Sandpile Dynamics Driven by Degree on Scale-Free Networks

We introduce a sandpile model driven by degree on scale-free networks, where the perturbation is triggered at nodes with the same degree. We numerically investigate the avalanche behaviour of sandpile driven by different degrees on scale-free networks. It is observed that the avalanche area has the same behaviour with avalanche size. When the sandpile is driven at nodes with the minimal degree, the avalanches of our model behave similarly to those of the original Bak-Tang-Wiesenfeld （BTW） model on scale-free networks. As the degree of driven nodes increases from the minimal value to the maximal value, the avalanche distribution gradually changes from a clean power law, then a mixture of Poissonian and power laws, finally to a Poisson-like distribution. The average avalanche area is found to increase with the degree of driven nodes so that perturbation triggered on higher-degree nodes will result in broader spreading of avalanche propagation.     

Influence of Blurred Ways on Pattern Recognition of a Scale-Free Hopfield Neural Network

We investigate the influence of blurred ways on pattern recognition of a Barabasi-Albert scale-free Hopfield neural network （SFHN） with a small amount of errors. Pattern recognition is an important function of information processing in brain. Due to heterogeneous degree of scale-free network, different blurred ways have different influences on pattern recognition with same errors. Simulation shows that among partial recognition, the larger loading ratio （the number of patterns to average degree P/ （k） ） is, the smaller the overlap of SFHN is. The influence of directed （large） way is largest and the directed （small） way is smallest while random way is intermediate between them. Under the ratio of the numbers of stored patterns to the size of the network PIN is less than O. 1 conditions, there are three families curves of the overlap corresponding to directed （small）, random and directed （large） blurred ways of patterns and these curves are not associated with the size of network and the number of patterns. This phenomenon only occurs in the SFHN. These conclusions are benefit for understanding the relation between neural network structure and brain function.     

A local-world evolving hypernetwork model

Complex hypernetworks are ubiquitous in the real system. It is very important to investigate the evolution mechanisms. In this paper, we present a local-world evolving hypernetwork model by taking into account the hyperedge growth and local-world hyperedge preferential attachment mechanisms. At each time step, a newly added hyperedge encircles a new coming node and a number of nodes from a randomly selected local world. The number of the selected nodes from the local world obeys the uniform distribution and its mean value is m. The analytical and simulation results show that the hyperdegree approximately obeys the power-law form and the exponent of hyperdegree distribution is γ = 2 + 1/m. Furthermore, we numerically investigate the node degree, hyperedge degree, clustering coefficient, as well as the average distance, and find that the hypernetwork model shares the scale-free and small-world properties, which shed some light for deeply understanding the evolution mechanism of the real systems.     

ANISOTROPIC CHARACTERISTICS OF DEMAGNETIZATION CURVE FOR NANOCRYSTALLINE Nd-Fe-B MAGNET CALCULATED BY MICROMAGNETICS

The demagnetization curves for nanocrystalline Nd-Fe-B magnets of a stoichiometric composition were calculated by making use of the finite element technique of micromagnetics. The curve, especially _iH_c, varies in a wide range with the direction of applied field if the grain number N is taken to be small. With the increase of N, the range becomes smaller and the average of _iH_c decreases and approaches a limit _iH_c(N=∞). _iH_c for finite N is larger than, or at least equal to, _iH_c(N=∞). J_r/J_s is weakly affected by N and the field direction. J_r/J_s(N=∞) decreases with the increase of grain size L. These are larger than the experimental values for the Nd-rich Nd_2.33Fe₁₄B_1.06Si_0.21 magnets by ～0.05. _iH_c(N=∞) increases with the increase of L, and is close to or somewhat smaller than the experimental values of the Nd-rich magnet, as would be expected. In contrast, the curve calculated for the non-interacting grain system (Stoner-Wohlfarth model) of N≥30 depends neither on the field direction nor on N.     

Poor rich demarcation of Matthew effect on scale-free systems and its application

In a scale-free network,only a minority of nodes are connected very often,while the majority of nodes are connected rarely. However,what is the ratio of minority nodes to majority nodes resulting from the Matthew effect In this paper,based on a simple preferential random model,the poor-rich demarcation points are found to vary in a limited range,and form a poor-rich demarcation interval that approximates to k/m ∈ [3,4]. As a result,the (cumulative) degree distribution of a scale-free network can be divided into three intervals: the poor interval,the demarcation interval and the rich interval. The inequality of the degree distribution in each interval is measured. Finally,the Matthew effect is applied to the ABC analysis of project management.     

