The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ ℬ s

In the present paper the author uses the function system Γ ℬ s constructed in Cantor bases to show upper bounds of the extreme and star discrepancy of an arbitrary net in the terms of the trigonometric sum of this net with respect to the functions of this system. The obtained estimations are inequalities of the type of Erdős-Turán-Koksma. These inequalities are very suitable for studying of nets constructed in the same Cantor system.

Electroencephalogram Analysis Based on Gramian Angular Field Transformation

This paper addresses the problem of motion imagery classification from electroencephalogram signals which related with many difficulties such on human state, measurement accuracy, etc. Artificial neural networks are a good tool to solve such kind of problems. Electroencephalogram is time series signals therefore, a Gramian Angular Fields conversion has been applied to convert it into images. GAF conversion was used for classification EEG with Convolutional Neural Network (CNN). GAF images are represented as a Gramian matrix where each element is the trigonometric sum between different time intervals. Grayscale images were applied for recognition to reduce numbers of neural network parameters and increase calculation speed. Images from each measuring channel were connected into one multi-channel image. This article reveals the possible usage GAF conversion of EEG signals to motion imagery recognition, which is beneficial in the applied fields, such as implement it in brain-computer interface.