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The work discusses the methodological basis and problems of modeling of world dynamics. Outlines approaches to the construction of a new simulation model of global development and the results of the simulation. The basis of the model building is laid empirical approach which based on the statistical analysis of the main socio-economic indicators. On the basis of this analysis identified the main variables. Dynamic equations (in continuous differential form) were written for these variables. Dependencies between variables were selected based on the dynamics of indicators in the past and on the basis of expert assessments, while econometric techniques were used, based on regression analysis. Calculations have been performed for the resulting dynamic equations system, the results are presented in the form of a trajectories beam for those indicators that are directly observable, and for which statistics are available. Thus, it is possible to assess the scatter of the trajectories and understand the predictive capability of this model.

This paper is dedicated to discussing methods of statistical modeling the outcomes of sport events and, particularly, matches with continuous time. We propose a simulation-based approach to predicting the outcome of a match, somehow medium between pure statistical methods and agent simulation of individual players. An example of retrospective prediction is given.

Numerical investigation of mixing non-isothermal streams of sodium coolant in a T-branch is carried out in the FlowVision CFD software. This study is aimed at argumentation of applicability of different approaches to prediction of oscillating behavior of the flow in the mixing zone and simulation of temperature pulsations. The following approaches are considered: URANS (Unsteady Reynolds Averaged Navier Stokers), LES (Large Eddy Simulation) and quasi-DNS (Direct Numerical Simulation). One of the main tasks of the work is detection of the advantages and drawbacks of the aforementioned approaches.

Numerical investigation of temperature pulsations, arising in the liquid and T-branch walls from the mixing of non-isothermal streams of sodium coolant was carried out within a mathematical model assuming that the flow is turbulent, the fluid density does not depend on pressure, and that heat exchange proceeds between the coolant and T-branch walls. Model LMS designed for modeling turbulent heat transfer was used in the calculations within URANS approach. The model allows calculation of the Prandtl number distribution over the computational domain.

Preliminary study was dedicated to estimation of the influence of computational grid on the development of oscillating flow and character of temperature pulsation within the aforementioned approaches. The study resulted in formulation of criteria for grid generation for each approach.

Then, calculations of three flow regimes have been carried out. The regimes differ by the ratios of the sodium mass flow rates and temperatures at the T-branch inlets. Each regime was calculated with use of the URANS, LES and quasi-DNS approaches.

At the final stage of the work analytical comparison of numerical and experimental data was performed. Advantages and drawbacks of each approach to simulation of mixing non-isothermal streams of sodium coolant in the T-branch are revealed and formulated.

It is shown that the URANS approach predicts the mean temperature distribution with a reasonable accuracy. It requires essentially less computational and time resources compared to the LES and DNS approaches. The drawback of this approach is that it does not reproduce pulsations of velocity, pressure and temperature.

The LES and DNS approaches also predict the mean temperature with a reasonable accuracy. They provide oscillating solutions. The obtained amplitudes of the temperature pulsations exceed the experimental ones. The spectral power densities in the check points inside the sodium flow agree well with the experimental data. However, the expenses of the computational and time resources essentially exceed those for the URANS approach in the performed numerical experiments: 350 times for LES and 1500 times for ·DNS.

The aim of the work was to study and develop methods of forecasting the dynamics of the human respiratory reactions, based on mathematical modeling. To achieve this goal have been set and solved the following tasks: developed and justified the overall structure and formalized description of the model Respiro-reflex system; built and implemented the algorithm in software models of gas exchange of the body; computational experiments and checking the adequacy of the model-based Lite-ture data and our own experimental studies.

In this embodiment, a new comprehensive model entered partial model modified version of physicochemical properties and blood acid-base balance. In developing the model as the basis of a formalized description was based on the concept of separation of physiologically-fi system of regulation on active and passive subsystems regulation. Development of the model was carried out in stages. Integrated model of gas exchange consisted of the following special models: basic biophysical models of gas exchange system; model physicochemical properties and blood acid-base balance; passive mechanisms of gas exchange model developed on the basis of mass balance equations Grodinza F.; chemical regulation model developed on the basis of a multifactor model D. Gray.

For a software implementation of the model, calculations were made in MatLab programming environment. To solve the equations of the method of Runge–Kutta–Fehlberga. It is assumed that the model will be presented in the form of a computer research program, which allows implements vat various hypotheses about the mechanism of the observed processes. Calculate the expected value of the basic indicators of gas exchange under giperkap Britain and hypoxia. The results of calculations as the nature of, and quantity is good enough co-agree with the data obtained in the studies on the testers. The audit on Adek-vatnost confirmed that the error calculation is within error of copper-to-biological experiments. The model can be used in the theoretical prediction of the dynamics of the respiratory reactions of the human body in a changed atmosphere.

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.

The proteins of the Major Histocompatibility Complex (MHC) play a key role in the functioning of the adaptive immune system, and the identification of peptides that bind to them is an important step in the development of vaccines and understanding the mechanisms of autoimmune diseases. Today, there are a number of methods for predicting the binding of a particular MHC allele to a peptide. One of the best such methods is NetMHCpan-4.0, which is based on an ensemble of artificial neural networks. This paper presents a methodology for qualitatively improving the underlying neural network underlying NetMHCpan-4.0. The proposed method uses the ensemble construction technique and adds as input an estimate of the Potts model taken from static mechanics, which is a generalization of the Ising model. In the general case, the model reflects the interaction of spins in the crystal lattice. Within the framework of the proposed method, the model is used to better represent the physical nature of the interaction of proteins included in the complex. To assess the interaction of the MHC + peptide complex, we use a two-dimensional Potts model with 20 states (corresponding to basic amino acids). Solving the inverse problem using data on experimentally confirmed interacting pairs, we obtain the values of the parameters of the Potts model, which we then use to evaluate a new pair of MHC + peptide, and supplement this value with the input data of the neural network. This approach, combined with the ensemble construction technique, allows for improved prediction accuracy, in terms of the positive predictive value (PPV) metric, compared to the baseline model.

