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

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Constructing an agent-based fungus

. . sofunctiondrives structure

Organism ‘develops’ ability to walk/hunt/forageIssues: localization-delocalization, efficient vs. adaptable

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. . .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

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history at time t

. . . . 0 1agent memory m = 2

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action-1

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n+1 t[ ]

f d

b e

c

a global outcome0 or 1

f d

b e

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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

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gent

s

0t=

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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

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A + ΔA < L

time: tτ

A(t) = L

A(t)

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A

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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

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n−1 t[ ]

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agent memory m = 2

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n+1 t[ ]

f d

b e

c

a

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2m

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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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