This study presents a method for recognizing and classifying micro-expressions using optical flow analysis and the YOLOv11 architecture. Unlike previous binary detection approaches, this research enables multi-class classification while considering gender differences, as facial expressions may vary between males and females. A novel optical flow algorithm and a discretization technique improve classification stability, while the Micro ROC-AUC metric addresses class imbalance. Experimental results show that the proposed method achieves competitive accuracy, with gender-specific models further enhancing performance. Future work will explore ethnic variations and advanced learning strategies for improved recognition.

Keywords: microexpressions, pattern recognition, optical flow, YOLOv11

In the introduction the relevance of the study of diffusion along grain boundaries in metals. The aim of the work was to develop a method for determining the diffusion coefficient of impurity atoms at the grain boundaries in metals based on the numerical solution of the model by Fisher. The methodology laid plotting the ratio of the depth of bulk diffusion and grain boundary diffusion on the ratio of the diffusion coefficients of impurity atoms in them. In the construction of numerical solutions available to simplify the modeling of the physical nature of the process of diffusion along grain boundaries. The technique may be used in experiments with widely varying parameters diffusion annealing. Examples of the application procedure. The estimation of the coefficient of grain-boundary diffusion of copper in polycrystalline nickel. Also calculated the ratio of maximal depth of diffusion of silver in the grain and the grain boundary in the SMC copper.

Keywords: diversification of management, production diversification, financial and economic purposes of a diversification, technological purposes of ensuring flexibility of production