Elementary components of electroencephalography signals viewed as prime numbers

Abstract

The disabling aspect of epilepsy disease is that it seems to be erratic and random in nature. Electroencephalogram (EEG) serves as an essential non-invasive tool to diagnose and manage epilepsy, allowing the physiological manifestations of irregular cortical excitability to be demonstrated. Certain prior EEG features related to seizure onset may facilitate seizure pattern predictions through mathematical models. A better understanding of these patterns can positively improve epilepsy management and, in turn, improve the quality of life of epilepsy patients. Thus, the goal of the current paper is to show that elementary EEG signals during a seizure can be perceived as prime numbers. First, the recorded EEG signals are written as a product of their elementary components through the Krohn - Rhodes decomposition technique. Following this, every elementary component of EEG signal is expressed in terms of a summation of their simpler parts via the Jordan - Chevalley decomposition process. Conversely, some prime numbers are decomposed similar to Jordan - Chevalley decomposition of elementary EEG signals and presented as Pseudo - Goldbach Theorem. Finally, the results demonstrate substantial evidence that the EEG signals follow a pattern similar to that of the distribution of prime numbers among positive integers.