Ce diaporama a bien été signalé.
Nous utilisons votre profil LinkedIn et vos données d’activité pour vous proposer des publicités personnalisées et pertinentes. Vous pouvez changer vos préférences de publicités à tout moment.

Evolution and Ecology of the Digital World

933 vues

Publié le

The overwhelming success of the web 2.0, with online social networks as key actors, has induced a paradigm shift in the nature of human interactions. The user-driven character of these services for the first time has allowed researchers to quantify large-scale social patterns. However, the mechanisms that determine the fate of networks at a system level are still poorly understood. For instance, the simultaneous existence of numerous digital services naturally raises the question under which conditions these services can coexist. In analogy to population dynamics, the digital world is forming a complex ecosystem of interacting networks whose fitnesses depend on their ability to attract and maintain users' attention, which constitutes a limited resource. In this paper, we introduce an ecological theory of the digital world which exhibits a stable coexistence of several networks as well as the domination of a single one, in contrast to the principle of competitive exclusion. Interestingly, our model also predicts that the most probable outcome is the coexistence of a moderate number of services, in agreement with empirical observations.

Publié dans : Sciences
  • Identifiez-vous pour voir les commentaires

  • Soyez le premier à aimer ceci

Evolution and Ecology of the Digital World

  1. 1. Kaj Kolja KLEINEBERG Marián BOGUÑÁ @KoljaKleineberg Universitat de Barcelona kkl@ffn.ub.edu EVOLUTION and Digital world Ecology of the
  2. 2. all digital services need Attention but our time is limited
  3. 3. The digital world forms a complex ECOSYSTEM with networks as competing species
  4. 4. Can we preserve digital diversity?
  5. 5. Evolution of isolated networks
  6. 6. Motivation Evolution Ecology 2.0 Summary & Outlook The topological evolution of large quasi-isolated OSN exhibits a dynamical percolation transition 7
  7. 7. Motivation Evolution Ecology 2.0 Summary & Outlook The topological evolution of large quasi-isolated OSN exhibits a dynamical percolation transition Dynamical percolation transition demands new class of growing network models. 7
  8. 8. Motivation Evolution Ecology 2.0 Summary & Outlook The pre-existing underlying social structure forms the backbone of the evolution of the OSN Online social network layer Traditional contact network layer Active Online & offline Passive Online & offline Susceptible Only offline 8
  9. 9. Motivation Evolution Ecology 2.0 Summary & Outlook The pre-existing underlying social structure forms the backbone of the evolution of the OSN Online social network layer Traditional contact network layer Active Online & offline Passive Online & offline Susceptible Only offline Mass media activation Viral activation Deactivation Viral reactivation 8
  10. 10. Motivation Evolution Ecology 2.0 Summary & Outlook Final snapshot of empirical network as proxy for underlying structure allows rigorous model validation Final snapshot Empirical evolution Extract snapshots Empirical data Model evolution Compare Final snapshot 9
  11. 11. Motivation Evolution Ecology 2.0 Summary & Outlook Final snapshot of empirical network as proxy for underlying structure allows rigorous model validation Final snapshot Empirical evolution Extract snapshots Empirical data Model evolution Compare Final snapshot Can we reproduce the entire topological evolution of the empirical network? 9
  12. 12. Motivation Evolution Ecology 2.0 Summary & Outlook Model precisely reproduces the entire topological evolution and reveals balance between virality and media influence Model results Parameters GCC model 2nd comp. model ASPL model x4 GCC Pokec 2nd comp. Pokec ASPL Pokec x4 103 104 105 106 0 20 40 60 80 100 120 140 N 10
