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Kaj Kolja KLEINEBERG
Marián BOGUÑÁ
@KoljaKleineberg
Universitat de Barcelona
kkl@ffn.ub.edu
EVOLUTIONand
Digital world
Ecologyof the
all digital services need
Attentionbut our time is limited
The digital world forms a complexECOSYSTEM
with networks as competing species
Can we preservedigital diversity?
Evolution of isolated networks
Motivation Evolution Ecology 2.0 Summary & Outlook
The topological evolution of large quasi-isolated OSNexhibits a dynamical percolation transition
Dynamical percolation transition demands new classof growing network models.
7
Motivation Evolution Ecology 2.0 Summary & Outlook
The topological evolution of large quasi-isolated OSNexhibits a dynamical percolation transition
Dynamical percolation transition demands new classof growing network models.
7
Motivation Evolution Ecology 2.0 Summary & Outlook
The pre-existing underlying social structureforms the backbone of the evolution of the OSN
Online social network layer
Traditional contactnetwork layer
ActiveOnline & offline
PassiveOnline & offlineSusceptibleOnly offline
8
Motivation Evolution Ecology 2.0 Summary & Outlook
The pre-existing underlying social structureforms the backbone of the evolution of the OSN
Online social network layer
Traditional contactnetwork layer
ActiveOnline & offline
PassiveOnline & offlineSusceptibleOnly offline
Mass media activation Viral activation
Deactivation Viral reactivation
8
Motivation Evolution Ecology 2.0 Summary & Outlook
Final snapshot of empirical network as proxy forunderlying structure allows rigorous model validation
Finalsnapshot
Empiricalevolution
Extractsnapshots
Empiricaldata
Modelevolution
Compare
Finalsnapshot
Can we reproduce the entire topological evolutionof the empirical network?
9
Motivation Evolution Ecology 2.0 Summary & Outlook
Final snapshot of empirical network as proxy forunderlying structure allows rigorous model validation
Finalsnapshot
Empiricalevolution
Extractsnapshots
Empiricaldata
Modelevolution
Compare
Finalsnapshot
Can we reproduce the entire topological evolutionof the empirical network?
9
Motivation Evolution Ecology 2.0 Summary & Outlook
Model precisely reproduces the entire topological evolutionand reveals balance between virality and media influence
Model results ParametersGCC model
2nd comp. model
ASPL model x4
GCC Pokec
2nd comp. Pokec
ASPL Pokec x4
103 104 105 1060
20
40
60
80
100
120
140
N
Virality is about four timesstronger thanmass media
Interplay between virality andmass media dynamicsis the main underlying principle of the OSN evolution.
10
Motivation Evolution Ecology 2.0 Summary & Outlook
Model precisely reproduces the entire topological evolutionand reveals balance between virality and media influence
Model results ParametersGCC model
2nd comp. model
ASPL model x4
GCC Pokec
2nd comp. Pokec
ASPL Pokec x4
103 104 105 1060
20
40
60
80
100
120
140
N
Virality is about four timesstronger thanmass media
Interplay between virality andmass media dynamicsis the main underlying principle of the OSN evolution.
10
Motivation Evolution Ecology 2.0 Summary & Outlook
Model precisely reproduces the entire topological evolutionand reveals balance between virality and media influence
Model results ParametersGCC model
2nd comp. model
ASPL model x4
GCC Pokec
2nd comp. Pokec
ASPL Pokec x4
103 104 105 1060
20
40
60
80
100
120
140
N
Virality is about four timesstronger thanmass media
Interplay between virality andmass media dynamicsis the main underlying principle of the OSN evolution.
10
Motivation Evolution Ecology 2.0 Summary & Outlook
Below a critical value of the viral parameterthe network becomes entirely passive
Λc
0.00 0.02 0.04 0.06 0.08
0.00
0.05
0.10
0.15
0.20
0.25
Λ
ΡA
Our model predicts the survival and death of onlinesocial networks.
11
Motivation Evolution Ecology 2.0 Summary & Outlook
Below a critical value of the viral parameterthe network becomes entirely passive
Λc
0.00 0.02 0.04 0.06 0.08
0.00
0.05
0.10
0.15
0.20
0.25
Λ
ΡA
Our model predicts the survival and death of onlinesocial networks.
11
Motivation Evolution Ecology 2.0 Summary & Outlook
The microscopic picture revealsthe role of strong and weak ties
N103 104 105 1060.00
0.05
0.10
0.15
0.20
Clustering
Data
Tie strength:
i j
Transmissibility: λij ∝ λ [•+ 1]η
Individuals have a higher tendency to subscribe ifinvited byweaker social contacts.
