Small World Effects in a Harmonious Unifying Hybrid Preferential Model Networks

Small worm effects in the harmonious unifying hybrid preferential model （HUHPM） networks are studied both numerically and analytically. The idea and method of the HUHPM is applied to three typical examples of unweighted BA model, weighted BBV model, and the TDE rnodel, so-called HUHPM-BA, HUHPM-BBV and HUHPM- TDE networks. Comparing the HUHPM with current typical models above, it is found that the HUHPM networks has the smallest average path length and the biggest average clustering coefficient. The results demonstrate that the HUHPM is more suitable not only for the un-iveighted models but also for the weighted models.     

A harmonious unifying hybrid preferential model and its universal properties for complex dynamical networks

To describe the real world which is a harmonious unification world with both de- terminism and randomness, we propose a harmonious unifying hybrid preferential model (HUHPM) of a certain class of complex dynamical networks. HUHPM is gov- erned only by the total hybrid ratio d/r according to the practical need. As some typical examples, the concepts and methods of the HUHPM are applied to the un-weighted BA model proposed by Barabási et al., the weighted BBV model pro- posed by Barat et al. and the weighted TDE model proposed by Wang et al. to get the so-called HUHPM-BA network, HUHPM-BBV network and HUHPM-TDE network. These HUHPM networks are investigated both analytically and numerically. It is found that the HUHPM reveals several universal properties, which more approach to the real-world networks for both un-weighted and weighted networks and have potential for applications.     

Sensitivity of Exponents of Three-Power Laws to Hybrid Ratio in Weighted HUHPM

The sensitivity of exponents of three-power laws for node degree, node strength and edged weight to hybrid ratio are studied analytically and numerically in the weighted harmonious unifying hybrid preferential model （HUHPM）, which is extended from an-weighted hybrid preferential attachment model we proposed previously [Chin. Phys. Lett. 22 （2005）719]. Our weighted HUHPMs plus the Barrat-Barthelemy-Vespignani model and the traffic-driven evolution model, respectively, are taken as two typical examples for demonstration and application of the HUHPM.     

An improved model for structural vulnerability analysis of power networks

Electric power networks have been studied as a typical example of real-world complex networks. Traditional models for structural vulnerability analysis appear to be all based on physical topological structure. In this paper, we depict a typical power network as a weighted graph based on electrical topology by introducing its bus admittance matrix, which embodies the important characteristics of power networks in a much more realistic structure. Furthermore, the numerical simulation for both the traditional dynamical model and the proposed electrical topological model are investigated based on the IEEE 300 bus system respectively. The comparison demonstrates that the improved model is more precise and highly efficient for the analysis of structural vulnerability of power networks.     

Weighted coupling for geographical networks: Application to reducing consensus time in sensor networks

Although many complex real-world networks are weighted, unweighted networks are used in many applications such as sensor networks. In this Letter it is shown using properly weighted networks the performance can be greatly enhanced by reducing the time necessary for the average consensus. Random geographical models are adapted as network models and a method based on mutually coupled phase oscillators is used for providing average consensus over the network. The consensus time is calculated by numerically solving the network's differential equations and monitoring the average error. The simulation results on some sample networks show that the consensus time is dramatically reduced when the proposed weights are used for the links of the underlying network.     

An LCOR model for suppressing cascading failure in weighted complex networks

Based on the relationship between capacity and load, cascading failure on weighted complex networks is investigated, and a load-capacity optimal relationship (LCOR) model is proposed in this paper. Compared with three other kinds of load-capacity linear or non-linear relationship models in model networks as well as a number of real-world weighted networks including the railway network, the airports network and the metro network, the LCOR model is shown to have the best robustness against cascading failure with less cost. Furthermore, theoretical analysis and computational method of its cost threshold are provided to validate the effectiveness of the LCOR model. The results show that the LCOR model is effective for designing real-world networks with high robustness and less cost against cascading failure.     

