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ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK
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作者 Shuxiong ZHANG Jie XIONG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期2051-2072,共22页
Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure onℝ^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈ℝ... Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure onℝ^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈ℝ^(d):∣x∣<u})=0}the radius of the largest empty ball centered at the origin of Zn.In this work,we prove that after suitable renormalization,Rn converges in law to some non-degenerate distribution as n→∈.Furthermore,our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk.This completes the results of Révész[13]for the critical binary branching Wiener process. 展开更多
关键词 empty ball DIMENSION branching random walk super-Brownian motion
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Strong invariance principle for a counterbalanced random walk
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作者 TAN Hui-qun HU Zhi-shui DONG Liang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第2期370-380,共11页
We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 wit... We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(v(n))with probability 1−p,where v(n)is a uniform random variable on{1;…;n−1}.We apply martingale method to obtain a strong invariance principle forS_(n). 展开更多
关键词 random walk MARTINGALE invariance principle
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Heat Kernel Estimates on Simple Random Walks and On-Diagonal Upper Bounds
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作者 Runquan Zuo Yuxiao Yan +2 位作者 Zishan Zhu Liwen Yao Qihao Han 《Journal of Applied Mathematics and Physics》 2024年第10期3613-3625,共13页
We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that t... We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that the heat kernel in higher dimensions converges rapidly. We also compute the constants involved in the estimate for the 1-dimensional heat kernel. Furthermore, we discuss the general case of on-diagonal estimates for the heat kernel. 展开更多
关键词 Heat Kernel Simple random walk On-Diagonal Estimate
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基于Random Walk算法的CT图像肺实质自动分割 被引量:4
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作者 王兵 顾潇蒙 +3 位作者 杨颖 董华 田学东 顾力栩 《计算机应用》 CSCD 北大核心 2015年第9期2666-2672,2681,共8页
针对复杂情况下肺实质的分割问题,提出了一种基于Random Walk算法对肺实质自动分割的方法。首先,根据胸部组织解剖学及其计算机断层扫描(CT)图像的影像学特征,在肺实质及其周围组织分别确定目标区域种子点和背景种子点位置;然后,使用Ran... 针对复杂情况下肺实质的分割问题,提出了一种基于Random Walk算法对肺实质自动分割的方法。首先,根据胸部组织解剖学及其计算机断层扫描(CT)图像的影像学特征,在肺实质及其周围组织分别确定目标区域种子点和背景种子点位置;然后,使用Random Walk算法对CT图像进行分割,提取近似肺区域的掩模;接下来,对掩模实施数学形态学运算,来进一步调整目标区域种子点和背景种子点的标定位置,使其适合具体的复杂情况;最后,再次使用Random Walk算法分割图像,得到最终的肺实质分割结果。实验结果显示,该方法与金标准的平均绝对距离为0.44±0.13 mm,重合率(DC)为99.21%±0.38%。与其他分割方法相比,该方法在分割精度上得到了显著提高。结果表明,提出的方法能够解决复杂情况下肺实质分割的问题,确保了分割的完整性、准确性、实时性和鲁棒性,分割结果和时间均可满足临床需求。 展开更多
关键词 胸部图像 计算机断层扫描 random walk算法 肺实质分割 种子点选择 数学形态学运算
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基于LBP的改进Random Walks算法在颅脑磁共振影像分割中的应用
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作者 刘伟 童同 +1 位作者 黄煜峰 冯焕清 《北京生物医学工程》 2013年第3期237-242,共6页
目的由于颅脑结构复杂且颅脑磁共振影像易受噪声、磁场不均匀性、部分容积效应等因素的影响,精确的脑组织分割方法仍需深入研究。方法本文提出一种基于Random Walks的改进算法以提高脑白质、脑灰质及脑脊液分割的准确性。通过引入局部... 目的由于颅脑结构复杂且颅脑磁共振影像易受噪声、磁场不均匀性、部分容积效应等因素的影响,精确的脑组织分割方法仍需深入研究。方法本文提出一种基于Random Walks的改进算法以提高脑白质、脑灰质及脑脊液分割的准确性。通过引入局部二值模式(local binary patterns,LBP)改进了传统Random Walks权重函数的构造,在反映相邻像素灰度变化信息的同时包含了局部图像的纹理信息,有利于合并同质区域并增强边缘轮廓的识别。本文还使用了灰度先验概率模型减少Random Walks种子点交互的次数。结果实验结果表明基于LBP的改进算法在多种不同水平的噪声及不均匀场作用下,能够有效识别磁共振影像中脑组织区域的边缘轮廓,并对噪声有良好的鲁棒性。结论基于LBP的改进Random Walks算法可精确分割颅脑磁共振影像。 展开更多
关键词 随机游走 局部二值模式 先验概率 脑组织 分割
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基于改进Random Walk算法的磁共振图像脑组织分割 被引量:1
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作者 吴德煌 刘伟 +3 位作者 赖凯 范亚 李传富 冯焕清 《数据采集与处理》 CSCD 北大核心 2011年第2期194-199,共6页
在Random Walk算法中,边的权重对算法分割性能有着重要的影响,针对原算法在计算权重时仅使用相邻像素灰度值变化信息的局限性,通过引入图像局部熵,使得权重函数同时反映相邻像素灰度变化信息和图像局部灰度离散度信息,增强算法对目标内... 在Random Walk算法中,边的权重对算法分割性能有着重要的影响,针对原算法在计算权重时仅使用相邻像素灰度值变化信息的局限性,通过引入图像局部熵,使得权重函数同时反映相邻像素灰度变化信息和图像局部灰度离散度信息,增强算法对目标内容和边界的识别能力。同时通过Fisher评价函数构造最佳分类阈值的选取法则,增强了算法的判别能力。实验表明改进后的算法对目标内容和边界的识别能力有较大提高,且对噪声具有更好的鲁棒性。 展开更多
关键词 图像分割 random walk算法 局部熵 最佳阈值选取
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基于Random Walks算法的心脏双源CT左心房分割 被引量:6
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作者 何昌保 马秀丽 余长明 《电子测量技术》 2016年第5期75-79,共5页
