Prime-like structures in EEG signal matrices: A framework for analysing EEG signals in epilepsy

Epilepsy is a neurological condition affecting millions worldwide. It is characterised by recurrent seizures. Electroencephalography remains one of the important investigations into the diagnosis and management of epilepsy, imaging electrical activities of the brain to outline patterns that precede seizures. Mathematical modeling of seizure patterns requires identifying specific antecedent features of seizures in EEG recordings. Better understanding of such patterns could contribute to better management and improvement in the quality of life for persons living with the condition. The research further proposes a new mathematical framework wherein simple signals from EEG can be imagined as an analog of primes, drawing their inspiration from number-theoretical and linear algebraic concepts. It is based on the definition of the GCD for EEG signal square matrices and a theorem that will prove the existence of infinitely many elementary EEG signals. The approach described below transforms the EEG data into square matrices and, by applying algebraic techniques, allows a systematic analysis of seizure activity. The results suggest that this framework provides a structured method for EEG signal processing, offering potential applications in seizure analysis and related neurological studies.