Koszul connections of flat EEG bundles for description of brain signal dynamics

The bio-electromagnetic inverse problem is the identification of electromagnetic sources based on signals recorded from Electroencephalography (EEG) or Magnetoencephalography (MEG) and physical equations with a minimum of priori information. Following initial applications in modelling epilepsy patie...

Full description

Saved in:

Bibliographic Details
Main Author:	Ab. Karim, Niki Anis
Format:	Thesis
Language:	English
Published:	2016
Subjects:	QH301 Biology
Online Access:	http://eprints.utm.my/id/eprint/77776/1/NikiAnisAbKarimPFS2016.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-utm-ep.77776
record_format	uketd_dc
spelling	my-utm-ep.777762018-07-04T11:44:24Z Koszul connections of flat EEG bundles for description of brain signal dynamics 2016-03 Ab. Karim, Niki Anis QH301 Biology The bio-electromagnetic inverse problem is the identification of electromagnetic sources based on signals recorded from Electroencephalography (EEG) or Magnetoencephalography (MEG) and physical equations with a minimum of priori information. Following initial applications in modelling epilepsy patients' electrical brain activity, extensive research has been done in processing massive amounts of signal data from patients while preserving as much information as possible. Improvements in analyzing EEG/MEG recordings have significant utility not just in epilepsy treatment and diagnosis, but neuro-cognitive research in general. The main objective of this research is to build structures holding visualized and flattened EEG data as differential geometric entities, and to extend these structures as a dynamical system dealing with the evolution of large amounts of point data about brain activity. One aspect of existing research involves EEG signal data recorded across a time interval and processed using fuzzy clustering techniques, resulting in point data sets representing areas of high electrical activity within the brain. Concepts in differential geometry are applied to these spaces as a dynamical and visualized approach to modelling the evolution of signal clusters in the brain over time. Initially, Flat EEG data sets are shown to be topological spaces, manifolds and vector spaces. Two vector bundle structures for the Flat EEG space are thus developed: one analogous to Minkowski space-time and the other based on the classical notion of spatial change over linear time. From there, Koszul connections were constructed for both vector bundles, and both are shown to have zero curvature. Having provided a continuous differential structure to Flat EEG data, the evolution of signal clusters as a discrete dynamical system is then interpolated into a continuous form, allowing an enhanced view of the brain's state changes over time. 2016-03 Thesis http://eprints.utm.my/id/eprint/77776/ http://eprints.utm.my/id/eprint/77776/1/NikiAnisAbKarimPFS2016.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:97508 phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QH301 Biology
spellingShingle	QH301 Biology Ab. Karim, Niki Anis Koszul connections of flat EEG bundles for description of brain signal dynamics
description	The bio-electromagnetic inverse problem is the identification of electromagnetic sources based on signals recorded from Electroencephalography (EEG) or Magnetoencephalography (MEG) and physical equations with a minimum of priori information. Following initial applications in modelling epilepsy patients' electrical brain activity, extensive research has been done in processing massive amounts of signal data from patients while preserving as much information as possible. Improvements in analyzing EEG/MEG recordings have significant utility not just in epilepsy treatment and diagnosis, but neuro-cognitive research in general. The main objective of this research is to build structures holding visualized and flattened EEG data as differential geometric entities, and to extend these structures as a dynamical system dealing with the evolution of large amounts of point data about brain activity. One aspect of existing research involves EEG signal data recorded across a time interval and processed using fuzzy clustering techniques, resulting in point data sets representing areas of high electrical activity within the brain. Concepts in differential geometry are applied to these spaces as a dynamical and visualized approach to modelling the evolution of signal clusters in the brain over time. Initially, Flat EEG data sets are shown to be topological spaces, manifolds and vector spaces. Two vector bundle structures for the Flat EEG space are thus developed: one analogous to Minkowski space-time and the other based on the classical notion of spatial change over linear time. From there, Koszul connections were constructed for both vector bundles, and both are shown to have zero curvature. Having provided a continuous differential structure to Flat EEG data, the evolution of signal clusters as a discrete dynamical system is then interpolated into a continuous form, allowing an enhanced view of the brain's state changes over time.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Ab. Karim, Niki Anis
author_facet	Ab. Karim, Niki Anis
author_sort	Ab. Karim, Niki Anis
title	Koszul connections of flat EEG bundles for description of brain signal dynamics
title_short	Koszul connections of flat EEG bundles for description of brain signal dynamics
title_full	Koszul connections of flat EEG bundles for description of brain signal dynamics
title_fullStr	Koszul connections of flat EEG bundles for description of brain signal dynamics
title_full_unstemmed	Koszul connections of flat EEG bundles for description of brain signal dynamics
title_sort	koszul connections of flat eeg bundles for description of brain signal dynamics
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2016
url	http://eprints.utm.my/id/eprint/77776/1/NikiAnisAbKarimPFS2016.pdf
_version_	1747817828177674240

Koszul connections of flat EEG bundles for description of brain signal dynamics

Similar Items