12
Motivation Evolution Ecology 2.0 Summary & Outlook
The microscopic picture revealsthe role of strong and weak ties
N103 104 105 1060.00
0.05
0.10
0.15
0.20
Clustering
Data
Tie strength:
i j
Transmissibility: λij ∝ λ [•+ 1]η
Individuals have a higher tendency to subscribe ifinvited byweaker social contacts.
12
Motivation Evolution Ecology 2.0 Summary & Outlook
Evolution of the digital society revealsbalance between viral and mass media influence
Underlying social structuredetermines topological
evolution
Balanceof viral and mass media
influence
Survival and deathof networks
Weak tieshave higher transmissibility
PRX 4, 031046, 2014
13
Ecology 2.0
Motivation Evolution Ecology 2.0 Summary & Outlook
Gause's law impeding the coexistence of species competingfor the same unique resource is often violated in nature
Gause's lawspecies competingfor same resourcecannot coexist
Rich-get-richereven slightestadvantage isamplified
Naturecommunities
contain handful ofcoexisting species
15
Motivation Evolution Ecology 2.0 Summary & Outlook
Digital ecosystem is formed by multiple networkscompeting for the attention of individuals
OSN 2
OSN 1
Underl.network
ActivePassiveSusceptible
Partial states}
Virality shareDistribution
between OSNsλi = ωi(ρ
a)λ
Rich-get-richermore active
networks obtainhigher share
Does rich-get-richer effect always lead to thedomination of a single network?
16
Motivation Evolution Ecology 2.0 Summary & Outlook
Digital ecosystem is formed by multiple networkscompeting for the attention of individuals
OSN 2
OSN 1
Underl.network
ActivePassiveSusceptible
Partial states}
Virality shareDistribution
between OSNsλi = ωi(ρ
a)λ
Rich-get-richermore active
networks obtainhigher share
Does rich-get-richer effect always lead to thedomination of a single network?
16
Motivation Evolution Ecology 2.0 Summary & Outlook
Digital ecosystem is formed by multiple networkscompeting for the attention of individuals
OSN 2
OSN 1
Underl.network
ActivePassiveSusceptible
Partial states}
Virality shareDistribution
between OSNsλi = ωi(ρ
a)λ
Rich-get-richermore active
networks obtainhigher share
Does rich-get-richer effect always lead to thedomination of a single network?
16
Motivation Evolution Ecology 2.0 Summary & Outlook
Digital ecosystem is formed by multiple networkscompeting for the attention of individuals
OSN 2
OSN 1
Underl.network
ActivePassiveSusceptible
Partial states}
Virality shareDistribution
between OSNsλi = ωi(ρ
a)λ
Rich-get-richermore active
networks obtainhigher share
Does rich-get-richer effect always lead to thedomination of a single network?
16
Motivation Evolution Ecology 2.0 Summary & Outlook
Nonlinear dynamics of network evolution can enablecoexistence despite rich-get-richer mechanism
Meanfield:
ρ̇ai = ρai
[λ ⟨k⟩ωi(ρ
a) [1− ρai ]− 1
]+
λ
νωi(ρ
a)ρsi
ρ̇si = −λ
νωi(ρ
a)ρsi
[1 + ν ⟨k⟩ ρai
]Rich-get-richer: ωi = [ρai ]
σ/∑
j [ρaj ]
σ → σ activity affinity
Unstable FPStable FP
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0Coexistence σ=0.8
ρ1a
ρ2a
Unstable FPStable FP
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0Domination σ=1.2
ρ1a
ρ2a
StableUnstable
0.50 0.75 1.00 1.25 1.500.00
0.25
0.50
0.75
Bifurcation diagram
ρ1a
0.0 0.5 1.0 1.5
0.50
0.75
σ
σ
ρ1,2
a
17
Motivation Evolution Ecology 2.0 Summary & Outlook
Nonlinear dynamics of network evolution can enablecoexistence despite rich-get-richer mechanism
Meanfield:
ρ̇ai = ρai
[λ ⟨k⟩ωi(ρ
a) [1− ρai ]− 1
]+
λ
νωi(ρ
a)ρsi
ρ̇si = −λ
νωi(ρ
a)ρsi
[1 + ν ⟨k⟩ ρai
]Rich-get-richer: ωi = [ρai ]
σ/∑
j [ρaj ]
σ → σ activity affinity
Unstable FPStable FP
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0Coexistence σ=0.8
ρ1a
ρ2a
Unstable FPStable FP
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0Domination σ=1.2
ρ1a
ρ2a
StableUnstable
0.50 0.75 1.00 1.25 1.500.00
0.25
0.50
0.75
Bifurcation diagram
ρ1a
0.0 0.5 1.0 1.5
0.50
0.75
σ
σ
ρ1,2
a
17
Motivation Evolution Ecology 2.0 Summary & Outlook
Maximum number of coexisting networksis determined by total virality and activity affinity
Overall attention to OSNs
Mor
e lik
ely
to e
ngag
ein
mor
e ac
tive
OS
Ns
Dom.2 coex.3 coex.4 coex.5 coex.
