The article describes the process of forming a feature space for a system that allows monitoring the performance of physical exercises and developing personal recommendations for correcting their performance based on the rules used by an expert trainer. Human Pose Estimation (HPE) methods are used to digitally represent exercise performance. The feature space should represent HPE data (coordinates of human body parts) as a set of feature values for making recommendations (for example, exercise intensity, user endurance). The feature space plays a central role in the development of such systems: the richer it is, the better the recommendations can be implemented.

For a linear-quadratic tracking problem with a target trajectory described by a linear dynamics, convergence of reinforcement learning using policy iteration method is investigated. A proof of convergence is given, and convergence rate is analyzed. Namely, it is proven that the policy iteration method converges and has a quadratic convergence rate under relaxed constraints on the initial control.

In this paper, we propose a compact textual representation of scanned 3D objects. This representation can be obtained from the original point cloud by extracting geometric primitives, forming a topological graph depicting the relative positions of the primitives in the object, and then converting the graph into a string of characters. Our experiments show that many objects can be described quite accurately as a set of geometric primitives. Furthermore, the proposed representation significantly reduces the memory footprint compared to the original point cloud. The object recognition problem can be solved by searching the database for the object whose textual representation is closest in terms of the Levenshtein distance to the textual representation of the object being recognized. Computational experiments show that the proposed representation enables achieving a fairly high recognition accuracy.

It is shown that any scaled mixture of multivariate normal distributions can be a stationary distribution in the multivariate stochastic difference equation (SDE) scheme—a first-order multivariate autoregression with random coefficients. A correspondence is established between the resulting mixture and the behavior of the coefficients generating the stationary distribution.