SOLUTION OF THE PROBLEM OF COMPUTATIONAL STABILITY AND CONSISTENCY OF SAMPLE ESTIMATES OF THE CORRELATION MATRIX OF OBSERVATIONS BY THE METHOD OF DYNAMIC REGULARIZATION

The problem of forming sample estimates of the correlation matrix of observations that satisfy the criterion "computational stability – consistency" is considered. The variants in which the direct and inverse asymptotic forms of the correlation matrix of observations are approximated by various types of estimates formed from a sample of a fixed volume are investigated. The consistency of computationally stable estimates of the correlation matrix for their static regularization was analyzed. The contradiction inherent in the problem of regularization of the estimates with a fixed parameter is revealed. The dynamic regularization method as an alternative approach is proposed, which is based on the uniqueness theorem for solving the inverse problem with perturbed initial data. An optimal mean-square approximation algorithm has been developed for dynamic regularization of sample estimates of the correlation matrix of observations, using the law of monotonic decrease in the regularizing parameter with increasing sample size. An optimal dynamic regularization function was obtained for sample estimates of the correlation matrix under conditions of a priori uncertainty with respect to their spectral composition. The preference of this approach to the regularization of sample estimates of the correlation matrix under conditions of a priori uncertainty is proved, which allows to exclude the domain of computational instability from solving the inverse problem and obtain its solution in real time without involving prediction data and additional computational cost for finding the optimal value of the regularization parameter. The application of the dynamic regularization method is shown for solving the problem of detecting a signal at the output of an adaptive antenna array in a nondeterministic clutter and jamming environment. The results of a computational experiment that confirm the main conclusions are presented.

FEATURES OF DIAGNOSTIC ARTIFICIAL NEURAL NETWORKS FOR HYBRID EXPERT SYSTEMS

In the proposed article, various methods of constructing an artificial neural network as one of the components of a hybrid expert system for diagnosis were investigated. A review of foreign literature in recent years was conducted, where hybrid expert systems were considered as an integral part of complex technical systems in the field of security. The advantages and disadvantages of artificial neural networks are listed, and the main problems in creating hybrid expert systems for diagnostics are indicated, proving the relevance of further development of artificial neural networks for hybrid expert systems. The approaches to the analysis of natural language sentences, which are used for the work of hybrid expert systems with artificial neural networks, are considered. A bulletin board is shown, its structure and principle of operation are described. The structure of the bulletin board is divided into levels and sublevels. At sublevels, a confidence factor is applied. The dependence of the values of the confidence factor on the fulfillment of a particular condition is shown. The links between the levels and sublevels of the bulletin board are also described. As an artificial neural network architecture, the «key-threshold» model is used, the rule of neuron operation is shown. In addition, an artificial neural network has the property of training, based on the application of the penalty property, which is able to calculate depending on the accident situation. The behavior of a complex technical system, as well as its faulty states, are modeled using a model that describes the structure and behavior of a given system. To optimize the data of a complex technical system, an evolutionary algorithm is used to minimize the objective function. Solutions to the optimization problem consist of Pareto solution vectors. Optimization and training tasks are solved by using the Hopfield network. In general, a hybrid expert system is described using semantic networks, which consist of vertices and edges. The reference model of a complex technical system is stored in the knowledge base and updated during the acquisition of new knowledge. In an emergency, or about its premise, with the help of neural networks, a search is made for the cause and the control action necessary to eliminate the accident. The considered approaches, interacting with each other, can improve the operation of diagnostic artificial neural networks in the case of emergency management, showing more accurate data in a short time. In addition, the use of such a network for analyzing the state of health, as well as forecasting based on diagnostic data using the example of a complex technical system, is presented.

THE DYNAMICS OF THE INTERFERENCE SITUATION IN THE DOWNLINK DIRECTION OF THE MOBILE COMMUNICATION NETWORK WITH CDMA TECHNOLOGY

The work is devoted to the investigation of inter-cell interference in the radio access network, provided that subscribers are moving in cells along the route indicated earlier. Very often, the trajectory of the movement of mobile stations coincides with the grid of city streets, where subscribers are moving in public transport. For a network where the cluster dimension is K = 1, the proposed methodology for studying changes in the level of intra-system interference at the input of the receiver of a mobile station when a subscriber is moving along the given path. The features of the situation where the control mode of the transmitter power of the base station is used in each cell, which provides a constant power level of the input signal when the subscriber is moving within the cell, are analyzed. The level of inter-cell interference is estimated as one of the factors on which the quality of services depends, namely, the signal-to-interference ratio at the input of the receiver of the mobile station. For specific trajectories of the movement of subscribers in neighboring cells, a law of changing the transmitter power of the base station was found, which interferes with the receiver of the mobile station in the neighboring cell. Estimated ratios are obtained for determining the level of interference when subscribers in neighboring cells are moving along parallel streets. This assessment of the dependence of the signal / interference ratio at the input of the subscriber's receiver on the speed and direction of its movement. This dependence shows that serious problems with the quality of service provided by the operator will not arise. Such an investigation allows modeling the cellular network in order to optimize the work on improving the services provided to mobile subscribers.

