“Un modelo basado en agentes para el estudio de la actividad en redes sociales online”
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“Un modelo basado en agentes para el estudio de la actividad en redes sociales online”

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Conferencia 13.agosto.2013 Seminario de Complejiad y Economía ...

Conferencia 13.agosto.2013 Seminario de Complejiad y Economía
“Un modelo basado en agentes para el estudio de la actividad en redes sociales online”

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  • 1. A Majority Rule model to simulate twitter-like activity in complex networks Arezky H. Rodríguez Academia de Matemáticas, Colegio de Ciencia y Tecnología Universidad Autónoma de la Ciudad de México (UACM) Yamir Moreno BIFI, Univ de Zaragoza Sandro Meloni BIFI, Univ de Zaragoza Instituto de BioComputación y Física de Sistemas Complejos. Supported by Grant “Programa de Fomento a la Movilidad de Investigadores del Gobierno de Aragón 2011”
  • 2. Outline: • Motivation. • The Model. • Views of the simulation using Netlogo. • First results. 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 2
  • 3. Protest in the connected society From New York to Istanbul, and Rio to Tunis, waves of social unrest have been sweeping across the world. Whatever they are called – Occupy Wall Street in New York (2011), 15M Movement in Spain (2011), the Jasmine Revolution in Tunisia (2010) or the Arab Spring (2010), and the Salad Uprising in Brazil (2013) – the mass mobilisations share several common features. Espousing public discontent over a range of sometimes unrelated, even conflicting issues, they were driven largely by new communication technologies coupled with an abiding distrust of government policies. 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 3
  • 4. Protest in the connected society Unlike the formal, planned protests of earlier times, the latest ones are, for the most part, informal and relatively spontaneous. As such, scientists say, they reflect a shift away from conventional social hierarchies towards what some call leaderless networks. Similar to demonstrations leading to the Arab Spring, the protests across 100 Brazilian cities were facilitated largely by social media such as Facebook and Twitter. 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 4
  • 5. A Majority Rule model to simulate twitter-like activity in complex networks Purpose: Characterize the dynamics of people activation on a network like Twitter as a function of different internal and external parameters. A person is considerer active when is broadcasting a message to her link neighbours. The influence of an external factor which initially influences the people on the network is considered. 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 5
  • 6. A Majority Rule model The Ambient: The formalism of agent-based models is used. People and their contacts are modeled as a weighted network of N nodes, where a node represents a person and the links of the network represent the real people connections with other persons. The parameter ωij account for the link weight between agent i and j. As a fist approximation it is considered the network with undirectional links. 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 6
  • 7. A Majority Rule model The external stimulus: There is an external stimuls (mass media, broadcasting radio station, problematic topic, etc) of intensity Wo which is percived by all the agents of the network. The intensity of the external stimulus exponentialy decreases on time with a factor ε. It pretends to simulate the damping on time of an initial stimulus due to memory lose. 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 7
  • 8. A Majority Rule model The Agents design: Each node is characterized by a vector of two parameters: (feeling-awkward?, active?) Parameter feeling-awkward? ∈{true, false} Parameter active? ∈{true, false} The parameters feeling-awkward? and active? of the nodes are coupled between them and also coupled with the feeling-awkward? and active? of their link neighbours in a way that will be explained later. 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 8
  • 9. A Majority Rule model The Agents design: Each agent possesses also a set of possitive real parameters βie, βiup, and βidown which account for the inner disposition of the agent i to become active following the external stimulus or following its link-neighbors, respectively. 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 9
  • 10. A Majority Rule model Initial conditions: All nodes have feeling-awkward? = false active? = false It is selected a number of nodes no and it is set active? = true It resembles certain amount of agents which react to the external stimuls Wo at t = 0. 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 10
