二分网上的靴襻渗流

靴襻渗流最早应用于统计物理学中研究磁铁因非磁性杂质导致磁有序的降低并最终消失的现象. 随着复杂网络研究的深入, 许多学者展开网络上的靴襻渗流研究. 在自然界中, 许多系统自然呈现出二分结构, 二分网络是复杂网络中的一种重要的网络模式. 本文通过建立动力学方程和计算机仿真模拟的方法研究二分网上的靴襻渗流, 关注的参数是二分网中两类节点初始的活跃比例和活跃阈值, 分别用f₁, f₂和Ω₁, Ω₂表示, 得到二分网两类节点终态活跃比例随初始活跃比例的变化会发生相变等结论. 同时 验证了动力学方程与仿真模拟的一致性.     

Percolation on bipartite scale-free networks

Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type. Such bipartite graphs appear in many social networks, for instance in affiliation networks and in sexual-contact networks in which both types of nodes show the scale-free characteristic for the degree distribution. During the depreciation process, an edge between nodes with degrees k and q is retained with a probability proportional to (kq)^−α, where α is positive so that links between hubs are more prone to failure. The removal process is studied analytically by introducing a generating functions theory. We deduce exact self-consistent equations describing the system at a macroscopic level and discuss the percolation transition. Critical exponents are obtained by exploiting the Fortuin-Kasteleyn construction which provides a link between our model and a limit of the Potts model.     

A general evolving model for growing bipartite networks

In this Letter, we propose and study an inner evolving bipartite network model. Significantly, we prove that the degree distribution of two different kinds of nodes both obey power-law form with adjustable exponents. Furthermore, the joint degree distribution of any two nodes for bipartite networks model is calculated analytically by the mean-field method. The result displays that such bipartite networks are nearly uncorrelated networks, which is different from one-mode networks. Numerical simulations and empirical results are given to verify the theoretical results.     

An evolving model of online bipartite networks

Understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e-commerce services nowadays. Recently, various attempts have been tried to propose different models, resulting in either power-law or exponential degree distributions. However, many empirical results show that the user degree distribution actually follows a shifted power-law distribution, the so-called Mandelbrot’s law, which cannot be fully described by previous models. In this paper, we propose an evolving model, considering two different user behaviors: random and preferential attachment. Extensive empirical results on two real bipartite networks, Delicious and CiteULike  , show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions. In addition, we introduce a structural parameter p$p$, to demonstrate that the hybrid user behavior leads to the shifted power-law degree distribution, and the region of power-law tail will increase with the increment of p$p$. The proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks.     

Effects of high-order correlations on personalized recommendations for bipartite networks

In this paper, we introduce a modified collaborative filtering (MCF) algorithm, which has remarkably higher accuracy than the standard collaborative filtering. In the MCF, instead of the cosine similarity index, the user-user correlations are obtained by a diffusion process. Furthermore, by considering the second-order correlations, we design an effective algorithm that depresses the influence of mainstream preferences. Simulation results show that the algorithmic accuracy, measured by the average ranking score, is further improved by 20.45% and 33.25% in the optimal cases of MovieLens and Netflix data. More importantly, the optimal value depends approximately monotonously on the sparsity of the training set. Given a real system, we could estimate the optimal parameter according to the data sparsity, which makes this algorithm easy to be applied. In addition, two significant criteria of algorithmic performance, diversity and popularity, are also taken into account. Numerical results show that as the sparsity increases, the algorithm considering the second-order correlation can outperform the MCF simultaneously in all three criteria.     

在二部无标度网上的两性疾病传播

利用易感-感染-易感(SIS)传播模型研究人类性接触网上的病毒传播.当仅仅考虑异性性接触时,该网络是一个二部的无标度网.对这个网络上的SIS传播模型,通过率方程的方法分析了男性感染率和女性感染率与传染阈值之间的关系,发现女性感染者与男性感染者之比由网络的拓扑和男女感染率之比所确定.这一结果表明性接触网的拓扑对性传染病传播的重要性.最后给出了支持理论结果的数值模拟. 关键词： 性传染病 两性性接触网 无标度网络 二部图     

Effect of attachment strategies on bipartite networks

Bipartite systems show remarkable variations in their topological asymptotic properties,e.g., in their degree distribution. Such variations depend on the underlying growthdynamics. A scenario of particular importance is when the two partitions of the bipartitestructure do not grow at an equal rate. Here, we focus on the case where one of thepartitions can be assumed to be fixed while the other partition grows in time as observedin the codon-gene or alphabet-word network. We show that subtle changes in growthdynamics, particularly in the attachment kernel, can lead to drastic changes of theemergent topological properties. We present a detail analysis of various growthstrategies, including sequential and parallel addition of nodes, as well as with andwithout replacement attachment kernels. Analytical results have been compared withstochastic simulations as well as with real systems showing in all cases an excellentagreement.     

