Worldwide Marine Transportation Network： Efficiency and Container Throughput

通过全球海洋的交通网络(WMTN ) 的全球结构的实验分析，我们发现 WMTN，一个小世界的网络，展出象指数一样学位分布。我们在此由采用一个简单定义调查 WMTN 的效率。与许多另外的交通网络相比， WMTN 拥有相对低的效率。由探索在拓扑的结构和容器产量之间的关系，而且，我们发现强壮的关联在整个学位和聚类的系数在容器之中存在。另外，考虑一艘轮船在一根真实发货线旅行的航行过程，我们获得一个海港的重量与概率由所有过去贡献了的总数成正比发货，这排队。

Message Spreading and Forget-Remember Mechanism on a Scale-Free Network

我们学习消息在一个没有规模的网络上传播，由介绍新奇忘记记得机制。消息，能指电子邮件的一个一般术语，新闻，谣言或疾病，等等，能被它的持有者忘记并且记得。消息被忘记并且记得的方法被 forget 管理并且分别地记得功能， F 和 R。F 和 R 是有关个人的家的历史时间 t 的功能以前的状态，也就是是活跃的(与消息) 或不活跃(没有消息) 。我们以传播能是有效的低传播率的系统的模拟表演被相应参数首先为 F 和 R 决定。

The Fractal Dimensions of Complex Networks

It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average ＇density＇ （p（r ） ） of complex networks follows a better power-law function as a function of distance r with the exponent dl, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.

Network Aggregation Process in Multilayer Air Transportation Networks

The air transportation network, one of the common multilayer complex systems, is composed of a collection of individual airlines, and each airline corresponds to a different layer. An important question is then how many airlines are really necessary to represent the optimal structure of a multilayer air transportation system. Here we take the Chinese air transportation network （CATN） as an example to explore the nature of multiplex systems through the procedure of network aggregation. Specifically, we propose a series of structural measures to characterize the CATN from the multilayered to the aggregated network level. We show how these measures evolve during the network aggregation process in which layers are gradually merged together and find that there is an evident structural transition that happened in the aggregated network with nine randomly chosen airlines merged, where the network features and construction cost of this network are almost equivalent to those of the present CATN with twenty-two airlines under this condition. These findings could shed some light on network structure optimization and management of the Chinese air transportation system.

A New Feature in Some Quasi-discontinuous Systems

Many systems can display a very short,rapid changing stage(quasi-discontinuous region)inside a relatively very long and slowly changing process.A quantitative definition for the"quasi-discontinuity"in these systems has been introduced.We have shown by a simplified model that extra-large Feigenbaum constants can be found inside some period-doubling cascades due to the quasi-discontinuity.As an example,this phenomenon has also been observed in Rose-Hindmash model describing neuron activities.

Quasi-attractors in a Piece-Wise Smooth Area-Preserving Map

In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map.This can lead to the appearance of such kinds of elliptic islands that attract the iterations from a set of initial values outside themselves,while behaving regularly inside.We suggest calling such islands quasi-attractors.

Macro-Behaviour of Agents＇ Opinion under Influence of an External Field

我们建议一个模型在对小世界网络的一个外部领域的影响下面学习意见的进化。代理人的意见和时间过去的相对变化率的宏行为被学习。外部领域被发现在造成意见 s (t) 平衡或增加起一个重要作用，并且没有外部领域的影响，相对变化率鲸鱼群妈(t) 表演时间跑的非线性的增加行为。而且，这非线性的增加行为独立于起始的条件，外部领域的力量和我们取消外部领域的时间。结果可以在我们的社会反映一些现象，例如在中国的宏控制或在我们的社会的大众媒体的功能。

Maximum Path Information and Fokker-Planck Equation

我们在场从 Maupertuis 的最少的行动的原则的归纳直接导出异常散开的非线性的佛克普朗克常数(FP ) 方程的一个严密方法由王求婚了[混乱， Solitons 和分数维图形 23 (2005 ) 1253 ] 为在 Markovian 演变的光滑或伪光滑的不规则的动力学过程。获得的 FP 方程可以拿二种不同却相等的形式。散开常数可以取决于两 q，这也被发现(Tsallis 熵的索引[J。Stat。Phys。52 (1988 ) 479 ] 并且时间 t ) 。

Effects of Variant Rates and Noise on Epidemic Spreading

We introduce variant rates,for both infection and recovery and noise into the susceptible-infected-removed(SIR)modelfor epidemic spreading.The changing rates are taken mainly due to the changing profiles of an epidemic during its evolution.However,the noise parameter which is taken from a given distribution,i.e.Gaussian can describe the fluctuations of the infection and recovery rates.The numerical simulations show that the SIR model with variant rates and noise and can improve the fitting with real SARS data in the near-stationary stage.

