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DETERMINING MEAN FIRST-PASSAGE TIME ON A CLASS OF TREELIKE REGULAR FRACTALS

第六届全国复杂网络会议 CCCN2010. DETERMINING MEAN FIRST-PASSAGE TIME ON A CLASS OF TREELIKE REGULAR FRACTALS. 报告人：林　苑 指导老师：章忠志 副教授 复旦大学 2010.10.17. PUBLICATIONS.

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DETERMINING MEAN FIRST-PASSAGE TIME ON A CLASS OF TREELIKE REGULAR FRACTALS

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  1. 第六届全国复杂网络会议 CCCN2010 DETERMINING MEAN FIRST-PASSAGE TIME ON A CLASS OF TREELIKE REGULAR FRACTALS 报告人：林　苑 指导老师：章忠志 副教授 复旦大学 2010.10.17

  2. PUBLICATIONS • [1] Lin Yuan(林苑), Wu Bin, Zhang Zhongzhi(指导教师). Exactly determining mean first-passage time on a class of regular fractals, Physical Review E, 2010, 82: 031140. • [2] Zhang Zhongzhi(指导教师), Lin Yuan(林苑), et al. Trapping in scale-free networks with hierarchical organization of modularity, Physical Review E, 2009, 80: 051120. • [3] Zhang Zhongzhi(指导教师), Lin Yuan(林苑), et al. Mean first-passage time for random walks on the T-graph, New Journal of Physics, 2009, 11: 103043. • [4] Zhang Zhongzhi(指导教师), Lin Yuan(林苑), et al. Average distance in a hierarchical scale-free network: an exact solution. Journal of Statistical Mechanics: Theory and Experiment, 2009, P10022. • [5] Zhang Zhongzhi(指导教师), Qi Yi, Zhou Shuigeng, Lin Yuan(林苑), and Guan Jihong. Recursive solutions for Laplacian spectra and eigenvectors of a class of growing treelike networks, Physical Review E, 2009, 80:016104. • [6] Zhang Zhongzhi(指导教师), Zhou Shuigeng, Xie Wenlei, Chen Lichao, Lin Yuan(林苑), and Guan Jihong. Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect, Physical Review E, 2009, 79:061113.

  3. OUTLINE

  4. INTRODUCTION ABOUT RANDOM WALKS -

  5. INTRODUCTION ABOUT RANDOM WALKS -

  6. INTRODUCTION ABOUT RANDOM WALKS -

  7. INTRODUCTION ABOUT RANDOM WALKS -

  8. INTRODUCTION ABOUT RANDOM WALKS -

  9. IMPORTANT MEASURES OF RANDOM WALKS

  10. APPLICATIONS OF RANDOM WALKS • PageRank algorithm • Community detection • Recommendation systems • Electrical circuits (resistances) • Information Retrieval • Natural Language Processing • Machine Learning • Graph partitioning • In economics: random walk hypothesis

  11. APPLICATIONS OF RANDOM WALKS • Applications in real life

  12. OUR WORK: TRAPPING PROBLEM • Imagine there are traps (or absorbers) on several certain vertices. • We are interesting the time of absorption. • For simplicity, we first consider the problem that only a single trap.

  13. Determining mean first-passage time on a class of treelike regular fractals, Lin Yuan, Wu Bin, Zhang Zhongzhi, Physical Review E, 2010, 82:031140

  14. 网络构成

  15. 网络构成

  16. 网络构成：另一种方法 网络的构成具有自相似性

  17. 具有单个陷阱的随机游走

  18. 计算平均游走时间 这个结论对一般的树 拉拉状网络均成立。

  19. 计算平均游走时间

  20. 计算平均游走时间 将每一代新增加的点进行分类，分别计算。

  21. 结论(1) • 平均随机游走时间服从幂率分布； • 网络的参数m影响网络的吸收效率：随着m的增大，网络的吸收效率增高。

  22. 全局平均随机游走时间 • 将任一点作为陷阱的平均吸收时间； • 即网络上任意两点的平均首达时间(MFPT)。 • 计算全局平均随机游走时间的经典方法：计算拉普拉斯的伪逆矩阵。 • 时间复杂度 O(n3) • 空间复杂度 O(n2)

  23. 全局平均随机游走时间

  24. 全局平均随机游走时间

  25. 全局平均随机游走时间

  26. 结论(2) • 全局平均随机游走时间同样服从幂率分布。 • 陷阱位置对网络的吸收效率没有实质影响，原因在于网络的构造。

  27. 网络构成：另一种方法 网络的构成具有自相似性

  28. 小结 • 提出一类树状分形 • 中间点作为陷阱的随机游走 • 全局随机游走时间 • 对自相似网络具有普适性

  29. Thank you

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