STRATEGIC INTERACTION OF PROVIDERS FOR DIFFERENTIATED INTERNET SERVICES

As computing and Internet connections become general-purpose technologies and services aimed at broad global markets, questions arise about the effectiveness of such markets in terms of public welfare, the participation of differentiated service providers and end-users. Motorola’s Iridium Global Communications project was completed in the 1990s due to similar issues, reaching the goal of technological connectivity for the first time. As Internet services are characterized by high innovation, differentiation and dynamism, they can use well-known models of differentiated products. However, the demand functions in such models are hyperbolic rather than linear. In addition, such models are stochastic and include providers with different ways of competing. In the Internet ecosystem, the links between Internet service providers (ISPs) as telecommunications operators and content service providers are important, especially high-bandwidth video content providers. As increasing bandwidth requires new investments in network capacity, both video content providers and ISPs need to be motivated to do so. In order to analyze the relationships between Internet service providers and content providers in the Internet ecosystem, computable models, based on the construction of payoff functions for all the participants in the ecosystem, are suggested. The introduction of paid content browsing will motivate Internet service providers to invest in increasing the capacity of the global network, which has a trend of exponential growth. At the same time, such a browsing will violate the principles of net neutrality, which provides grounds for the development of new tasks to minimize the violations of net neutrality and maximize the social welfare of the Internet ecosystem. The models point to the importance of the efficiency of Internet service providers, the predictability of demand and the high price elasticity of innovative services.

ON THE ACCELERATION OF OPTIMIZATION METHODS FOR THE PROBLEM OF SYNTHESIS OF MULTILAYER OPTICAL COATINGS

Five ways to speed up the multidimensional search in order to solve the problem of synthesis of multilayer optical coatings by using the methods of zero and first orders have been considered. The first way is to use an analytical derivative for the target quality function of the multilayer coating. It allows us to calculate accurately (within the computer arithmetic) the value of the gradient of a smooth objective function and generalized gradient of a non-smooth objective one. The first way requires the same number of arithmetic operations as well as finite-difference methods of calculating the gradient and the generalized gradient. The second way is to use a speedy finding of the objective function gradient using the prefix- and suffix-arrays in the analytical method of calculating the gradient. This technique allows us to reduce the number of arithmetic operations thrice for large-scale problems. The third way is the use of tabulating the values of trigonometric functions to calculate the characteristic matrices. This technique reduces the execution time of multiplication operations of characteristic matrices ten times depending on the computer’s specifications. For some computer architectures, this advantage is more than 140 times. The fourth method is the use of the golden section method for the one-dimensional optimization in the problems of synthesis of optical coatings. In particular, when solving one partial problem it is shown that the ternary search method requires approximately 40% more time than the golden section method. The fifth way is to use the effective implementation of multiplication of two matrices. It lies in changing the order of the second and third cycles for the well-known method of multiplying two matrices and fixing in a common variable value of the element of the first matrix. This allows us to speed up significantly the multiplication operation of two matrices. For matrices having 1000 x 1000 dimension the acceleration is from 2 to 15 times, depending on the computer's specifications.

DETERMINATION OF MODEL PARAMETERS OF ROCKET STABILIZATION SYSTEM IN FLIGHT

The dynamic characteristics of the system that includes the controlled object and the regulator largely depend on the choice of the control law, which is determined based on the nominal values of the parameters of the mathematical model of the stabilization process and its priority indicator. Due to the deviation of the missile parameters and, accordingly, the model from the nominal values, the designers set the safety factors based on the most unfavorable conditions, which negatively affects the overall performance, in particular, the relative weight of the payload. Therefore, there is a need to develop algorithms for adjustment that is identification model parameters during the flight using the signals of measuring devices and the capabilities of on-board computers. This will increase the efficiency of methods of choosing the control law based on such indicators as stabilization accuracy, stability margin and power requirements of the actuator. The aim of the article is to develop methods for refining the parameters of the rocket stabilization system in the yawing plane, which are based on the use of current data of measuring devices of the part of coordinates of the state vector, and verify the effectiveness of refinement in terms of the above indicators. A linear stationary model of a system for stabilizing the perturbed motion of a rocket taking into account the inertia of the actuator in the form of ordinary fifth-order differential equations is adopted. Two approaches are proposed to approximate the model parameters to their actual values. In the first in the model parameter space there is a minimum of the integral of the distance between the points of the trajectory according to the signals of the measuring devices and the trajectory obtained by modeling the perturbation compensation process. In the second, the actual values of the parameters are the result of solving a system of nonlinear equations, which includes data from measuring devices and the corresponding data obtained by simulation. On the example of space rocket parameters it is shown that the choice of the control law based on the actual coefficients of the model leads to a significant reduction of deviations from the set value of the system stability margin, stabilization error and power of the actuator.

