DISCRETE AND CONTINUOUS MODELS AND APPLIED COMPUTATIONAL SCIENCE

Currently, an increasing number of fiber-optic communication lines are reaching the end of their predetermined service life, yet the quality indicators of these lines still allow for continued operation. To extend the actual operational life of these lines, it is necessary to conduct high-quality monitoring of both the current status of all components and the dynamics of key indicators. This article proposes a method for addressing the challenge of maintaining communication network reliability while continuing to use optical cables after their warranty period has expired. A study of random values of the attenuation coefficient and polarization mode dispersion of an optical fiber, supported by actual operational data from a network segment, shows high temporal stability in the attenuation coefficient and polarization mode dispersion of optical fiber type G.652. This conclusion allows us to discuss the continued operation of optical cables after the warranty period. To analyze the key aging metric, mathematical models are used that take into account the physical and chemical properties of cables as well as the conditions of their proof-tests. Using an example related to the current state of Russian fiber optic networks, we calculate the number of emergency reserve elements necessary to maintain the reliability of their operation. Practical recommendations for the placement of emergency reserve are also provided.

Chronic non-communicable diseases account for more than 70% of global mortality statistics. The main share is made up of diseases of the cardiovascular system. Adequate preventive measures—impact on controllable and conditionally controllable risk factors—can reduce the contribution of these diseases to the structure of mortality. A significant effect can be achieved with an adequately selected level of physical activity, but doctors do not always recommend specific actions to patients. This article describes a prototype of a cognitive assistant for constructing personalized plans for therapeutic physical exercises for relatively healthy people and people suffering from cardiovascular diseases. The developed system consists of two main components: a cardiovascular risk assessment module and an exercise planning module. The risk assessment module consists of a knowledge base and an argumentative reasoning algorithm. Its task is to identify risk factors and levels, which is dual in nature: in the case of monitoring a relatively healthy user, the risk of developing cardiovascular disease is assessed, while in the case of interaction of the system with a user with cardiovascular disease, the risk of complications of a chronic form is assessed—development of a cardiovascular event. The exercise planning module includes an exercise database and a scheduler algorithm. The planning algorithm selects optimal therapeutic physical exercises according to optimal criteria, in order to form a plan that will not harm the patient and will increase his physical performance. The developed mechanism allows you to create training scenarios for users with any level of initial training, taking into account the available sports equipment, the preferred location for training (home, street, gym) and at any level of the cardiovascular continuum.

In this paper, we study a queuing system with a single-capacity storage device and queue updating. An update is understood as the following mechanism: an application that enters the system and finds another application in the drive destroys it, taking its place in the drive. It should be noted that systems with one or another update mechanism have long attracted the attention of researchers, since they have important applied significance. Recently, interest in systems of this kind has grown in connection with the tasks of assessing and managing the age of information. A system with a queue update mechanism similar to the one we are considering has already been studied earlier in the works of other authors. However, in these works we were talking about the simplest version of the system with Poisson flow and exponential maintenance. In this paper, we consider a phase-type flow and maintenance system. As a result of our research, we developed a recurrent matrix algorithm for calculating the stationary distribution of states of a Markov process describing the stochastic behavior of the system in question, and obtained expressions for the main indicators of its performance.

This article continues the cycle of works by the authors devoted to the problem of the age of information (AoI), a metric used in information systems for monitoring and managing remote sources of information from the control center. The theoretical analysis of information transmission systems requires a quantitative assessment of the “freshness” of information delivered to the control center. The process of transferring information from peripheral sources to the center is usually modeled using queuing systems. In this paper, a queuing system with phase-type distributions is used to estimate the maximum value of the information age, called the peak age. This takes into account the special requirement of the transmission protocol, which consists in the fact that information enters the system in groups of random size. For this case, an expression is obtained for the Laplace–Stieltjes transformation of the stationary distribution function of the peak age of information and its average value. Based on the results of analytical modeling, a numerical study of the dependence of the average value of the peak age of information on the system load was carried out. The correctness of the expressions obtained was verified by comparing the analytical results with the results of simulation modeling.

Superconducting properties of twisted tri-layer graphene (TTG) are studied within the scope of the chiral model based on using the unitary matrix

In this article, we propose fourth- and fifth-order two-step iterative methods for solving the systems of nonlinear equations in

Earlier we developed a stable fast numerical algorithm for solving ordinary differential equations of the first order. The method based on the Chebyshev collocation allows solving both initial value problems and problems with a fixed condition at an arbitrary point of the interval with equal success. The algorithm for solving the boundary value problem practically implements a single-pass analogue of the shooting method traditionally used in such cases. In this paper, we extend the developed algorithm to the class of linear ODEs of the second order. Active use of the method of integrating factors and the d’Alembert method allows us to reduce the method for solving second-order equations to a sequence of solutions of a pair of first-order equations. The general solution of the initial or boundary value problem for an inhomogeneous equation of the second order is represented as a sum of basic solutions with unknown constant coefficients. This approach ensures numerical stability, clarity, and simplicity of the algorithm.

The problem of summation of Fourier series in finite form is formulated in the weak sense, which allows one to consider this problem uniformly both for classically convergent and for divergent series. For series with polynomial Fourier coefficients

Various approaches to calculating normal modes of a closed waveguide are considered. A review of the literature was given, a comparison of the two formulations of this problem was made. It is shown that using a self-adjoint formulation of the problem of normal waveguide modes eliminates the occurrence of artifacts associated with the appearance of a small imaginary additive to the eigenvalues. The implementation of this approach for a rectangular waveguide with rectangular inserts in the Sage computer algebra system is presented and tested on hybrid modes of layered waveguides. The tests showed that our program copes well with calculating the points of the dispersion curve corresponding to the hybrid modes of the waveguide.

The paper considers a single-line retrial queueing system with an unreliable server. Queuing systems are called unreliable if their servers may fail from time to time and require restoration (repair), only after which they can resume servicing customers. The input of the system is a simple Poisson flow of customers. The service time and uptime of the server are distributed exponentially. An incoming customer try to get service. The server can be free, busy or under repair. The customer is serviced immediately if the server is free. If it is busy or under repair, the customer goes into orbit. And after a random time it tries to get service again. The study is carried out by the method of asymptotically diffusion analysis under the condition of a large delay of requests in orbit. In this work, the transfer coefficient and diffusion coefficient were found and a diffusion approximation was constructed.

The paper presents a new multimodal approach to analyzing the psycho-emotional state of a person using nonlinear classifiers. The main modalities are the subject’s speech data and video data of facial expressions. Speech is digitized and transcribed using the Scribe library, and then mood cues are extracted using the Titanis sentiment analyzer from the FRC CSC RAS. For visual analysis, two different approaches were implemented: a pre-trained ResNet model for direct sentiment classification from facial expressions, and a deep learning model that integrates ResNet with a graph-based deep neural network for facial recognition. Both approaches have faced challenges related to environmental factors affecting the stability of results. The second approach demonstrated greater flexibility with adjustable classification vocabularies, which facilitated post-deployment calibration. Integration of text and visual data has significantly improved the accuracy and reliability of the analysis of a person’s psycho-emotional state