2023.3

The article discusses the development of a system for identifying the channel of information leakage from a document photo taken from a computer screen via digital watermarks integrated into the image on the monitor. The article also presents the results of an experimental study to prove the properties of the algorithm and its resistance to deliberate attacks.

Recurrent sequences over a set of integers are considered, in which arbitrary superpositions of polynomial functions and functions close to polynomial ones are used as generating functions, — almost polynomial recurrent sequences. A series of functions of the form b · ji(x) is distinguished. Each of these functions, together with polynomial functions, allows us to construct generating functions that make it possible to determine almost polynomial recurrent sequences that simulate calculations on Minsky machines. Based on this result, algorithmically unsolvable problems related to these almost polynomial recurrent sequences are formulated. Consequences are obtained that significantly expand the range of functions capable of generating recurrent sequences with algorithmically unsolvable problems.

This paper is devoted to the problem of separation of mixtures of probability distributions. An optimization method is proposed as an alternative to the EM-algorithm (Expectation-Maximization) for statistical estimation of mixture parameters. The idea of approximating the distribution of increments (logarithms) of financial data by a mixture of normal laws is considered. The practical application of such an approximation to the problems of calculating and predicting volatility, as well as to the problem of calculating the risk measure (Value at Risk), is presented. The results obtained allow us to conclude that the application of mixtures of normal distributions to the description of financial data is adequate.

The article deals with localization methods of inverse magnetoencephalography tasks. Localization methods are important in real clinical practice. During neurosurgical interventions, various areas of the brain can be damaged, including non-recoverable areas. Since the location of functional areas in the human brain is individual, the doctor must be able to localize these areas in the preoperative period with high accuracy. The developed methods serve the solution of such an important problem.

Similarity transformations are the main part of matrix theory, which studies numerous classes of special matrices. Accordingly, there are many ways of describing such classes. In most cases, one can verify whether a matrix belongs to the required class by a rational calculation, that is, by a finite algorithm using only arithmetical operations.

The use of a large number of drones set us the tasks of correct, transparent, and high-performance modeling of their collective activity within the framework of swarm behavior. For this, an example of transitioning from the description of the control system of a single drone to the behavior of a swarm of identical drones based on Hadamard algebra (product) was developed and given. It was found that the use of such an approach increases the performance of the model by dozens of times and allows modeling of swarm systems with a very large number of agents.

We study the existence of an implicit function, defined by an equation G(x, σ) = 0, in a neighborhood of an abnormal point (x0, σ0). We prove that if some λ-truncation of the mapping F(x) = G(x, σ0) is regular in a certain direction, then the sought implicit function exists.