Table of contents

A digital watermark embedding algorithm robust against any changes of a video container format with the use of a three-dimensional (3D) discrete cosine transform is proposed. For embedding the three-dimensional (3D) method based on Koch and Zhao's two-dimensional (2D) method is applied. The image of a digital watermark and its digital hologram as embedded information are used. Embedding is carried out in a YUV color scheme. Computer-simulation experiments are made. The proposed method proved to be robust against attacks of video container format changes.

Mathematical modeling of socium as mechanical system with the material components determined by parts of system with qualitatively excellent complexes of properties concerning production, storage and consumption of production is considered. Existence of objectively operating feedback in the representing system is established. The mathematical model formed in work appears the nonlinear system of the ordinary differential equations and is far-reaching expansion of classical models Lotka and Volterra. The mathematical analysis shows existence of a fixed point in phase space of solutions of system and gives for her analytical expressions. Results of private numerical modeling of the offered model are presented. Results of modeling show manifestations of difficult oscillatory dynamics of phase trajectories of the solution of system and serve as an essential argument of an explanation of real oscillatory processes in the history of social systems.

Rationale and objectives. The paper aims at the decrease of requirements to a test sample size while estimating the entropy of long codes with dependent digits. Materials and methods. Codes in the Hamming space instead of typical codes are used that is equal to an exponential decrease of a number of controlled code states. Results. Usage of beta distributions instead of normal ones for describing the Hamming distances allows overcoming the restrictions of the previously applied GOST R 52633.3 algorithm. A nomogram generated for fast and reliable computations appeared linear in logarithmic coordinates that makes its usage simple and convenient. Conclusions. The calculation of the entropy of long codes by Shannon method is not possible in practice as it is a task with exponential computational complexity. The usage of the Hamming codes instead of normal ones results in a decrease of the computational complexity to a linear one. The application of beta distributions for describing the Hamming statistics allows overcoming normality test restrictions for initial data. The proposed fast method of computing the entropy is becoming common.

The solution of equations and systems of equations over real, complex, rational and integer numbers is a classic topic of research in various areas of mathematics for several thousand years. In the last 20 years, the so-called universal algebraic geometry has been actively developed, in which systems of equations over arbitrary algebraic systems are researched. Many practically important problems on finite graphs, finite fields, and finite orders can be formulated as problems related to solving systems of equations over these systems, which leads to the need to develop algebraic geometry. Many modern models of informational defence represents by graphs and partial orders (posets). This article presents polynomial algorithms for constructing radical and coordinate partial order of systems of equations over finite partial orders in a language without constants.

The article deals with the reliability problem of information systems and contains the developed method for assessing the fault-tolerance of data transmission systems and mathematical model that allows to obtain the probability of failure at different levels of information systems.

The game task of confrontation of the attacked hardware-redundant dynamic system with an attacking enemy operating in conditions of incomplete information about the behavior of the attacked enemy in the process of conflict was posed and solved numerically and analytically.

The attacking party aspires to increase the intensity of the failures of the components of the attacked system at the expense of its attack resources, up to its total failure. The attacked party, due to the corresponding strategy of redistribution of reserve blocks of the hardware-redundant dynamic system between the failed main blocks at the appropriate instants of time, strives to maximize the probability of failure-free operation of the attacked system at the end of the confrontation (game) with the attacking enemy.

Behavior of the system under attack in the process of conflict is approximated by the Markov process, and the number of operable states is equal to the number of failed functional blocks that do not exceed the number of standby blocks. As a payment function in the game in question, the probability of failure-free operation of the attacked system is used by the time the game ends. The solution of the game is the vector of the system setup moments after the corresponding failures of the functional blocks and the set of reservation vectors corresponding to the instantaneous settings of the system being attacked, which maximizes the probability of system failure during the conflict.

