In this paper, we consider an optimal control problem for a system of linear first-order hyperbolic equations in which the inhomogeneity in the right-hand side is determined from the controlled linear system of ordinary differential equations with constant delay. The coefficient matrix at phase variables in the system of ordinary differential equations depends on the control function. The cost functional is linear. On the basis of the exact increment formula (without remainder terms) of the cost functional, the problem is reduced to the optimal control problem of a system of ordinary differential equations. The result is formulated in the form of a non-classical variational optimality condition. The proposed problem reduction significantly reduces the amount of calculations when using numerical optimization methods. An illustrative example is given.

A great number of solutions of the Einstein field equation are known. They describe the gravitational field in the empty space-time, in the space-time with electromagnetic field and for a ball filled with a liquid under pressure. The present work is devoted to gravitational field generated by some mass distribution. One of the simplest cases is considered, when mass is uniformly distributed inside a ball and is not moving. The boundary problem for the Einstein equation is formulated. Solution outside the ball is the Schwartzschild solution in vacuum. The coordinates at which the Schwartzschild solution is written are different from the coordinates used in equations for components of the metric tensor inside the ball. Relations between internal and external coordinates are found on the ball surface. They allow to use the Schwartzschild solution for formulation of boundary conditions for internal solution. The solution of the boundary problem is found for the case of weak field. This solution can be used as an example in the analysis of laws of conservation for the gravitational field, in which interaction of mass with field generated by the mass gives a contribution to momentum and energy of the gravitational field.

This paper discusses bifurcational phenomena in a control system with pulse-width modulation of the first kind. We show that the transition from a regular dynamics to chaos occurs in a sequence of classical supercritical period doubling and border collision bifurcations. As a parameter is varied, one can observe a cascade of doubling of the cyclic chaotic intervals, which are associated with homoclinic bifurcations of unstable periodic orbits. Such transition are also refereed as merging bifurcation (known also as merging crisis). At the bifurcation point, the unstable periodic orbit collides with some of the boundaries of a chaotic attractor and as a result, the periodic orbit becomes a homoclinic. This condition we use for obtain equations for bifurcation boundaries in the form of an explicit dependence on the parameters. This allow us to determine the regions of stability for periodic orbits and domains of the existence of four-, two- and one-band chaotic attractors in the parameter plane.

Despite the many advantages offered by Host Intrusion Detection Systems (HIDS), they are rarely adopted in mainstream cybersecurity strategies. Unlike Network Intrusion Detection Systems, a HIDS is the last layer of defence between potential attacks and the underlying OSs. One of the main reasons behind this is its poor capabilities to adequately protect against zero-day attacks. With the rising number of zero-day exploits and related attacks, this is an increasingly imperative requirement for a modern HIDS. In this paper variational long short-term memory — recurrent autoencoder approach which improves zero-day attack detection is proposed. We have practically implemented our model using TensorFlow and evaluated its performance using benchmark ADFA-LD and UNM datasets. We have also compared the results against those from notable publications in the area.

This article presents an analysis of transfer matrix method (TMM) and scattering matrix method (SMM) for determining reflection and transmission coefficients of thin films. Investigated single layer structures of semiconductor materials (Si, Ge, GaAs), noble metals (Ag, Au, Cu) and multilayer structure of Si. Numeric results were getting in two diapason wavelengths: λ = 0.2067–0.8267 µm and λ = 0.2–20 µm. In this work obtained with TMM and SMM the reflection and transmission coefficient of layer structures. Numerical results of reflection coefficients of all investigation structures were exactly match with literature data. But results we got for the transmission coefficients did not match of literature data for the both of method. This mismatch is investigated, as we assume from some of normalization coefficient, corresponding a refractive index of right side of medium which we didn’t take into account.

