In this paper, classical iterative learning models are extended by including the factors of fatigue and rest. The existing approaches to model fatigue and rest from various fields –– education, production, sports, and medicine –– are analyzed, and the need to include these factors in the models is justified accordingly. Mathematical models are proposed to describe learning level dynamics during rest periods, considering the reduced efficiency of acquiring skills due to fatigue. Ten models of growing complexity are studied: from simple models without any fatigue effects to complex ones with the probabilities of skill acquisition and forgetting depending on time and rest periods. As is shown, the breaks of optimal duration allow improving the terminal learning level. In the model with fatigue, rest, and no forgetting, the optimal time to start rest is independent of the probability of skill acquisition as a function of time and lies at the middle of the experience acquisition interval. The models proposed are intended for predicting performance and optimizing training programs, production processes, and training cycles. This study emphasizes the need to consider biological and cognitive constraints when designing adaptive learning systems.

This paper is devoted to analytical approaches to path planning with obstacles. Two analytical modeling principles are compared for obstacles in a scene: the methods of potentials and R-functional modeling. The functional voxel design principle of complex computational processes is presented on an illustrative example of modeling of the R-function for the union/intersection of the domains of two functions. The fundamentals of arithmetic operations over local geometrical characteristics describing the components of a homogeneous unit vector of a local function are discussed. The denormalization principle of such components is demonstrated for application in arithmetic operations constituting an R-function. The scene is modeled by the layout of concentric objects and a local function describing the target by a funnel surface at a given point. A dynamic formation algorithm is considered for the final local function of the union of the funnel and scene surfaces at a current point. The final local function is used to determine the components of the direction vector of gradient-based motion to the target.

Проанализирована академическая успеваемость студентов МГТУ им. Н. Э. Баумана и её связь с их активностью в социальной сети ВКонтакте. С помощью методов машинного обучения выделены различные траектории успеваемости, отражающие динамику образовательных достижений. На основе анализа подписок студентов идентифицированы маркерные сообщества, характеризующие преобладание студентов, относящихся к определённым категориям успеваемости. С применением теории графов выполнена кластеризация сообществ, выявившая структурные группы интересов студентов. Для каждой траектории построены стохастические векторы долей интересов к кластерным сообществам, позволившие определить кластеры сообществ, статистически значимо связанные с конкретными траекториями успеваемости. Полученные результаты подтвердили наличие связи между цифровым поведением студентов и их академическими результатами, что способствует разработке моделей прогнозирования успеваемости с учётом интересов студентов в социальных сетях.