共查询到18条相似文献,搜索用时 171 毫秒
1.
分析新节点边对网络无标度性的影响.虽然亚线性增长网络瞬态平均度分布尾部表现出了幂律分布性质,但是,这个网络的稳态度分布并不是幂律分布,由此可见,计算机模拟预测不出网络稳态度分布,它只能预测网络的瞬态度分布.进而建立随机增长网络模型,利用随机过程理论得到了这个模型的度分布的解析表达式,结果表明这个网络是无标度网络. 相似文献
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考察了供应链网络的基本特征,提出了节点到达过程是更新过程、新增入边和出边数是具有Bernoulli分布随机变量的供应链型有向网络.研究了这类网络节点的瞬态度分布和稳态平均度分布.利用更新过程理论对这类网络进行了分析,获得了网络节点瞬态度分布和网络稳态平均度分布的解析表达式.分析表明, 虽然这类网络节点的稳态度分布不存在,但是网络的稳态平均度分布具有双向幂律性.
关键词:
复杂网络
入度
出度
度分布 相似文献
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受某些实际网络节点数按几何级数增长现象的启发,构造了每个时间步中按当前网络规模成比例地同时加入多个节点的节点数加速增长的网络模型.研究表明,在增长率不是很大的情况下网络度分布仍然是幂律的,但在不同的增长率r下幂律指数是不同的.得到了幂律指数介于2到3之间可调的无标度网络模型,并解析地给出了幂律指数随增长率变化的函数关系.数值模拟还显示,网络的平均最短距离随r减小而簇系数随r增大.
关键词:
复杂网络
无标度网络
生长网络模型
节点数加速增长网络模型 相似文献
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分析新节点边对网络无标度性的影响.虽然亚线性增长网络瞬态平均度分布尾部表现出了幂律分布性质,但是,这个网络的稳态度分布并不是幂律分布,由此可见,计算机模拟预测不出网络稳态度分布,它只能预测网络的瞬态度分布.进而建立随机增长网络模型,利用随机过程理论得到了这个模型的度分布的解析表达式,结果表明这个网络是无标度网络.
关键词:
复杂网络
无标度网络
小世界网络
度分布 相似文献
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k光子Jaynes-Cummings模型的亚Poisson光子统计特性研究 总被引:9,自引:4,他引:5
本文利用量子电动力学理论,首次对 k 光子 Jaynes-Cummings 模型中单模激光场的稳态亚 Poisson 光子统计性质进行了系统研究.结果表明:在一般情况下,激光上能级相对泵浦参量 xa 具有一个确定的阈值 xat;当 xa>xat时,光场呈现亚 Poisson 光子统计;当 xa>>xat时,光场呈现出深度且完全恒定的亚 Poisson 光子统计.在特殊情况下,阈值 xat-0,这时在激光腔内将直接诱发亚 Poisson 光子统计.随着 k(k≥2)值增加,阈值 xat降低,光场亚 Poisson 光子统计程度增强. 相似文献
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本文以一维均匀环为基础, 通过添加有限数量的长程连接构造出了一维有限能量约束下的空间网络, 环上任意节点i与j之间存在一条长程连接的概率满足pijα dij-α (α≥ 0),其中dij为节点i与j之间的网格距离, 并且所有长程连接长度总和受到总能量∧=cN(c≥ 0)的约束, N为网络节点总数.通过研究该空间网络上的随机游走过程,存在最优幂指数α0 使得陷阱问题的平均首达时间最短.进一步研究发现,平均首达时间与网络规模N之间存在着幂律关系, 随着网络规模N和总能量∧的增加,最优幂指数α0单调增加,并趋近最优值1.5. 相似文献
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建立非线性择优连接非均齐超网络演化模型,研究非均齐超网络演化机制和拓扑性质.使用Poisson过程理论和连续化方法对模型进行分析,给出超网络超度的特征方程.利用超度特征方程不仅证明网络稳态平均超度分布存在,而且获得超度分布的解析表达式.分析表明这个网络具有"富者愈富"现象.仿真实验和理论分析相符合.随着网络规模的增大,这个动态演化的非均齐超网络的超度分布表现出拉直指数分布的特征,而不一定是幂律分布.结果表明"富者愈富"不一定导致幂律分布. 相似文献
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不同于经典扩散模型中节点传染力等同于节点度k的假定, 基于交通流量的病毒扩散模型中, 各个节点的传染力可以等同于节点实际介数bk. 利用平均场近似方法, 提出基于交通流量SIS病毒修正扩散模型. 根据修正SIS模型, 以最小搜索信息路由为例, 重新研究病毒传播率β, 平均发包率λ同传播阈值βc, 平稳状态病毒密度ρ之间的关系. 理论分析与实验结果均表明, 当网络拓扑和路由策略一定时, 传播阈值βc为实际介数bk的均值<bk>与其平方的均值<bk2>的比值. 而稳定状态时感染密度ρ同感染同病毒传播率β, 平均发包率λ 以及λ =1时节点实际介数的均值<bλ=1> 的乘积倒数存在幂率关系. 相似文献
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Ginestra Bianconi 《Pramana》2008,70(6):1135-1142
The structural entropy is the entropy of the ensemble of uncorrelated networks with given degree sequence. Here we derive
the most probable degree distribution emerging when we distribute stubs (or half-edges) randomly through the nodes of the
network by keeping fixed the structural entropy. This degree distribution is found to decay as a Poisson distribution when
the entropy is maximized and to have a power-law tail with an exponent γ → 2 when the entropy is minimized.
