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PMC Biophysics paper review - Hsu and Hsu
You may have seen on our RSS feed of latest articles the publication of a very interesting paper in PMC Biophysics by Hsu and Hsu. Prof. John Straub gives us a bit of background, and highlights the work's particular merits.
Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion
David Hsu and Murielle Hsu
PMC Biophysics 2009, 2:6 (13 July 2009)
Sometimes it pays to borrow. A problem frequently encountered in science is to describe the behavior of a few experimental variables when these are coupled to many other variables about which we know very little. How does one infer relationships between the experimental variables in a rigorous way, with minimal ad hoc assumptions?
In the 1960’s, Robert Zwanzig and Hazime Mori independently addressed exactly this problem in describing the motion of large, slower moving particles in a “bath” of many smaller particles (the Brownian particle problem). Using “projection operators”, they showed that the equation of motion for the larger particles has the form of a generalized Langevin equation. This equation breaks down the forces acting on the larger (“Brownian”) particles into three contributions: one due to direct interactions between Brownian particles, a second due to frictional drag on the Brownian particles due to the bath, and a third which causes random fluctuations in Brownian particle trajectories due to collisions with bath particles.
Over time, Zwanzig-Mori projection operators have proven extremely useful in nonequilibrium statistical mechanics. Now David and Murielle Hsu have adapted projection operators to the analysis of electroencephalograms (EEG). In “Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion”, they show that EEG dynamics also obeys a generalized Langevin equation. They point out that the parameters of this equation represent macroscopic properties, and then, most ingeniously, they identify two variational principles that allow these parameters to be extracted from experimental data. The variational principles of Hsu and Hsu open the way for practical application of the generalized Langevin equation to a wide array of real life problems, not just EEG dynamics. We can look forward to interesting results.
Posted by Morag Hickman at 11:52 Comments (0)