香港中文大学：由耦合演化驱动的网络结构与相分离行为（PPT讲稿）Disconnected-connected network transitions and phase separation driven by coevolving dynamics

Disconnected-connected network transitions and phase separation driven by coevolving dynamics 由耦合演化驱动的网络结构与相分离行为 Pak Ming Hui许伯铭 Department of Physics香港中文大学物理系 The Chinese University of Hong Kong In collaborations with Oliver Graser顾皓森(CUHK Chen Xu许晨( Soochow University CCCN 2010 (15-17 October 2010, Suzhou

Disconnected-connected network transitions and phase separation driven by coevolving dynamics 由耦合演化驱动的网络结构与相分离行为 Pak Ming Hui 许伯铭 Department of Physics The Chinese University of Hong Kong 香港中文大学 物理系 In collaborations with: Oliver Gräser 顾皓森 (CUHK) Chen XU许晨 (Soochow University) CCCN 2010 (15-17 October 2010, Suzhou)

Dynamic models Two dynamics (SIS, SIR Influencing one opInion another formation), or games (PD, SG,.) COMPUTER SIMULATIONS 中心 COEVOLVING NEW SYSTEM FEATURES? THEORIES NETWORKS REAL (group dynamics SYSTEMS To read more on the topic in general Perc and Szolnoki, Biosystems 99, 109(2009) Szabo and Fath, Physics Reports 446, 97(2007) Gross and blasius, J.R. Soc. Interface 5, 259(2008)

Dynamic models (SIS,SIR, opinion formation), or games (PD,SG,…) NETWORKS (group dynamics) NEW FEATURES? COMPUTER SIMULATIONS THEORIES REAL SYSTEMS COEVOLVING SYSTEM Two dynamics influencing one another To read more on the topic in general: Perc and Szolnoki, Biosystems 99, 109 (2009) Szabo and Fath, Physics Reports 446, 97 (2007) Gross and Blasius, J. R. Soc. Interface 5, 259 (2008)

Dynamic models (SIS, SIR, opinion Two dynamics formation), or influencing one another games (PD, SG, .) COMPUTER SIMULATIONS 中哈( NEW FEATURES? THEORIES NETWORKS (group REAL dynamics SYSTEMS The general ideas have been applied to Adaptive epidemic models: e.g., Gross et al., PRL 96, 208701(2006); Shaw and Schwartz, PRE71, 066101(2008 Opinion formation models: e.g., Vazquez et al., PRL 100, 108702 (2008); Nardini et al.. PRL100,158701(2008) Wars and human conflicts: e.g. Bohorquez et al., Nature 462, 911(2009); Zhao etal,PRL103,148701(2009)

Dynamic models (SIS,SIR, opinion formation), or games (PD,SG,…) NETWORKS (group dynamics) NEW FEATURES? COMPUTER SIMULATIONS THEORIES REAL SYSTEMS COEVOLVING SYSTEM Two dynamics influencing one another The general ideas have been applied to: Adaptive epidemic models: e.g., Gross et al., PRL 96, 208701 (2006); Shaw and Schwartz, PRE 71, 066101 (2008) Opinion formation models: e.g., Vazquez et al., PRL 100, 108702 (2008); Nardini et al., PRL 100, 158701 (2008) Wars and human conflicts: e.g. Bohorquez et al., Nature 462, 911 (2009); Zhao et al., PRL 103, 148701 (2009)

Dynamic models (SIS, SIR, opinion Two dynamics formation), or influencing one another games (PD, SG, .) COMPUTER SIMULATIONS 中哈( NEW FEATURES? THEORIES NETWORKS (group REAL dynamics SYSTEMS And more. (from PM Huis group) Modeling of guilds in online games World of Warcraft and LA street gangs- Zhao et al., PRE 79, 066117(2009) Effects of social group dynamics on contagion(You tube downloads foreign exchange rates, flu)-Zhao et al., PRE 81, 056107(2010)

Dynamic models (SIS,SIR, opinion formation), or games (PD,SG,…) NETWORKS (group dynamics) NEW FEATURES? COMPUTER SIMULATIONS THEORIES REAL SYSTEMS COEVOLVING SYSTEM Two dynamics influencing one another And more…(from PM Hui’s group): Modeling of guilds in online games (World of Warcraft) and LA street gangs – Zhao et al., PRE 79, 066117 (2009) Effects of social group dynamics on contagion (YouTube downloads, foreign exchange rates, flu) – Zhao et al., PRE 81, 056107 (2010)

Co-evolving Modeling-"Job Hunting Model An agent looks for a group that he thinks he could contribute a group assess the agent to see if he can contribute to the group After joining group agent has a better understanding of the group and assess the group (Can I really contribute? If agent is unhappy with the group agent will quit! If agent feels OK with the group, he still wants to find a better group If he finds a better group, he will switch group if not, he stays Team formation model (agents with skills that complement each other) against kinship(buddy-buddy ) model