  13. 13. Motivation Evolution Ecology 2.0 Summary & Outlook Model precisely reproduces the entire topological evolution and reveals balance between virality and media influence Model results Parameters GCC model 2nd comp. model ASPL model x4 GCC Pokec 2nd comp. Pokec ASPL Pokec x4 103 104 105 106 0 20 40 60 80 100 120 140 N Virality is about four times stronger than mass media 10
  14. 14. Motivation Evolution Ecology 2.0 Summary & Outlook Model precisely reproduces the entire topological evolution and reveals balance between virality and media influence Model results Parameters GCC model 2nd comp. model ASPL model x4 GCC Pokec 2nd comp. Pokec ASPL Pokec x4 103 104 105 106 0 20 40 60 80 100 120 140 N Virality is about four times stronger than mass media Interplay between virality and mass media dynamics is the main underlying principle of the OSN evolution. 10
  15. 15. Motivation Evolution Ecology 2.0 Summary & Outlook Below a critical value of the viral parameter the 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 11
  16. 16. Motivation Evolution Ecology 2.0 Summary & Outlook Below a critical value of the viral parameter the 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 online social networks. 11
  17. 17. Motivation Evolution Ecology 2.0 Summary & Outlook The microscopic picture reveals the role of strong and weak ties N 103 104 105 106 0.00 0.05 0.10 0.15 0.20 Clustering Data Tie strength: i j Transmissibility: λij ∝ λ [• + 1]η 12
  18. 18. Motivation Evolution Ecology 2.0 Summary & Outlook The microscopic picture reveals the role of strong and weak ties N 103 104 105 106 0.00 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 if invited by weaker social contacts. 12
  19. 19. Motivation Evolution Ecology 2.0 Summary & Outlook Evolution of the digital society reveals balance between viral and mass media influence Underlying social structure determines topological evolution Balance of viral and mass media influence Survival and death of networks Weak ties have higher transmissibility PRX 4, 031046, 2014 13
  20. 20. Ecology 2.0
  21. 21. Motivation Evolution Ecology 2.0 Summary & Outlook Gause's law impeding the coexistence of species competing for the same unique resource is often violated in nature Gause's law species competing for same resource cannot coexist Rich-get-richer even slightest advantage is amplified Nature communities contain handful of coexisting species 15
  22. 22. Motivation Evolution Ecology 2.0 Summary & Outlook Digital ecosystem is formed by multiple networks competing for the attention of individuals OSN 2 OSN 1 Underl. network Active Passive Susceptible Partial states} 16
  23. 23. Motivation Evolution Ecology 2.0 Summary & Outlook Digital ecosystem is formed by multiple networks competing for the attention of individuals OSN 2 OSN 1 Underl. network Active Passive Susceptible Partial states} Virality share Distribution between OSNs λi = ωi(ρa)λ 16
  24. 24. Motivation Evolution Ecology 2.0 Summary & Outlook Digital ecosystem is formed by multiple networks competing for the attention of individuals OSN 2 OSN 1 Underl. network Active Passive Susceptible Partial states} Virality share Distribution between OSNs λi = ωi(ρa)λ Rich-get-richer more active networks obtain higher share 16
  25. 25. Motivation Evolution Ecology 2.0 Summary & Outlook Digital ecosystem is formed by multiple networks competing for the attention of individuals OSN 2 OSN 1 Underl. network Active Passive Susceptible Partial states} Virality share Distribution between OSNs λi = ωi(ρa)λ Rich-get-richer more active networks obtain higher share Does rich-get-richer effect always lead to the domination of a single network? 16