1 2 3 4 5 60.0
0.5
1.0
1.5
λ/λc1
σ
How many networks can coexist
Gause's law is violated as networks can coexistdespite rich-get-richer mechanism.
18
Motivation Evolution Ecology 2.0 Summary & Outlook
Maximum number of coexisting networksis determined by total virality and activity affinity
Overall attention to OSNs
Mor
e lik
ely
to e
ngag
ein
mor
e ac
tive
OS
Ns
Dom.2 coex.3 coex.4 coex.5 coex.
1 2 3 4 5 60.0
0.5
1.0
1.5
λ/λc1
σ
How many networks can coexist
3 networks
2 networks
1 network
Stable configurations
Gause's law is violated as networks can coexistdespite rich-get-richer mechanism.
18
Motivation Evolution Ecology 2.0 Summary & Outlook
Maximum number of coexisting networksis determined by total virality and activity affinity
Overall attention to OSNs
Mor
e lik
ely
to e
ngag
ein
mor
e ac
tive
OS
Ns
How many networks can coexist
1 2 3 4 5 6 7 8 9 100.0
0.5
1.0
1.5
λ/λc1
σ
Dom.2 coex.3 coex.4 coex.5 coex.
3 networks
2 networks
1 network
Stable configurations
Gause's law is violated as networks can coexistdespite rich-get-richer mechanism.
18
Motivation Evolution Ecology 2.0 Summary & Outlook
Maximum number of coexisting networksis determined by total virality and activity affinity
Overall attention to OSNs
Mor
e lik
ely
to e
ngag
ein
mor
e ac
tive
OS
Ns
How many networks can coexist
1 2 3 4 5 6 7 8 9 100.0
0.5
1.0
1.5
λ/λc1
σ
Dom.2 coex.3 coex.4 coex.5 coex.
3 networks
2 networks
1 network
Stable configurations
Gause's law is violated as networks can coexistdespite rich-get-richer mechanism.
18
Motivation Evolution Ecology 2.0 Summary & Outlook
Noise and the shape of the basin of attraction limitobserved digital diversity starting from empty networks
Multi stabilityseveral stablefixed points
Noisein full dynamical
model
Dom.Coex.
2 4 6 8 100.0
0.4
0.8
1.2
λ/λc1
σ
Reachability for 2 networks
→ Effective critical lines for more networks saturate atsuccessively lower values σi,eff
c
Evenwithout precise knowledge of the empiricalparameters our theory predictsmoderate diversity.
19
Motivation Evolution Ecology 2.0 Summary & Outlook
Noise and the shape of the basin of attraction limitobserved digital diversity starting from empty networks
Multi stabilityseveral stablefixed points
Noisein full dynamical
model
Dom.Coex.
2 4 6 8 100.0
0.4
0.8
1.2
λ/λc1
σ
Reachability for 2 networks
→ Effective critical lines for more networks saturate atsuccessively lower values σi,eff
c
Evenwithout precise knowledge of the empiricalparameters our theory predictsmoderate diversity.
19
Motivation Evolution Ecology 2.0 Summary & Outlook
Noise and the shape of the basin of attraction limitobserved digital diversity starting from empty networks
Multi stabilityseveral stablefixed points
Noisein full dynamical
model
Dom.Coex.
2 4 6 8 100.0
0.4
0.8
1.2
λ/λc1
σ
Reachability for 2 networks
→ Effective critical lines for more networks saturate atsuccessively lower values σi,eff
c
Evenwithout precise knowledge of the empiricalparameters our theory predictsmoderate diversity.
19
Motivation Evolution Ecology 2.0 Summary & Outlook
Reachability of the coexistence solutiondepends on the influence of mass media
Reachabilityprobability to
coexist
Mass mediainfluences thereachability 0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
ν
Probability coex.
Recall: µi = λi/ν, small ν means high media influence
The influence ofmass media enhances the observeddigital diversity.
