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Canonical Distribution

2010
E=−            σi σj
                i,j

       Ising Model

2010
∆E < 0P (∆E) = 1
       ∆E > 0then
       p(∆E) = 1 − e−β∆E




2010
2010
2010
From a single attracting state to
       multiple attracting states.




2010
2010
Spin glass: random spin-spin
       interaction generates a spatially
       random but temporally ordered
       states.




2010
2010
T


           Tc




       M

2010
Scale Free Correlations in Starling Flocks, A
       Cavagna et al. PNAS (2010)


2010
2010
Self-Organized Criticality(SOC)




       Sandpile Model
           P.Bak
                                                              Avalanche size
          P.Bak, C. Tang, K. WiesenFeld. Self-Organized Criticality: An Explanation of 1/f Noise.
          Physical Review Letters. Volume 59, Number 4, July 1987.




2010
by Hide Sakaguchi et al. 2005
2010
NKmodel: a complete phase space of
       K=3 N=6




2010
2010
2010
Developmental abnormality, called
       metaplasia, exhibits the same restricted
       pathways of aberrant differentiation.




2010
lambda-parameter (C.Langton)

2010
Per Bak’s memory as a SOC
       and so on.




2010
How the fluctuation propagates through a system?




2010
What about avalanche in the high
       dimensional space?




2010

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