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Effective least squares approximation method for estimating the rhythm function of cyclic random process
(2025) Lupenko, Serhii; Wiatr, Małgorzata; Metelski, Andrzej
The work is devoted to a problem of the rhythm function estimation of a cyclic random process, which is based on the least squares approximation methods instead of well-known interpolation approach. Analytical dependencies between errors of estimation of a discrete rhythm function and errors of segmentation of a cyclic random process into cycles and zones were constructed. This made it possible to develop a procedure for calculating and controlling errors of estimating rhythm function of a cyclic random process as certain functions of errors of the segmentation method. The general problem of least squares approximation of the rhythm function of a cyclic random process is formulated as a problem of optimal selection of a parametric function derived from a predetermined class of functions that satisfy the necessary and sufficient conditions of the rhythm function of a cyclic random process. New parametric classes of rhythm characteristics of cyclic random processes such as parametric monomials of degree k, parametric logarithmic functions and parametric exponential functions have been built. The advantage of considered method over well-known interpolation approach refers to the improvement of accuracy of rhythm function estimation and reduction of the rhythm function estimation parameters’ number. For example, in presented computer simulation experiment for the parametric class of monomials of degree 2, average value of the mean square errors for 500 simulations in the case of the interpolation is over 40 times higher than the corresponding value for approximation. Moreover, for that parametric class, the number of estimated parameters is almost equal to doubled number of considered cycles in the case of piecewise linear interpolation and is reduced to 1 for least square approximation. The results obtained in the work constitute the basis for improvement of rhythm-adaptive methods and spectral analysis of cyclic random processes, including the area of statistical methods for detecting hidden cyclic structures of the investigated cyclic stochastic signals with an irregular rhythm.
ОСВІТНІ ЦИФРОВІ ПЛАТФОРМИ ТА ОБ'ЄКТИВНІСТЬ ОЦІНЮВАННЯ СТУДЕНТІВ
(2024-05) Ільєнко, Оксана
Онтологічно-орієнтовані системи керування контентом інформаційно-навчальних Web-порталів : монографія
(Амерікан Юніверсіті Київ, 2024) Tytenko, Sergiy
Монографія присвячена розробці моделей та методів керування навчальним контентом на основі онтологічного підходу. У роботі досліджується структурування, моделювання та автоматизація побудови інформаційно-навчальних систем, що відповідають сучасним освітнім вимогам. Книга буде корисна для науковців, розробників навчальних платформ, освітніх адміністраторів, викладачів і студентів, які цікавляться питаннями розробки інтелектуальних систем навчання, а також для тих, хто працює над покращенням якості контенту та індивідуалізацією навчальних середовищ.
GRAPH USER INTERFACES FOR ENHANCING EXPLORATORY LEARNING: AN OVERVIEW
(2023-10-30) Tytenko, Andrii; Tytenko, Sergiy
Exploratory learning is a key methodology in education. This text highlights the role of Graph User Interfaces (Graph UI) in enhancing exploratory learning by providing interactive, graph-structured data representations. Tracing from Euler's work to modern applications, graph structures simplify complex data, aiding cognitive engagement and navigational abilities. Studies show that Graph UI can optimize educational processes, enhancing knowledge acquisition and innovative application through an intuitive, visually structured learning environment. The promising future of exploratory learning through Graph UI invites more research and development to unlock its potential for insightful and accessible learning experiences.
GENERATIVE AI AND PROMPT ENGINEERING IN EDUCATION
(2023-10-30) Kakun, Artem; Tytenko, Sergiy
The development of generative AIs and the variability of their use are still at the level of research and active development simultaneously. However, it has already become clear that the emergence of generative AI significantly impacts many industries, including education. In this study, we explore the potential applications of generative AI in education, such as personalized learning tools and AI-powered study resources. We also delve into the critical role of prompt engineering in ensuring effective communication between users and AI systems, leading to improved educational outcomes. In addition, we identify the challenges and risks associated with integrating artificial intelligence technologies into the educational environment, including data privacy, security issues, andpotential AI “hallucinations”. By thoroughly exploring these topics, this study aims to highlight the opportunities and limitations of generative AI and prompt engineering in education.