Surveying network community structure in the hidden metric space

Most real-world networks from various fields share a universal topological property as community structure. In this paper, we propose a node-similarity based mechanism to explore the formation of modular networks by applying the concept of hidden metric spaces of complex networks. It is demonstrated that network community structure could be formed according to node similarity in the underlying hidden metric space. To clarify this, we generate a set of observed networks using a typical kind of hidden metric space model. By detecting and analyzing corresponding communities both in the observed network and the hidden space, we show that the values of the fitness are rather close, and the assignments of nodes for these two kinds of community structures detected based on the fitness parameter are extremely matching ones. Furthermore, our research also shows that networks with strong clustering tend to display prominent community structures with large values of network modularity and fitness.     

Estimating the clustering coefficient in scale-free networks on lattices with local spatial correlation structure

When we study the architecture of networks of spatially extended systems the nodes in the network are subject to local correlation structures. In this case, we show that for scale-free networks the traditional way to estimate the clustering coefficient may not be meaningful. Here we explain why and propose an approach that corrects this problem.     

Detecting overlapping communities based on vital nodes in complex networks

Detection of community structures in the complex networks is significant to understand the network structures and analyze the network properties. However, it is still a problem on how to select initial seeds as well as to determine the number of communities. In this paper, we proposed the detecting overlapping communities based on vital nodes algorithm(DOCBVA), an algorithm based on vital nodes and initial seeds to detect overlapping communities. First, through some screening method, we find the vital nodes and then the seed communities through the pretreatment of vital nodes. This process differs from most existing methods, and the speed is faster. Then the seeds will be extended. We also adopt a new parameter of attribution degree to extend the seeds and find the overlapping communities. Finally, the remaining nodes that have not been processed in the first two steps will be reprocessed. The number of communities is likely to change until the end of algorithm. The experimental results using some real-world network data and artificial network data are satisfactory and can prove the superiority of the DOCBVA algorithm.     

Fairness and throughput performance of infrastructure IEEE 802.11 networks with hidden-nodes

The fairness behavior and throughput performance of IEEE 802.11 distributed coordination function and request-to-send/clear-to-send channel access scheme in the presence of hidden nodes are investigated. A mathematical model which accurately predicts a user’s throughput performance and packet collision probability in non-saturated traffic and asymmetric hidden node environments is developed. The model allows us to see many interesting results in networks with hidden nodes. In an asymmetric hidden node network environment, the network fairness performance depends on the traffic load. In low traffic conditions, users get their fair share of the resources. However, in moderate-to-high traffic conditions, users that experience less number of hidden nodes dominate the network, causing badly located stations in a network to starve. In addition, the performance of request-to-send/clear-to-send channel access scheme, which is developed as a solution to hidden node problem, in networks with hidden nodes, is also estimated. It is shown that request-to-send/clear-to-send contention resolution scheme greatly improves the network fairness performance in hidden node scenarios. The developed model enables us to more accurately estimate the performance of practical wireless local area networks, where hidden node occurrence is common. Theoretical analysis presented in the paper is validated with simulation results.     

定向传输水声通信网络介质访问控制协议

针对水声通信网络吞吐量低、通信隐蔽性差、隐藏终端等问题,提出一种定向传输水声通信网络介质访问控制(Medium Access Control,MAC)协议。协议中各节点采用定向模式传输数据,不需要邻节点位置等先验信息。通过发送节点顺序连续发送传输请求(Request To Send,RTS)信号、维护邻节点相对位置信息表及定向虚拟载波监测等技术实现网络高效无碰撞运行。本协议可有效解决水声通信网络中存在的由非对称增益导致的隐藏终端问题,增加网络覆盖范围,提高通信隐蔽性。仿真结果表明,所提MAC协议能够显著提高水声通信网络吞吐量性能。     

States and transitions in mixed networks

A network is named as mixed network if it is composed of N nodes, the dynamics of some nodes are periodic, while the others are chaotic. The mixed network with all-to-all coupling and its correspond- ing networks after the nonlinearity gap-condition pruning are investigated. Several synchronization states are demonstrated in both systems, and a first-order phase transition is proposed. The mixture of dynamics implies any kind of synchronous dynamics for the whole network, and the inixed networks may be controlled by the nonlinearity gap-condition pruning.     

