Neural Dynamics: Criticality, Cooperation, Avalanches and Entrainment between Complex Networks Page: 1
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xx: XX - Chap. 1 - 2012/5/22 - 11:43 - page 1
Neural Dynamics: Criticality, Cooperation, Avalanches
and Entrainment between Complex Networks
P. Grigolini, M. Zare, A. Svenkeson, B. J. West
The discovery of avalanches in neural systems  has aroused substantial inter-
est among neurophysiologists and, more generally, among researchers in complex
networks  as well. The main purpose of this chapter is to provide evidence in
support of the hypothesis that the phenomenon of neural avalanches  is generated
by the same cooperative properties as those responsible for a surprising effect that
we call cooperation-induced synchronization, illustrated in . The phenomenon
of neural entrainment  is another manifestation of the same cooperative property.
We also address the important issue of the connection between neural avalanches
and criticality. Avalanches are thought to be a manifestation of criticality, and
especially self-organized criticality [5, 6]. At the same time, criticality is accom-
panied by long-range correlation  and a plausible model for neural dynamics
is expected to account for the astounding interaction between agents separated by
relatively large distances. General agreement exists in the literature that brain func-
tion rests on these crucial properties, and the phase transition theory for physical
phenomena  is thought to afford the most important theoretical direction for fur-
ther research work on this subject. In this theory criticality emerges at a specific
single value of a control parameter, designated by the symbol Kc. In this chapter
we illustrate a theoretical model generating avalanches, long-range correlation and
entrainment, as a form of cooperation-induced synchronization, over a wide range
of values of the control parameter K, thereby suggesting that the form of criticality
within the brain is not the ordinary criticality of physical phase transitions but is
instead the extended criticality recently introduced by Longo and co-workers 
to explain biological processes.
Cooperation is the common effort of the elements of a network for their mutual
benefit. We use the term cooperation in the same loose sense as that adopted, for
instance, by Montroll  to shed light on the equilibrium condition realized by
the interacting spins of the Ising model. Although the term cooperation, frequently
used in this chapter, does not imply a network's cognition, we follow the conceptual
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Grigolini, Paolo; Zare, Marzieh; Svenkeson, Adam & West, Bruce J. Neural Dynamics: Criticality, Cooperation, Avalanches and Entrainment between Complex Networks, chapter, May 22, 2012; [Hoboken, New Jersey]. (digital.library.unt.edu/ark:/67531/metadc177272/m1/1/: accessed July 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.