Adaptive Traffic and Dynamical Networks: From Plants to People
• Methods:agents (i.e. decision-making particles) + networks (i.e. connectivity)empirical + simulation + analytics
• Empirical:Dynamical evolution of nutrient networks in fungal and slime-mold systemsAVMs and supply networks in the brainAngiogenesis in cancer tumour growthVirus spreading on networksSupply chains, flow of cases in judicial systemsFlow of rumours around FX currency markets
• Issues:Flow of objects on network: group formation & crowding, congestionFeedback onto network structure: structure vs functionWhat is ‘best’ ?
optimal, fault tolerant or just ‘good enough’centralized vs decentralizedcompetitive vs. cooperative
How to control, manage, design ?
http://sbs-xnet.sbs.ox.ac.uk/complexity/ complexity_splash_2003.asp
Mark Fricker, Paul Summers, Pak Ming Hui, Charley Choe, David Smith, Chiu Fan Lee, Tim Jarrett, Sean Gourley, Neil Johnson
NC
P
C
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Constructing an agent-based fungus
. . sofunctiondrives structure
Organism ‘develops’ ability to walk/hunt/forageIssues: localization-delocalization, efficient vs. adaptable
QuickTime™ and a decompressor
are needed to see this picture.
. . .should I try a short-cutthrough the centre?
If cost c of using central hub is non-linear, we find:Abrupt changes in optimal network structure, which are induced by small changes in c
Diverse set of structurally inequivalent networks, which are functionally equivalent
centralized vs decentralized ? Phys. Rev. Lett. 2005
If cost c of using central hub is non-linear, we find:Abrupt changes in optimal network structure, which are induced by small changes in c
Diverse set of structurally inequivalent networks, which are functionally equivalent
Efficient, but deadly . . . .
cancer: angiogenesis brain: AVM, aneurysm
updated history at time t +1
. . . . 1 0
€
n−1 t[ ]
S
history at time t
. . . . 0 1agent memory m = 2
action+1
action-1
€
n+1 t[ ]
f d
b e
c
a global outcome0 or 1
f d
b e
c
a
strategyspace
Evolutionary Minority Game (EMG) Phys. Rev. Lett. ‘99
agent’s strategy/‘gene’ p mutates
time: tτ
agent’s performance or ‘wealth’
time
kp0 10.5kp0 10.5
dist
ribut
ion
of a
gent
s
0t=
0.5
steady stateself-organized segregation into
Anti-crowds and Crowds
p = probability agent follows common information: past history, news, rumor (right or wrong)
p p
coin-toss
basic Minority Game (MG)crowding/congestion reduced by- acting ‘dumb’- choosing second-best- mis-information- heterogeneity in abilities, e.g. m
agent memory m
hybrid
EMG
typical fluctuation size
Evolutionary Minority Game (EMG) Phys. Rev. Lett. ‘99
General global resource level L (e.g. # seats)A(t)
L N = 100 agents wish to access resource (e.g. attend bar)
L
‘freezing’of evolution
€
A + ΔA < L
time: tτ
A(t) = L
A(t)
€
A
€
ΔA
system’s time evolution
Phys. Rev. E (2004)
Distribution of duration ofextreme large changes in
variable-N evolutionary MG
-4
∆ t
largest changes/crashes are ‘different’ -7
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history at time t+1
. . . . 1 0
€
n−1 t[ ]
S
agent memory m = 2
S
€
n+1 t[ ]
f d
b e
c
a
€
2m
€
22m
histories
strategies
11 10 01 00
-1 -1 -1 -1
-1 -1 -1 +1 . . . .
-1 -1 +1 +1 . . . .
-1 +1 +1 +1 . . . .
+1 +1 +1 +1
f d
b e
c
a
action+1
action-1
history at time t
. . . . 0 1
global outcome0 or 1
memory m
volatility
Memory m 2m+1 << N.s 2m+1 ~ N.s 2m+1 >> N.sCrowd
sizelarge medium ~ 1
Anticrowdsize
small medium ~ 0
Net crowd –anticrowdpair size
large>> 1
small small~ 1
# crowd -anticrowd
pairs
~ 2m
<< N~ 2m
< N< 2m
~ N
random
crowd - anticrowd pairs executeuncorrelatedrandom walks
sum of variances
walk step-size
# of walks
typical fluctuation sizeMinority Game:
Each agent has s=2,3,4,.. strategieswith memory-length m
€
2mhistories
11 10 01 00
-1 -1 -1 -1
-1 -1 -1 +1 . . . .
-1 -1 +1 +1 . . . .
-1 +1 +1 +1 . . . .
+1 +1 +1 +1
Hub Capacity L=40
Add in agent decision-making . . . .
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