On the degree distribution of projected networks mapped from bipartite networks

Many real-world systems can be represented by bipartite networks. In a bipartite network, the nodes are divided into two disjoint sets, and the edges connect nodes that belong to different sets. Given a bipartite network (i.e. two-mode network) it is possible to construct two projected networks (i.e. one-mode networks) where each one is composed of only one set of nodes. While network analyses have focused on unipartite networks, considerably less attention has been paid to the analytical study of bipartite networks. Here, we analytically derive simple mathematical relationships that predict degree distributions of the projected networks by only knowing the structure of the original bipartite network. These analytical results are confirmed by computational simulations using artificial and real-world bipartite networks from a variety of biological and social systems. These findings offer in our view new insights into the structure of real-world bipartite networks.     

Clustering coefficient and community structure of bipartite networks

Many real-world networks display natural bipartite structure, where the basic cycle is a square. In this paper, with the similar consideration of standard clustering coefficient in binary networks, a definition of the clustering coefficient for bipartite networks based on the fraction of squares is proposed. In order to detect community structures in bipartite networks, two different edge clustering coefficients LC₄ and LC₃ of bipartite networks are defined, which are based on squares and triples respectively. With the algorithm of cutting the edge with the least clustering coefficient, communities in artificial and real world networks are identified. The results reveal that investigating bipartite networks based on the original structure can show the detailed properties that is helpful to get deep understanding about the networks.     

Comparison of methods for the detection of node group membership in bipartite networks

Most real-world networks considered in the literature have a modular structure. Analysis of these real-world networks often are performed under the assumption that there is only one type of node. However, social and biochemical systems are often bipartite networks, meaning that there are two exclusive sets of nodes, and that edges run exclusively between nodes belonging to different sets. Here we address the issue of module detection in bipartite networks by comparing the performance of two classes of group identification methods – modularity maximization and clique percolation – on an ensemble of modular random bipartite networks. We find that the modularity maximization methods are able to reliably detect the modular bipartite structure, and that, under some conditions, the simulated annealing method outperforms the spectral decomposition method. We also find that the clique percolation methods are not capable of reliably detecting the modular bipartite structure of the bipartite model networks considered.     

基于二分图的温度网络拓扑性质研究

利用中国地区435个台站1961—2002年逐日平均温度序列,将温度变化发生在9天时间尺度上的特征编码在网络中,通过研究二分图温度网络(BGT网络)中节点与项目的关系,揭示出9天时间尺度上温度变化的特征及其在空间上的拓扑统计性质.网络中各节点RRRD, RrDD, eeed, DRRD, DDRR等所代表的温度波动模态在网络中异常频发,对9天尺度温度变化的预报有一定的指导意义.统计网络的节点度分布,集群系数等拓扑结构特征量,发现BGT网络服从正态分布特征.BGT网络项目内节点度的多样性大体上 关键词： 二分图温度网络 气候系统 拓扑结构     

Personal recommendation via unequal resource allocation on bipartite networks

In this paper, we present a recommendation algorithm based on the resource-allocation progresses on bipartite networks. In this model, each node is assigned an attraction that is proportional to the power of its degree, where the exponent β is an adjustable parameter that controls the configuration of attractions. In the resource-allocation process, each transmitter distributes its each neighbor a fragment of resource that is proportional to the attraction of the neighbor. Based on a benchmark database, we find that decreasing the attractions that the nodes with higher degrees are assigned can further improve the algorithmic accuracy. More significantly, numerical results show that the optimal configuration of attractions subject to accuracy can also generate more diverse and less popular recommendations.     

