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Dynamical Coevolution Model with Power-Law Strength

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Dynamical Coevolution Model with Power-Law Strength I. Introduction II. Model III. Results IV. Pathological region V. Summary Sungmin Lee, Yup Kim – PowerPoint PPT presentation

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Title: Dynamical Coevolution Model with Power-Law Strength


1
Dynamical Coevolution Model with Power-Law
Strength
  • I. Introduction
  • II. Model
  • III. Results
  • IV. Pathological region
  • V. Summary

Sungmin Lee, Yup Kim Kyung Hee Univ.
2
I. Introduction
The "punctuated equilibrium" theory
Instead of a slow, continuous movement, evolution
tends to be characterized by long periods of
virtual standstill ("equilibrium"), "punctuated"
by episodes of very fast development of new forms
S.J.Gould (1972)
The Bak-Sneppen evolution model
P.Bak and K.sneppen PRL 71,4083 (1993)
Lowest fitness
PBC
0.2 0.3 0.15 0.4 0.45 0.7 0.9 0.35 0.1 0.55 0.75 0.5 0.8 0.65 0.6 0.25
0.2 0.3 0.15 0.4 0.45 0.7 0.9 0.95 0.47 0.22 0.75 0.5 0.8 0.65 0.6 0.25
New lowest fitness
3
Snapshot of the stationary state
M.Paczuski, S.Maslov, P.Bak PRE 53,414 (1996)
Avalanche - subsequent sequences of
mutations through fitness below a certain
threshold
Distribution of avalanche sizes in the critical
state
1d 2d
1.07(1) 1.245(10)
4
Summary of previous works
H.Flyvbjerg et al. PRL 71, 4087 (1993)
? Mean Field


? Random Network
K.Christensen et al. PRL 81, 2380 (1998)


S.Lee and Y.Kim PRE 71, 057102 (2005)
? Scale-free Network




5
R.Cafiero et al. PRE 60, R1111 (1999)
neighbors of the active site are chosen
from power-law decreasing function of the
distance
(degree exponent)
6
II. Model
- 1d lattice with N sites (PBC) - A random
fitness equally distributed between 0 and 1, is
assigned to each site.
the lowest fitness value
0.2
0.3
0.11
0.4
0.45
0.7
0.9
0.01
0.1
0.55
0.75
0.5
Choose update size from
reassign new fitness values
7
III. Results
8
1D 2D
0.66702(3) 0.328855(4)
cf)
9
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10
cf)
1D 2D
1.07(1) 1.245(10)
11
(No Transcript)
12
IV. Pathological region
ex)
13
V. Summary
? We study modified BS model with power-law
strength.
? We measure the critical fitness, avalanche size
distribution and degree distribution.
? The property of critical fitness changes at
. (cf. BS on SFN )
? The degree exponent is different from the
strength exponent unlike Havlins
network model because updates are locally
occurred in our model.
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