Fuzzy topographic topological mapping for localisation simulated multiple current sources of MEG

Ahmad, Tahir; Ahmad, Robiah; Rahman, Wan Eny Zarina Wan Abdul; Yun, Liau Li; Zakaria, Fauziah

doi:10.1080/09720502.2008.10700565

Cited by 14 publications

(9 citation statements)

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“…It consists of four topological spaces, namely, magnetic contour plane (MC), base magnetic plane (BM), fuzzy magnetic field (FM), and topographic magnetic field (TM). e FTTM is developed to determine the location of a simulated neuromagnetic current source [2] as shown in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Graph of Fuzzy Topographic Topological Mapping in relation to k-Fibonacci Sequence

Shukor

Ahmad

Idris

et al. 2021

Journal of Mathematics

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A generated n-sequence of fuzzy topographic topological mapping, FTTM n , is a combination of n number of FTTM’s graphs. An assembly graph is a graph whereby its vertices have valency of one or four. A Hamiltonian path is a path that visits every vertex of the graph exactly once. In this paper, we prove that assembly graphs exist in FTTM n and establish their relations to the Hamiltonian polygonal paths. Finally, the relation between the Hamiltonian polygonal paths induced from FTTM n to the k-Fibonacci sequence is established and their upper and lower bounds’ number of paths is determined.

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Section: Introductionmentioning

confidence: 99%

Graph of Fuzzy Topographic Topological Mapping in relation to k-Fibonacci Sequence

Shukor

Ahmad

Idris

et al. 2021

Journal of Mathematics

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“…The cerebral cortex has a total surface area of about 2500 cm 2 , folded in a complicated way, so that it fits into the cranial cavity formed by the skull of the brain. There are at least 1010 neurons in the cerebral cortex (Ahmad et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

“…Currently there is only a method for solving this problem, namely Bayesian that needs a priori information (data based model) and it is time consuming (Tarantola and Vallete, 1982). On the other hand, FTTM is a novel model for solving neuromagnetic inverse problem (Ahmad et al, 2008). It does not need a priori information and it is less time consuming.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Finite Sequence of Fuzzy Topographic Topological Mapping

Ahmad¹,

Jamian

Talib

2010

Journal of Mathematics and Statistics

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Problem statement: Fuzzy Topographic Topological Mapping (FTTM) was developed to solve the neuromagnetic inverse problem. FTTM consisted of four topological spaces and connected by three homeomorphisms. FTTM 1 and FTTM 2 were developed to present 3-D view of an unbounded single current source and bounded multicurrent sources, respectively. FTTM 1 and FTTM 2 were homeomorphic and this homeomorphism will generate another 14 FTTM. We conjectured if there exist n elements of FTTM, then the numbers of new elements are n⁴-n. Approach: In this study, the conjecture was proven by viewing FTTMs as sequence and using its geometrical features. Results: In the process, several definitions were developed, geometrical and algebraic properties of FTTM were discovered. Conclusion: The conjecture was proven and some features of the sequence appear in Pascal Triangle

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“…Literature review: Fuzzy Topographic Topological Mapping (FTTM) is a novel model for solving neuromagnetic inverse problem (Ahmad et al, 2008). The model is consists of four elements, Magnetic Contour Plane (MC), Base Magnetic Place (BM), Fuzzy Magnetic Field (TM) and Topographic Magnetic Field (TM) each homeomorphic to each other .…”

Section: Fig 1: Eeg Projectionmentioning

confidence: 99%

Topological Conjugacy Between Seizure and Flat Electroencephalography

M.¹

2010

American Journal of Applied Sciences

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Problem statement: Seizure and Flat EEG which are modeled as two distinct dynamical systems share the same dynamics in the topological viewpoint. Approach: Motions of seizure and Flat EEG of the dynamical systems were written as set points. A function that maps between these two sets is then built. By using topological conjugacy, they are shown to share the same dynamics. Results: Seizure and Flat EEG were shown to share the same dynamics along with other properties such as order isomorphic, homeomorphic and the unique representation of any event during seizure as an open set. Conclusion: This study shows that the dynamics of seizure can be transported to Flat EEG.

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Fuzzy topographic topological mapping for localisation simulated multiple current sources of MEG

Cited by 14 publications

References 1 publication

Graph of Fuzzy Topographic Topological Mapping in relation to k-Fibonacci Sequence

Graph of Fuzzy Topographic Topological Mapping in relation to k-Fibonacci Sequence

Generalized Finite Sequence of Fuzzy Topographic Topological Mapping

Topological Conjugacy Between Seizure and Flat Electroencephalography

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