Imperfect targeted immunization in scale-free networks

Scale-free networks are prone to epidemic spreading. To provide cost-effective protection for such networks, targeted immunization was proposed to selectively immunize the hub nodes. In many real-life applications, however, the targeted immunization may not be perfect, either because some hub nodes are hidden and consequently not immunized, or because the vaccination simply cannot provide perfect protection. We investigate the effects of imperfect targeted immunization in scale-free networks. Analysis and simulation results show that there exists a linear relationship between the inverse of the epidemic threshold and the effectiveness of targeted immunization. Therefore, the probability of epidemic outbreak cannot be significantly lowered unless the protection is reasonably strong. On the other hand, even a relatively weak protection over the hub nodes significantly decreases the number of network nodes ever getting infected and therefore enhances network robustness against virus. We show that the above conclusions remain valid where there exists a negative correlation between nodal degree and infectiousness.     

Grand Canonical Ensembles of Sparse Networks and Bayesian Inference

Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical models for exchangeable networks in the sparse limit, i.e., with the total number of links scaling linearly with the total number of nodes. The approach is grand canonical, i.e., the number of nodes of the network is not fixed a priori: it is finite but can be arbitrarily large. In this way the grand canonical network ensembles circumvent the difficulties in treating infinite sparse exchangeable networks which according to the Aldous-Hoover theorem must vanish. The approach can treat networks with given degree distribution or networks with given distribution of latent variables. When only a subgraph induced by a subset of nodes is known, this model allows a Bayesian estimation of the network size and the degree sequence (or the sequence of latent variables) of the entire network which can be used for network reconstruction.     

一种基于离散数据从局部到全局的网络重构算法

网络的结构和功能彼此相互影响,网络上的功能往往体现为网络上的动力学过程,网络上的动力学过程通过网络中的行为表象数据进行体现.因此,根据网络上可观测的相关数据对网络结构进行重构将成为可能.本文拟解决如何根据网络上可观测的离散数据还原网络拓扑结构的问题,提出了在网络局部利用每一条离散数据对应节点的相似程度来推测节点间发生连边的可能性,通过多条离散数据重构网络各个局部拓扑并将由多条数据得到的局部拓扑进行叠加,最终重构出整个网络的全局拓扑结构的算法.为了验证算法的可行性与准确性,在小世界、无标度和随机网络中进行了网络重构实验,通过在三种不同类型及不同规模的网络中进行网络重构实验可以看出,网络重构算法在不同类型网络中的表现也不同,且网络的平均度值也会影响网络重构算法对数据的要求.为了验证算法的适用性,对三个实际网络进行了网络重构实验,结果显示算法能够适用实际较大规模网络的重构.该算法具有很好的适用性和准确度,适合不同类型网络的拓扑结构重构场景.     

Adaptive synchronization of weighted complex dynamical networks through pinning

This paper considers the problem of controlling weighted complex dynamical networks by applying adaptive control to a fraction of network nodes. We investigate the local and global synchronization of the controlled dynamical network through the construction of a master stability function and a Lyapunov function. Analytical results show that a certain number of nodes can be controlled by using adaptive pinning to ensure the synchronization of the entire network. We present numerical simulations to verify the effectiveness of the proposed scheme. In comparison with feedback pinning, the proposed pinning control scheme is robust when tested by noise, different weighting and coupling structures, and time delays.     

Reconstruction of a random phase dynamics network from observations

We consider networks of coupled phase oscillators of different complexity: Kuramoto–Daido-type networks, generalized Winfree networks, and hypernetworks with triple interactions. For these setups an inverse problem of reconstruction of the network connections and of the coupling function from the observations of the phase dynamics is addressed. We show how a reconstruction based on the minimization of the squared error can be implemented in all these cases. Examples include random networks with full disorder both in the connections and in the coupling functions, as well as networks where the coupling functions are taken from experimental data of electrochemical oscillators. The method can be directly applied to asynchronous dynamics of units, while in the case of synchrony, additional phase resettings are necessary for reconstruction.     

Detecting and describing the modular structures of weighted networks

In the functional properties of complex networks, modules play a central role. In this paper, we propose a new method to detect and describe the modular structures of weighted networks. In order to test the proposed method, as an example, we use our method to analyse the structural properties of the Chinese railway network. Here, the stations are regarded as the nodes and the track sections are regarded as the links. Rigorous analysis of the existing data shows that using the proposed algorithm, the nodes of network can be classified naturally. Moreover, there are several core nodes in each module. Remarkably, we introduce the correlation function $G_{rs}$, and use it to distinguish the different modules in weighted networks.     

