Analysis of Results of Digital Electroencephalography and Digital Vectors of Coronavirus Images upon Applying the Theory of Covariance Functions

• Published in: Symmetry (Basel) Vol. 15; no. 7; p. 1330
• Main Authors: Skeivalas, Jonas, Paršeliūnas, Eimuntas, Paršeliūnas, Audrius, Šlikas, Dominykas
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.06.2023
• Subjects: Analysis; Coronaviruses; Correlation coefficients; Covariance; covariance function; COVID-19; Digital imaging; Electrodes; Electroencephalography; Estimators; Health aspects; Mathematical analysis; Matrices (mathematics); Parameters; Pixels; quantised interval; SARS-CoV-2; Standard deviation
• DOI: 10.3390/sym15071330
• ISSN: 2073-8994

This paper analyses the structures of covariance functions of digital electroencephalography measurement vectors and digital vectors of two coronavirus images. For this research, we used the measurement results of 30-channel electroencephalography (E1–E30) and digital vectors of images of two SARS-CoV-2 variants (cor2 and cor4), where the magnitudes of intensity of the electroencephalography parameters and the parameters of the digital images of coronaviruses were encoded. The estimators of cross-covariance functions of the digital electroencephalography measurements’ vectors and the digital vectors of the coronavirus images and the estimators of auto-covariance functions of separate vectors were derived by applying random functions constructed according to the vectors’ parameter measurement data files. The estimators of covariance functions were derived by changing the values of the quantised interval k on the time and image pixel scales. The symmetric matrices of correlation coefficients were calculated to estimate the level of dependencies between the electroencephalography measurement results’ vectors and the digital vectors of the coronavirus images. The graphical images of the normalised cross-covariance functions for the electroencephalography measurement results’ vectors and the digital vectors of the coronavirus images within the period of all measurements are asymmetric. For all calculations, a computer program was developed by applying a package of Matlab procedures. A probabilistic interdependence between the results of the electroencephalography measurements and the parameters of the coronavirus vectors, as well as their variation on the time and image pixel scales, was established.