1. Simulating the Social Processes of Science Leiden| 9 April 2014 INGENIO [CSIC-UPV] Ciudad Politécnica de la Innovación | Edif 8E 4º Camino de Vera s/n 46022 Valencia tel +34 963 877 048 fax +34 963 877 991 DIFFUSION OF SCIENTIFIC KNOWLEDGE: A PERCOLATION MODEL Elena M. Tur With P Zeppini and K Frenken www.ingenio.upv.es

2. 2 How do social pressure and assortativity affect the process of diffusion? How do their effect interact with the social network structure? How do local effects dictate global diffusion through the overall network structure? Main contribution: introducing social pressure in a model of diffusion with different network structures Focus 2

3. 3 Spread of rumors (Zanette, 2002) Online spreading of behavior (Centola, 2010) Opinion dynamics (Shao et al., 2009) Paradigm shift in science (Brock and Durlauf, 1999) How to approach the problem (Zeppini and Frenken, 2013) Heterogeneity of agents Externalities Social network Percolation (Solomon et al., 2000) Diffusion of ideas

4. 4 Percolation in a social network

5. 5

6. 6

7. 7 Small world (Watts and Strogatz, 1998) Starting with a regular lattice, with nodes and edges per node, rewire each edge at random with probability High clustering coefficient, low average path length Social network

8. 8 Percolation without social pressure

9. 9 SOCIAL PRESSURE

10. 10 The unwilling to adopt can be persuaded Network externalities: shared language, shared experiences, shared beliefs… Increasing amount of evidence Conformity (Asch,1958) Weariness Why social pressure?

11. 11 Modelling social Pressure

12. 12 Parameters for the simulations 12

13. 13 Percolation with social pressure

14. 14 Clustering with social pressure

15. 15 The 45º line is no longer an upper bound to diffusion Diffusion increases Percolation thresholds decrease Differences between networks are reduced Percolation with social pressure

16. 16 ASSORTATIVITY People tend to be friends with similar people

17. 17 Modelling assortativity Most unwilling to adopt Most willing to adopt

18. 18 No critical transition from non-diffusion to diffusion Diffusion size scales linearly with diffusion size No effect of the network structure (well-mixed population) Percolation with assortativity

19. 19 Percolation with social pressure and assortativity

20. 20 Does assortativity help diffusion?

21. 21 Does assortativity help diffusion? (2)

22. 22 CONCLUSIONS

23. 23 Social pressure changes the behavior of the percolation process: higher diffusion size, lower percolation thresholds The effect of social pressure is different for different network structures: critical transition in small worlds and lattices With social pressure, clustering becomes beneficial for diffusion: reduced differences between networks Assortativity removes the effect of the network structure: all behave as a well-mixed population Assortativity can help or hamper diffusion depending on the setting Conclusions

24. 24 Future work and limitations

25. 25 THANK YOU INGENIO [CSIC-UPV] Ciudad Politécnica de la Innovación | Edif 8E 4º Camino de Vera s/n 46022 Valencia tel +34 963 877 048 fax +34 963 877 991