NUMERICAL INVESTIGATION OF THERMOMECHANICAL PROCESSES UNDER SHORT-PULSED LASER IRRADIATION OF A HALF-SPACE

The laser irradiation of metallic surfaces by intense heat sources is used for the generation of short probing pulses, which propagate into thin specimens and enable one to estimate their structure and mechanical properties within the framework of the classical acoustic approach. High thermal stresses and residual strains occur during the short-term irradiation of the surface of a construction by an energy source of high density. In the present work, we solve the axially symmetric problem of a half-space under thermomechanical loading. We take into account the influence of volume and inelastic characteristics of separate phases on the residual stress-strain state of the half-space. The statement of the problem includes: Cauchy relations, equations of motion, heat conduction equation, initial conditions, thermal and mechanical boundary conditions. The thermomechanical behavior of an isotropic material is described by the Bodner-Partom unified model of flow. The problem is solved with using the finite element technique. The numerical realization of our problem is performed with the help of step-by-step time integration. The equations of motion are integrated by the Newmark method. The residual stress-strain state is described using the method of numerical solution of the axisymmetric dynamic problem for a half-space under thermomechanical loading and the flow model. We established that microstructural transformations, which are taken into account due to the thermophase volume strain and dependence of inelastic characteristics of the material on the phase composition, significantly reduce residual inelastic strain and promote the appearance of compressive stresses. The three-zone region of residual stresses field formation is obtained.

MODELS AND METHODS OF INFORMATION TECHNOLOGY OF ADVANCED NEONOTAL SCREENING

The paper considers the problems of informational implementation of neonatal screening of newborns in order to improve the overall picture of the nation's health and prevent the development of hereditary diseases. The methodology for solving the problems of complete neonatal screening is based on the methods and mathematical apparatus of discrete mathematics, web technologies, data warehouses, and data mining methods. An information model of the dynamic processes of neonatal screening is proposed, based on the specific processing of data presented by a tuple, which contains coherent sequential processes for obtaining the results of tests for blood analysis of newborns, conducting genetic studies and determining pathologies and deviations from an expanded list (currently up to 44 indicators for the purpose of exiting for more than 60). The block diagram of information support of information technology in the decision support system for carrying out neonatal screening of hereditary metabolic diseases is presented. On the basis of LLC «CDC «PHARMBIOTEST», the research of the algorithm for performing sequential procedures of neonatal screening was carried out. The described algorithm of actions has been tested and fully tested for the continuity of information flows, the stability of the information model graph. As a result of the research, the sufficiency and completeness of the chronological indicators of the processing of information flows have been proved. The criteria for confirming the authenticity of methods for obtaining a diagnosis have been developed.

INVESTIGATION OF THE IMPACT OF DELAY IN ONE MATHEMATICAL MODEL OF WORLD DEVELOPMENT DYNAMICS

There is a large number of works devoted to the dynamics of world development. But very few of them have clear abstract mathematical models of the corresponding processes. This work is devoted to further deepening and mathematical abstraction of the study of world development process. The qualitative analysis of linear and modified nonlinear model in the form of systems of inhomogeneous differential equations is carried out. Their steady states are calculated, explicit analytical solutions are presented. For the first time, a model taking into account the time delay factor is proposed, which is written in the form of functional-differential equations with argument deviation. It is shown that with such an introduction to the model of a delayed argument, the system can be reduced to a system of linear inhomogeneous differential equations with constant coefficients without delay, and the stability of the steady state of the system equilibrium under study will be affected only by linear terms of equations without argument deviation. This fact well correlates with the socio-economic interpretation of this problem. In the future, the work will focus on studying the influence of not one but several factors of time lag, when the model is presented as a system of functional-differential equations with several different deviating arguments in equations responsible for the dynamics of a particular process dynamics of world development.

EXPERT DECISION-MAKING SYSTEMS

An approach to making complex technical and economic decisions is proposed in cases where there is insufficient (or no) information about the experimental statistical data necessary for the construction of regression models of criterion functions. The situation is aggravated when a decision is made according to several conflicting quality criteria. In conditions of an acute shortage of experimental data, it is proposed to obtain the necessary information («quasi-experimental» data) from experts - specialists with sufficient experience in making decisions for the class in question. A qualified specialist (expert) with sufficient experience in making decisions for this class can perform a thought experiment. He must imagine what, in his opinion, the levels of criterion functions will be at various reference points of factors. The method is based on an individual opinion (postulate), expressed by a specialist-expert about the estimated value, based on his professional experience. To assess a certain quantitative characteristic, the postulates of not one, but several persons competent in this issue are used. It is assumed that the «true» value of the unknown quantitative characteristic is within the range of expert assessments and the «generalized» collective opinion is more reliable. To solve the problem under consideration, a multicriteria optimization approach is taken using a nonlinear trade-off scheme. This study makes it possible to identify the main trends in the development of multi-criteria decision-making systems in the absence (or lack) of experimental data. A model example is given.