相似文献
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In this paper, a new evolving model with tunable attractiveness is presented. Based on the Barabasi—Albert (BA) model, we introduce the attractiveness of node which can change with node degree. Using the mean-field theory, we obtain the analytical expression of power-law degree distribution with the exponent γ ∈ (3,∞). The new model is more homogeneous and has a lower clustering coefficient and bigger average path length than the BA model. 相似文献
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Sander?Dommers Cristian?Giardinà Remco?van?der?Hofstad 《Journal of statistical physics》2010,141(4):638-660
We study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit
of the pressure when the mean degree is finite (degree exponent τ>2), for which the random graph has a tree-like structure. For this, we closely follow the analysis by Dembo and Montanari
(Ann. Appl. Probab. 20(2):565–592, 2010) which assumes finite variance degrees (τ>3), adapting it when necessary and also simplifying it when possible. Our results also apply in cases where the degree distribution
does not obey a power law. 相似文献
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《Physics letters. A》2006,360(1):174-178
Large-scale acquisition technologies in mRNA abundance (gene expression) have provided new opportunities to better understand many complex biological processes. Lately, it has been reported that the observed gene expression data in several organisms significantly deviates from a Poisson distribution and follows a power-law or fat-tailed distribution. Here, we show that a simple stochastic model of gene expression with intrinsic and extrinsic noise derives the stationary power-law distribution using the Stratonovich calculus. Furthermore, we connect the experimental measure of the power-law exponent with the value of the mRNA decay. Finally, we compare the results with other models where stochastic equations were used within the Ito interpretation. 相似文献
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Betweenness centrality in finite components of complex networks 总被引:1,自引:0,他引:1
We use generating function formalism to obtain an exact formula of the betweenness centrality in finite components of random networks with arbitrary degree distributions. The formula is obtained as a function of the degree and the component size, and is confirmed by simulations for Poisson, exponential, and power-law degree distributions. We find that the betweenness centralities for the three distributions are asymptotically power laws with an exponent 1.5 and are invariant to the particular distribution parameters. 相似文献
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This paper studies and predicts the number growth of China's mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well. 相似文献
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This work is devoted to the study of the scaling, and the consequent power-law behavior, of the correlation function in a mutation-replication model known as the expansion-modification system. The latter is a biology inspired random substitution model for the genome evolution, which is defined on a binary alphabet and depends on a parameter interpreted as a mutation probability. We prove that the time-evolution of this system is such that any initial measure converges towards a unique stationary one exhibiting decay of correlations not slower than a power-law. We then prove, for a significant range of mutation probabilities, that the decay of correlations indeed follows a power-law with scaling exponent smoothly depending on the mutation probability. Finally we put forward an argument which allows us to give a closed expression for the corresponding scaling exponent for all the values of the mutation probability. Such a scaling exponent turns out to be a piecewise smooth function of the parameter. 相似文献
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A.-H. Sato T. Hayashi 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,76(4):529-535
We investigate an association between a power-law
relationship of constituents’ flows (mean versus standard deviation) and their
covariance matrix on a directed bipartite network.
We propose a Poisson mixture
model and a method to infer states of the constituents’ flows on such a
bipartite network from empirical observation without a priori
knowledge on the network structure. By using a proposed parameter estimation
method with high frequency financial data we found that the scaling
exponent and simultaneous cross-correlation matrix have a positive
correspondence relationship. Consequently we conclude that the scaling
exponent tends to be 1/2 in the case of desynchronous (specific
dynamics is dominant), and to be 1 in the case of synchronous (common
dynamics is dominant). 相似文献