Cosma Shalizi
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[edit] Bio
Cosma Shalizi (CMU, Statistics, Bio) is giving a talk at our
[edit] Event
May 16th complexity videoconference on "Statistical methods for complex systems." Abstract: A summary of the tools people should use to study complex systems, covering statistical learning and data-mining, time series analysis, cellular automata, agent-based models, evaluation techniques and simulation, information theory and complexity measures.
1:30-3:00 UCI 3030 Anteater I&R Bldg UCLA 285 Powell Library UCSD 260 Galbraith Hall
See: "Methods and Techniques of Complex Systems Science: An Overview", chapter 1 (pp. 33-114) in Thomas S. Deisboeck and J. Yasha Kresh (eds.), Complex Systems Science in Biomedicine (NY: Springer, 2006).
Optimal Nonlinear Prediction of Random Fields on Networks Published 2003 Discrete Mathematics and Theoretical Computer Science 11-31
Under our Tools and Methods for our Probability distributions we have a link to his Maximum Likelihood Estimation for q-Exponential (Tsallis) Distributions as it applies, for example, to city size distributions.
[edit] Notebook on Feedback Networks
Under Cosma's Social Networks notebook is a useful comment on
- Douglas R. White, Natasa Kejzar, Constantino Tsallis, Doyne Farmer and Scott White, "A generative model for feedback networks", cond-mat/0508028 = Physical Review E 73 (2006): 016119 [Cosma: I find the growth model here very interesting, because it breaks with the now-usual "preferential attachment" mechanism. I think this model would repay very careful attention, both dynamically (could one map this onto preferential attachment in some meaningful way?) and statistically (what is the limiting degree distribution, and how does it vary with the growth parameters?).]
For our Network_tools he has provided the basis for a maximal likelihood estimation (MLE) procedure for Degree distributions that Mark Handcock may be able to program within the dnet package for R.
Cosma has a notebook entry for complexity and an interesting if not yet productive dialog with Tsallis. Tsallis replied to http://intersci.ss.uci.edu/wiki/pw/Buchanan_s_NewScientist_article.pdf Buchanan's New Scientist article, August 2005, reviewing q-entropy, but the editors eliminated 90% of the original letter (see below), here reprinted:
http://intersci.ss.uci.edu/wiki/pw/Tsallis__Letter_to_the_Editor__Full_Version_.pdf Original 2005 Letter to the Editor of The New Scientist about the Buchanan review.
http://intersci.ss.uci.edu/wiki/pw/Tsallis__Letter_to_the_Editor__Short_version_.pdf The Letter to the Editor of The New Scientist magazine about the Buchanan review, as shortened for issue 2518, 24 September 2005, page 25.
Scott White's Review of Buchanan
The literature on nonextensive physics (see below)
[edit] Tsallis Response
29 July 2007 (PDT)
Thanks for all this information. A few remarks:
1) I certainly enjoyed reading Scott's fair viewpoint!
2) Letters to the Editor of New Scientist cannot be of more of about 200 words (I was not aware of that when I wrote the full version). This is why only the short version came out.
3) The most convenient link to the literature of nonextensive statistics is the regularly updated bibliography at http://tsallis.cat.cbpf.br/biblio.htm (it is exactly the same that you and Scott quote, excepting for the fact that this one is always regularly updated)
4) One of the most impressive experimental verifications of the predictions of q-statistics concerns cold atoms in dissipative optical lattices. Eric Lutz made an analytical prediction in 2003 http://prola.aps.org/abstract/PRA/v67/i5/e051402, and it was verified in 2006 by a London team: see PRL here attached. http://intersci.ss.uci.edu/wiki/pw/DouglasBergaminiRenzoni06.pdf
5) I conjectured in 1999 (Brazilian Journal of Physics 29, 1; see Figure 4 http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97331999000100002&lng=pt&nrm=iso&tlng=en) (i) that a longstanding quasi-stationary state (QSS) was expected in LONG-range interacting Hamiltonian systems (one of the core problems of statistical mechanics), and (ii) that this QSS should be described by q-statistics instead of Boltzmann-Gibbs statistics. Point (i) was quickly verified by many groups around the world.
But I had to wait (hearing of course lots of skeptical remarks by colleagues!) for 9 looooooong years in order to see (ii). It is now done since about one month: see the last figure of the 2007 http://intersci.ss.uci.edu/wiki/pw/0706.4021v2.pdf attachment by Pluchino, Rapisarda and myself. Instead of the celebrated Maxwellian (Gaussian) distribution of velocities (valid for SHORT-range interactions), one sees a q-Gaussian!
Cheers,
Constantino
drw, see also: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97331999000100009&lng=pt&nrm=iso
[edit] MLE for q
Shalizi, Cosma. 2007 Maximum Likelihood Estimation for q-Exponential (Tsallis) Distributions. http://www.cscs.umich.edu/~crshalizi/research/tsallis-MLE
NONEXTENSIVE STATISTICAL MECHANICS AND THERMODYNAMICS: BIBLIOGRAPHY January 2007
[edit] Tutorial in R for Discrete Distributions
Using the new discrete estimator and producing sampling distribution plots
