dynamics are presented for the Russian Federation. As studies have shown, the value of human capital increased rapidly until 2008, in the future there was a period of stabilization, but after 2014 there is a negative dynamics of this value.

Выполнено математическое моделирование величины и структуры человеческого капитала РФ. Построен прогноз его динамики до 2025 г. с использованием двумерного уравнения переноса, в котором учтены время и возраст демографических элементов, а также прогнозные объемы бюджетных и частных инвестиций в человеческий капитал, полученные по многослойной нейросетевой модели. Построенные прогнозы удовлетворяют заданной точности.

Предложена методика решения задачи логистики топливоснабжения региона, включающая в себя взаимосвязанные задачи маршрутизации, кластеризации, оптимального распределения ресурсов и управления запасами. Расчеты проведены на примере системы топливоснабжения Удмуртской Республики.

В работе представлен подход к моделированию транспортных потоков в условиях светофорного регулирования. Разработана компьютерная имитационная мультиагентная модель транспортных потоков, которая включает три основных агента: автомобиль, светофор, генератор. Разработан расчетный имитационный алгоритм движения автомобилей по дорожным полосам и имитационный алгоритм их поведения на перекрестках. Компьютерная мультиагентная модель и имитационный расчетный алгоритм поведения автомобилей в транспортной сети реализованы в виде интеллектуальной аналитической системы, которая также включает в себя базу данных по характеристикам движения автомобилей, спроектированную в среде СУБД MS SQL, и модуль визуализации всех процессов.Компонентами имитационной модели транспортных потоков являются система координат (карта), сами динамические объекты (автомобиль, светофор, генератор входного потока автомобилей), счетчик временных интервалов и алгоритм движения автомобилей. В процессе моделирования транспортных потоков в системе фиксируются необходимые выходные параметры модели.На примере одного из дорожных участков города Ижевска продемонстрированы возможности реализованной модели. Разработанная компьютерная имитационная мультиагентная модель позволяет рассчитывать показатели средней длины очереди транспортных средств в любое время суток с учетом интенсивности входных транспортных потоков.

This paper presents a programming and computing suite which comprises regional socio-economic parameters database (gross regional product, physical capital, human capital and their investment volume), an analytical subsystem which renders mathematical models of parameters’ analysis and forecasting, as well as visual representation unit of modeling and forecasting results. In view of the results, a system research report is built, providing information on socio-economic condition of the region. The calculations are performed by the example of the Udmurt Republic.

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The problem of social clustering being studied in the paper is one of the main subtasks; its solution is an integral part of analysis and prognosis of socio-economic processes. Analysis and systematization of knowledge in the field of applying neural network modelling to regional system social clustering problem solving are implemented. It was demonstrated that today, the main factor of economic growth is human capital, which is composed of quantitative and qualitative features. The main quantitative element is population replacement which has a bearing on human capital development sustainability. Qualitative component has several aspects in it: healthcare, culture, education and science are among them. To estimate human capital structure, the population is divided into social clusters by these aspects. It was also shown that since social cluster is an attribute of sociogenesis, processes of social clustering themselves are the result of people social interactions. Social cluster is a specific state of social entity which includes description of not only entity’s objects, but the processes which led to its structural development and interactions with social environment. As part of the study, a conclusion was made that neural networks enable one to apply cluster analysis to the society. Neural networks prove notable capabilities to solve poorly formalized tasks; they are resistant to frequent environmental changes and effective to use when working with a large amount of incomplete or contradictory information. While studying the issue, it was observed that structural and statistical features of social clusters reflect aggregation of their elements. The structure of a social cluster is a characteristic which represents a conjunction of stable connections which provide its unity. Under different external and internal changes, the main properties of social clusters are preserved. The grading of social demographic elements by health condition and cultural and educational level is set, in accordance with which collecting a statistical data to solve the clustering problem is implemented.