The influence of tie strength on evolutionary games on networks: An empirical investigation

Extending previous work on unweighted networks, we present here a systematic numerical investigation of standard evolutionary games on weighted networks. In the absence of any reliable model for generating weighted social networks, we attribute weights to links in a few ways supported by empirical data ranging from totally uncorrelated to weighted bipartite networks. The results of the extensive simulation work on standard complex network models show that, except in a case that does not seem to be common in social networks, taking the tie strength into account does not change in a radical manner the long-run steady-state behavior of the studied games. Besides model networks, we also included a real-life case drawn from a coauthorship network. In this case also, taking the weights into account only changes the results slightly with respect to the raw unweighted graph, although to draw more reliable conclusions on real social networks many more cases should be studied as these weighted networks become available.     

Average weighted receiving time in recursive weighted Koch networks

Motivated by the empirical observation in airport networks and metabolic networks, we introduce the model of the recursive weighted Koch networks created by the recursive division method. As a fundamental dynamical process, random walks have received considerable interest in the scientific community. Then, we study the recursive weighted Koch networks on random walk i.e., the walker, at each step, starting from its current node, moves uniformly to any of its neighbours. In order to study the model more conveniently, we use recursive division method again to calculate the sum of the mean weighted first-passing times for all nodes to absorption at the trap located in the merging node. It is showed that in a large network, the average weighted receiving time grows sublinearly with the network order.     

Synchronization in Triangled Complex Networks

Using a tunable clustering coefficient model without changing the degree distribution, we investigate the effect of clustering coefficient on synchronization of networks with both unweighted and weighted couplings. For several typical categories of complex networks, the more triangles are in the networks, the worse the synchronizability of the networks is.     

Statistical Ensembles for Economic Networks

Economic networks share with other social networks the fundamental property of sparsity. It is well known that the maximum entropy techniques usually employed to estimate or simulate weighted networks produce unrealistic dense topologies. At the same time, strengths should not be neglected, since they are related to core economic variables like supply and demand. To overcome this limitation, the exponential Bosonic model has been previously extended in order to obtain ensembles where the average degree and strength sequences are simultaneously fixed (conditional geometric model). In this paper a new exponential model, which is the network equivalent of Boltzmann ideal systems, is introduced and then extended to the case of joint degree-strength constraints (conditional Poisson model). Finally, the fitness of these alternative models is tested against a number of networks. While the conditional geometric model generally provides a better goodness-of-fit in terms of log-likelihoods, the conditional Poisson model could nevertheless be preferred whenever it provides a higher similarity with original data. If we are interested instead only in topological properties, the simple Bernoulli model appears to be preferable to the correlated topologies of the two more complex models.     

Recursive weighted treelike networks

We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical results indicate that the resulting networks have power-law distributions of degree, strength, weight and betweenness, a scale-free behavior for degree correlations, logarithmic small average path length and diameter with network size. The obtained properties are in agreement with empirical data observed in many real-life networks, which shows that the presented model may provide valuable insight into the real systems.     

Entropy and HUHPM approach for complex networks

The general formulas of the network for the power exponents of the degree distribution and the entropy are presented based on an open Liouville equation for the driven network. The proposed harmonious unifying hybrid preferential models (HUHPM) have been studied using the obtained formalism, in which the simulating results are quite consistent with the theoretical results.     

Scaling of average receiving time and average weighted shortest path on weighted Koch networks

In this paper we present weighted Koch networks based on classic Koch networks. A new method is used to determine the average receiving time (ART), whose key step is to write the sum of mean first-passage times (MFPTs) for all nodes to absorption at the trap located at a hub node as a recursive relation. We show that the ART exhibits a sublinear or linear dependence on network order. Thus, the weighted Koch networks are more efficient than classic Koch networks in receiving information. Moreover, average weighted shortest path (AWSP) is calculated. In the infinite network order limit, the AWSP depends on the scaling factor. The weighted Koch network grows unbounded but with the logarithm of the network size, while the weighted shortest paths stay bounded.     

