Extremal dynamics on dynamically changing networks with power-law weights

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Extremal dynamics on dynamically changing
networks with power-law weights

• I. Introduction
• II. Motivation
• III. Model
• IV. Results
• V. Summary

Sungmin Lee, Yup Kim Kyung Hee Univ.
? ??? ?????? ???? ?????? (KRF-2004-015-C00185)?
??? ?? ???????.
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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)
Self-organized critical steady state
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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
At each time step, the ecology is updated by
(i) locating the site with the lowest fitness
and mutating it by assigning a new random number
to that site, and
(ii) changing the landscapes of the two
neighbors by assigning new random numbers to
those sites
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
Snapshot of the stationary state
M.Paczuski, S.Maslov, P.Bak PRE 53,414 (1996)
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Gap, Critical fitness and avalanche
The lowest fitness at step s
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)
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Summary of previous work
? Mean Field


? Random Network


? Scale-free Network








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II. Motivation
(1) Study for a characteristic of
evolution when the influence strength or
interacting structures of biospecies are
dynamically changed with power-law weights.
(2) Are the structures changed dynamically
with power-law weights still Scale-free
network in steady state?
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III. Models
lowest fitness
0.2
0.3
0.11
0.4
0.45
0.7
0.9
0.01
0.1
0.55
0.75
0.5
remove links
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 (number of links) from
0.2
0.3
0.11
0.4
0.15
0.47
0.29
0.21
0.8
0.51
0.28
0.5
reassign new links and new fitness
- 1d lattice with N sites (PBC) - A random
fitness equally distributed between 0 and 1, is
assigned to each site. - At each time step, the
ecology is updated by (i) locating the site i
with the lowest fitness (ii) removing its
links (ii) choosing the update size from
power-law distritubion (iii) connecting the
site i with sites within the update size (iv)
reassign new random numbers to those sites and i.
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IV. Results
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V. Summary
? We study punctuated equilibrium properties
of Bak-Sneppen (BS) model on two different
one dimensional geometric structures,
regular lattice and random network.
? We measure the critical fitness and avalanche
size distribution.