A simple model based on a kinetic-type equation is proposed to describe the spread of a virus in space through the migration of virus carriers from a certain center. The consideration is carried out on the example of three countries for which such a one-dimensional model is applicable: Russia, Italy and Chile. The geographical location of these countries and their elongation in the direction from the centers of infection (Moscow, Milan and Lombardia in general, as well as Santiago, respectively) makes it possible to use such an approximation. The aim is to determine the dynamic density of the infected in time and space. The model is two-parameter. The first parameter is the value of the average spreading rate associated with the transfer of infected moving by transport vehicles. The second parameter is the frequency of the decrease of the infected as they move through the country, which is associated with the passengers reaching their destination, as well as with quarantine measures. The parameters are determined from the actual known data for the first days of the spatial spread of the epidemic. An analytical solution is being built; simple numerical methods are also used to obtain a series of calculations. The geographical spread of the disease is a factor taken into account in the model, the second important factor is that contact infection in the field is not taken into account. Therefore, the comparison of the calculated values with the actual data in the initial period of infection coincides with the real data, then these data become higher than the model data. Those no less model calculations allow us to make some predictions. In addition to the speed of infection, a similar “speed of recovery” is possible. When such a speed is found for the majority of the country's population, a conclusion is made about the beginning of a global recovery, which coincides with real data.

The numerical methods used to simulate the evolution of hydrodynamic systems require the considerable use of computational resources thus limiting the number of possible simulations. The data-driven simulation technique is one promising approach to the development of heuristic models, which may speed up the study of such models. In this approach, machine learning methods are used to tune the weights of an artificial neural network that predicts the state of a physical system at a given point in time based on initial conditions. This article describes an original neural network architecture and a novel multi-stage training procedure which create a heuristic model of a two-phase flow in a heterogeneous porous medium. The neural network-based model predicts the states of the grid cells at an arbitrary timestep (within the known constraints), taking in only the initial conditions: the properties of the heterogeneous permeability of the medium and the location of sources and sinks. The proposed model requires orders of magnitude less processor time in comparison with the classical numerical method, which served as a criterion for evaluating the effectiveness of the trained model. The proposed architecture includes a number of subnets trained in various combinations on several datasets. The techniques of adversarial training and weight transfer are utilized.

Finding PageRank vector is of great scientific and practical interest due to its applicability to modern search engines. Despite the fact that this problem is reduced to finding the eigenvector of the stochastic matrix $P$, the need for new algorithms is justified by a large size of the input data. To achieve no more than linear execution time, various randomized methods have been proposed, returning the expected result only with some probability close enough to one. We will consider two of them by reducing the problem of calculating the PageRank vector to the problem of finding equilibrium in an antagonistic matrix game, which is then solved using the Grigoriadis – Khachiyan algorithm. This implementation works effectively under the assumption of sparsity of the input matrix. As far as we know, there are no successful implementations of neither the Grigoriadis – Khachiyan algorithm nor its application to the task of calculating the PageRank vector. The purpose of this paper is to fill this gap. The article describes an algorithm giving pseudocode and some details of the implementation. In addition, it discusses another randomized method of calculating the PageRank vector, namely, Markov chain Monte Carlo (MCMC), in order to compare the results of these algorithms on matrices with different values of the spectral gap. The latter is of particular interest, since the magnitude of the spectral gap strongly affects the convergence rate of MCMC and does not affect the other two approaches at all. The comparison was carried out on two types of generated graphs: chains and $d$-dimensional cubes. The experiments, as predicted by the theory, demonstrated the effectiveness of the Grigoriadis – Khachiyan algorithm in comparison with MCMC for sparse graphs with a small spectral gap value. The written code is publicly available, so everyone can reproduce the results themselves or use this implementation for their own needs. The work has a purely practical orientation, no theoretical results were obtained.

This paper focuses on the problem of modeling and analyzing dynamic regimes, both regular and chaotic, in systems of coupled populations in the presence of random disturbances. The discrete Ricker model is used as the initial deterministic population model. The paper examines the dynamics of two populations coupled by migration. Migration is proportional to the difference between the densities of two populations with a coupling coefficient responsible for the strength of the migration flow. Isolated population subsystems, modeled by the Ricker map, exhibit various dynamic modes, including equilibrium, periodic, and chaotic ones. In this study, the coupling coefficient is treated as a bifurcation parameter and the parameters of natural population growth rate remain fixed. Under these conditions, one subsystem is in the equilibrium mode, while the other exhibits chaotic behavior. The coupling of two populations through migration creates new dynamic regimes, which were not observed in the isolated model. This article aims to analyze the dynamics of corporate systems with variations in the flow intensity between population subsystems. The article presents a bifurcation analysis of the attractors in a deterministic model of two coupled populations, identifies zones of monostability and bistability, and gives examples of regular and chaotic attractors. The main focus of the work is in comparing the stability of dynamic regimes against random disturbances in the migration intensity. Noise-induced transitions from a periodic attractor to a chaotic attractor are identified and described using direct numerical simulation methods. The Lyapunov exponents are used to analyze stochastic phenomena. It has been shown that in this model, there is a region of change in the bifurcation parameter in which, even with an increase in the intensity of random perturbations, there is no transition from order to chaos. For the analytical study of noise-induced transitions, the stochastic sensitivity function technique and the confidence domain method are used. The paper demonstrates how this mathematical tool can be employed to predict the critical noise intensity that causes a periodic regime to transform into a chaotic one.