Group-like algebraic structures of fuzzy topographic topological mapping for solving neuromagnetic inverse problem

Fuzzy Topographic Topological Mapping (FTTM) is a novel mathematical model for solving neuromagnetic inverse problem. It is given as a set of mathematical operations, namely topological transformations with four components and connected by three different algorithms. At this moment, Fuzzy Topographi...

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Main Author:	Liau, Li Yun
Format:	Thesis
Language:	English
Published:	2006
Subjects:	QD Chemistry
Online Access:	http://eprints.utm.my/id/eprint/78176/1/LiauLiYunPFS20061.pdf
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id	my-utm-ep.78176
record_format	uketd_dc
spelling	my-utm-ep.781762018-07-25T08:19:08Z Group-like algebraic structures of fuzzy topographic topological mapping for solving neuromagnetic inverse problem 2006-12 Liau, Li Yun QD Chemistry Fuzzy Topographic Topological Mapping (FTTM) is a novel mathematical model for solving neuromagnetic inverse problem. It is given as a set of mathematical operations, namely topological transformations with four components and connected by three different algorithms. At this moment, Fuzzy Topographic Topological Mapping 1 (FTTM 1) and Fuzzy Topographic Topological Mapping 2 (FTTM 2), which are used to solve the inverse problem for determining single current source and multiple current sources respectively, have been developed. The purpose of this research is to establish the topological and the algebraic structures of the components of FTTM 1 and FTTM 2. Firstly, the topological structures of the components of FTTM 2 were established and the homeomorphisms between the components of FTTM 2 were shown by using the proving techniques of the topological structures of the components of FTTM 1 and the homeomorphisms between the components of FTTM 1, then followed by the establishment of the algebraic structures of the components of FTTM 1 and FTTM 2. In the process, several definitions and theorems of group theory were adopted and the proving technique by construction was highlighted. In addition, FTTM was then generalized as a set which led to the proving the existence of infinitely many forms of FTTM. Finally, these structures were interpreted physically in order to study the information content of the inverse problem for determining single and multiple current sources. 2006-12 Thesis http://eprints.utm.my/id/eprint/78176/ http://eprints.utm.my/id/eprint/78176/1/LiauLiYunPFS20061.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:81863 phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QD Chemistry
spellingShingle	QD Chemistry Liau, Li Yun Group-like algebraic structures of fuzzy topographic topological mapping for solving neuromagnetic inverse problem
description	Fuzzy Topographic Topological Mapping (FTTM) is a novel mathematical model for solving neuromagnetic inverse problem. It is given as a set of mathematical operations, namely topological transformations with four components and connected by three different algorithms. At this moment, Fuzzy Topographic Topological Mapping 1 (FTTM 1) and Fuzzy Topographic Topological Mapping 2 (FTTM 2), which are used to solve the inverse problem for determining single current source and multiple current sources respectively, have been developed. The purpose of this research is to establish the topological and the algebraic structures of the components of FTTM 1 and FTTM 2. Firstly, the topological structures of the components of FTTM 2 were established and the homeomorphisms between the components of FTTM 2 were shown by using the proving techniques of the topological structures of the components of FTTM 1 and the homeomorphisms between the components of FTTM 1, then followed by the establishment of the algebraic structures of the components of FTTM 1 and FTTM 2. In the process, several definitions and theorems of group theory were adopted and the proving technique by construction was highlighted. In addition, FTTM was then generalized as a set which led to the proving the existence of infinitely many forms of FTTM. Finally, these structures were interpreted physically in order to study the information content of the inverse problem for determining single and multiple current sources.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Liau, Li Yun
author_facet	Liau, Li Yun
author_sort	Liau, Li Yun
title	Group-like algebraic structures of fuzzy topographic topological mapping for solving neuromagnetic inverse problem
title_short	Group-like algebraic structures of fuzzy topographic topological mapping for solving neuromagnetic inverse problem
title_full	Group-like algebraic structures of fuzzy topographic topological mapping for solving neuromagnetic inverse problem
title_fullStr	Group-like algebraic structures of fuzzy topographic topological mapping for solving neuromagnetic inverse problem
title_full_unstemmed	Group-like algebraic structures of fuzzy topographic topological mapping for solving neuromagnetic inverse problem
title_sort	group-like algebraic structures of fuzzy topographic topological mapping for solving neuromagnetic inverse problem
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2006
url	http://eprints.utm.my/id/eprint/78176/1/LiauLiYunPFS20061.pdf
_version_	1747817925619744768

Group-like algebraic structures of fuzzy topographic topological mapping for solving neuromagnetic inverse problem

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