http://arxiv.org/abs/1204.0576
This
is in poor English but the cool part is the link to Dynamic Quantum
Clustering and fractals. The fractal diffusion equation is almost
exactly the same as the regular diffusion equation except that it uses a
dimension that is not necessarily an integer. / And/or it introduces
all sorts of fractal based approaches to the dimension, not just one,
each corresponding to a family of solutions.
The researchers were able to generate data that very closely matches EEG patterns. Deciphering signals in EEG data is a major obstacle to developing new interfaces for the disabled and next-generation human interface devices.
Dynamic quantum clustering is the name for using the Schrodinger /
higher wave equations for de-clustering noisy data. The wave equations for DQC are all based off the diffusion
equation, except they use an imaginary diffusion coefficient, turning Probability into Psi (sqrt Probability.)
What this fundamentally means is that DQC + fractals most likely
applies to the same case. Now because this research is using only the Schrod eq while other clustering papers have used more advanced equations, I'm assuming it might not be state of the art, and since DQC
is well known in ML circle, it should be the case that neurobiologists likely
well know about the overlap already. But I haven't read all the latest
EEG papers so to find this confirmation at the level of the diffusion
equation is indication enough that DQC+fractals is likely also valid or at least related.
Either way, there is a connection between the Lagrangian formalism and neurobiology, which is interesting in and of itself.
