Abstract
Fuzzy Topographic Topological Mapping, shortly FTTM, is a model for solving neuromagnetic inverse problem. FTTM consist of four topological spaces and connected by three homeomorphisms. FTTM 1 and FTTM 2 were developed topresent 3-D view of an unbounded single current source and bounded multicurrent sources, respectively. Liau Li Yun (2006) showed that FTTM 1 and FTTM 2 are homeomorphic and this homeomorphism will generate another 14 FTTM. She then conjectured if there exist n elements of FTTM then the numbers of new elements are n4 − n . The 1purpose of this paper is to study the geometrical features of FTTM. In the process, several definitions were developed which may be used to prove the conjecture. This paper will show the proof of the conjecture and their extension result.
Highlights
The human brain (Figure 1a) is the most important structure in our body
By examining cube in FTTM, we can realize that cube is come from the combination of two terms FTTM in
Definition 6 can be expressed as follows and Table 2 shows sequence of FTTM2/n and its new elements
Summary
The human brain (Figure 1a) is the most important structure in our body. It is the most complex organized structure known to exist. Magnetoencephalography (MEG) is a recording of magnetic fields produced by electrical activity of the neurons in the brain. Magnetic field readings obtained from SQUID give information for the process to determine location, direction and magnitude of a current source. There is only a method for solving this problem, namely Bayesian that needs a priori information (data based model) and it is time consuming [9]. FTTM is a novel model for solving neuromagnetic inverse problem [7] It does not need a priori information and it is not time consuming. Its mathematical structure is compiled in [5], its algorithm is written in [2] and its performance is reported extensively in [8]
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