Some fundamental properties for regular element of electroencephalography signals semigroup during epileptic seizure
DOI:
https://doi.org/10.11113/mjfas.v11n1.335Keywords:
EEG, semigroup, regular element,Abstract
Electroencephalography (EEG) is a record of electrical activity along the scalp. It is measures voltage fluctuations resulting from ionic current flows within the neurons of the brain. EEG is most often used to diagnose epilepsy, which causes understandable abnormalities in EEG readings. The mathematical analysis of EEG signals assists medical specialists by providing a clarification of the brain activity being observed, so increasing the information about the structure and function of the human brain. EEG signals during epileptic seizure can be viewed as a semigroup of square matrices under matrix multiplication, and every element in that semigroup is shown to be regular. In this paper, we will present some main properties of regular element of EEG signals during epileptic seizure.References
Fisher, R.S., W.v.E. Boas, W. Blume, C. Elger, P. Genton, P. Lee, and J. Engel, Epileptic seizures and epilepsy: definitions proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE). Epilepsia, 470-472 (2005) 46(4).
Gastaut, H., Clinical and Electroencephalographical Classification of Epileptic Seizures. Epilepsia, 102-112 (1970) 11(1).
Ahmad, T., R.A. Fairuz, F. Zakaria, and H. Isa. Selection of a subset of EEG channels of epileptic patient during seizure using PCA. in Proceedings of the 7th WSEAS International Conference on Signal Processing, Robotics and Automation. (2008): World Scientific and Engineering Academy and Society (WSEAS).
Niedermeyer, E. and F.L. Da Silva, Electroencephalography: basic principles, clinical applications, and related fields. (2005): Lippincott Williams & Wilkins.
Zakaria, F. and T. Ahmad, Tracking The Storm In The Brain. , in Presented at Kolokium Jabatan Matematik. (2007): UTM Skudai Johor.
Fauziah, Z., Dynamic Profiling Of EEG Data During Seizure Using Fuzzy Information Space, in Mathematics. (2008), Universiti Teknologi Malaysia,Skudai: Malaysia.
Binjadhnan, F.A.M. and T. Ahmad, EEG Signals during Epileptic Seizure as a Semigroup of Upper Triangular Matrices. American Journal of Applied Sciences, (2010) 7(4).
Putcha, M.S., Linear algebraic monoids. Vol. 133. (1988): Cambridge University Press.
Almeida, J., S.W. Margolis, and M.V. Volkov, The pseudovariety of semigroups of triangular matrices over a finite field. Theoretical Informatics and Applications, 31-48 (2005) 39(1).
Kambites, M., On the Krohn–Rhodes complexity of semigroups of upper triangular matrices. International Journal of Algebra and Computation, 187-201 (2007) 17(01).
Clifford, A.H. and G.B. Preston, The algebraic theory of semigroups. 2. Vol. 7. (1967): Amer Mathematical Society.
Krohn, K. and J. Rhodes, Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines. Transactions of the American Mathematical Society, 450-464 (1965) 116.
Howie, J.M., Fundamentals of semigroup theory. (1995): Clarendon Oxford.
Binjadhnan, F.A.M., Krohn-Rhodes Decomposition for Electroencephalography Signals during Epileptic Seizure., in Mathematics. (2011), Universiti Teknologi Malaysia, Skudai: Malaysia.
Kambites, M. and B. Steinberg, Wreath Product Decompositions for Triangular Matrix Semigroups. Semigroups and Formal Languages, 129-144 (2005).
Barja, A.O., T. Ahmad, and F.A. Binjadhnan, Regular Element for a Semigroup of Electroencephalography Signals During Epileptic Seizure. Journal of Applied Sciences, 1781-1785 (2014) 14(15).