20
Motivation Evolution Ecology 2.0 Summary & Outlook
Reachability of the coexistence solutiondepends on the influence of mass media
Reachabilityprobability to
coexist
Mass mediainfluences thereachability 0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
ν
Probability coex.
Recall: µi = λi/ν, small ν means high media influence
The influence ofmass media enhances the observeddigital diversity.
20
Motivation Evolution Ecology 2.0 Summary & Outlook
Ecological theory of the digital world explains whywe observe a moderate number of coexisting networks
Coexistencedespite
rich-get-richer
Moderateobserved diversity
Media effectscontrols observed
diversity
arxiv:1410.8865, 2014
21
Summary & Outlook
Motivation Evolution Ecology 2.0 Summary & Outlook
Multiscale theory of the digital world revealsconditions for sustaining digital diversity
Individuals Interacting Worldwide
Mod
el Strength ofsocial ties
Res
ult Weak ties
have highertransmissibility
Viral + mediaeffect & under-lying structure
Viral effect is about fourtimes stronger
Rich-get-richer& diminishingreturns
Coexistance of amoderate numberof services
Network of net-works & effectiveactivity
Local networks canprevail under certainconditions
Focu
s
12
3
101 - 102 105 - 106 106 - 109 >109
Ord
er
Isolatednetwork networks
PRX 4, 031046, 2014 arxiv:1410.8865, 2014 To appear23
Motivation Evolution Ecology 2.0 Summary & Outlook
Multiscale theory of the digital world revealsconditions for sustaining digital diversity
Individuals Interacting Worldwide
Mod
el Strength ofsocial ties
Res
ult Weak ties
have highertransmissibility
Viral + mediaeffect & under-lying structure
Viral effect is about fourtimes stronger
Rich-get-richer& diminishingreturns
Coexistance of amoderate numberof services
Network of net-works & effectiveactivity
Local networks canprevail under certainconditions
Focu
s
12
3
101 - 102 105 - 106 106 - 109 >109
Ord
er
Isolatednetwork networks
PRX 4, 031046, 2014 arxiv:1410.8865, 2014 To appear23
Motivation Evolution Ecology 2.0 Summary & Outlook
Multiscale theory of the digital world revealsconditions for sustaining digital diversity
Individuals Interacting Worldwide
Mod
el Strength ofsocial ties
Res
ult Weak ties
have highertransmissibility
Viral + mediaeffect & under-lying structure
Viral effect is about fourtimes stronger
Rich-get-richer& diminishingreturns
Coexistance of amoderate numberof services
Network of net-works & effectiveactivity
Local networks canprevail under certainconditions
Focu
s
12
3
101 - 102 105 - 106 106 - 109 >109
Ord
er
Isolatednetwork networks
PRX 4, 031046, 2014 arxiv:1410.8865, 2014 To appear23
Motivation Evolution Ecology 2.0 Summary & Outlook
Multiscale theory of the digital world revealsconditions for sustaining digital diversity
Individuals Interacting Worldwide
Mod
el Strength ofsocial ties
Res
ult Weak ties
have highertransmissibility
Viral + mediaeffect & under-lying structure
Viral effect is about fourtimes stronger
Rich-get-richer& diminishingreturns
Coexistance of amoderate numberof services
Network of net-works & effectiveactivity
Local networks canprevail under certainconditions
Focu
s
12
3
101 - 102 105 - 106 106 - 109 >109
Ord
er
Isolatednetwork networks
PRX 4, 031046, 2014 arxiv:1410.8865, 2014 To appear23
Just as a monopoly in economy is a threat to free markets, the lack of
poses a threat to the digital diversity
freedom of information.
Motivation Evolution Ecology 2.0 Summary & Outlook
IMAGE CREDITS
Oil field: http://www.rgvnewswire.com/wp-content/uploads/2014/12/energy-oil_rig-1.jpg
Cat attention: David CornejoHand icon: Irene HoffmanNetwork: Adam BeasleyBoxing gloves: Gabriele FumeroSummary icon: Stefan ParnarovLayer icon: MentaltoyBalance icon: Roman Kovbasyuk
Death symbol: Mila RedkoTeam icon: Joshua JonesMegaphone: Alex Auda SamoraSocial media chalk:mkhmarketing.wordpress.comflower: Nishanth Joiscables: jerry john
deer: Rob & Dawn ShrewsburyMoney sack: Lemon LiuNo: P.J. Onoridices: Drew Ellis3 arrows: Juan Pablo Bravo
26
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