Second in today’s “e-mails from Eric” department is this announcement of a talk by Jack Cowan, a mathematics professor at U. Chicago. The talk, scheduled for 16:00 on Tuesday, 3 April in room 46-3189, is abstracted as follows:
We have recently found a way to describe large-scale neural activity in terms of non-equilibrium statistical mechanics [Buice & Cowan, in preparation]. This allows us to calculate (perturbatively) the effects of fluctuations and correlations on neural activity. Major results of this formulation include a role for critical branching, and the demonstration that there exist non-equilibrium phase transitions in neocortical activity, which are in the same universality class as directed percolation. This result leads to explanations for the origin of many of the scaling laws found in LFP, EEG, fMRI, and in ISI distributions, and provides a possible explanation for the origin of alpha, beta, gamma, delta and theta waves. It also leads to ways of calculating how correlations can affect neocortical activity, and therefore provides a new tool for investigating the connections between neural dynamics, cognition and behavior.
I suspect I’ve already seen some of these results, in the video “Spontaneous pattern formation in large scale brain activity: what visual migraines and hallucinations tell us about the brain” (2006). The one review of that video is, depressingly enough, a muddled remark about “observers” in quantum mechanics and what they must mean for consciousness (and you’ll probably catch me ranting about that, anon). Fortunately, the video itself is much more informative.
For a quick primer, see “Hallucinatory neurophysics” at Sean Carroll‘s old blog, Preposterous Universe.
UPDATE (11 June 2007): Yes, I ranted more about the “quantum mind.” See here and here.
Eric just sent along the following summary of our upcoming sessions:
This Friday at NECSI is Info Theory again: we’ll be talking specifically about the coordinate-dependence of differential (continuous) entropy and more generally, discussing the rest of Part III of Shannon’s paper. The next topic after that will be “Error-Correcting Codes in Biology“, which will probably take a few weeks at least â€” we’ll first cover the relevant sections of Ash (or Reza or whatever people prefer) and then talk about the biological basics.
This next Monday is Stat Mech and I will be reviewing the ensembles we have covered so far and talking at NECSI about the Gibbs-canonical and grand-canonical ensembles. Depending on time I will prove (in a physicist way) that all of the ensembles are equivalent within their own ranges of assumptions â€” so this may take one or two lectures. After that I will probably assign some homework so that we can get experience working with these tools.
Links added by me, because this is Xanadu 2.0, after all.
Yesterday evening, we had our first seminar session on the group theory track, led by Ben Allen. We covered the definition of groups, semigroups and monoids, and we developed several examples by transforming a pentagon. After a brief interlude on discrete topology and â€” no snickers, please â€” pointless topology, Ben introduced the concept of generators and posed several homework questions intended to lead us into the study of Lie groups and Lie algebras.
Notes are available in PDF format, or as a gzipped tarball for those who wish to play with the original LaTeX source. Likewise, the current notes for the entropy and information-theory seminar track (the Friday sessions) are available in both PDF and tarball flavors.
Our next session will be Friday afternoon at NECSI, where we will continue discussing Claude Shannon’s classic paper, A/The Mathematical Theory of Communication (1948). The following Monday, Eric will treat us to the grand canonical ensemble.
Welcome to Science After Sunclipse, a blag devoted (more or less) to discussing mathematics and physics. Your hosts, including a soft-spoken and ever-humble Order of the Molly recipient (me), currently run a seminar series grandly entitled the “Do It Yourself University”. Typically hosted at the New England Complex Systems Institute, our sessions cover topics in statistical physics, information theory, topology and. . . well. . . whatever else strikes our collective fancy.
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