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Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion

We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that has the form of a generalized Langevin equatio...

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Detalles Bibliográficos
Autores principales: Hsu, David, Hsu, Murielle
Formato: Texto
Lenguaje:English
Publicado: BioMed Central 2009
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2728514/
https://www.ncbi.nlm.nih.gov/pubmed/19594920
http://dx.doi.org/10.1186/1757-5036-2-6
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author Hsu, David
Hsu, Murielle
author_facet Hsu, David
Hsu, Murielle
author_sort Hsu, David
collection PubMed
description We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that has the form of a generalized Langevin equation (GLE), which requires knowledge only of macroscopic properties. The macroscopic properties can be extracted from experimental data by one of two possible variational principles. These variational principles are our principal contribution to the formalism. Potential applications are discussed, including applications to the theory of critical phenomena in the brain, Granger causality and Kalman filters. PACS code: 87.19.lj
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spelling pubmed-27285142009-08-19 Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion Hsu, David Hsu, Murielle PMC Biophys Research Article We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that has the form of a generalized Langevin equation (GLE), which requires knowledge only of macroscopic properties. The macroscopic properties can be extracted from experimental data by one of two possible variational principles. These variational principles are our principal contribution to the formalism. Potential applications are discussed, including applications to the theory of critical phenomena in the brain, Granger causality and Kalman filters. PACS code: 87.19.lj BioMed Central 2009-07-13 /pmc/articles/PMC2728514/ /pubmed/19594920 http://dx.doi.org/10.1186/1757-5036-2-6 Text en Copyright © 2009 Hsu and Hsu http://creativecommons.org/licenses/by/2.0 This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( (http://creativecommons.org/licenses/by/2.0) ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Hsu, David
Hsu, Murielle
Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion
title Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion
title_full Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion
title_fullStr Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion
title_full_unstemmed Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion
title_short Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion
title_sort zwanzig-mori projection operators and eeg dynamics: deriving a simple equation of motion
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2728514/
https://www.ncbi.nlm.nih.gov/pubmed/19594920
http://dx.doi.org/10.1186/1757-5036-2-6
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