针对在传统的CT介入式治疗过程中,胸腔中软组织较多软组织的厚度和注射的造影剂在心脏中呈现的不均匀分布,导致在采用CT成像的图像中胸腔内部各组织之间存在边界模糊或者确实等状况,本文提出一种采用形态重构和随机行走相结合的分割方... 针对在传统的CT介入式治疗过程中,胸腔中软组织较多软组织的厚度和注射的造影剂在心脏中呈现的不均匀分布,导致在采用CT成像的图像中胸腔内部各组织之间存在边界模糊或者确实等状况,本文提出一种采用形态重构和随机行走相结合的分割方法。首先利用形态学开闭运算对图像进行化简,并使得心脏CT腔体边界分离,进而使得各个组织组织分离,再结合Random walks算法。从而使得不需要标记太多种子点的情况下提高了分割的速度和准确性,实验证明该方法能够达到预期的目标。 展开更多
关键词 双源CT 形态学重构 random walks算法
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基于Random-Walk算法的DR图像分割方法 被引量:1
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作者 丰国栋 徐雪 周荷琴 《北京生物医学工程》 2009年第5期449-453,共5页
本文算法对原图像进行快速Mallat小波分解得到骨干图后,利用其高频子带梯度信息优化边的权重,并在概率阈值的准则下对争议区域做进一步划分,最后把最大到达概率所在类的标签赋予未标定顶点,并扩展到原图像,得到分割边界。用微软GrabCut... 本文算法对原图像进行快速Mallat小波分解得到骨干图后,利用其高频子带梯度信息优化边的权重,并在概率阈值的准则下对争议区域做进一步划分,最后把最大到达概率所在类的标签赋予未标定顶点,并扩展到原图像,得到分割边界。用微软GrabCut分割数据库图像和实际DR图像对该算法进行了验证,该算法能快速而有效地分割出特定的图像,适用于DR图像的分割,为进行组织增强和进一步提高DR图像质量打下基础。 展开更多
关键词 DR 图像分割 randomwalk算法 骨干图 概率阈值准则
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Immunization for scale-free networks by random walker 被引量:7
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作者 胡柯 唐翌 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第12期2782-2787,共6页
Based on the random walk and the intentional random walk, we propose two types of immunization strategies which require only local connectivity information. On several typical scale-free networks, we demonstrate that ... Based on the random walk and the intentional random walk, we propose two types of immunization strategies which require only local connectivity information. On several typical scale-free networks, we demonstrate that these strategies can lead to the eradication of the epidemic by immunizing a small fraction of the nodes in the networks. Particularly, the immunization strategy based on the intentional random walk is extremely efficient for the assortatively mixed networks. 展开更多
关键词 immunization strategy scale-free network random walk intentional random walk
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ASYMPTOTIC PROPERTIES OF A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME 被引量:4
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作者 Yuejiao WANG Zaiming LIU +1 位作者 Quansheng LIU Yingqiu LI 《Acta Mathematica Scientia》 SCIE CSCD 2019年第5期1345-1362,共18页
We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoti... We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate. 展开更多
关键词 branching random walk random ENVIRONMENT quenched MOMENTS WEIGHTED MOMENTS
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CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME 被引量:6
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作者 高志强 刘全升 汪和松 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期501-512,共12页
We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environmen... We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn(A) be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn (-) with appropriate normalization. 展开更多
关键词 Branching random walk random environment in time central limit theorems
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Random walk search in unstructured P2P 被引量:4
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作者 Jia Zhaoqing You Jinyuan +1 位作者 Rao Ruonan Li Minglu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第3期648-653,共6页
Unstructured P2P has power-law link distribution, and the random walk in power-law networks is analyzed. The analysis results show that the probability that a random walker walks through the high degree nodes is high ... Unstructured P2P has power-law link distribution, and the random walk in power-law networks is analyzed. The analysis results show that the probability that a random walker walks through the high degree nodes is high in the power-law network, and the information on the high degree nodes can be easily found through random walk. Random walk spread and random walk search method (RWSS) is proposed based on the analysis result. Simulation results show that RWSS achieves high success rates at low cost and is robust to high degree node failure. 展开更多
关键词 unstructured P2P search random walk search random walk spread power-law network.
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A random walk evolution model of wireless sensor networks and virus spreading 被引量:3
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作者 王亚奇 杨晓元 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第1期154-160,共7页