基于深度反向投影的感知增强超分辨率重建模型

以SRCNN（super-resolution convolutional neural network）模型为代表的超分辨率重建模型通常都有很高的PSNR（peak signal to noise ratio）和SSIM（structural similarity）值，但其在视觉感知上并不令人满意，而以SRGAN为代表的拥有高感知质量的GAN（generative adversarial networks）模型却很容易产生大量的伪细节，这表现在其PSNR和SSIM值通常都较低。针对上述问题，提出了一种基于深度反向投影的感知增强超分辨率重建模型。该模型采用双尺度自适应加权融合特征提取模块进行特征提取，然后通过深度反向投影进行上采样，最终由增强模块增强后得到最终输出。模型采用残差连接与稠密连接，有助于特征的共享以及模型的有效训练。在指标评价上，引入了基于学习的LPIPS（learned perceptual image patch similarity）度量作为新的图像感知质量评价指标，与PSNR、SSIM一起作为模型评价指标。实验结果表明，模型在测试数据集上PSNR、SSIM、LPIPS的平均值分别为27.84、0.7320、0.1258，各项指标均优于对比算法。     

A Mixed Mechanism of Weighted-Driven and Inner Selection in Networks

For most networks, the weight of connection is changing with their attachment and inner affinity. By introducing a mixed mechanism of weighted-driven and inner selection, the model exhibits wide range power-law distributions of node strength and edge weight, and the exponent can be adjusted by not only the parameter δ but also the probability q. Furthermore, we investigate the weighted average shortest distance, clustering coefficient, and the correlation of our network. In addition, the weighted assortativity coefficient which characterizes important information of weighted topological networks has been discussed, but the variation of coefficients is much smaller than the former researches.     

Improving consensus and synchronizability of networks of coupled systems via adding links

The problem of improving the consensus and synchronizability for weighted networks of dynamic systems via adding links among them is investigated in this paper. A weighted network entropy is introduced to measure the homogeneity of the weighted networks. The relationship between the homogeneity and the consensus and synchronizability is analyzed. A solution scheme is proposed to improve the consensus and synchronizability of the weighted networks through maximizing their homogeneity via adding as few links as possible. Weighted networks created from the Barrat model are tested by using the proposed scheme, and two commonly used link-adding approaches are selected to compare with this scheme. Computer simulation results show that the proposed link-adding scheme can enhance the consensus and the synchronizability of the weighted networks effectively and efficiently.     

一类高聚类系数的加权无标度网络及其同步能力分析

针对真实世界中大规模网络都具有明显聚类效应的特点, 提出一类具有高聚类系数的加权无标度网络演化模型, 该模型同时考虑了优先连接、三角结构、随机连接和社团结构等四种演化机制. 在模型演化规则中, 以概率p增加单个节点, 以概率1–p增加一个社团. 与以往研究的不同在于新边的建立, 以概率φ在旧节点之间进行三角连接, 以概率1–φ进行随机连接. 仿真分析表明, 所提出的网络度、强度和权值分布都是服从幂律分布的形式, 且具有高聚类系数的特性, 聚类系数的提高与社团结构和随机连接机制有直接的关系. 最后通过数值仿真分析了网络演化机制对同步动态特性的影响, 数值仿真结果表明, 网络的平均聚类系数越小, 网络的同步能力越强. 关键词： 无标度网络 加权网络 聚类系数 同步能力     

粉末涂料电脑配色的人工神经网络模型

提出一种基于多层BP人工神经网络的粉末涂料配方预测模型;用BP算法人工神经网络建立粉末涂料反射样品的标准色度参数与配方浓度参数之间的映射关系。把人工神经网络的配方预测模型应用到典型的粉末涂料样品的测配色实验过程中。实验结果表明,基于多隐层BP网的模型可以实现粉末涂料样品的配方浓度空间与标准三刺激值颜色空间的相互映射,对64个节点的平均训练精度达到了1个CIELAB色差单位。     

Synchronization in weighted complex networks: Heterogeneity and synchronizability

Synchronization in different types of weighted networks based on a scale-free weighted network model is investigated. It has been argued that heterogeneity suppresses synchronization in unweighted networks [T. Nishikawa, A.E. Motter, Y.C. Lai, F.C. Hoppensteadt, Phys. Rev. Lett. 91 (2003) 014101]. However, it is shown in this work that as the network becomes more heterogeneous, the synchronizability of Type I symmetrically weighted networks, and Type I and Type II asymmetrically weighted networks is enhanced, while the synchronizability of Type II symmetrically weighted networks is weakened.