Today, skin cancer is one of the leading causes of death in the world. Diagnosing skin cancer early is critical to increasing potential survival. Therefore, it is relevant to develop highprecision intelligent auxiliary diagnostic systems for detecting skin cancer in the early stages. Ensemble learning is one of the current and promising methods for increasing the accuracy of intelligent classification systems by reducing the dispersion and variability of predictions of individual components of the overall system. The work proposes an ensemble intelligent system for analyzing heterogeneous dermatological data based on multimodal neural networks. The accuracy of the developed ensemble system was 85.92 %, which is 1.85 percentage points higher than the average accuracy of individual multimodal architectures for classifying heterogeneous dermatological data. The developed system can be used as a high-precision auxiliary diagnostic tool to help make a medical decision, which will increase the chance of early detection of pigmented oncological pathologies.

The paper is devoted to the problem of optimizing gas condensate mining in the process of developing a given number of wells in a field. The essence of the problem is such a distribution of control actions, which are wells pressures, at which, for a given fixed rate of gas mixture mining, maximum gas condensate extraction is ensured at a certain planning horizon. A formalized formulation of the problem is carried out and it is shown that it reduces to a nonlinear programming problem with essentially nonlinear objective function and constraints. Two different approaches to finding the optimal solution are proposed. The first of them is based on solving the original optimization problem, and the second one — on simplifying it in order to reduce the computational costs of finding a solution. A numerical example of gas condensate mining for five wells is presented and a comparison of the obtained modeling results for these two algorithms is performed.

The article describes a general integral model of the inflow and outflow of a dynamic system, the parameters of which are stochastic in nature. For this type of dynamic systems, the general principle of dynamic balance is formulated, and the concepts of interval dynamic balance of integral volumes of inflow and outflow as well as the concept of dynamic balance characteristic are introduced. The class of stochastic dynamic processes and systems of inflow and outflow that satisfy the principle of dynamic balance is quite wide (the spread of viral epidemics and the dynamics of morbidity in medicine, processes of changes in the size and structure of the population in demography, the dynamics of supply and demand in the economy, etc.). The possibilities of using the proposed model for constructing short-term and long-term forecasts are demonstrated using examples of the spread of the COVID-19 epidemic in Moscow and Saint Petersburg, as well as using the example of forecasting the growth of the Earth population and population of countries. The results of computational experiments on constructing retrospective forecasts of the state of dynamic systems using the method of dynamic trends of stochastic parameters of the integral model and using the classical ARIMA method are presented. A comparative analysis of forecasting accuracy is provided.

We have developed a microscopic version of general concealed voter model (GCVM). Original GCVM uses only statistical-physical methods, while our new approach starts with a real network. A microscopic model is suitable for any two-layer network (with internal ans external layers) satisfying the definition given in the paper. We conduct a series of simulations with different network structures and found that a cyclic external structure prolongs consensus time in comparison with a complete external structure. Moreover, a cyclic external structure has a positive impact on a winning rate, and this result is different from the one obtained in the macroscopic version of GCVM. The possible reasons for this difference are discussed in the paper. Additionally, we propose and validate the hypothesis that there exists a strong linear relationship between a consensus time and pairwise average shortest paths $d$ in the network structure. We performed a controlled variable approach to validate the impact of each individual parameter on key performance indicators (KPIs) including a consensus time and winning rate. Furthermore, we assess the influence of parameter combinations on KPIs by analyzing the results using the K-means algorithm. We conclude that certain parameter combinations can have a significant impact on the consensus time.

Traditionally, the principle of maximum entropy is used to find unknown distribution of random variables. In decision theory, this principle is used primarily in situations of uncertainty regarding the probability distribution of hypotheses about the “state of the environment”, where the environment is understood as a set of parameters that influence the result of the decision made. This paper considers the use of the principle of maximum entropy for a different purpose, namely for the purpose of optimal distribution of resources of various types. A proof of theorems is given that make it possible to create algorithms for solving various problems of resource allocation based on the principle of maximum entropy, as well as examples of solving demonstrative problems.