In this paper, considering both cluster heads and sensor nodes, we propose a novel evolving a network model based on a random walk to study the fault tolerance decrease of wireless sensor networks (WSNs) due to node... In this paper, considering both cluster heads and sensor nodes, we propose a novel evolving a network model based on a random walk to study the fault tolerance decrease of wireless sensor networks (WSNs) due to node failure, and discuss the spreading dynamic behavior of viruses in the evolution model. A theoretical analysis shows that the WSN generated by such an evolution model not only has a strong fault tolerance, but also can dynamically balance the energy loss of the entire network. It is also found that although the increase of the density of cluster heads in the network reduces the network efficiency, it can effectively inhibit the spread of viruses. In addition, the heterogeneity of the network improves the network efficiency and enhances the virus prevalence. We confirm all the theoretical results with sufficient numerical simulations. 展开更多
关键词 wireless sensor network random walk network efficiency virus spreading
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Some Probability Properties of Random Walk in Time-Random Environment 被引量:3
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作者 ZhangXiao-min LiBo 《Wuhan University Journal of Natural Sciences》 CAS 2004年第2期139-143,共5页
A general formulation of the stochastic model for random walk in time-random environment and an equivalent definition is established in this paper. Moreover, some basic probability relations similar to the classical c... A general formulation of the stochastic model for random walk in time-random environment and an equivalent definition is established in this paper. Moreover, some basic probability relations similar to the classical case which are very useful in the corresponding research of fractal properties are given. At the end, a typical example is provided to show the recurrence and transience. Key words random environment - random walk in timerandom environment - skew product Markov chain CLC number O 211.6 Foudation item: Supported by the National Natural Science Foundation of China (10371092) and Foundation of Wuhan University.Biography: Zhang Xiao-min (1977-), male, Ph. D candidate, research direction: stochastic processes and random fractal. 展开更多
关键词 random environment random walk in timerandom environment skew product Markov chain
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RENEWAL THEOREM FOR(L,1)-RANDOM WALK IN RANDOM ENVIRONMENT 被引量:2
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作者 洪文明 孙鸿雁 《Acta Mathematica Scientia》 SCIE CSCD 2013年第6期1736-1748,共13页
We consider a random walk on Z in random environment with possible jumps {-L,…, -1, 1}, in the case that the environment {ωi : i ∈ Z} are i.i.d.. We establish the renewal theorem for the Markov chain of "the envi... We consider a random walk on Z in random environment with possible jumps {-L,…, -1, 1}, in the case that the environment {ωi : i ∈ Z} are i.i.d.. We establish the renewal theorem for the Markov chain of "the environment viewed from the particle" in both annealed probability and quenched probability, which generalize partially the results of Kesten (1977) and Lalley (1986) for the nearest random walk in random environment on Z, respectively. Our method is based on (L, 1)-RWRE formulated in Hong and Wang the intrinsic branching structure within the (2013). 展开更多
关键词 random walk in random environment renewal theorem multitype branchingprocess in random environment COUPLING
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Random walk modeling of wake dispersion for the exhaust tower of an underground tunnel in urban area 被引量:2
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作者 JIANG Wei\|mei\+1, YU Hong\|bin\+1, LI Xin\+2 (1.Department of Atmospheric Sciences, Nanjing University, Nanjing 210093, China 2.LAPC, Institute of Atmospheric Physics,Chinese Academy of Sciences, Beijing 100029, China) 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 1999年第4期474-479,共6页
In this paper, some experimental studies on the impact of effluent from an exhaust tower of an underground tunnel with special construction are reported. By measuring the flow field downstream of the tower in NJU mete... In this paper, some experimental studies on the impact of effluent from an exhaust tower of an underground tunnel with special construction are reported. By measuring the flow field downstream of the tower in NJU meteorological wind tunnel, some flow characteristics in the make area were established. Based on these, an advanced random\|walk dispersion model was set up and applied successfully to the simulation of dispersion in the wake area. The modelling results were in accordance with wind tunnel measurements. The computed maximum of ground surface concentration in the building case was a factor of 3-4 higher than that in the flat case and appeared much closer to the source. The simulation indicated that random walk modelling is an effective and practical tool for the wake stream impact assessment. 展开更多