  • 11. A Majority Rule model Initial conditions: Three ways of select the initially active nodes no are implemented: • Random •Target with higher connectivity first (hcf). •Target with lower connectivity first (lcf). 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 11
  • 12. A Majority Rule model Temporal evolution: Each time-step agent updates its values of feeling-awkward? and active?, in this order. •Agent feeling-awkward?(t) = ƒ(own active?(t -1), neighbours active?(t -1)) •Agent active?(t) = ƒ(own active?(t - 1), own feeling-awkward?(t)) 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 12
  • 13. A Majority Rule model Temporal updating: It is implemented two secuential updating: •Syncronous (in Parallel): all network nodes update its feeling-awkward? first and then all network nodes update its active? •Asyncronous – Random (resembling continuous updating): all network nodes are ordering in a list in random order (each time) and following this order each node updates its feeling-awkward? and inmediatelly updates its active? value. 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 13
  • 14. A Majority Rule model Details: Mathematical expresions: up i Q =1−e up i up i −(βie Wo f (t )+β W ) up i W =∑ j neighbours ωij s j (t ) Si = 1 for agent i with active? = true Si = 0 for agent i with active? = false 19/08/13 Q down i W −βidown W down i =1−e down i =∑ j neighbours ωij (1−s j (t)) f (t)=e Seminario de Complejidad y Economía CEIICH-UNAM −ϵ t 14
  • 15. A Majority Rule model Details: Agents update its feeling-awkward? according to: feeling-awkward?(t) =ƒ(own active?(t-1), neighbours active?(t-1)) Agents update its active? according to: active?(t) = ƒ(own active?(t-1), own feeling-awkward?(t)) if feeling-awkward? = false → active?(t) = active?(t – 1) if feeling-awkward? = true → active?(t) = not active?(t - 1) 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 15
  • 16. Parameters used: βie= βiup= βidown = 1 Wo =1 ωij = 1 asyncronous-random updating The simulation ends when all agents have feeling-awkward? = false 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 16
  • 17. Results: Erdös-Rényi network of 10 000 nodes. Each point is an average over 1000 runs. Asyncronous-random updating. Absorving states and trapped states Tipping points!! 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 17
  • 18. Results: Erdös-Rényi network of 10 000 nodes. Each point is an average over 1000 runs. Asyncronous-random updating. Absorving states and trapped states Tipping points!! 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 18
  • 19. Caracterizing the tipping points: Diversity Index DI = Entropy Information 1 ∑i P S =−∑i P i log 2 ( P i ) 2 i Amount of posible states you have in your system. 19/08/13 Amount of information your system containts. Seminario de Complejidad y Economía CEIICH-UNAM 19
  • 20. Results: Erdös-Rényi network of 10 000 nodes. Each point is an average over 1000 runs. Asyncronous-random updating. Absorving states and trapped states Tipping points!! 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 20
  • 21. Results: Erdös-Rényi network of 10 000 nodes. Each point is an average over 1000 runs. Asyncronous-random updating. Absorving states and trapped states Tipping points!! 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 21
  • 22. Results: Scale-Free network of 10 000 nodes. Each point is an average over 1000 runs. Asyncronous-random updating. Absorving states and trapped states Tipping points!! 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 22
  • 23. Results: Scale Free network of 10 000 nodes. Each point is an average over 1000 runs. Asyncronous-random updating. Absorving states and trapped states Tipping points!! 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 23
  • 24. Results: Scale Free network of 10 000 nodes. Each point is an average over 1000 runs. Asyncronous-random updating. Absorving states and trapped states Tipping points!! 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 24
  • 25. Further explorations: • Report the activation distribution: amount of neighbors which are active when the agent becomes active • Tipping points as a function of the initial stimulus intensity W o • Tipping points as a function of the network size • Trapped states characterization • β distributions dependences • Syncronous vs Asyncronous-random updating 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 25
  • 26. Further explorations: • Social agents have roles • Social agents are autonomous • Social agents interact locally with a few number of neighbors Necessity of other models!! Explanation rather than prediction Gracias.... 19/08/13 Seminario de Complejidad y Economía CEIICH-UNAM 26