Rosenblatt’s First Theorem and Frugality of Deep Learning

The Rosenblatt’s first theorem about the omnipotence of shallow networks states that elementary perceptrons can solve any classification problem if there are no discrepancies in the training set. Minsky and Papert considered elementary perceptrons with restrictions on the neural inputs: a bounded number of connections or a relatively small diameter of the receptive field for each neuron at the hidden layer. They proved that under these constraints, an elementary perceptron cannot solve some problems, such as the connectivity of input images or the parity of pixels in them. In this note, we demonstrated Rosenblatt’s first theorem at work, showed how an elementary perceptron can solve a version of the travel maze problem, and analysed the complexity of that solution. We also constructed a deep network algorithm for the same problem. It is much more efficient. The shallow network uses an exponentially large number of neurons on the hidden layer (Rosenblatt’s A-elements), whereas for the deep network, the second-order polynomial complexity is sufficient. We demonstrated that for the same complex problem, the deep network can be much smaller and reveal a heuristic behind this effect.     

基于节点相关性的网络不动点理论研究

现代复杂的通信网络内部存在着广泛的幂律现象，网络节点之间存在相关特性. 根据这种相关特性，提出了网络不动点理论. 将Banach不动点理论引入网络模型，证明了网络不动点理论的正确有效性. 证明过程是把通信网络看作由路径预测算法产生的似马尔可夫链的路由节点迭代序列形成的网络空间. 由节点相关性可知，此空间中的节点序列相对越长就越能折射出搜索的目标所在，预测准确率也会逐步增加，可以更好地进行目标定位、数据挖掘等. 通过某种路由准则的算子从源节点最终映射到的目的节点与Banach空间的不动点相对应，即为网络空间的不动点. 当网络发展到能为用户提供真正的无处不在的连接时，网络不动点理论的物理特性将非常明显. 因为网络规模越大，节点间的群体作用越显著，就越能显现网络不动点理论的物理特性. 关键词： 计算机网络 长程相关 不动点 幂律     

A local-world heterogeneous model of wireless sensor networks with node and link diversity

In this paper, we present a novel local-world model of wireless sensor networks (WSN) with two kinds of nodes: sensor nodes and sink nodes, which is different from other models with identical nodes and links. The model balances energy consumption by limiting the connectivity of sink nodes to prolong the life of the network. How the proportion of sink nodes, different energy distribution and the local-world scale would affect the topological structure and network performance are investigated. We find that, using mean-field theory, the degree distribution is obtained as an integral with respect to the proportion of sink nodes and energy distribution. We also show that, the model exhibits a mixed connectivity correlation which is greatly distinct from general networks. Moreover, from the perspective of the efficiency and the average hops for data processing, we find some suitable range of the proportion p of sink nodes would make the network model have optimal performance for data processing.     

花簇分形无标度网络中节点影响力的区分度

大量研究表明分形尺度特性广泛存在于真实复杂系统中, 且分形结构显著影响网络上的传播动力学行为. 虽然复杂网络的节点传播影响力吸引了越来越多学者的关注, 但依旧缺乏针对分形网络结构的节点影响力的系统研究. 鉴于此, 本文基于花簇分形网络模型, 研究了分形无标度结构上的节点传播影响力. 首先, 对比了不同分形维数下的节点影响力, 结果表明, 当分形维数很小时, 节点影响力的区分度几乎不随节点度变化, 很难区分不同节点的传播影响力, 而随着分形维数的增大, 从全局和局域角度都能很容易识别网络中的超级传播源. 其次, 通过对原分形网络进行不同程度的随机重连来分析网络噪声对节点影响力区分度的影响, 发现在低维分形网络上, 加入网络噪声之后能够容易区分不同节点的影响力, 而在无穷维超分形网络中, 加入网络噪声之后能够区分中间度节点的影响力, 但从全局和局域角度都很难识别中心节点的影响力. 所得结论进一步补充、深化了基于花簇分形网络的节点影响力研究, 研究结果对实际病毒传播的预警控制提供了一定的理论借鉴.     

