Abstract
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.
Highlights
The human brain (Fig. 1a) is the most important structure in our body
We have introduced that two and three terms Fuzzy Topographic Topological Mapping (FTTM) in FTTMn can produce cubes
It is impossible to continuing develop cube from the combination of five or more terms FTTM
Summary
The human brain (Fig. 1a) is the most important structure in our body. It is the most complex organized structure known to exist. There are four lobes in both halves of the cortex: Frontal, pariental, temporal and occipital. The outermost layer of the brain is called the cerebral cortex. The cerebral cortex has a total surface area of about 2500 cm, 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)
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