Information technologies have become increasingly used in various fields, be it document management or payment systems. One of the most popular and promising technologies is cryptocurrency. Since they require ensuring the security and reliability of data in the system, most of them use blockchain and complex cryptographic protocols, such as zero-knowledge proof protocols (ZKP). Therefore, an important aspect for achieving the security of these systems is verification, since it can be used to assess the system's resistance to various attacks, as well as its compliance with security requirements. This paper will consider both the concept of verification itself and the methods for its implementation. A comparison of methods for identifying a proof suitable for zero-knowledge protocols is also carried out. And as a result, a conclusion is made that an integrated approach to verification is needed, since choosing only one method cannot cover all potential vulnerabilities. In this regard, it is necessary to apply various verification methods at various stages of system design.

Keywords: cryptocurrency, blockchain, verification, formal method, static analysis, dynamic method, zero-knowledge proof protocol

This paper proposes a novel model of computer network behavior that incorporates weighted multi-label dependencies to identify rare anomalous events. The model accounts for multi-label dependencies not previously encountered in the source data, enabling a "preemptive" assessment of their potential destructive impact on the network. An algorithm for calculating the potential damage from the realization of a multi-label dependency is presented. The proposed model is applicable for analyzing a broad spectrum of rare events in information security and for developing new methods and algorithms for information protection based on multi-label patterns. The approach allows for fine-tuning the parameters of multi-label dependency accounting within the model, depending on the specific goals and operating conditions of the computer network.

Keywords: multi-label classification, multi-label dependency, attribute space, computer attacks, information security, network traffic classification, attack detection, attribute informativeness, model, rare anomalous events, anomalous events

The article is devoted to the development of an innovative neural network decision support system for firefighting in conditions of limited visibility. A comprehensive approach based on the integration of data from multispectral sensors (lidar, ultrasonic phased array, temperature and hygrometric sensors) is presented. The architecture includes a hybrid network that combines three-dimensional convolutional and bidirectional LSTM neurons. To improve the quality of processing, a cross-modal attention mechanism is used to evaluate the physical nature and reliability of incoming signals. A Bayesian approach is used to account for the uncertainty of forecasts using the Monte Carlo dropout method. Adaptive routing algorithms allow for quick response to changing situations. This solution significantly improves the efficiency of firefighting operations and reduces the risk to personnel.

Keywords: mathematical model, intelligence, organizational model, gas and smoke protection service, neural networks, limited visibility, fire department, management, intelligent systems, decision support

Problem statement. When modeling a complex technical system, the issues of parameter estimation are of primary importance. To solve this problem, it is necessary to obtain a methodology that allows eliminating errors and inaccuracies in obtaining numerical parameters. Goal. The article is devoted to a systematic analysis of the methodology for estimating the parameters of a complex technical system using the interval estimation method. The research method. A systematic analysis of the methods of using interval estimates of numerical parameters is carried out. The decomposition and structuring of the methods were carried out. Results. The expediency of using a methodology for describing the parameters of a complex technical system using the interval estimation method is shown. An analysis of the use of various interval estimation models is presented. Practical significance. Application in the analysis and construction of complex systems is considered as a practical application option. The method of estimating the parameters of a complex technical system using the interval estimation method can be used as a practical guide.

Keywords: interval estimation, parameter estimation, numerical data, fuzzy data, complex technical systems

This paper is devoted to the theoretical analysis and comparative characteristics of methods and algorithms for automatic identity verification based on the dynamic characteristics of a handwritten signature. The processes of collecting and preprocessing dynamic characteristics are considered. An analysis of classical methods, including hidden Markov models, support vector machines, and modern neural network architectures, including recurrent, convolutional, and Siamese neural networks, is conducted. The advantages of using Siamese neural networks in verification tasks under the condition of a small volume of training data are highlighted. Key metrics for assessing the quality of biometric systems are defined. The advantages and disadvantages of the considered methods are summarized, and promising areas of research are outlined.