The differential game model is reduced to a multi-step matrix model with given probabilities of the states of the attacking enemy. Numerical algorithms for calculating the vector of reservation for the attacked system that maximizes the probability of its trouble-free operation by the end of the game and for solving the game problem in question are presented in a form convenient for implementation on a personal computer.

Two mathematical models have been built to describe the behavior of an information system with a client-server architecture without and taking into account the ultimate reliability of the monitoring system and the restoration of the failed component of the system under consideration. The behavior of the information system in the presence of failures and the restoration of the performance of components is approximated by a Markov process and is described by a system of differential equations with variable coefficients. The solution of the obtained differential equations by numerical methods on computers allows the research of various characteristics of the reliability of information systems such as "client-server" in a wide range of changes in failure rates and restoration of system components.

The article is connected with a problem of the organization of purposeful movement, actual for various spheres of activity. Described is one of ways of the decision of this problem on an example of imitation of purposeful movement of packages in a network of data transmission. For routing samples are used. Sample ST it n of the parameters. These parameters are coordinates of a point in n-dimensional space. The state Si of each communication channel too has n the current parameters. The packet is transmitted over a channel for which the Euclidean distance from Si to ST is minimal. The simulation model is implemented on GPSSW. The results of the experiments showed the possibility and feasibility of using samples for routing. The samples can be used to select the routes of purposeful movement on the oriented graphs in systems for various purposes: technical, economic, social.

In this article, we show that the concept of graph compression is important for the study of universal equivalence of simple graphs (not necessarily finite) and graph algebraic structures.

The article is based on the monitoring faults problem of information systems and contains the mathematical model description of the process for monitoring faulty parameters for network equipment, which takes into account the probability dependence of events on a time intervals, and offers a method of probabilistic forecasting of the state of network failure.

Static biometric patterns such as fingerprint, iris and face are difficult to keep secret. Since the open pattern has a little potential replacement options stealing a strange open biometrics provides great opportunities for compromising systems. Authentication on the basis of electroencephalogram pattern (EEG) is the most secure kind of biometric security. The present study aims to develop a method of biometric authentication by the EEG data with high accuracy. Several neural network EEG pattern verification algorithms have been tested. A method for verification of the human EEG pattern based on a modified Bayes hypothesis formula has been developed. The following error indicators FAR <10^-4 with FRR = 0.062 were achieved.

This work was supported by the Russian Foundation for Basic Research (RFBR) and the Government of the Omsk Region (grant 18-41-550002).

The article deals with the problem of calculating the frequency of network motifs with a help of Rand-ESU algorithm. We have established that while using a Rand-ESU algorithm, it is necessary to cut off (to thin out) the network motifs only on the last level of ESU-tree (and therefore, an implementation of the algorithm requires the construction of almost entire ESU-tree). Examples of calculations are given, they demonstrate, that other strategies to cut-off sampling lead to larger distance errors in calculation.

The problem of calculating the frequencies of network motifs on three and four nodes in large networks is considered. Telecommunications networks, cell molecular networks are investigated. The sizes of the investigated networks are hundreds of thousands of nodes and connections. These networks are represented in the form of directed and undirected simple graphs. Exact calculating requires huge computational resources for such large graphs. A method for calculating the frequencies of network motifs using the Monte Carlo method with control of an accuracy of calculations is proposed. The proposed effective method minimizes the value of the coefficient of variation.

A study of the duration of transients processes in random graphs with preferred attachment was carried out, during which it was found out that for some random graphs transient processes can last very long. For some known growing graphs the absence of stationary distribution of the vertices attachment degree has been found out for the first time. This makes the calculation methods and the techniques for analyzing transient processes up-to-date, because real networks modelled by this graphs, do not have stationary characteristics either. Real networks having stationary characteristics, can for a long time, even if they are too large, stay in the transient mode which does not let estimate these networks by stationary solutions. While modeling these networks, the methods for analyzing the transient modes are also urgent as they provide for controlling the errors of stationary solutions application. The paper gives the example of the stationary solution error control for a random graph, widely used in modeling of growing networks.