Chapter 6 Size
does not always matter
This is fractal
Resemblances
The indeterminate scale
Quite normal rareness
Can criticality
be autonomous?
Foreseeable avalanches
Optimum and permissive
We are entangled!
The world is a handkerchief
· For galleries of fractal images, some of them
natural: www.armoniafractal.com/, www.microbialart.com/, local.wasp.uwa.edu.au/~pbourke/fractals/,lightbox.time.
com/2012/09/19/finding-beauty-fractal-patterns-on-earth-as-seen-from-space/#1
The Sierpinski gasket is
described at matap.dmae.upm.es and www.efg2.com; Wikipedia provides some
alternative methods of constructing this fractal.
Visit
mathworld.wolfram.com and en.wikipedia.org to see more on the dragon curve.
See also a detailed
description in
® Reviews of
Modern Physics 81, 333 (2009) by Jacobo Aguirre, Ricardo L. Viana
and Miguel A.F. Sanjuan.
Lear how to estimate the
dimension of a fractal: local.wasp.uwa.edu.au/ ~pbourke/fractals/fracdim/. There
is a list of mathematical and natural fractals by dimension in Wikipedia.
® "Dynamic similarity, the dimensionless
science", Physics Today, page 42, September 2011, elaborates on concepts
related to self-similarity and scale invariance.
A remarkable case of
fractal in number theory is in www.mathcs.emory.edu/
~ono/, www.aimath.org, or esciencecommons.blogspot.com.
· On power law descriptions, see
® “A brief history of generative models for power law
and lognormal distributions” by Michael Mitzenmacher, Internet Mathematics 1, 226 (2004), already mentioned, and
recall the book (Random House 2010) quoted before by Nassim N. Taleb on the
impact of rare “black swan” events and on our tendency to rationalize them too
simply a posteriori; and
® “Pareto versus lognormal: A maximum entropy test”,
Marco Bee, Massimo Riccaboni, and Stefano Schialvo, Physical Review E 84, 026104 (2011).
· On the possible causes that populations should be
distributed according to Zipf’s law, see:
eclectic.ss.uci.edu/~drwhite/pub/CitiesWhiKejTsal.pdf;
® “Hierarchy in social organization”, by Sergey V.
Buldyrev, N.V. Doholyan, S. Erramilli, M. Hong, J.Y. Kim, G. Malescio and E.
Eugene Stanley, Physica A 330,
653 (2003);
® “The size, scale, and shape of cities”, Michael
Batty, Science 319, 769
(2008);
® “A unified theory of urban living”, Luis M.A.
Bettencourt and Geoffrey B. West, Nature
467, 912 (2010). (The site www.geohive.com has data that we used for the
figures.)
· For power laws concerning linguistics, see
® George K. Zipf, Human
behavior and the principle of least effort (Addison-Wesley, Cambridge,
1949), interpreting that a minimization of the efforts of both hearer and
speaker in a conversation may lead to power–law distribution laws;
® Ramón Ferrer i Cancho and Ricard V. Solé, “Least
effort and the origins of scaling in human language,” in Proceedings of the National Academy of Science of the U.S.A. 100,
788 (2003); and
® “True reason for Zipf’s law in language”, Dahui
Wang, Menghui Li, and Zengru Di, Physica
A 358, 545 (2005), which questions
whether power–laws are indeed a characteristic of all written languages.
Concerning Zipf’s law
and related issues, see also www.nslij–genetics.org.
The intriguing question
of language dynamics is addressed in
® “Statistical physics of language dynamics”, by
Vittorio Loreto et al., Journal of
Statistical Mechanics: Theory and Experiment P04006 (2011).
· On terrorism and the like,
® “Pattern in escalations in insurgent and terrorist
activity”, by Neil Johnson et al., Science
333, 81 (2011), illustrates how to look for clues that may help in
predicting attacks and the evolution of wars, and see
® “Attitudes and action: Public opinion and the
occurrence of international terrorism”, by Alan B. Krueger and Jitka Malecková,
Science 325, 1534 (2009) on
the relevance of public opinion on terrorism.
· A relatively simple description of the complex
physical processes that lead to earthquakes can be found in
® “The physics of earthquakes”, Hiroo Kanamory and
Emily E. Brodsky, Physics Today, June
2001, page 34. See also
® “Statistical physics of fracture, friction, and
earthquakes”, by Hikaru Kawamura, Takahiro Hatano, Naoyuki Kato, Soumyajyoti
Biswas, and Bikas K. Chakrabarti, Review
of Modern Physics 84, 839 (2012).
For recent models and
simulations, see also
® “Understanding earthquakes”, Paul Segall, Science 336, 676 (2012) and
references therein
· Concerning the mentioned work on bird flocks, see
® “Scale−free correlations in starling flocks”,
Andrea Cavagna, Alessio Cimarelli, Irene Giardina, Giorgio Parisi, Raffaele
Santagati, Fabio Stefanini, and Massimiliano Viale, Proceedings of the National Academy of Science of the U.S.A. 107,
11865 (2010), and a video at www.youtube.com/watch?v=IqWngtticAc which shows
interaction between starlings and the peregrine falcon.
