2024.3

Type I diabetes, also known as insulin-dependent diabetes, is a serious disease. There are two main approaches to the management of patients with this disease: the use of insulin pens and various types of insulin (such as ultrashort, short-acting and long-acting insulins) or the use of an insulin pump with ultrashort insulin. An important task remains the development of a reliable system for the accurate calculation of insulin doses using insulin pens in the treatment of type I diabetes. In this study, we investigate the accuracy of calculating insulin doses based on historical data. To solve this problem, we propose using various artificial intelligence (AI) methods, including decision trees, gradient acceleration, support vector machine (SVM) methods and various neural network architectures. We are conducting a comparative analysis of these approaches to determine their effectiveness.

The traffic load balancing problem is relevant in modern networks that have many alternative routes between any pair of nodes. Balancing provides a uniform load of network resources. The paper proposes a method for adaptive queueing policy configuration on a switch to get a uniform queue load on the switch output ports. Because modern applications require the data transmission delay to be around milliseconds, reinforcement learning method DQN was applied to solve the problem. An experimental study demonstrated the convergence of the proposed method during the training to uniform queue load at output ports.

One of the main tools for describing and predicting the occurrence of events is survival analysis, which allows you to predict not only the probability and time of events but also the changing of probability over time. This article presents Survivors, an open-source Python library that helps solve problems of survival analysis, build individual forecasts of survival and risk functions, investigate data dependencies, evaluate the quality of forecasts, and conduct experimental studies. The library uses new methods of constructing tree-based models of survival analysis with high sensitivity to real datasets. In particular, the paper presents a new histogram approach for searching the best split of censored data. The models can handle categorical and missing values, cases of informative censorship, and multimodal time distribution. The paper describes the architecture and components of the library, the features of the software implementation, and an experimental comparison with existing libraries of survival analysis.

A one-line queueing system with three incoming Poissonian flows is studied. Service time distributions are general and absolutely continuous for each flow. The first class requirements have nonpreemptive priority over the second class requirements and preemptive-repeat-different priority over the third class requirements. The second class requirements have nonpreemptive priority over the third class requirements. The heavy traffic limiting distribution of the queue length for the third class is obtained while the system load tends to 1 and time tends to infinity.

The paper considers the asymptotic behavior of the reserve of an organization subjected to risk in the case when the number of factors leading to loss is random. Burr distribution is considered as loss distribution. An asymptotic comparison of the activities of such organizations is carried out in terms of the necessary additional number of such factors (asymptotic deficiency). Two examples illustrating tne obtained results are presented. The first example concerns extreme order statistics, and the second one deals with the truncated Poisson and binomial distributions.

The concept of steady-state solutions of the Navier–Stokes equation is defined. Such solutions expand the concept of stationary, exponentially decrease in time, have a constant spatial velocity field and constant pressure in the absence of external fields. The method of their construction is considered, and the problem of Taylor vortices is solved. A mathematical model of a tornado is proposed. Within the framework of this model, a steady-state solution is obtained as an eigenfunction of the problem in the form of a vortex. Based on the Navier–Stokes equation, a model of the formation of the structure of a gas cloud is proposed. It is shown that due to the Coriolis force, spiral arms arise from flows of gas moving outward. It is proved that the number of arms m is even, and their structure does not depend on the angular velocity of rotation. A formula is obtained for the spiral twist angle depending on the cloud parameters for the case of m=2.

The paper considers inverse problems for hyperbolic equation with singular perturbation in which the function entering the source is unknown. The existence of inverse problems solutions is proved, numerical methods for inverse problems solving are developed and the results of computational experiments illustrating effectiveness of numerical methods are presented.

Technique of data preparation for hemodynamic calculations in a quasi-one-dimensional approximation on complex spatial graphs of elastic vessels is considered. A method is described for the automatic construction of volumetric (3D) models of graphs of the vascular system according to their frame models. The main approaches to carrying out calculations in parallel with the visualization of their results on volumetric models are discussed.