国际贸易网络

1. 国际贸易网络 樊瑛 北京师范大学系统科学学院 2013.07.08

2. 复杂网络简介

3. Complicated Simple Complex System

4. Complex systems

5. Complex Systems Complex systems are all around us: • economies • nature: ant, bee, bird colonies • little robots

6. Internet 相互作用与复杂性 晶格 全局相互作用 ? 平均场 扩散

7. 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)

8. 为什么研究复杂网络？ •复杂系统不能够用分析的方法去研究， 必须考虑个体之间的关联和作用； •理解复杂系统的行为应该从理解系统相互作用网络的拓扑结构开始； •网络拓扑结构的信息是构建系统模型、研究系统性质和功能的基础。

9. 为什么研究复杂网络？ 复杂网络是研究复杂系统的一种角度和方法，它关注系统中个体相互关联的作用的拓扑结构，是理解复杂系统性质和功能的基础。

10. Complex systems Made of many non-identical elements connected by diverse interactions. NETWORK 复杂网络 复杂网络是对复杂系统的一种抽象 同质性？（个体、相互作用）

11. 复杂网络的数学描述 • 网络G=（V, E），由点集V（G）和边集E（G）组成的一个图，可分为无向、有向和加权网络 • 令ei∈ E（G），每条边ei有V（G）中的一对点(u,v)与之对应； 如果任意(u,v)与(v,u)对应同一条边，则称为无向网络，否则为有向网络； 如果任意∣ei ∣ =1，则称为无权网络，否则为加权网络。 • 链接矩阵及拉普拉斯矩阵

12. 技术网络 WWW 因特网 电力网

13. 社会网络 科学引文网 朋友关系网 演员网 科学家合著网

14. 交通运输网络 城市公共交通网 航空网 道路交通网

15. 神经网络 生态、生物网络 生态网络 蛋白质相互作用网络 基因网络 新陈代谢网络

16. 不同领域的复杂网络 • 社会网：演员合作网，朋友网，姻亲关系网，科研合作网，Email网，短信网… • 生物网：食物链网，神经网，新陈代谢网，蛋白质网，基因网络… • 信息网络：WWW，专利使用，论文引用，… • 技术网络：电力网，Internet，电话线路网， • 交通运输网：航线网，铁路网，公路网，自然河流网 • 经济系统：投入产出网，国际贸易，…

17. 网络研究的历史 • 1736，欧拉：哥尼斯堡七桥 • 1950，Erdos, Renyi: 随机图论 • 1998，Strogatz； 1999，Barabasi: 小世界和无标度网络

18. 复杂网络的兴起 • 计算机技术的发展： • 使我们有可能对大规模的网络进行实证研究 • 普适性的发现： • 许多实际网络具有相同的定性性质 • 且已有的理论不能描述和解释 • 理论研究的发展 • 小世界网络 (Small World Network), 无标度网络 (Scale-free Network) • 统计物理学的研究手段 • 应用领域的丰富 • 社会经济系统、生命生态系统等

19. 复杂网络研究所关心的问题 • 如何建立复杂网络？网络研究中的反问题 • 如何定量刻画复杂网络？ • 网络结构的描述及其性质 • 网络是如何发展成现在这种结构的？ • 网络演化模型 • 网络特定结构的后果是什么？正问题 • 网络结构的鲁棒性 • 网络上的动力学行为和过程

20. 国际贸易网络World Trade Network

21. 1 What Is World Trade Network?

22. Our Global Village Under the world economy, the trading relation between countries havemultiple influence. The influence can widely transmitted to other countries.

23. What Is World Trade Network? Or International Trade Network, World Trade Web… Network Construction Binary Directed export Weighted All value / the cut-off value (Kastelle et al., 2006; Kastelle, 2009) or (Tzekina et al., 2008; Kali and Reyes, 2007) (Fagiolo et al., 2007; Fagiolo et al., 2008; Fagiolo et al., 2010)

24. About World Trade Network World Trade Network( 2003-2012 )

25. See World Trade Network 2010 World Trade Network in our eyes Communities Note: By using of Weighted Extremal Optimization algorithm and Coarse Graining process

26. See World Trade Network 2010 World Trade Network in our eyes Centrality of Vertices

27. 2 What Is Bootstrap Percolation?

28. Bootstrap Percolation on Lattice • Sites’ States: • active “ ” or inactive “ ” , • Update Rules: • Initial Active Probability: • Active Threshold: • Proportion of Sites are Active: START … f=0.2

29. First Introduced • Study the diminution and eventual destruction of magnetic order by non-magnetic impurities in a magnet. • - J. Chalupa, P.L.Leath, G.R.Reich, Bootstrap percolation on a bethe lattice, J.Phys.C: Solid State Phys. 12 (1979) L31–L35. • Application • An useful model to describe complex phenomena • The neuronal activity (Eckmann et al., 2007; Soriano et al., 2008; Goltsev et al., 2009); • Hydrogen mixtures (Adler et al., 1987); • The dynamics of the glass transition (Nakanishi and Takano,1986;Ertel et al., 1988; Sellitto et al., 2005; Toninelli et al., 2006); • The magnetic alloys (Kogut and Leath, 1981).

30. Bootstrap Percolation on Complex Networks • Vertices’ States: • active “ ” or inactive “ ” • Update Rules: • Initial Active Probability: • Active Threshold: • Proportion of Sites are Active: START f=0.2

31. Bootstrap Percolation on Complex Networks (G.J. Baxter et al. Phys.Rev.E, 82:011103, 2010.) Fig. 1. Phase diagram in the f-p plane networks with finite second moment of the degree distribution Fig.2. Probability that an arbitrarily chosen vertex is (a) active and (b) in a giant connected component of active vertices Erdős-Rényi graph of mean degree 5, with k=3.

32. Bootstrap Percolation on Bipartite Networks (Wan Baohui et al. Acta Phys.Sin., 61(16):166402, 2012.) Update Rules of Vertex 2 N1=2000,N2=1600 Ώ1=10, Ώ2=9 f1=f2, Ώ1=10 F2=0.2, Ώ1=10, Ώ2=9

33. Bootstrap Percolation 3 +World Trade Network=?

34. Trading relations are so important !!! How can we explore the impact of trading relations?

35. Basic Assumptions • Vertices States： • Normal state • Abnormal state • Transmission in Edges： • Along the country’s commodities and services' export flows. • Country influence system by restricting imports or changing export. • Transmission Process：in a short term, discrete in time • Topology Distance Rather Than Geographical Distance

36. Rules Step1 Step2 Step3 Step4 For each i, if (Rule.1.) ;or (Rule.2.) ; it will become abnormal. ( A: Abnormal Neighbors)

37. Case: USA, China and Japan Final Scope of Impact (Rule.1.)

38. Case: USA, China and Japan Final Scope of Impact (Rule.2.)

39. Case: USA, China and Japan Phase Transition (Rule.1.) (a) disconnecting unilateral trading relation (b) disconnecting bilateral trading relation

40. Case: USA, China and Japan Phase Transition (Rule.2.) (a) disconnecting unilateral trading relation (b) disconnecting bilateral trading relation

41. 2 1 Case: USA, China and Japan Conclusions In Our Case: The China’s export to United States and Japan is even more important. Relations between China, USA and Japan are more important than random cases. They are important, too.

43. Thank you!