The poster available below was presented at ECCS '06 and shows an application of Mutual Information to the Vicsek model of self propelled particles. The Vicsek model is an excellent example of a multi-disciplinary complex system, it was originally invented to model the flocking of birds but will actually model the collective motion of many organisms and is amazingly simple. The Vicsek model is also connected to the Edwards Wilkinson model of surface deposition and so has connections to sand pile models, turbulence and non-equilibrium statistical mechanics in general.
Mutual information is an exciting method that tests the similarity between two data sets. Originally developed as part of information theory by Claude Shannon in 1949 it is at its maximum when both data sets appear random (a mix of 1s and 0s with 0.5 probability each) but are identical and is at a minimum when both data sets are identical and uniform (all 1s or all 0s with probability 1) or when both data sets are random and completely different. Read on if interested!
Two oral presentations were given at the spring EGU meeting in Vienna. The first, titled "Quantifying spatial correlation in the turbulent solar wind flow using mutual information: simultaneous in-situ spacecraft observations from WIND and ACE." was given in the session "Nonlinear time series analysis in the geosciences". This talk is mostly about how mutual information can beused to show correlation in turbulent flow. It uses the Vicsek model as an example of how MI can be used on limited data and then goes on to show some results using "real world" data taken from the solar wind.
The second talk was titled "Mutual information as a measure of the spatial correlation properties of the turbulent solar wind as seen by WIND and ACE." which was part of the "Coupling between regions and scales: the future is multipoint and multi-instrument" session. The talk has a quick introduction to MI and then shows how Coronal Mass Ejections (CMEs) and turbulence are measured by MI; the results include a brief comparison of MI and linear correlation and also an example of possible anisotropy measurement in the solar wind.
These presentations are available in PDF format below:
(Warning: the embedded videos wont play and the presentation was written to be accompanied by description from the author so may not make compete sense)
(Warning: the presentation was written to be accompanied by description from the author so may not make compete sense)
At the 34th EPS Conference on Plasma Physics in Warsaw, Poland, I presented the poster below which received a commendation in the Itoh prize. The poster shows work continued from the two talks above. We find that the correlation measured between two point measurements of solar wind variables, density and magnetic field, fall at different rates. The mutual information measurements we make also fall at different rates, the differences between the MI measurements and the correlation measurements highlight the importance of non linear interatctions in this process. The correlation and MI measured between the magnetic field and velocity indicate (as expected from previous measurements) that there is Alfvénic turbulence present, but that it is between more pressure dominated behaviour. The effect of solar activity on this effect is now being investigated as the higher pressure, higher magnet field magnitude events occur with increased frequency at solar maximum.