Keywords: verification, signature, machine learning, dynamic characteristic, hidden Markov models, support vector machine, neural network approach, recurrent neural networks, convolutional neural networks, siamese neural networks, type I error

The principles of biophilic design are becoming a key component of the architectural design of medical facilities due to the well-known psychological impact of natural elements on patients and medical staff. The inclusion of natural elements, such as the use of plants, natural light and shade, colors found in nature, and naturally occurring patterns and curves, in medical facilities has been shown to create a psychologically safe environment that promotes the health and well-being of patients and staff. This article explores the fundamental principles of biophilic design, the scientific evidence supporting its therapeutic effects, and practical examples of its use in healthcare settings to improve psychological health and well-being. This work contributes to the existing body of knowledge on biophilic design by providing an up-to-date review of recent research and real-world applications, including challenges

Keywords: biophilia, biophilic design, sustainable architecture, healthcare architecture, well-being, sustainability, biophilic architecture

The practice of producing optical interference coatings shows that when using new thin-film materials, obtaining optical products with specified quality function requirements depends on the accuracy of their refractive index. The results of its evaluation on large frequency crystals differ, which does not allow narrowband filters with the required technical parameters. This article proposes an approach to estimating the parameters of the refractive index of a thin film based on solving the inverse synthesis problem, which is based on the experimental determination of the thickness of sprayed films using an X-ray fluorescence coating thickness analyzer and data on the reflection coefficient spectrum obtained using a broadband spectrophotometer. The numerical modeling carried out during the study showed that even if there are 5% tolerances for estimating the thickness of coatings, a fairly accurate determination of the refractive index can be expected. The correctness of the results of using this approach was verified by using a thin film with a known refractive index, which was also determined using the proposed method of numerical modeling of the reflection spectrum of the digital twin coating.

Keywords: interference coating, numerical modeling, reflection coefficient spectrum

The article forms the task of hierarchical classification of texts, describes approaches to hierarchical classification and metrics for evaluating their work, examines in detail the local approach to hierarchical classification, describes different approaches to local hierarchical classification, conducts a series of experiments on training local hierarchical classifiers with various vectorization methods, compares the results of evaluating the work of trained classifiers.

Keywords: classification, hierarchical classification, local classification, hierarchical presicion, hierarchical recall, hierarchical F-measure, natural language processing, vectorization

Разработан алгоритм и составлена программа на языке программирования Python для расчета численных значений оптимального оператора фильтрации с запаздыванием для L-марковского процесса с квазирациональной спектральной плотностью, являющегося обобщением марковского процесса с рациональным спектром. В основе построения оптимального оператора фильтрации с запаздыванием лежит спектральная теория случайных процессов. Расчетная формула оператора фильтрации была получена с использованием теории L-марковских процессов, методов вычисления стохастических интегралов, теории функций комплексного переменного и методов тригонометрической регрессии. Рассмотрен интересный с точки зрения управления сложными стохастическими системами пример L-марковского процесса (сигнала) с квазирациональным спектром. За основу при построении математической модели оптимального оператора фильтрации с запаздыванием была взята тригонометрическая модель. Показано, что значения оператора фильтрации с запаздыванием представляются линейной комбинацией значений принимаемого сигнала в определенные моменты времени и значений синусоидальных и косинусоидальных функций в те же моменты. Установлено, что числовые значения оператора фильтрации существенно зависят от параметра β совместной спектральной плотности принимаемого и передаваемого сигналов, в связи с чем в работе рассматривались три разные задачи прохождения сигнала через разные физические среды. Установлено, что абсолютная величина действительной части оператора фильтрации на всех трех интервалах изменения срока запаздывания и во всех трех средах превышает абсолютную величину мнимой части в среднем в два и более раз. Построены графики зависимости действительных и мнимых частей оператора фильтрации от срока запаздывания τ, а также трехмерные графики зависимости самого оператора фильтрации с запаздыванием от срока запаздывания. Дано физическое обоснование полученным результатам.

