Computer Tools in Education

Solution of Two-Criteria Project Scheduling Problems Using Methods of Tropical Optimization

Nikolai Krivulin — 2026-03-31

The paper considers two-criteria problems to schedule a project that consists in performing a given set of activities with restrictions on the start and end times of the activities. The maximum time of the working cycle and the spread of the start time of activities that need to be minimized are taken as the optimality criteria of the plan for one of the problems. The other problem is to minimize the total duration of the project and the spread of the start time of activities. The solution of the problems is based on representation in terms of tropical algebra, which studies algebraic systems with idempotent operations. By applying methods of tropical optimization, results are obtained that analytically describe all Pareto-optimal solutions to the considered problems in parametric form. Illustrative numerical examples of solving two-criteria problems for a project of three activities are given.

Computer Visualization of Field Lines of Constant Electric and Constant Magnetic Fields

Alexander Liapzev — 2026-03-31

A method is proposed for constructing a picture of the field lines of constant electric and magnetic fields based on the numerical solution of a system of differential equations followed by visualization by graphs in three-dimensional space. It is shown that the application of this method makes it possible to understand and demonstrate some qualitative features of the field lines, due in particular to the symmetry of the systems under consideration. The examples considered show that even for the simplest systems studied in electrostatics and magnetostatics courses, the pattern of field lines can be complex and sometimes unpredictable.

On the Hybrid Approach for Cardiac Electrophysiology Modeling Utilizing Spectral Neural Operators

Eugene Shchetinin — 2026-03-31

Purpose. To investigate the applicability of a hybrid approach combining spectral neural operators with classical numerical methods for accelerated cardiac electrophysiology simulation in the bidomain formulation.

Materials and methods. The bidomain model is considered on rectangular anisotropic 3D domains with the ten Tusscher-Panfilov ionic model. A hybrid scheme is investigated: an autoregressive Fourier neural operator (AR-FNO) approximates the nonlinear parabolic evolution of the transmembrane potential, while the elliptic coupling equation is solved by the conjugate gradient method. Gradient-aware training is employed to improve wavefront reproduction accuracy.

Results. On test 3D anisotropic slabs with a 2 ms time step, a conduction velocity error of 3–6 % relative to the reference finite element solution was obtained. An ablation study of individual method components was performed. Limitations were identified: error accumulation during prolonged autoregressive rollout and accuracy dependence on time step size.

Conclusion. The principal feasibility of applying hybrid neural network architectures for computational electrophysiology problems on model domains is demonstrated. The applicability boundaries and directions for further research are identified.

Hybrid Method for User Feedback Analysis and Dynamic Weight Optimization of Key Parameters in AI Systems

Ma Danting — 2026-03-31

Understanding user preferences plays a crucial role in personalized services and intelligent systems. This understanding is achieved through feedback mechanisms in various forms, with natural language being the most preferred format. However, this approach requires precise identification of key features from user feedback and dynamic optimization of feature weights to enhance system decision-making accuracy. Traditional methods face significant limitations in extracting key feedback features from natural language texts and adapting weight distribution effectively. This paper presents a novel method for extracting key features from user feedback and distributing their weights based on preliminary multi-iteration interaction between the user and the AI system. This method integrates four main modules: YAKE-based feature extraction, personalized TF-IDF weight modeling, semantic fusion of vector representations with feature classification, and dynamic weight distribution for key features. Thus, a direct mapping mechanism is created from user feedback to the set of feature weights involved in building the decision-making model in AI systems. The novelty of the method lies in the development of a YAKE keyword extraction algorithm with improved semantic and feature density; a TF-IDF weight calculation algorithm integrating historical user preferences and weight personalization; a feature classification mechanism based on semantic similarity; and optimization of feature extraction and weight distribution processes. An emotional state prediction system with continuous data collection from 16 users over 30 days was used to test the method. The results showed that the proposed method achieves an emotion prediction accuracy of 78.4%, which is 23% higher than baseline methods. A significant increase in user satisfaction with the system's predictions and a substantial reduction in the time to achieve stable feature weight distribution are noted.

Models for automatic generation of educational tasks: a comparative analysis

Dmitry Butenko — 2026-03-31

The article presents a comparative analysis of models for the automatic generation of assessment tasks for university courses in the context of a growing mismatch between student and instructor numbers and an increase in cases of academic dishonesty.
The aim of the study is to compare existing generation models according to three criteria — task variability, effort required for implementation, and explainability of results — in order to reduce instructors’ workload while preserving the quality of the educational process.
The methodology includes an analysis of publications from 2020–2025 and a classification of models into template-based, grammar-based, statistical, graph-based, recurrent neural networks, evolutionary algorithms, and large language models (LLMs).
Key findings: LLMs outperform alternative approaches in the diversity of generated content and computational efficiency when pre-trained models are used. Template-based and grammar-based systems are constrained by low variability, evolutionary algorithms require significantly more time, and recurrent networks are inferior in maintaining semantic coherence. Critical drawbacks of LLMs are limited explainability and a tendency to hallucinate, which necessitates mandatory expert oversight of outputs.
The work has practical relevance for developers of educational systems and for instructors seeking to scale instruction while retaining pedagogical control.