关键词 exhaust tower air pollution in urban area atmospheric dispersion random walk modelling
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Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap 被引量:2
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作者 张静远 孙伟刚 陈关荣 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第3期525-529,共5页
In this paper, we study the scaling for the mean first-passage time (MFPT) of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from... In this paper, we study the scaling for the mean first-passage time (MFPT) of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks. 展开更多
关键词 mean first-passage time random walks Koch networks
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Modelling of the behavior of marine oil spills: applications based on random walk techniques 被引量:2
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作者 Li, Zhi-Wei Mead, Christopher T. Zhang, Shu-Shen 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2000年第1期3-8,共6页
A numerical model has been developed to simulate the transport and fate of oil spilled at sea. The model combines the transport and fate processes of spilled oil with the random walk technique. Oil movement under th... A numerical model has been developed to simulate the transport and fate of oil spilled at sea. The model combines the transport and fate processes of spilled oil with the random walk technique. Oil movement under the influence of tidal currents, wind driven currents, and turbulent eddies is simulated by the PLUME RW dispersion model developed by HR Wallingford. The weathering processes in the model represent physical and chemical changes of soil slicks with time, and comprise mechanical spreading, dispersion, evaporation and emulsification. Shoreline stranding is determined approximately using a capacity method for different shoreline types. This paper presents details of the model, and describe the results of various sensitivity tests. The model is suitable for oil spill contingency planning. 展开更多
关键词 oil spill MODELLING random walk technique CLC number: TQ021 4 Document code: A
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Application of random walk model to fit temperature in 46 gamma world cities from 1901 to 1998 被引量:3
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作者 Shaomin Yan Guang Wu 《Natural Science》 2010年第12期1425-1431,共7页
Very recently, we have applied the random walk model to fit the global temperature anomaly, CRUTEM3. With encouraging results, we apply the random walk model to fit the temperature walk that is the conversion of recor... Very recently, we have applied the random walk model to fit the global temperature anomaly, CRUTEM3. With encouraging results, we apply the random walk model to fit the temperature walk that is the conversion of recorded tem-perature and real recorded temperature in 46 gamma world cities from 1901 to 1998 in this study. The results show that the random walk model can fit both temperature walk and real recorded temperature although the fitted results from other climate models are unavailable for comparison in these 46 cities. Therefore, the random walk model can fit not only the global temperature anomaly, but also the real recorded temperatures in various cities around the world. 展开更多
关键词 GAMMA World CITIES Global WARMING Modeling random walk TEMPERATURE Change
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Competition between two kinds of information among random-walking individuals 被引量:1
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作者 刘真真 王兴元 王茂基 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第4期625-630,共6页
A model is proposed to describe the competition between two kinds of information among N random-walking individuals in an L x L square, starting from a half-and-half mixture of two kinds of information. Individuals re... A model is proposed to describe the competition between two kinds of information among N random-walking individuals in an L x L square, starting from a half-and-half mixture of two kinds of information. Individuals remain or change their information according to their neighbors' information. When the moving speed of individuals v is zero, the two kinds of information typically coexist, and the ratio between them increases with L and decreases with N. In the dynamic case (v 〉 0), only one information eventually remains, and the time required for one information being left scales as Td -v^αL^β^γ. 展开更多
关键词 information spread random walk complex networks power law
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