IMPROVING FACE RECOGNITION MODELS USING METRIC LEARNING, LEARNING RATE SCHEDULERS, AND AUGMENTATIONS

Face recognition is one of the main tasks of computer vision, which is relevant due to its practical significance and great interest of wide range of scientists. It has many applications, which has led to a huge amount of research in this area. And although research in the field has been going on since the beginning of the computer vision, good results could be achieved only with the help of convolutional neural networks. In this work, a comparative analysis of facial recognition methods before convolutional neural networks was performed. A metric learning approach, augmentations and learning rate schedulers are considered. There were performed bunch of experiments and comparative analysis of the considered methods of improvement of convolutional neural networks. As a result a universal algorithm for training the face recognition model was obtained. In this work, we used SE-ResNet50 as the only neural network for experiments. Metric learning is a method by which it is possible to achieve good accuracy in face recognition. Overfitting is a big problem of neural networks, in particular because they have too many parameters and usually not enough data to guarantee the generalization of the model. Additional data labeling can be time-consuming and expensive, so there is such an approach as augmentation. Augmentations artificially increase the training dataset, so as expected, this method improved the results relative to the original experiment in all experiments. Different degrees and more aggressive forms of augmentation in this work led to better results. As expected, the best learning rate scheduler was cosine scheduler with warm-ups and restarts. This schedule has few parameters, so it is also easy to use. In general, using different approaches, we were able to obtain an accuracy of 93,5 %, which is 22 % better than the baseline experiment. In the following studies, it is planned to consider improving not only the model of facial recognition, but also detection. The accuracy of face detection directly depends on the quality of face recognition.

ON THE UPPER AND LOWER RESOLVING FUNCTIONS IN GAME PROBLEMS OF DYNAMICS

The quasi-linear conflict-controlled processes of general form are studied. The theme for investigation is the problem of the trajectories approaching a given cylindrical set. The research is based on the method of upper and lower resolving functions. The main attention is paid to the case when Pontryagin’s condition does not hold, moreover, the bodily part of the terminal set is non-convex. A scheme of the method is proposed, which allows, in the case of non-convexity of the body part, to fix some point in it, namely the aiming point, and to realize the process of approach. Sufficient conditions are obtained for solving the problem of approach for different classes of strategies. In so doing, the Hayek stroboscopic strategies that prescribe control by N.N. Krasovskii are applied. The process of approach goes on in two stages — active and passive. On the active stage the upper resolving function of second type is accumulated and after the moment of switching the lower resolving function of second type is used. These functions allow constructing a measurable control of second player on the basis of the theorems on measurable choice, in particular, the Filippov-Castaing theorem. The obtained results for generalized quasi-linear processes make it possible to encompass a wide range of functional-differential systems as well as the systems with fractional and partial derivatives. Possibilities for development of the offered technique are specified.

COMPARATIVE ANALYSIS OF THE EFFICIENCY OF CONSTANT POWER THROTTLED ROCKET ENGINES FOR INTERORBITAL FLIGHTS TO GEOSTATIONAR

Carrying out low-thrust transfers of spacecrafts in the near-earth space from intermediate elliptic to the geostationary orbit using electric rocket engines seems to be one of the most important tasks of modern cosmonautics. Electric rocket engines, whose specific impulse of the reactive jet is an order of magnitude more than in chemical RD, are preferable for interorbit flights with a maximum payload in the case when a significant increase in the duration of the maneuver is permissible. Ability to throttling the rocket engine thrust is traditionally considered as one of the ways to reduce both the engine mass and the required fuel assumptions for performing the specified maneuver. Using the concept of an ideal-rocket engine provides the upper estimates of the payload mass of interborbital flights for the given power level. Accounting for the properties of real engines leads to the need of considering the mathematical models with more strict limits on control functions. A study of the efficiency of three modes of thrust control of an electric propulsion rocket engine was carried out when performing practically interesting spacecraft flights from highly elliptical intermediate near-earth orbits to geostationary orbits. A mathematical model of constant power relay rocket engine has been built. The formulation of the variational problem of the Maer type is given about the execution of a given dynamic maneuver for the throttled and unregulated electric rocket engines of constant power. Using the Pontryagin maximum principle, an analysis of the optimal control functions was carried out, for which the final relations were written out, which allowed to write down the system of differential equations of the optimal movement of the spacecraft, equipped with relay electric rocket engine. The obtained numerical and quality results of the study of the effectiveness of various modes of thrust control of an electric propulsion engine to increase the payload of a given orbital maneuver confirmed the correctness of mathematical models of throttled and relay engines and, in general, the efficiency of using solutions of the averaged equations of optimal motion of a spacecraft for numerical solution of the corresponding boundary value problems in an exact formulation.