复杂网络研究现状与前瞻.ppt

Toward a Universal Understanding of Human Mobility and Social Networks,胡延庆 郇迪 张江 黎勇 樊瑛 王有贵 狄增如 北京师范大学管理学院系统科学系 北京师范大学复杂性研究中心 2010.10 苏州,Background and Motivation,Empirical Results of Mobility Animals and Human Beings Understanding Why Social Networks Distance Distribution of Social Links Maximum Entropy Yields It Toward Universal Understanding of Both Mobility and Social Networks,Mobility Pattern,Pattern: most of the studies on animal mobility pattern including experimental data and theoretic analysis found that their mobility pattern follow the Levy flight:,Levy flight search patterns of wandering albatrosses, Nature 381, (1996) Revisiting Levy flight search patterns of wandering albatrosses, bumblebees and deer, NATURE| Vol 449|25 October 2007 Scaling laws of marine predator search behaviour, Nature (2008 ),Human Mobility,D. Brockmann, L. Hufnagel and T. Geisel, The scaling laws of human travel, Nature, 439, 462-465, (2006).,-1.59,Human Mobility,1.75,Understanding individual human mobility patterns Marta C. Gonzalez, Cesar A. Hidalgo & Albert-Laszlo Barabasi, NATURE| Vol 453|5 June 2008,Optimizing the success of random searches G. M. Viswanathan*, Sergey V. Buldyrev*, Shlomo Havlin*, M. G. E. da Luzk, E. P. Raposok# & H. Eugene Stanley*, NATURE |VOL 401 | 28 OCTOBER 1999 |,Fish in Lvy-flight foraging Gandhimohan M. Viswanathan Lvy flights are a theoretical construct that has attracted wide interdisciplinary interest. Empirical evidence shows that the principle applies to the foraging of marine predators. NATURE|Vol 465|24 June 2010,Understanding Why,Search Efficiency Number of target Sites Visited to the Total Distance Tranversed,Exploration and Preferential return,(i) Exploration: with probability the individual moves to a new location (ii) Preferential return: with probability,Complex Networks,complex networks are the backbone of complex systems every complex system is a network of interaction among numerous smaller elements understanding a complex system = break down into parts + reassemble network anatomy is important to characterize because structure affects function (and vice-versa) ex: structure of social networks prevent spread of diseases control spread of information (marketing, fads, rumors, etc.),Binary Network: Node-Link Weighted Network Link weight Spatial Network Geometrical or Geographical Structure,Spatial Properties of Social Networks,Discovering What Understanding Why Investigating Its Impacts Navigability Synchronization Traffic Dynamics Epidemic Process,Distance Is Not Dead: Social Interaction and Geographical Distance in the Internet era,Distance Is Not Dead: Social Interaction and Geographical Distance in the Internet era,Empirical Results,D.Liben-Nowell, J. Novak, R. Kumar, P. Raghavan, and A. Tomkins. PNAS 102, 11623-11628, (2005).,Empirical results R. Lambiotte and his cooperators: 2.5 million mobile phone customers Physica A. 387(2008),P(d) d-1,The distribution of geographic distance between friends is,Investigating its Effects -Navigation,Social Networks Milgram: Six degrees of separation. Travers, J. and Milgram, S., Sociometry. 32, 425-443 (1969). Kleinberg: Kleinberg, J. M. Navigation in a small world. Nature. 406, 845 (2000),Synchronization,Synchronizability,Topology,Traffic Dynamics,Getting information through social network,Understanding Why Do the Networks Possess Spatial Scaling Properties,Understanding Why Do the Networks Possess Spatial Scaling Properties,Maximization of Entropy,?,W=cL 下的理论分析,1,1,Mobility & Network,One Levy Flights,Infinit Levy Flights,Home-Return Effect,Human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time independent characteristic travel distance and a significant probability to return t