We present the Julia package Manifolds.jl , providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Riemannian manifold, such as the circle, the sphere, symmetric positive definite matrices, or one of the models for hyperbolic spaces. We introduce a common interface, available in ManifoldsBase.jl , with which new manifolds, applications, and algorithms can be implemented. We demonstrate the utility of Manifolds.jl using Bézier splines, an optimization task on manifolds, and principal component analysis on nonlinear data. In a benchmark, Manifolds.jl outperforms all comparable packages for low-dimensional manifolds in speed; over Python and Matlab packages, the improvement is often several orders of magnitude, while over C/C++ packages, the improvement is two-fold. For high-dimensional manifolds, it outperforms all packages except for Tensorflow-Riemopt, which is specifically tailored for high-dimensional manifolds.

The man-machine interface (MMI) is one of the most exciting areas of contemporary research. To make the MMI as convenient for a human as possible, it is desirable that efficient algorithms for recognizing body language are developed. This paper presents a system for quick and effective recognition of gestures of hand body language, based on data from a specialized glove equipped with ten sensors. In the experiment, 10 people performed 22 hand body language gestures. Each of the 22 gestures was executed 10 times. Collected data were preprocessed in multiple ways and three machine learning algorithms were designed based on classifiers (probabilistic neural network, support vector machine, and k-nearest neighbors algorithm) trained and tested by a tenfold cross-validation technique. The best designed classifiers gained effectiveness of gesture recognition at κ = 98.24% with a very short time of testing, below 1 ms. The experiments confirm that efficient and quick recognition of hand body language is possible.

The implementation of the concept based on the SOA paradigm appeared to be significant problem associated with the issue of monitoring and visualization of communication between the various elements of the system during the execution of business processes. The monitoring process as a collection of messages (logs) is a technique known and used. However, collate and read what the state and what messages leading up to it give you relevant information. Ways of gathering such information, especially visualization of the communication with their advantages, will be described in this article as new. This will be the first to create a universal, expandable, multiagent platform to collect information about events and history of the state changes of distributed components. This solution keeps information about the real, global sequence of events occurring on different machines (not necessarily synchronized with clocks) and connections between them.