FRACTAL GRAPHICS FOR VIRTUAL ENVIRONMENT GENERATION

Progress in hardware and software development is impressively fast. The main reason of computer graphics fast improvement is a full experience that can be reached though visual representation of our world. Therefore, the most interesting problem of it is a realistic image with high quality and resolution, which often requires procedural graphics generation. The article analyzes simplicity of a fractal and mathematics abstraction. Mathematics describes not only accuracy and logic but also beauty of the Universe. Mountains, clouds, trees, cells do not fit into the world of Euclidean geometry. They cannot be described by its methods. But fractals and fractal geometry solve that problem. Fractals are fairly simple equations on a sheet of paper with bright, unusual images, and, above all, they explain things. Fractal is a figure in the space, which consists of statistical character as the whole. It is self-similar, and therefore looks ‘roughly’ same and does not depend on its scale. So, any complex object can be called a fractal, if it has the same shape, as the parts it consists of. Fractal is abstract, and it helps to translate any algebraic problem into geometric, where solution is always obvious. A lot of researches in the field of fractal graphics has been carried out, but there are still issues that deserve considerable attention and more perfect solutions. The main purpose of the work is codes development with object-oriented programming languages for fractal graphics rendering. The article analyzes simplicity of a fractal and mathematics abstraction. Procedural generation was described as a method of algorithmic data generation for 3D models and textures creation. Code was written with general-purpose programming language Python, which renders step by step creation of fractal composition and variations of fractal images. Fractal generation used for modeling is part of realism in computer graphics In summary, procedural generation is very important for video games, as it can be used to automatically create large amount of game content. The random generation of natural looking landscapes is based on geometric computer generated images Created compositions can be used in computer science for image compression, in medicine for the study of the cellular level of organs, etc.

CRYPTOGRAPHIC AUTHENTICATION PROTOCOL ZERO-KNOWLEDGE SECRET ON ELLIPTIC CURVES USING PUBLIC KEYS AND RANDOM MESSAGES

We propose a cryptographic protocol with zero-knowledge proof (ZKP) on elliptic curves (EC) using public keys and random messages, allowing to establish the truth of a statement not conveying any additional information about the statement itself. The cryptographic protocols based on zero-knowledge proof allow identification, key exchange and other cryptographic operations to be performed without leakage of sensitive information during the information exchange. The implementation of the cryptographic protocol of the zero-knowledge proof on the basis of the mathematical apparatus of elliptic curves allows to significantly reduce the size of the protocol parameters and increase its cryptographic strength (computational complexity of the breaking). The security of cryptosystems involving elliptic curves is based on the difficulty of solving the elliptic curve discrete logarithm problem. We determine the completeness and correctness of the protocol and give an example of the calculation is given. The cryptographic protocol was modeled in the High-Level Protocol Specification Language, the model validation and verification of the protocol were also performed. The software verification of the cryptographic protocol was performed using the software modules On the Fly Model Checker and Constraint Logic based Attack Searcher. In order to validate the cryptographic protocol resistance to intruder attacks, we used the Security Protocol Animator package for Automated Validation of Internet Security Protocols and Applications. The security of the proposed cryptographic protocol ZKP EC is based on the difficulty of solving the elliptic curve discrete logarithm problem). The recommended elliptical curves according to DSTU 4145-2002 may be used to implement such cryptographic protocol.

ANALYTICAL EVALUATION OF THE NUMERICAL VALUES OF THE HUBBLE CONSTANT AND MAIN SPATIAL-ENERGY CHARACTERISTICS OF THE OBSERVABLE UNIVERSE

Since the baryonic matter of the observable Universe consists mainly of protons and neutrons, then the numerical value of its mass can be represented and calculated on the basis of an additive-multiplicative golden algebraic fractal, based on golden algebraic fractals of the masse of proton, neutron, and muon. Based on an analytical estimate of the mass of the observable Universe, using the law “Planck’s Universal Proportions”, an analytical estimate of the Hubble constant and the main spatial-energy characteristics of the observed Universe is obtained. An analytical estimate of the Hubble constant is consistent with the experimental data of Planck’s mission, SDSS-III Baryon Oscillation Spectroscopic Survey, DES Collaboration. The objectivity of the experimental estimation of the Hubble constant from the H0LiCOW, Riess et al, Hubble Space Telescope collaborations does not raise any doubts. This means that the Hubble constant describes two similar, but different physical processes and has at least two values. The value of the Hubble constant from the collaborations Planck’s mission, SDSS-III Baryon Oscillation Spectroscopic Survey, DES Collaboration describes the process of rotation of the space of the observed Universe, and the value of the Hubble constant from the collaborations H0LiCOW, Riess et al, Hubble Space Telescope describes the process of rotation of substance in the space of the observed Universe. It is shown that after the Big Bang, the space of the observable Universe made one incomplete revolution of at 345 degrees, and the substance in it made one complete revolution of approximately 379 degrees. New estimates are given: of the gravitational constant, of the Planck energy, of the Planck acceleration, of the Planck force, of the gravity factor of the observable Universe, of the Planck temperature, of the angular velocity of rotation of the space of the observable Universe. Estimates of temperature and wavelength of thermal radiation of the observable Universe, as the Hubble sphere, are given.