Co-evolving Modeling – “Job Hunting Model” • An agent looks for a group that he thinks he could contribute • A group assess the agent to see if he can contribute to the group • After joining group, agent has a better understanding of the group and assess the group (Can I really contribute?) • If agent is unhappy with the group, agent will quit! • If agent feels OK with the group, he still wants to find a better group • If he finds a better group, he will switch group; if not, he stays • Team formation model (agents with skills that complement each other) against kinship (buddy-buddy) model

Main Empirical Results from Data Sets: Online guilds and offline street gangs World of warcraft World of warcraft LA gangs 1000 All guilds in all servers All guilds in all servers All gang (a) (b) 1000 s 100 0.7 -0.55 92 106 500 110°im0 L LL 10 100 10 1000 Wow guild size Cumulative gang size distribution N(s)for all Cumulative size distribution distribution of la guilds in 3 servers S1, S2, Inset: Churn vs guild size Street gangs with all S3(put together) in Oct ethnicity put together 2005 Total members 5214 Total players: 76686 Small data sets Steps even in N(s>s Data from: Ducheneaut and Yee(Palo alto Research Center)

Main Empirical Results from Data Sets: Online guilds and Offline street gangs Wow Guild size distribution N(s) for all guilds in 3 servers S1, S2, S3 (put together) in Oct 2005 Total players: 76686 Cumulative size distribution Inset: Churn vs guild size Cumulative gang size distribution of LA Street gangs with all ethnicity put together Total members: 5214 Small data sets Steps even in N(s’>s) Data from: Ducheneaut and Yee (Palo Alto Research Center)

All guilds in all servers Server: S1 N=766861000 (a) (b) N=24033 kinship model 100200 200 1o108 6100 s Server: S2 Server: S3 1000 N=24477 N=28176 100k200 200 ∧ u口日 0o10 100 250 s 10 WoW Empirical data (blue)& Team-formation Modeling Results(red) Cumulative guild size distribution and Churn vs guild size N from data is taken as input (data in oct 2005

WoW Empirical data (blue) & Team-formation Modeling Results (red) Cumulative guild size distribution and Churn vs guild size N from data is taken as input (data in Oct 2005) N=76686 N=24033 N=24477 N=28176

100 All gangs (e) ∧ N=5214 t10 10 100 1000 Cumulative gang size distribution Data(blue)and team-formation modeling results(red) Dashed line(kinship/ buddy-buddy model) See APS News item June 2009) http:/physics.aps.org/synopsis-for/10.1103/physreve.79.066117 for an news item reporting our work

Cumulative gang size distribution Data (blue) and team-formation modeling results (red) Dashed line (kinship/”buddy-buddy” model) N=5214 See APS News item (June 2009) http://physics.aps.org/synopsis-for/10.1103/PhysRevE.79.066117 for an news item reporting our work

Here, we use an adaptive snowdrift game as an example to illustrate how coupled dynamics influence each other and explicit coupled transitions in the form of disconnected to connected network transition(structural) highly cooperative to lower cooperative population(functional) segregated phase to mixed-character phase(population characteristics frozen to continously evolving(dynamical) how one could approach such problems analytically what to look at in formulating a theory and its validity what a proper theory can inform us about the properties of the system

Here, we • use an adaptive snowdrift game as an example to illustrate… -- how coupled dynamics influence each other and explicit coupled transitions in the form of • disconnected to connected network transition (structural) • highly cooperative to lower cooperative population (functional) • segregated phase to mixed-character phase (population characteristics) • frozen to continously evolving (dynamical) -- how one could approach such problems analytically -- what to look at in formulating a theory and its validity -- what a proper theory can inform us about the properties of the system

Snowdrift Game SDG)[1 ☆ Scenario Two drivers heading home in opposite directions Blocked by a snowdrift Each driver: 2 actions/characters C( cooperate")= to shovel the snowdrift D(“noto- operate”)OR‘ defect(in prisoner's dilemma language)=not to shovel [1]J M. Smith, Evolution and the Theory of Games( cambridge Univ Press 1982). In other contexts, the"game of chicken

Snowdrift Game (SDG) [1] ◼ Two drivers heading home in opposite directions ◼ Blocked by a snowdrift ◼ Each driver: 2 actions/characters C (“cooperate”) = to shovel the snowdrift D (“not-to-operate”) OR “defect”(in prisoner’s dilemma language) = not to shovel ❖Scenario: [1] J. M. Smith, Evolution and the Theory of Games ( Cambridge Univ. Press 1982). In other contexts, the “game of chicken