· On the relation between the shape of the
distribution and the correlations among the variables involved, see
® “Non–Gaussian distributions under scrutiny”,
Thierry Dauxois, Journal of Statistical
Mechanics: Theory and Experiment N08001 (2007), and for other related
interesting details, see
® “Power laws, Pareto distributions and Zipf’s law”,
Mark E.J. Newman, Contemporary Physics
46, 323 (2005);
® el libro de Per Bak ya citado;
® Self–organized
criticality: Emergent complex behavior in physical and biological systems,
Henrik J. Jensen (Cambridge Lecture Notes in Physics 1998);
® “The power of design”, Mark Newman, Nature 405, 412 (2000);
® Complexity
and Criticality, Kim Christensen and Nicholas R. Moloney (World Scientific
2005), and www.complexityandcriticality.com.
· The sand pile automaton is in www.cmth.bnl.gov/~maslov/Sandpile.htm,
and the possible applications of self–organization in various contexts is
described in en.wikipedia.org/wiki/self–organization and in the links listed on
this page.
· The “Burridge–Knopoff model” for earthquakes is
described with detail in www.fisfun.uned.es/~mar/LSC/terremot.htm,
mathworld.wolfram.com/burridge–knopoffmodel.html and
lec.ugr.es/~julyan/papers/quakeletter/quakeletter.html.
· On apparent avalanches, see
® “Understanding scale invariance in a minimal model
of complex relaxation phenomena“, Pablo I. Hurtado, Joaquín Marro and Pedro L.
Garrido, Journal of Statistical
Mechanics: Theory and Experiment P02004 (2006).
· The relation between fame and merit is studied in
® “On the Google–fame of scientists and other
populations”, James P. Bagrow and Daniel ben–Avraham, which is part of the book
Modeling Cooperative Behavior in the
Social Sciences, edited by Pedro Garrido, Joaquín Marro and Miguel A. Muñoz
(American Institute of Physics, New York 2005).
· For an alternative to self–organized criticality,
compatible with a simple scenario described in class, see
® “The ‘robust yet fragile’ nature of the Internet”,
John C. Doyle et al., Proceedings of the
National Academy of Sciences of the U.S.A. 102, 14497 (2005).
· Concerning optimization, see
® The traveling
salesman problem, Gerhard Reinelt (Springer, Berlin 1994) and the webs
www.nada.kth.se/~viggo/problemlist/ and mathworld.wolfram.com/ TravelingSalesmanProblem.html;
and
® “Solving the traveling–salesman problem by a
statistical–physics method”, Usami Yoshiyuki et al., Computers in Physics 10, 525 (1996), which applies
renormalization–group ideas (Chapter 4) to the salesman problem.
· For Euler’s graphs:
www.infovis.net/printMag.php?num=137&lang=1.
· On networks:
® “Exploring complex networks”, Steven H. Strogatz, Nature 410, 268 (2001);
® Linked,
Albert–László Barabási (Perseus Pub., Cambridge, MA 2002);
® “The ‘new’ science of networks”, Duncan J. Watts, Annual Review of Sociology 30,
243 (2004);
® “The physics of networks”, in Physics Today, page 33, November 2008, Mark E. J. Newman;
® Networks: An
Introduction, Mark E. J. Newman (Oxford Univ. Press, 2010);
® Networks,
crowds, and markets: Reasoning about a highly connected world, David Easley
and Jon Kleinberg (Cambridge University Press, New York 2010).
See also, on the variety
of possible applications:
® Nathan Eagle, Michael Macy and Rob Claxton in
“Network diversity and economic development”, Science 328, 1029 (2010), showing strong correlation between
the economic development of a community and the diversity of the relationships
between its individuals;
® the several interesting comments and articles on
complex systems in Nature Physics 8,
January 2012, and the web pages.physics.cornell.edu/~sethna/Stat Mech/ComputerExercises/SmallWorld/SmallWorld.html;
® the viewpoint
by Sitabhra Sinha in Physics 4,
8 (2011) on the work “All scale-free networks are sparse”, by Charo I. Del
Genio, Thilo Gross, and Kevin E. Bassler, Physical Review Letters 107, 178701 (2011).
· Concerning social proximity, see
® Six Degrees:
The Science of a Connected Age, Duncan J. Watts (Norton, New York 2003),
and
® “Separating you and me? 4.74 degrees” by John
Markoff and Somini Sengupta, The New York Times, 21 November 2011 (www.nytimes.com/2011/11/22/techno
logy/between-you-and-me-4-74-degrees.html?_r=0).
·
En relación con la Web en España,
® Ricardo Baeza-Yates, Carlos Castillo y
Vicente López, “Características de la Web de España”, en El profesional de la información 15 (número 1), 6 (2006).
Nota: véanse
las referencias y enlaces que se incluyen en las dispositivas del curso, que a
menudo completan las anteriores.