Generalization of the graph of fuzzy topographic topological mapping
DOI:
https://doi.org/10.11113/mjfas.v11n4.395Keywords:
FTTM, Sequence of FTTM, Elements Order, Graph of FTTM,Abstract
In 1999, Tahir et. al. developed the Fuzzy Topographic Topological Mapping to determine the location of epileptic foci in epilepsy disorder patients. The model which consists of topological and fuzzy structure is composed into three mathematical algorithms. There are two FTTMs up to now, namely FTTM version 1 and FTTM version 2. FTTM version 1 is homeomorphic to FTTM version 2. The homeomorphism of FTTM can be presented using graphs. In this paper, we generalized the graph of FTTM. In other words, we will prove that, if there exist k versions of FTTM, the new elements will produce a graph of degree 8k3+8k-24.
References
Chao, D., Shen, X. and Xia, Y., (2013). From Acupuncture to Interaction between-Opioid Receptors and Na (+) Channels: A Potential Pathway to Inhibit Epileptic Hyperexcitability. Evidence-based complementary and alternative
medicine: eCAM, 2012: 216016–216016.
Mirza, N., Vasieva, O., Marson, A. G. and Pirmohamed, M. (2011). Exploring the genomic basis of pharmacoresistance in epilepsy: an integrative analysis of large-scale gene expression profiling studies on brain tissue from epilepsy surgery. Human molecular genetics, 20(22): 4381–4394.
Giorgi, F. S., Pizzanelli, C., Pelliccia, V., Di Coscio, E., Maestri, M., Guida, M., Iacopini, E., Iudice, A. and Bonanni, E., (2013). A Clinical-EEG Study of Sleepiness and Psychological Symptoms in Pharmacoresistant Epilepsy Patients Treated with Lacosamide. Epilepsy research and treatment.
Singh, P., Kaur, R., Saggar, K., Singh, G. and Kaur, A., (2013). Qualitative and Quantitative Hippocampal MRI Assessments in Intractable Epilepsy. BioMed research international.
Hosseini, S., Akbarzadeh-T, M. and Naghibi-Sistani, M., (2013). Qualitative and Quantitative Evaluation of EEG Signals in Epileptic Seizure Recognition. International Journal of Intelligent Systems and Applications (IJISA).
Fisher, R. S., Boas, W. v. E., Blume, W., Elger, C., Genton, P., Lee, P. and Engel, J., (2005) Epileptic seizures and epilepsy: definitions proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE). Epilepsia. 46(4): 470–472.
Schindler, K., Gast, H., Goodfellow, M. and Rummel, C., (2012). On seeing the trees and the forest: Single-signal and multisignal analysis of periictal intracranial EEG. Epilepsia. 53(9): 1658–1668.
Lerche, H., Shah, M., Beck, H., Noebels, J., Johnston, D. and Vincent, A. , (2012). Ion channels in genetic and acquired forms of epilepsy. The Journal of physiology. 591.4.
Altenmüller, D.-M., Hebel, J. M., Rassner, M. P., Volz, S., Freiman, T. M., Feuerstein, T. J. and Zentner, J., (2013). Locally Applied Valproate Enhances Survival in Rats after Neocortical Treatment with Tetanus Toxin and Cobalt Chloride. BioMed research international.
McNamara, J. O. , (1994). Cellular and molecular basis of epilepsy. The Journal of Neuroscience. 14(6): 3413–3425.
Shorvon, S. D., (2005). Handbook oF Epilepsy Treatment Forms, Causes and Therapy in Children and Adults 2nd edition. Massachusetts, USA: Blackwell Publishingl.
Guo, Y., Baum, L. W., Sham, P. C., Wong, V., Ng, P. W., Lui, C. H. T., Sin, N. C., Tsoi, T. H., Tang, C. S., Kwan, J. S. et al. , (2012) Two-stage genome-wide association study identifies variants in CAMSAP1L1 as susceptibility loci for epilepsy in Chinese. Human molecular genetics. 21(5): 1184–1189.
Ahmad, T., Shah, R., Zakaria, F. and Yun, L. L., (2000). Development Of Detection Model For Neuromagnetic Field. Proceedings of BIOMED. Kuala Lumpur: Universiti Malaysia. 119–121.
Yun, L. L., (2001). Homeomorfisma Antara Melalui Struktur Permukaan Riemann serta Deduksi Teknik Pembuktiannya bagi Homeomorfisma pemetaan Topologi Topografi kabur (FTTM). M.sc. thesis. University Teknologi Malaysia.
Zakaria, F., (2002). Algorithma Penyelesaian Masalah Songsang Arus Tunggal Tak Terbatas MEG. M.sc. thesis. University Technology Malaysia.
Yun, L. L., (2006). Algebraic Structures of Fuzzy Topographic Topological Mapping for Solving Neuromagnetic Inverse Problem. PhD. thesis. University Teknologi Malaysia.
Ahmad, T., Shah, R., Yun, L. L., Zakaria, F. and Zarina, W. E. , (2005). Homeomorphism of Fuzzy Topographic Topological Mapping (FTTM). Matematika. 1(21): 35– 42.
Ahmad, T., Jamian, S. S. and Talib, J., (2010). Generalized Finite Sequence of Fuzzy Topographic Topological Mapping. Journal of Mathematics and Statistics. 6(2): 151– 156
Sayed, M., and Ahmad,T,. (2013). Graph of Finite Sequence of fuzzy Topographic topological Mapping. Journal of Mathematics and Statistics. 9(1): 18– 23.
Sayed, M. and Ahmad, T., (2013). On Properties of the Graph of Fuzzy Topographic Topological Mapping. Malaysian Journal of Fundamental and Applied and Applied Sciences. 9(3):139-142.
