This paper presents a probabilistic-temporal modeling approach for analyzing data processing stages in a personalized recommendation system for digital heritage collections. The methodology is based on (Graphical Evaluation and Review Technique) GERT network formalism, which enables the representation of complex probabilistic workflows with feedbacks and alternative branches. For each processing stage, corresponding GERT-schemes were developed, and equivalent transfer functions were derived. Using Laplace transform inversion techniques, probability density functions of processing time were recovered, followed by the calculation of key statistical metrics, including expectation, standard deviation, and quantiles. The results demonstrate that the proposed approach allows for detailed temporal performance evaluation, including the estimation of time exceedance probabilities at each stage. This provides a quantitative basis for optimizing recommendation system design and highlights the applicability of GERT-based modeling to intelligent data-driven services in the cultural domain.

This article investigates the use of visual cues, such as colour coding, to enhance educational materials and optimise students’ learning. The aim of the study was to examine how colour coding (CC) of selected components of a task influenced students’ cognitive engagement (CE) when solving algorithmic problems. We present experimental results from studies using eye-tracking techniques, which provide fine-grained behavioural indicators serving as proxy insights into learners’ cognitive processes. The findings reveal that the distribution of visual attention—measured through fixation time percentage, fixation count in areas of interest (AOIs), and the sequence in which task components were viewed—differed significantly between colour-coded and black-and-white task formats. Furthermore, analysis of two key eye-tracking indicators—fixation duration total (FDT) and average fixation duration (FDA)—suggests an increased level of cognitive engagement in students who had difficulty understanding the presented concepts while solving the colour-coded tasks. These results indicate that colour coding may help sustain students’ attention and engagement, especially when they face challenges in interpreting educational materials or engaging in complex problem-solving tasks.