Two—phase flow in correlated pore—throat random porous media

We have constructed a porous media model in which there are percolation clusters with varying percolation probability P and correlated site-bonds. Taking into account both the pore and the throat geometry, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme. The simulation results show that the VF structure varies with the correlation parameter ε, the viscosity ratio M and the percolation probability P. The smaller the correlation parameter ε, the greater the deviation of the normalized size distribution of the invaded throat N_inv(r) from the truncated Rayleigh distribution. For a larger viscosity ratio M, the VF pattern looks like a diffusion-limited-aggregation structure in percolation clusters. The fractal dimension D increases with the increase of the percolation probability P and the correlation parameter ε. The velocity distribution f(α) of VF in percolation clusters is of a parabola-like curve. The tail of the distribution (large α) is longer for a larger correlation parameter ε. For a smaller ε, the distribution is very sharp. The sweep efficiency E decreases along with the decrease of the correlation parameter ε and the increase of the network size L_nz. E has a minimum as L_nz increases up to the maximum no matter what the values of P, M and ε. The E～ L_nz curve has a frozen zone and an active zone. The geometry and the topology of the porous media have strong effects on the displacement processes and the structure of VF.     

The principle of the Internet evolving and the conjecture of the optimal structure of Internet

In this paper we will give the statistical characteristics and general principles of an optimal structure of the Internet, which is a scale-free network. Since the purpose of the Internet is to allow fast and easy communication, the average path length is used to measure the performance of the network, and the number of edges of the network is used as a metric of its cost. Based on this, the goal of this Internet optimization problem is to obtain the highest performance with the lowest cost. A multi goal optimization problem is proposed to model this problem. By using two empirical formulas of and , we are able to find the statistical characteristics of the optimal structure. There is a critical power law exponent α _c for the Internet with power law degree distribution, at which the Internet can obtain a relatively good performance with a low cost. We find that this α _c is approximately 2.1.     

Random and Preferential Attachment Networks with Aging

A new model for network generation is proposed by considering both the preferential and random attachments with aging. The connectivity distribution is obtained with the mean-field theory. The simulation results show that the model can be used to generate such networks with different topology structures as random and scale-free ones. The networks with different densities (i.e., the average connectivity degrees) can also be generated by the model.     

Pair correlations in scale-free networks

Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi－Albert (BA) scale-free model with both analytical results and simulations, and find two neighbouring regions, a disassortative one for low degrees and a neutral one for high degrees. The average degree of the neighbours of a randomly picked node is expected to diverge in the limit of infinite network size. As a generalization of the concept of correlation, we also study the correlations of other scalar properties, including age and clustering coefficient. Finally we propose a correlation measurement in bipartite networks.     

Stability of Random Networks under Evolution of Attack and Repair

With a simple model, we study the stability of random networks under the evolution of attack and repair. We introduce a new quantity, i.e. invulnerability I（s）, to describe the stability of the system. It is found that the network can evolve to a stationary state. The stationary value Ic has a power-law dependence on the initial average degree （κ）, with the slope about -1.5. In the stationary state, the degree distribution is a normal distribution, rather than a typical Poisson distribution for general random graphs. The clustering coefficient in the stationary state is much larger than that in the initial state. The stability of the network depends only on the initial average degree （κ）, which increases rapidly with the decrease of （κ）.     

Modeling the IPv6 internet AS-level topology

To measure the IPv6 internet AS-level topology, a network topology discovery system, called Dolphin, was developed. By comparing the measurement result of Dolphin with that of CAIDA’s Scamper, it was found that the IPv6 Internet at AS level, similar to other complex networks, is also scale-free but the exponent of its degree distribution is 1.2, which is much smaller than that of the IPv4 Internet and most other scale-free networks. In order to explain this feature of IPv6 Internet we argue that the degree exponent is a measure of uniformity of the degree distribution. Then, for the purpose of modeling the networks, we propose a new model based on the two major factors affecting the exponent of the EBA model. It breaks the lower bound of degree exponent which is 2 for most models. To verify the validity of this model, both theoretical and experimental analyses have been carried out. Finally, we demonstrate how this model can be successfully used to reproduce the topology of the IPv6 Internet.     

Traffic of packets with non-homogeneously selected destinations in scale-free network

In this paper, we study the information traffic flow in communication networks with scale-free topology. We consider the situation arising when packets are delivered to non-homogeneously selected destinations. It is found that the network capacity R_c increases with the increase of 〈k〉 (average degree of destination nodes) under local routing strategy. In contrast, R_c is essentially independent of 〈k〉 under shortest path strategy. Based on this finding, an integrated routing strategy that can enhance network capacity is proposed by combining the two strategies.     

Transport between multiple users in complex networks

We study the transport properties of model networks such as scale-free and Erd?s-Rényi networks as well as a real network. We consider few possibilities for the trnasport problem. We start by studying the conductance G between two arbitrarily chosen nodes where each link has the same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G, with a power-law tail distribution $\Phi_{\rm SF}(G)\sim G^{-g_G}$ , where g_G=2λ-1, and λ is the decay exponent for the scale-free network degree distribution. The power-law tail in Φ_SF(G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erd?s-Rényi networks where the tail of the conductivity distribution decays exponentially. We develop a simple physical picture of the transport to account for the results. The other model for transport is the max-flow model, where conductance is defined as the number of link-independent paths between the two nodes, and find that a similar picture holds. The effects of distance on the value of conductance are considered for both models, and some differences emerge. We then extend our study to the case of multiple sources ans sinks, where the transport is defined between two groups of nodes. We find a fundamental difference between the two forms of flow when considering the quality of the transport with respect to the number of sources, and find an optimal number of sources, or users, for the max-flow case. A qualitative (and partially quantitative) explanation is also given.     

