determining mean first-passage time on a class of treelike regular fractals
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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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
第六届全国复杂网络会议 CCCN2010
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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.
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OUTLINE11:33:12
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INTRODUCTION ABOUT RANDOM WALKS
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INTRODUCTION ABOUT RANDOM WALKS
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INTRODUCTION ABOUT RANDOM WALKS
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INTRODUCTION ABOUT RANDOM WALKS
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INTRODUCTION ABOUT RANDOM WALKS
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IMPORTANT MEASURES OF RANDOM WALKS
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APPLICATIONS OF RANDOM WALKSPageRank algorithmCommunity detectionRecommendation systemsElectrical circuits (resistances) Information RetrievalNatural Language ProcessingMachine LearningGraph partitioning In economics: random walk
hypothesis
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Applications in real life
APPLICATIONS OF RANDOM WALKS
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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.
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Determining mean first-passage time on a class of treelike regular fractals, Lin Yuan, Wu Bin, Zhang Zhongzhi, Physical Review E, 2010, 82:031140
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网络构成
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网络构成
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网络构成:另一种方法
网络的构成具有自相似性
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具有单个陷阱的随机游走
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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。
这个结论对一般的树 拉拉状网络均成立。
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计算平均游走时间
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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。
将每一代新增加的点进行分类,分别计算。
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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。
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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)
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全局平均随机游走时间
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全局平均随机游走时间
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全局平均随机游走时间
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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。
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网络构成:另一种方法
网络的构成具有自相似性
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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
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Thank you
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