  26. 26. Motivation Evolution Ecology 2.0 Summary & Outlook Nonlinear dynamics of network evolution can enable coexistence despite rich-get-richer mechanism Meanfield: ˙ρa i = ρa i [ λ ⟨k⟩ ωi(ρa ) [1 − ρa i ] − 1 ] + λ ν ωi(ρa )ρs i ˙ρs i = − λ ν ωi(ρa )ρs i [ 1 + ν ⟨k⟩ ρa i ] Rich-get-richer: ωi = [ρa i ]σ/ ∑ j[ρa j ]σ → σ activity affinity 17
  27. 27. Motivation Evolution Ecology 2.0 Summary & Outlook Nonlinear dynamics of network evolution can enable coexistence despite rich-get-richer mechanism Meanfield: ˙ρa i = ρa i [ λ ⟨k⟩ ωi(ρa ) [1 − ρa i ] − 1 ] + λ ν ωi(ρa )ρs i ˙ρs i = − λ ν ωi(ρa )ρs i [ 1 + ν ⟨k⟩ ρa i ] Rich-get-richer: ωi = [ρa i ]σ/ ∑ j[ρa j ]σ → σ activity affinity Unstable FP Stable FP 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Coexistence σ=0.8 ρ1 a ρ2 a Unstable FP Stable FP 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Domination σ=1.2 ρ1 a ρ2 a Stable Unstable 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 Bifurcation diagram ρ1 a 0.0 0.5 1.0 1.5 0.50 0.75 σ σ ρ1,2 a 17
  28. 28. Motivation Evolution Ecology 2.0 Summary & Outlook Maximum number of coexisting networks is determined by total virality and activity affinity Overall attention to OSNs Morelikelytoengage inmoreactiveOSNs Dom. 2 coex. 3 coex. 4 coex. 5 coex. 1 2 3 4 5 6 0.0 0.5 1.0 1.5 λ/λc 1 σ How many networks can coexist 18
  29. 29. Motivation Evolution Ecology 2.0 Summary & Outlook Maximum number of coexisting networks is determined by total virality and activity affinity Overall attention to OSNs Morelikelytoengage inmoreactiveOSNs Dom. 2 coex. 3 coex. 4 coex. 5 coex. 1 2 3 4 5 6 0.0 0.5 1.0 1.5 λ/λc 1 σ How many networks can coexist 3 networks 2 networks 1 network Stable configurations 18
  30. 30. Motivation Evolution Ecology 2.0 Summary & Outlook Maximum number of coexisting networks is determined by total virality and activity affinity Overall attention to OSNs Morelikelytoengage inmoreactiveOSNs How many networks can coexist 1 2 3 4 5 6 7 8 9 10 0.0 0.5 1.0 1.5 λ/λc 1 σ Dom. 2 coex. 3 coex. 4 coex. 5 coex. 3 networks 2 networks 1 network Stable configurations 18
  31. 31. Motivation Evolution Ecology 2.0 Summary & Outlook Maximum number of coexisting networks is determined by total virality and activity affinity Overall attention to OSNs Morelikelytoengage inmoreactiveOSNs How many networks can coexist 1 2 3 4 5 6 7 8 9 10 0.0 0.5 1.0 1.5 λ/λc 1 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 coexist despite rich-get-richer mechanism. 18
  32. 32. Motivation Evolution Ecology 2.0 Summary & Outlook Noise and the shape of the basin of attraction limit observed digital diversity starting from empty networks Multi stability several stable fixed points Noise in full dynamical model Dom. Coex. 2 4 6 8 10 0.0 0.4 0.8 1.2 λ/λc 1 σ Reachability for 2 networks 19
  33. 33. Motivation Evolution Ecology 2.0 Summary & Outlook Noise and the shape of the basin of attraction limit observed digital diversity starting from empty networks Multi stability several stable fixed points Noise in full dynamical model Dom. Coex. 2 4 6 8 10 0.0 0.4 0.8 1.2 λ/λc 1 σ Reachability for 2 networks → Effective critical lines for more networks saturate at successively lower values σi,eff c 19
  34. 34. Motivation Evolution Ecology 2.0 Summary & Outlook Noise and the shape of the basin of attraction limit observed digital diversity starting from empty networks Multi stability several stable fixed points Noise in full dynamical model Dom. Coex. 2 4 6 8 10 0.0 0.4 0.8 1.2 λ/λc 1 σ Reachability for 2 networks → Effective critical lines for more networks saturate at successively lower values σi,eff c Even without precise knowledge of the empirical parameters our theory predicts moderate diversity. 19
  35. 35. Motivation Evolution Ecology 2.0 Summary & Outlook Reachability of the coexistence solution depends on the influence of mass media Reachability probability to coexist Mass media influences the reachability 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 20
