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     Research Journal of Applied Sciences, Engineering and Technology


Group Complexity for Semigroup of Electroencephalography Signals during Epileptic Seizure

1Ameen Omar Ali Barja, 1Tahir Bin Ahmad and 2Faisal Abdurabu Mubarak Binjadhnan
1Department of Mathematical Science and Ibnu Sina Institute for Fundamental Science Studies, Nanotechnology Research Alliance, Faculty of Science, Universiti Teknologi Malaysia, Skudai 81310, Johor, Malaysia
2Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla 50511, Yemen
Research Journal of Applied Sciences, Engineering and Technology  2015  2:150-157
http://dx.doi.org/10.19026/rjaset.11.1701  |  © The Author(s) 2015
Received: March ‎19, ‎2015  |  Accepted: April ‎1, ‎2015  |  Published: September 15, 2015

Abstract

Electroencephalography (EEG) signals during epileptic seizure can be viewed as a semigroup of upper triangular matrices under matrix multiplication. In this study, we will provide a novel algebraic structure for EEG signals during epileptic seizure and then find out the group complexity. In this case, the novel structure of EEG signals during seizure is investigated for potential and Average Potential Differences (APD).

Keywords:

Electroencephalography, group complexity, semigroup,


References

  1. Abarbanel, H., R. Davis, G.J. Macdonald and W. Munk, 1985. Bispectra. Defense Technical Information Center, Document ADA 150870, 1984.
  2. Ahmad, T., R.S. Ahmad, W.E.A.W. Abdul Rahman, L.L. Yun and F. Zakaria, 2008. Fuzzy topographic topological mapping for localisation simulated multiple current sources of MEG. J. Interdiscipl. Math., 11(3): 381-393.
  3. Ahmad, T., M. Ghanbari, M. Askaripour and N. Behboodiyan, 2012. Detection of epilepsy from EEG signal during seizure using heuristic algorithm of fixed point iterations. Res. J. Appl. Sci. Eng. Technol., 4(19): 3584-3587.
    CrossRef    
  4. Almeida, J., S.W. Margolis and M.V. Volkov, 2005. The pseudovariety of semigroups of triangular matrices over a finite field. Theor. Inform. Appl., 39(1): 31-48.
    CrossRef    
  5. Barja, A., T. Ahmad and F. Binjadhnan, 2014. Regular element for a semigroup of electroencephalography signals during epileptic seizure. J. Appl. Sci., 14(15): 1781-1785.
    CrossRef    
  6. Binjadhnan, F. and T. Ahmad, 2010. Semigroup of EEG signals during epileptic seizure. J. Appl. Sci., 10(14): 1466-1470.
    CrossRef    
  7. Faisal, B., 2011. Krohn-Rhodes decomposition for electroencephalography signals during epileptic seizure. Ph.D. Thesis, Universiti Teknologi Malaysia, Skudai.
  8. Gastaut, H., 1970. Clinical and electroencephalographical classification of epileptic seizures. Epilepsia, 11(1): 102-112.
    CrossRef    PMid:5268244    
  9. Howie, J.M., 1995. Fundamentals of Semigroup Theory. London Mathematical Society Monographs. New Series 12, Clarendon Press, Oxford University Press, New York, pp: 351.
  10. Kambites, M., 2007. On the Krohn-Rhodes complexity of semigroups of upper triangular matrices. Int. J. Algebra Comput., 17(01): 187-201.
    CrossRef    
  11. Krohn, K. and J. Rhodes, 1965. Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines. T. Am. Math. Soc., 116: 450-464.
    CrossRef    
  12. Krohn, K. and J. Rhodes, 1968. Complexity of finite semigroups. Ann. Math., 88(1): 128-160.
    CrossRef    
  13. Magiorkinis, E., K. Sidiropoulou and A. Diamantis, 2010. Hallmarks in the history of epilepsy: Epilepsy in antiquity. Epilepsy Behav., 17(1): 103-108.
    CrossRef    PMid:19963440    
  14. Michel, C.M., M.M. Murray, G. Lantz, S. Gonzalez, L. Spinelli and R. Grave De Peralta, 2004. EEG source imaging. Clin. Neurophysiol., 115(10): 2195-2222.
    CrossRef    PMid:15351361    
  15. Niedermeyer, E. and F.H.L. Da Silva, 2005. Electroencephalography: Basic Principles, Clinical Applications and Related Fields. Wolters Kluwer Health, Philadelphia, PA.
    PMCid:PMC1193547    
  16. Okninski, J., 1998. Semigroups of Matrices. World Scientific, Singapore.
    CrossRef    
  17. Putcha, M.S., 1988. Linear Algebraic Monoids. Cambridge University Press, Cambridge.
    CrossRef    PMid:3370038    
  18. Rhodes, J., 1968. The fundamental lemma of complexity for arbitrary finite semigroups. B. Am. Math. Soc., 74(6): 1104-1109.
    CrossRef    
  19. Rhodes, J. and R. Tilson, 1968. Algebraic Theory of Finite Semigroups. Structure Number and Structure Theorems for Finite Semigroups. Academic Press, New York, pp: 125-208.
  20. Selvaraj, K. and P. Sivaprakasam, 2014. Focused attention analysis of meditating and non-meditating brains in time and frequency domains using EEG data. Res. J. Appl. Sci. Eng. Technol., 7(17): 3671-3676.
  21. Zakaria, F. and T. Ahmad, 2007. Tracking the storm in the brain. Presented at Kolokium Jabatan Matematik, UTM Skudai, March 21, 2007.
  22. Zakaria, F.B.H., 2008. Dynamic profiling of electroencephalographic data during seizure using fuzzy information space. Ph.D. Thesis, Universiti Teknologi Malaysia.

Competing interests

The authors have no competing interests.

Open Access Policy

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Copyright

The authors have no competing interests.

ISSN (Online):  2040-7467
ISSN (Print):   2040-7459
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