Computer Tools in Education

Nikolai Alexandrovich Vavilov (1952–2023)

Sun, 15 Oct 2023 00:00:00 +0000

On September 14, 2023, in St. Petersburg, at the age of 71, Nikolai Aleksandrovich Vavilov, a member of the editorial board of our journal, an outstanding mathematician and professor at St. Petersburg University, suddenly died.

Attack Detection in Critical Infrastructures on the Base of Analysis of States

Vasily Desnitsky — Sun, 15 Oct 2023 00:00:00 +0000

An approach to revelation of attacks in critical infrastructures by means of graphoriented modeling methods is disclosed in the article. The approach has two main steps. At the preliminary step through the use of machine learning methods, it performs a processing of logs, i.e. primary information characterizing the operation of the infrastructure in order to build the graph of states and transitions of the infrastructure. At the exploitation step, the constructed graph is traversed to detect those states in which the system is under attack of a certain type. During the functioning, wrong transitions between the correct states of the infrastructure are detected, which in turn can be used to deduce a fact of an attack. The conducted experiments on data from datasets describing the exploitation of two industrial critical systems confirmed the soundness of the developed attack revelation mechanism, and demonstrated the large stability degree of the mechanism to possible losses of data fragments containing primary data from the system for the attack detection.

Applications of Tropical Mathematics to Neural Network Architecture

Anna Petrova, Victoria Kazakevich — Sun, 15 Oct 2023 00:00:00 +0000

Using the methods provided by tropical mathematics we can simplify the structure of a neural network, which increases its explainability, without decreasing its accuracy. This paper aims to explore the use of tropical functions in neural networks and compare their efficiency with classical ones. Theoretical framework of tropical mathematics is a semiring with idempotent addition, which is a natural approach to piecewise-linear neural networks, e.g. networks with ReLU activation. Within this approach, piecewise-linear convex function is a tropical polynomial, and general piecewise-linear functions are tropical rational functions. Thus a layer of a neural network with linear preactivation and ReLU activation can be viewed as a vector-valued tropical rational function, which in turn can be represented by two tropical layers. Two tropical layers were implemented, and five tropical architectures were constructed. The models were trained on a heart disease dataset, aiming to determine the presence of heart disease. All models had the same hyperparameters. Each of the models was trained for 100 epochs using Adam and SGD optimizers. The results of the comparison showed that the best accuracy was achieved by a mixed-architecture model using two linear layers. The comparison results showed that the best accuracy was achieved by a mixed-architecture model with two linear layers with a min-layer and a max-layer in between. This accuracy was achieved by using an Adam optimizer. The classical model scored 77.3% and the tropical 77.7%.

System integration and optimization of security in a multilayer virtual network

Shchegoleva Nadezhda, Jasur Kiyamov — Sun, 15 Oct 2023 00:00:00 +0000

In modern distributed systems, especially in the field of blockchain and cloud computing, ensuring reliable and efficient consensus is a critical task. This paper discusses a combined consensus approach based on a combination of P-BFT and RAFT protocols. The purpose of this study is to explore the possibilities of a combined P-BFT and RAFT consensus approach to improve reliability, performance and security in distributed registries and cloud systems. The principles of operation and characteristics of each protocol are explored, as well as their joint use to achieve agreement in a distributed environment. In the course of the work, the advantages and prospects of the combined P-BFT and RAFT approach are analyzed, support for various trust models is considered, as well as the integration of data protection mechanisms to ensure security and privacy. The results of the study suggest that the combined P-BFT and RAFT consensus approach demonstrates high performance and reliability in distributed registries and cloud systems. The proposed approach has prospects for application in various areas where a reliable and secure consensus is required to ensure the efficient operation of distributed systems.

Software Level of the Computer Network Monitoring System with Additional Anomaly Diagnostics Module

Maxim Avilov — Sun, 15 Oct 2023 00:00:00 +0000

This article describes the software architecture level of the computer network operation monitoring system with an anomaly diagnostics module. A software solution for this level of network monitoring system architecture is proposed. Also, the article reflects the results of tests of compliance with the requirements to the architecture of the monitoring system of computer network operation with an anomaly diagnostics module: the ability to cluster anomalies in the network, manual and automatic control of forming scenarios of impact on nodes, the ability to scale the network monitoring system, the availability of separate data storage for statistics and scenarios impact on nodes and other requirements. In addition, this article presents the results of testing the developed software solution. The tests were conducted to cluster computer network anomalies and forming scenarios of impact on the observed unstable network nodes. The results show that the developed software allows you to cluster anomalies in the computer network, as well as during additional diagnostics of unstable nodes to form scenarios of impact on such nodes.

Development of a Software Platform for Testing Application Solutions Based on Container Virtualization Technolog

Olga Polovikova, Anastasia Manicheva, Vera Zuravleva — Sun, 15 Oct 2023 00:00:00 +0000

This article analyzes the problem of collecting and storing the program solutions of students that can be directly executed, tested. Container-based virtualization technologies are proposed to solve the problem. Each software development is automatically deployed in one or more isolated docker-containers. The approach has been tested in practice. A software platform for publishing ready-made application solutions has been designed and developed.The platform services allow testing ready-made developments of different level and complexity, analyzing the applied technologies and approaches, evaluating the performance of the used methods and algorithms. The software platform is implemented on the basis of client-server web- application. The problem of deploying and running the portal application stack without additional server hardware and resource-intensive technologies is solved by using hypervisor-based virtualization. The virtual machine for the developed web- application was created on the basis of a software hypervisor. The analysis of resource virtualization types obtained in the framework of the research allows us to draw conclusions about the applicability of the used technologies for solving other practical tasks.

Number Theory for Mathematics Instruction of Teacher Candidates in the Digital Era

Sergei Abramovich — Sun, 15 Oct 2023 00:00:00 +0000

The paper presents technology-enhanced activities with triangular, square, and other polygonal numbers arranged in basic geometric shapes — equilateral and isosceles triangles and squares. Computational algorithms for the summation of such numbers within each geometric structure have been developed and discussed. In some cases, algebraic identities between certain numeric entries of the shapes have been formulated and proved computationally. The activities, supported by WolframAlpha, and Maple, are recommended for the use by instructors of technology-motivated mathematics teacher education courses. The paper emphasizes the value of technology-immune/technology-enabled mathematical problem solving in the modern-day teaching topics of elementary number theory across multiple grade levels and educational programs. The paper argues that the power of digital tools allows future teachers of mathematics, in the context of elementary number theory, to appreciate the use of simple algorithms in achieving sophisticated computational outcomes.