  36. 36. Motivation Evolution Ecology 2.0 Summary & Outlook Reachability of the coexistence solution depends on the influence of mass media Reachability probability to coexist Mass media influences the reachability 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 of mass media enhances the observed digital diversity. 20
  37. 37. Motivation Evolution Ecology 2.0 Summary & Outlook Ecological theory of the digital world explains why we observe a moderate number of coexisting networks Coexistence despite rich-get-richer Moderate observed diversity Media effects controls observed diversity arxiv:1410.8865, 2014 21
  38. 38. Summary & Outlook
  39. 39. Motivation Evolution Ecology 2.0 Summary & Outlook Multiscale theory of the digital world reveals conditions for sustaining digital diversity Individuals Interacting Worldwide Model Strength of social ties Result Weak ties have higher transmissibility Viral + media effect & under- lying structure Viral effect is about four times stronger Rich-get-richer & diminishing returns Coexistance of a moderate number of services Network of net- works & effective activity Local networks can prevail under certain conditions Focus 12 3 101 - 102 105 - 106 106 - 109 >109 Order Isolated network networks PRX 4, 031046, 2014 arxiv:1410.8865, 2014 To appear 23
  40. 40. Motivation Evolution Ecology 2.0 Summary & Outlook Multiscale theory of the digital world reveals conditions for sustaining digital diversity Individuals Interacting Worldwide Model Strength of social ties Result Weak ties have higher transmissibility Viral + media effect & under- lying structure Viral effect is about four times stronger Rich-get-richer & diminishing returns Coexistance of a moderate number of services Network of net- works & effective activity Local networks can prevail under certain conditions Focus 12 3 101 - 102 105 - 106 106 - 109 >109 Order Isolated network networks PRX 4, 031046, 2014 arxiv:1410.8865, 2014 To appear 23
  41. 41. Motivation Evolution Ecology 2.0 Summary & Outlook Multiscale theory of the digital world reveals conditions for sustaining digital diversity Individuals Interacting Worldwide Model Strength of social ties Result Weak ties have higher transmissibility Viral + media effect & under- lying structure Viral effect is about four times stronger Rich-get-richer & diminishing returns Coexistance of a moderate number of services Network of net- works & effective activity Local networks can prevail under certain conditions Focus 12 3 101 - 102 105 - 106 106 - 109 >109 Order Isolated network networks PRX 4, 031046, 2014 arxiv:1410.8865, 2014 To appear 23
  42. 42. Motivation Evolution Ecology 2.0 Summary & Outlook Multiscale theory of the digital world reveals conditions for sustaining digital diversity Individuals Interacting Worldwide Model Strength of social ties Result Weak ties have higher transmissibility Viral + media effect & under- lying structure Viral effect is about four times stronger Rich-get-richer & diminishing returns Coexistance of a moderate number of services Network of net- works & effective activity Local networks can prevail under certain conditions Focus 12 3 101 - 102 105 - 106 106 - 109 >109 Order Isolated network networks PRX 4, 031046, 2014 arxiv:1410.8865, 2014 To appear 23
  43. 43. 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.
  44. 44. 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 Cornejo Hand icon: Irene Hoffman Network: Adam Beasley Boxing gloves: Gabriele Fumero Summary icon: Stefan Parnarov Layer icon: Mentaltoy Balance icon: Roman Kovbasyuk Death symbol: Mila Redko Team icon: Joshua Jones Megaphone: Alex Auda Samora Social media chalk: mkhmarketing.wordpress.com flower: Nishanth Jois cables: jerry john deer: Rob & Dawn Shrewsbury Money sack: Lemon Liu No: P.J. Onori dices: Drew Ellis 3 arrows: Juan Pablo Bravo 26

×