A uniform framework of projection and community detection for one-mode network in bipartite networks

Projection is a widely used method in bipartite networks. However, each projection has a specific application scenario and differs in the forms of mapping for bipartite networks. In this paper, inspired by the network-based information exchange dynamics, we propose a uniform framework of projection. Subsequently, an information exchange rate projection based on the nature of community structures of a network(named IERCP) is designed to detect community structures of bipartite networks. Results from the synthetic and real-world networks show that the IERCP algorithm has higher performance compared with the other projection methods. It suggests that the IERCP may extract more information hidden in bipartite networks and minimize information loss.     

An analytic approach to the measurement of nestedness in bipartite networks

We present an index that measures the nestedness pattern of bipartite networks, a problem that arises in theoretical ecology. Our measure is derived using the sum of distances of the occupied elements in the incidence matrix of the network. This index quantifies directly the deviation of a given matrix from the nested pattern. In the simplest case the distance of the matrix element a_i,j is d_i,j=i+j, the Manhattan distance. A generic distance is obtained as d_i,j=(i^χ+j^χ)^1/χ. The nestedness index is defined by ν=1−τ, where τ is the “temperature” of the matrix. We construct the temperature index using two benchmarks: the distance of the complete nested matrix that corresponds to zero temperature and the distance of the average random matrix where the temperature is defined as one. We discuss an important feature of the problem: matrix occupancy ρ. We address this question using a metric index χ that adjusts for matrix occupancy.     

Effect of the social influence on topological properties of user-object bipartite networks

Social influence plays an important role in analyzing online users’ collective behaviors[Salganik et al., Science 311, 854 (2006)]. However, the effect of the socialinfluence from the viewpoint of theoretical model is missing. In this paper, by takinginto account the social influence and users’ preferences, we develop a theoretical modelto analyze the topological properties of user-object bipartite networks, including thedegree distribution, average nearest neighbor degree and the bipartite clusteringcoefficient, as well as topological properties of the original user-object networks andtheir unipartite projections. According to the users’ preferences and the global rankingeffect, we analyze the theoretical results for two benchmark data sets, Amazon andBookcrossing, which are approximately consistent with the empirical results. This worksuggests that this model is feasible to analyze topological properties of bipartitenetworks in terms of the social influence and the users’ preferences.     

Identifying missing and spurious connections via the bi-directional diffusion on bipartite networks

Link prediction and spurious link detection in complex networks have attracted increasing attention from both physical and computer science communities, due to their wide applications in many real systems. Related previous works mainly focus on monopartite networks while these problems in bipartite networks are not yet systematically addressed. Containing two different kinds of nodes, bipartite networks are essentially different from monopartite networks, especially in node similarity calculation: the similarity between nodes of different kinds (called inter-similarity) is not well defined. In this letter, we employ the local diffusion processes to measure the inter-similarity in bipartite networks. We find that the inter-similarity is asymmetric if the diffusion is applied in different directions. Accordingly, we propose a bi-directional hybrid diffusion method which is shown to achieve higher accuracy than the existing diffusion methods in identifying missing and spurious links in bipartite networks.     

Inseparability criteria for continuous bipartite quantum states

We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under study. The violation of any inequality of this series is a sufficient condition for entanglement. Previously known entanglement conditions are shown to be special cases of our approach.     

Quantum nondemolition circuit for testing bipartite complementarity

We present a quantum circuit that implements a nondemolition measurement of complementary single- and bipartite properties of a two-qubit system: entanglement and single-partite visibility and predictability. The system must be in a pure state with real coefficients in the computational basis, which allows a direct operational interpretation of those properties. The circuit can be realized in many systems of interest to quantum information.     

General monogamy inequality for bipartite qubit entanglement

We consider multipartite states of qubits and prove that their bipartite quantum entanglement, as quantified by the concurrence, satisfies a monogamy inequality conjectured by Coffman, Kundu, and Wootters. We relate this monogamy inequality to the concept of frustration of correlations in quantum spin systems.     

Synthetic popularity reflects chemical reactivity

Large and diverse databases of chemical reactions contain statistically significant information about the propensities of molecules to undergo specific chemical transformations. It is shown that this information can be quantified to reflect reaction thermodynamics/kinetics and can be used to construct primitive (yet accurate) reactivity indices from the counts of reported reactions involving molecules/molecular positions of interest. These indices correlate with frontier orbital (FO) populations or Hammett σ and ρ parameters for a range of reactions involving aromatic substrates. These findings suggest that large chemical databases are not only a historical repository of chemical knowledge but also tools with which one can make useful chemical predictions. Copyright © 2009 John Wiley & Sons, Ltd.