Keywords: random process, L-Markov process, noise, delayed filtering, spectral characteristic, filtering operator, trigonometric trend, standardized approximation error

A mathematical model has been constructed, an algorithm has been developed, and a program has been written in the Python programming language for calculating the numerical values of the optimal filtering operator with a forecast for an L-Markov process with a quasi-rational spectrum. The probabilistic model of the filtering operator formula has been obtained based on the spectral analysis of L-Markov processes using methods for calculating stochastic integrals, the theory of analytical functions of a complex variable, and methods for correlation and regression analysis. Considered an example of L-Markov process, the values of the optimal filtering operator with a forecast for which it was possible to express in the form of a linear combination of the values of the process at some moments of time and the sum of numerical values of cosines and sines at the same moments. The basis for obtaining the numerical values of the filtering operator was the mathematical model of trigonometric regression with 16 harmonics, which best approximates the process under study and has a minimum

Keywords: random process, L-Markov process, prediction filtering, spectral characteristics, filtering operator

The article describes the process of developing a volumetric display for information and communication interaction in the Arctic, where traditional means of visualization and communication face the challenges of extreme climate, isolation and limited infrastructure. An analysis of the main areas of using volumetric in the Arctic zone is carried out. The main disadvantages of methods for creating a volumetric image in existing 3D displays are considered. Taking into account the main tasks to be solved - creating the illusion of a three-dimensional object for a group of people (more than 2 people) at a wide viewing angle - a description and analysis of two main developed configurations of the optical system is given, the latter of which meets the requirements, ensuring stable operation in Arctic conditions and opening up prospects for implementation in remote and hard-to-reach regions of the Far North.

Keywords: volume display, arctic zone, 3D image, system analysis, lens, optical system, computer modeling

The paper considers the synthesis of a non-stationary automatic control system for braking the wheels of a heavy vehicle using the generalized Galerkin method. The research method under consideration is used to solve the problem of synthesizing a non-stationary system whose desired program motion is specified at the output of a nonlinear element. The paper presents the results of studying the impact of non-stationarity on the parameters of the fixed part of the system (object) on the deterioration of the quality of the transient process. For critical operating conditions, the parameters of the controller were recalculated, and the results of accounting for non-stationarity and re-synthesis were evaluated.

Keywords: automatic control system, regulator, braking system, unsteadiness of parameters, generalized Galerkin method

The article proposes the development of a mathematical model that includes an integrated approach to modeling the interaction of surfaces, taking into account the geometric features of the groove. An important aspect of the novelty of the work is its validation based on experimental data. To describe the movement of the lubricant in the working gap, a model is used that describes the movement of a truly viscous lubricant, including the continuity equation. The calculations and experiments performed have confirmed the adequacy of the proposed model, which indicates the possibility of its practical application for engineering analysis and design. The results of this work made it possible to improve the understanding of the mechanism of movement of the lubricant in radial sliding bearings having a polymer coating with an axial groove on the shaft surface. Studies have also shown that the presence of a groove on the shaft surface affects the pressure distribution, which, in turn, affects the tribotechnical parameters of the bearing. The introduction of the groove helps to distribute the lubricant more efficiently over the working gap, increase the bearing capacity of the bearing, reduce the coefficient of friction and reduce wear on the contact surfaces.

Keywords: radial bearing, wear resistance assessment, antifriction polymer coating, groove, hydrodynamic mode, verification

This paper proposes a mathematical model of the laminar flow of a truly viscous lubricant in the clearance of a radial plain bearing with a nonstandard support profile. The influence of a fluoroplastic-containing polymer coating and a groove on the shaft surface is considered, taking into account nonlinear effects, which improves the accuracy of the description of hydrodynamic processes. Thin-film approximations and continuity equations are used to determine the hydrodynamic pressure, load capacity, and friction coefficient. A comparison with existing calculation models demonstrated improved performance prediction. The results demonstrate the feasibility of ensuring stable shaft floatation, confirming the applicability of the developed model for engineering calculations of bearings with a polymer coating and a groove.

Keywords: radial plain bearing, mathematical modeling, true viscous lubricant, polymer composite coating, hydrodynamic regime, tribotechnical characteristics

The article considers the parameter identification issues of linear non-stationary dynamic systems adaptive models using the example of a linearized adjustable model of a DC motor with independent excitation. A new method for estimating the parameters of adjustable models from a small number of observations is developed based on projection identification and the apparatus of linear algebra and analytical geometry. To evaluate the developed identification method, a comparison of the transient processes of the adaptive model of a DC motor with independent excitation with the obtained parameter estimates with reference characteristics was carried out. The efficiency of the proposed identification method in problems of DC electric drive control is shown.

Keywords: DC motor, projection identification, dynamic system parameter estimation, adaptive model of non-stationary dynamic system