China Institute of Atomic Energy Beijing 102413 202163
广泛交叉的网络科学 及其发展前景 方锦清 中国原子能科学研究院 China Institute of Atomic Energy, Beijing 102413 2021/6/3 ppt 1
两个重要发现 小世界现象( The Small World Effect,1998) “What a small world!” Indeed, we all are connected through a short chain of acquaintances. The most popular manifestation of such “small world effect” is the so-called “Six degree of separation” concept 无标度特性( The Scale-free feature,1999) 2021/6/3 ppt 6
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Erdös-Rényi model (1960) Connect with probability p p=1/6 N=10 k ~ 1. 5 Pál Erdös (1913 -1996) Poisson distribution - Democratic - Random 2021/6/3 ppt 8
Small-world networks N = 1000 • Large clustering coeff. • Short average path length Watts & Strogatz, Nature 2021/6/3 393, 440 (1998) ppt 9
无标度特性 Scale-free networks Nodes: Actors Web-pages Trans. stations Links: Movies Hyper-links Power lines 2021/6/3 Barabasi & Albert, Science 286, 509 (1999)ppt 10
Single-scale small-world networks Proc Nat Acad Sci USA 97, 11149 (2000) 2021/6/3 ppt 11
无标度特性的形成机制 (1) 网络不断增长: 通过加入新节点 GROWTH: add a new node with m links WWW : addition of new documents Citation : publication of new papers (2) 新节点偏好与度高的节点连接 New nodes prefer to link to highly connected nodes. 择优连接: the probability that a node connects to a node with k links is proportional to k. WWW : linking to well known sites Citation : citing again highly cited papers P(k) ~k -3 Barabási & Albert, Science 286, 509 (1999) 2021/6/3 ppt 12
生命复杂性的金字塔 Life’s Complexity Pyramid (Zoltán N. Oltvai and Albert-László Barabási, Science, 298(2002)763) 2021/6/3 ppt 15
GENOME protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle 2021/6/3 ppt 16
有关文献:网络形成的的物理机 制和研究方法 Steven H. Strogatz, Exploring Complex Networks, Nature, 2001, Vol. 410, 268 -276. R. Albet and A. L. Barabasi, Statistical Mechanics of Complex Networks, Rev. Mod. Phys. , 2002, Vol. 74, pp 48 -97 M. E. J. Newman, The Structure Function of Complex Networks, SIAM Review, 2003, Vol. 45, No. 2, pp 167 -256. 2021/6/3 ppt 20
2. 1 HUHPM的主要结果 Exponent of node degree power-law HUHPM-BA HUHPM- BBV HUHPM- TDE Ø Ø Fang J J Q, Q, 2021/6/3 Bi Q, Li Progress Y, Y, Y, in Advances in Complex Systems, Vol. 10, No. 2 (2007) 117 -141 et al, Science in China Series G, 2007, 50(3): 379 -396. et al, Chin. Phys. Lett. , 2007, 24(1): 279~ 283. Nature Science, 2007, 17(7): 761 -774. ppt 24
Left: Comparison of Average path length Right: Comparison of Clustering coefficient C ( HUHPM model with d/r=1/1 and <k>=4) 2021/6/3 ppt 25
2. 2 UHNM 主要结果 r C versus d/r (a) fd =1/1, m = 30; (b) fd =1/1, m = 10; (c) fd =1/10, m = 2. 2021/6/3 ppt 26
有权UHNM- BBV网络中 rc vs (dr,gr). 2021/6/3 ppt 27
d/r三种典型 作模式 r C vs (fd , gr) (weighted network ) d/r =1/99, 2021/6/3 d/r=1/1, 19/1 ppt d/r 28
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Some Papers Yong Li , Jin-Qing Fang , Qiao Bi , and Qiang Liu. Entropy Characteristic on Harmonious Unifying Hybrid Preferential Networks,Entropy, 2007, 9: 73 -82 Fang Jin-Qing, Bi Qiao, Ly, Yong, Advances in theoretical models of network science, Front. Phys. China, 2007, 1: 109 -124. Liu Qiang, Fang Jinqing, Li yong, Commun. Theor. Phys. 2007, 47: 752 -758. Bi Qiao, and Fang Jinqing, Entropy and HUHPM approach for complex networks, Physica A, in press (2007). Wu-jie Yuan Xiao-Su Luo, Pin- Qun Jiang , Bi-Hong Wang, Jin-Qing Fang, Transition to Chaos in Small World Dynamical Network , Physica A, 2007, in press。 Sun Weiguan, XU Cong–Xiang, Li Chang-Ping, Fang Jin-qing, Synchroniuzation and Bifurcation of General Complex Dynamical Networks, Commun. Theor. Phys. 2007, 47: 1073 -1075. 2021/6/3 ppt 31
III. 统一混合变速增长模型 Unified Hybrid Variable Growing Network Model 因为许多实际网络,不论是节点增减和边的连接数随时间 的发展速度都是不一样的, 有增、有减、正常、异常等情 况,而且还空间变化,如中国四川汶川抗震救灾网每时每 刻不断变化,而高技术网络、因特网、人类社会关系网、 通讯网等等通常也是随时间空间在变化着。 In many real-world networks such as the Intemel, World Wide Web, collaboration, citation, telephone exchanges, engineering, society, metabolism, biology, gene regulatory network ( e. g. , the network of regulatory proteins that control gene expression in bacteria), etc. . The number of links grow in time in a nonlinear fashion. 2021/6/3 ppt 33
典型的变速生长模式 确定性增长: P=Const 随机性增长: 0 ≤ p(t) ≤ 1。 变速类型 : [1] Sen P. Phys. Rev. E, 2004, 69: 46107. [2]Mattick J S. Gagen G M. Science, 2005 307: 856 [3]Gagen G M. Mattick J S. Phys. Rev. E, 2005, 72: 16123. [4]David M D S, Jukka P O, Neil F J. ar. Xiv, 2007, physics/0701339. 2021/6/3 ppt 35
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2005年 2021/6/3 ppt 49
1 E-3 1 E-4 2021/6/3 ppt 50
四个基本方程 2021/6/3 ppt 54
Master Equation of the QID 2021/6/3 ppt 55
QID Fokker-Plank Equation由 量子Fokker-Plank 方程作用在初始输入QID上 的演化算子来描述。 2021/6/3 ppt 56
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纳米相干网络 Hexagonal nanowire network The 5 th order The 2 nd order 2021/6/3 ppt 61
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群集系统中的同步问题研究 (动态网络系统) Birds Flocking Fish Swarming 2021/6/3 ppt 66
An Adaptive Velocity Model Hesitate, and move slow! Local order parameter: 2021/6/3 ppt 68
Convergence Probability the probability that a group of N initially randomly distributed agents will finally converge to a global convergence state. 2021/6/3 ppt 70
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