一种基于文本互信息的金融复杂网络模型

复杂网络能够解决许多金融问题,能够发现金融市场的拓扑结构特征,反映不同金融主体之间的相互依赖关系.相关性度量在金融复杂网络构建中至关重要.通过将多元金融时间序列符号化,借鉴文本特征提取以及信息论的方法,定义了一种基于文本互信息的相关系数.为检验方法的有效性,分别构建了基于不同相关系数(Pearson和文本互信息)和不同网络缩减方法(阈值和最小生成树)的4个金融复杂网络模型.在阈值网络中提出了使用分位数来确定阈值的方法,将相关系数6等分,取第4部分的中点作为阈值,此时基于Pearson和文本互信息的阈值模型将会有相近的边数,有利于这两种模型的对比.数据使用了沪深两地证券市场地区指数收盘价,时间从2006年1月4日至2016年12月30日,共计2673个交易日.从网络节点相关性看,基于文本互信息的方法能够体现出大约20%的非线性相关关系;在网络整体拓扑指标上,本文计算了4种指标,结果显示能够使所保留的节点联系更为紧密,有效提高保留节点的重要性以及挖掘出更好的社区结构;最后,计算了阈值网络的动态指标,将数据按年分别构建网络,缩减方法只用了阈值方法,结果显示本文提出的方法在小世界动态和网络度中心性等指标上能够成功捕捉到样本区间内存在的两次异常波动.此外,本文构建的地区金融网络具有服从幂律分布、动态稳定性、一些经济欠发达地区在金融地区网络中占据重要地位等特性.     

Deep Link-Prediction Based on the Local Structure of Bipartite Networks

Link prediction based on bipartite networks can not only mine hidden relationships between different types of nodes, but also reveal the inherent law of network evolution. Existing bipartite network link prediction is mainly based on the global structure that cannot analyze the role of the local structure in link prediction. To tackle this problem, this paper proposes a deep link-prediction (DLP) method by leveraging the local structure of bipartite networks. The method first extracts the local structure between target nodes and observes structural information between nodes from a local perspective. Then, representation learning of the local structure is performed on the basis of the graph neural network to extract latent features between target nodes. Lastly, a deep-link prediction model is trained on the basis of latent features between target nodes to achieve link prediction. Experimental results on five datasets showed that DLP achieved significant improvement over existing state-of-the-art link prediction methods. In addition, this paper analyzes the relationship between local structure and link prediction, confirming the effectiveness of a local structure in link prediction.     

基于全卷积金字塔残差网络的能谱CT图像降噪研究

传统CT采用积分式探测器采集投影数据,反映的是物体的平均衰减特性,会在一定程度上造成信息损失,无法对物体进行较好的定性定量测量。基于光子计数探测器的能谱CT通过设定多个能量响应阈值能够探测不同能量范围内的X射线光子,采集更多被测物体的物质组成信息,有助于识别不同物理特性的材料,基于此,能谱CT被广泛的应用于小病灶、低对比度结构以及微细结构的成像。然而将整个能谱划分为多个能量段进行数据采集时,范围较窄能量范围内的有效光子数比例相对降低,导致图像中包含较多的噪声,图像质量较差,影响能谱CT的临床应用。为了有效的抑制能谱CT不同能量段内重建图像中的噪声,提出了一种基于深度学习的能谱CT图像降噪方法。我们将全卷积网络和金字塔残差网络结合为全卷积金字塔残差网络(FCPRN),实验中,利用能谱CT在不同的能量范围扫描小鼠样本,使用FDK算法和基于压缩感知的Split-Bregman算法进行重建并分别作为训练数据和标签数据训练全卷积金字塔残差网络。为了验证网络的降噪性能,选取了常见的降噪网络模型denoising convolutional neural networks(DNCN)以及residual encoder decoder convolutional neural network (REDCNN)进行对比,训练三种网络的使用的数据和实验配置都是完全相同的,实验结果表明训练模型可以有效抑制不同能量范围内重建图像的噪声,且使用的全卷积金字塔残差网络的降噪性能优于其他网络模型。模型训练好后,可以对FDK算法重建出的图像进行降噪,由此提高能谱CT图像降噪效率,保证能谱CT重建图像的质量。     

LCH: A local clustering H-index centrality measure for identifying and ranking influential nodes in complex networks

Identifying influential nodes in complex networks is one of the most significant and challenging issues, which may contribute to optimizing the network structure, controlling the process of epidemic spreading and accelerating information diffusion. The node importance ranking measures based on global information are not suitable for large-scale networks due to their high computational complexity. Moreover, they do not take into account the impact of network topology evolution over time, resulting in limitations in some applications. Based on local information of networks, a local clustering H-index (LCH) centrality measure is proposed, which considers neighborhood topology, the quantity and quality of neighbor nodes simultaneously. The proposed measure only needs the information of first-order and second-order neighbor nodes of networks, thus it has nearly linear time complexity and can be applicable to large-scale networks. In order to test the proposed measure, we adopt the susceptible-infected-recovered (SIR) and susceptible-infected (SI) models to simulate the spreading process. A series of experimental results on eight real-world networks illustrate that the proposed LCH can identify and rank influential nodes more accurately than several classical and state-of-the-art measures.