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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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Formato: | Texto |
Lenguaje: | English |
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BioMed Central
2009
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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 |
format | Text |
id | pubmed-2728514 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2009 |
publisher | BioMed Central |
record_format | MEDLINE/PubMed |
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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