Decomposing the Krohn-Rhodes Form of Electroencephalography (EEG) Signals Using Jordan-Chevalley Decomposition Technique

Amirul Aizad Ahmad Fuad,Tahir Ahmad

doi:10.3390/axioms10010010

Abstract

This paper explores how electroencephalography (EEG) signals in the Krohn-Rhodes form can be decomposed further using the Jordan-Chevalley decomposition technique. First, the recorded EEG signals of a seizure were transformed into a set of matrices. Each of these matrices was decomposed into its elementary components using the Krohn-Rhodes decomposition method. The components were then further decomposed into semisimple and nilpotent matrices using the Jordan-Chevalley decomposition. These matrices—which are the extended building blocks of elementary EEG signals—provide evidence that the EEG signals recorded during a seizure contain patterns similar to that of prime numbers.

Highlights

Introduction and MotivationElectroencephalography (EEG)Epilepsy is a common neurological disease that, according to the World Health Organization, affects approximately 1% of the world’s population [1]
The elementary EEG signals can be written as a sum of their simpler parts, which is similar to prime numbers where some primes can be written as a sum of two primes
The results provide a substantial manifestation that the EEG signals contain some patterns similar to prime numbers

Summary

Introduction and Motivation

Epilepsy is a common neurological disease that, according to the World Health Organization, affects approximately 1% of the world’s population [1]. The author concluded that MC is a plane that contains information This prompted Binjadhnan [14] to execute the Krohn-Rhodes decomposition on a set of square matrices of EEG signals during a seizure, MCn (R). The results showed that the EEG signals that arose during an epileptic seizure do not occur randomly Instead, they were ordered patterns with simple algebraic structures, namely periodic semigroups, affine scaling groups and the diagonal groups. The results are discussed, where the elementary EEG signals are further decomposed using the Jordan-Chevalley decomposition technique. We offer our concluding remarks and possible future studies

Semigroup of EEG Signals during a Seizure

Jordan-Chevalley Decomposition of EEG Signals during a Seizure

Main Results

Conclusions