Jordan-chevalley decomposition of recorded electroencephalography signals during epileptic seizures
Also available in printed version
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| Format: | Doctoral thesis |
| Language: | English |
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Universiti Teknologi Malaysia
2025
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| Online Access: | https://utmik.utm.my/handle/123456789/43346 |
| Abstract | Abstract here |
| _version_ | 1854975119081865216 |
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| author | Amirul Aizad Ahmad Fuad |
| author2 | Tahir Ahmad, supervisor |
| author_facet | Tahir Ahmad, supervisor Amirul Aizad Ahmad Fuad |
| author_sort | Amirul Aizad Ahmad Fuad |
| description | Also available in printed version |
| format | Doctoral thesis |
| id | utm-123456789-43346 |
| institution | Universiti Teknologi Malaysia |
| language | English |
| publishDate | 2025 |
| publisher | Universiti Teknologi Malaysia |
| record_format | dspace |
| record_pdf | Abstract |
| spelling | utm-123456789-433462025-08-21T14:19:07Z Jordan-chevalley decomposition of recorded electroencephalography signals during epileptic seizures Amirul Aizad Ahmad Fuad Tahir Ahmad, supervisor Science Also available in printed version Epilepsy is a disease that can be identified by its main features that are the recurrent and unpredictable electrical discharges of the cerebral cortex that trigger disturbances in brain functions. It can be diagnosed through a noninvasive tool called electroencephalography (EEG), which records the electrical signals emanated by the brain. The recorded signals provide important information about brain functions in terms of observed electrical potentials. This information is critical especially for diagnosing brain disorders, particularly epilepsy. In fact, EEG signals during epileptic seizures can form a semigroup of upper triangular matrices under matrix multiplication. This semigroup can be represented as the product of its elementary components through the Krohn-Rhodes decomposition technique. The representation of EEG signals in terms of the product of its elementary components is somehow connected to how any positive integer can be written as a product of prime numbers. In this study, the elementary EEG signals are shown to act as the building blocks of EEG signals, similar to the prime numbers being the building blocks of the positive integers. The primary goal of this research is to describe and view the elementary components of EEG signals during epileptic seizures as prime numbers. Firstly, the well-ordered property of prime numbers hints at a similar attribute to be found in the case of elementary EEG signals. Therefore, a new way of ordering matrices, namely the precede operator, is introduced to achieve this goal, and several theorems are developed in the process. Secondly, the elementary EEG signals are decomposed via the Jordan-Chevalley decomposition technique, which produces the summation of its simpler parts and reveals that it resonates with one of the main properties of prime numbers, particularly the Twin-Prime Conjecture. Finally, the decomposition method is implemented on the real EEG data of three patients. In this way, the theoretical framework of the EEG signals� building blocks is developed. In short, it is obtained that the ordered property of the elementary EEG signals and its representation through the Jordan-Chevalley decomposition exhibits similar properties with certain results in prime numbers as anticipated by the Krohn-Rhodes semigroup theory. The results hint that, due to their similar properties, the EEG signals could have a similar pattern to that of prime numbers. shafika UTM 341 p. Thesis (Ph.D (Matematik)) - Universiti Teknologi Malaysia, 2021 2025-03-11T05:36:21Z 2025-03-11T05:36:21Z 2021 Doctoral thesis https://utmik.utm.my/handle/123456789/43346 vital:146189 valet-20220405-12429 ENG Closed Access UTM Complete Unpublished Completion application/pdf Universiti Teknologi Malaysia |
| spellingShingle | Science Amirul Aizad Ahmad Fuad Jordan-chevalley decomposition of recorded electroencephalography signals during epileptic seizures |
| thesis_level | PhD |
| title | Jordan-chevalley decomposition of recorded electroencephalography signals during epileptic seizures |
| title_full | Jordan-chevalley decomposition of recorded electroencephalography signals during epileptic seizures |
| title_fullStr | Jordan-chevalley decomposition of recorded electroencephalography signals during epileptic seizures |
| title_full_unstemmed | Jordan-chevalley decomposition of recorded electroencephalography signals during epileptic seizures |
| title_short | Jordan-chevalley decomposition of recorded electroencephalography signals during epileptic seizures |
| title_sort | jordan chevalley decomposition of recorded electroencephalography signals during epileptic seizures |
| topic | Science |
| url | https://utmik.utm.my/handle/123456789/43346 |
| work_keys_str_mv | AT amirulaizadahmadfuad jordanchevalleydecompositionofrecordedelectroencephalographysignalsduringepilepticseizures |