Apollonian packings as physical fractals

The Apollonian packings (APs) of spheres are fractals that result from a space-filling procedure. We discuss the finite size effects for finite intervals s?∈?[s _min,?s _max] between the largest and the smallest sizes of the filling spheres. We derive a simple analytical generalization of the scale-free laws, which allows a quantitative study of such physical fractals. To test our result, a new efficient space-filling algorithm has been developed which generates random APs of spheres with a finite range of diameters: the correct asymptotic limit s _min/s _max?→?0 and the known APs' fractal dimensions are recovered and an excellent agreement with the generalized analytic laws is proved within the overall range of sizes.     

The average path length for a class of scale-free fractal hierarchical lattices: Rigorous results

With the help of the recurrence relations derived from the self-similar structure, we obtain the closed-form solution for the average path length of a class of scale-free fractal hierarchical lattices (HLs) with a general parameter q, which are simultaneously scale-free, self-similar and disassortative. Our rigorous solution shows that the average path length of the HLs grows logarithmically as in the infinite limit of network size of N_t and that they are not small worlds but grow with a power-law relationship to the number of nodes.     

用户需求行为对互联网动力学整体特性的影响

由Internet构成的复杂网络的动力学特性主要受到用户需求行为的影响,具备时域的统计规律性. 通过对区域群体用户需求行为的时域实验统计分析,发现用户对Web网站的访问频度及其生成的二分网络的入度分布也呈现幂律分布和集聚现象,其幂指数介于1.7到1.8之间. 建立了虚拟资源网络VRN和物理拓扑网络PTN双层模型,分析了双层模型映射机理,并对网络用户需求行为进行建模. 虚拟资源网络VRN对物理拓扑网络PTN映射过程的不同机理,模拟了Internet资源网络到物理网络的不同影响模式. 幂律分布的用户需求特性会 关键词： 复杂网络 无标度拓扑 用户需求 相变     

Scale-free networks by super-linear preferential attachment rule

A network growth model with geographic limitation of accessible information about the status of existing nodes is investigated. In this model, the probability Π(k) of an existing node of degree k is found to be super-linear with Π(k)∼k^α and α>1 when there are links from new nodes. The numerical results show that the constructed networks have typical power-law degree distributions P(k)∼k^−γ and the exponent γ depends on the constraint level. An analysis of local structural features shows the robust emergence of scale-free network structure in spite of the super-linear preferential attachment rule. This local structural feature is directly associated with the geographical connection constraints which are widely observed in many real networks.     

Improved SNR in linear reordered 2D bSSFP imaging using variable flip angles

This article presents a variable flip-angle approach for balanced steady-state free precession (bSSFP) imaging, which allows increases in signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) while keeping specific absorption rate (SAR) constant or reduces SAR for given CNR and SNR. The gain in SNR is achieved by utilizing the higher signal in the transient phase. Flip-angle variation during the echo train is realized using a trigonometric function with M steps (ramp length). Variation is combined with a linear k-space reordering such that outer parts of k-space are sampled using a lower flip angle α_min, while the central part of k-space is acquired with a higher flip angle α_max. No additional preparation or dummy cycles are applied prior to data acquisition. Several variation schemes with different starting flip angles α_min and ramp length M are considered. For example, using α_min=1° and M=96, α_max can be set to 47° without exceeding SAR limits at 3 T and gaining up to 50% in SNR, while, conventionally, α=34° is the maximal possible flip angle. Resolution seems unaffected in volunteer imaging. In all cases, no transient artifacts due to flip-angle variation were observed. This article demonstrates the use of flip-angle variations in bSSFP to increase SNR and CNR while keeping SAR constant, which is especially important at higher field strengths. Flip-angle variation can also be combined with other methods such as parallel imaging techniques for further SAR reduction.     

Antiferromagnetic Ising model in scale-free networks

The antiferromagnetic Ising model in uncorrelated scale-free networks has been studied by means of Monte Carlo simulations. These networks are characterized by a connectivity (or degree) distribution P(k) ∼k^-γ. The disorder present in these complex networks frustrates the antiferromagnetic spin ordering, giving rise to a spin-glass (SG) phase at low temperature. The paramagnetic-SG transition temperature T_c has been studied as a function of the parameter γ and the minimum degree present in the networks. T_c is found to increase when the exponent γ is reduced, in line with a larger frustration caused by the presence of nodes with higher degree.