Long Division Unites or Long Union Divides:a Model for Social Network Evolution

A remarkable phenomenon in the time evolution of many networks such as cultural,political,national and economic systems is the recurrent transition between the states of union and the division of nodes.We propose a phenomenological modeling,inspired by the maxim"long union divides and long division unites"to investigate the evolutionary characters of these networks composed of the entities whose behaviors are dominated by these two events.The nodes are endowed with quantities such as identity,ingredient,richness(power),openness(connections),age,distance,and interaction,which determine collectively the evolution in a probabilistic way.Depending on a tunable parameter,the time evolution of this model is mainly an alternative domination of union or division state,with a possible state of final union dominated by one single node.

A Confined Chaotic Motion of a Kicked Particle

Different types of models for describing the motion of a kicked ion were suggested and studied. It is shown that certain kinds of jumping behavior of the exerting electromagnetic field can lead to a type of noninvertible property, which changes this conservative system into a 'quasi-dissipative' one. The quasi-dissipative behaviors allow the particle to move along a confined chaotic 'quasi-attractor' in many regions of the parameter space. If the exerting electromagnetic field is discontinuous but the system is still invertible, it will take an unbounded chaotic diffusion with similar parameter values. We hope that this discovery could provide a helpful idea for confining the plasma.

English and Chinese language frequency time series analysis

<Abstract>English and Chinese language frequency time series (LFTS) were constructed based on an English and two Chinese novels. Methods of statistical hypothesis testing were adopted to test the nonlinear properties of the LFTS. Results suggest the series exhibited non-normal, auto-correlative, and stationary characteristics. Moreover, we found that LFTS follow the power law distributions, and thereby we investigated the fractal structure, long range correlation, and intermittency, which indicated the self-similarity features of LFTS, and also provided hints that human societies are likely to share some universal properties.

Thermoequilibrium statistics for a finite system with energy nonextensivity

A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ , we derive an explicit form for the distribution functions by regulating λ , and then explore the nontrivial relationship between these functions and energy nonextensivity, as well other system parameters such as system size. A variational entropy function is also derived from these distribution functions.

Binary opinion dynamics with noise on random networks

Two kinds of noise strategies in binary opinion dynamics on ER random networks are discussed. Random noise p1 in the initial configuration plays a role in redistributing the opinion states associated with the network. Under synchronous updating, the system can attain a stable state within few time steps. The fraction of nodes with changed opinion states F decreases exponentially with time, and the ratio of one of the two opinion states R remains almost unchanged during the evolution. The average ratio <R> crosses at the half-half initial concentration under different p1. For noise in the dynamical evolution p2, the system can reach a steady state with small fluctuations. With larger p2, more nodes have changed opinion states at each updating and more nodes with opposite opinions coexist. If p2 is greater than 0.5, the two opinions coexist with equal support.

A mean-field Bak-Sneppen model with varying interaction strength

We propose a mean-field Bak-Sneppen (MFBS) model with varying interaction strength. The interaction strength, here denoted by α, specifies the degree of interaction, and varies smoothly between 0 for no interaction and 1 for full interaction (restoring the original BS model). Our simulations of the MFBS model reveal some interesting features. When α is non-zero, the MFBS model can evolve to a self-organized critical (SOC) state. The critical exponent of the avalanche size distribution, α, is insensitive to changes in α. The critical exponent of average avalanche size, α, and the avalanche dimension exponent, D, both increase slightly with α < 0.5 but remain constant if α > 0.5. The critical threshold fc decreases almost linearly with α.

Structure and collaboration relationship analysis in a scientific collaboration network

We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship parameter to measure the collaboration between scientists. The collaboration relationship parameter of two scientists depends not only on the connection weights between the nodes, but also on the network's structure. The stability of the network's structure in terms of different edge removal strategies is also studied. According to the parameter, we find that a community structure exists in this type of network.

Emergence of Community Structure in the Adaptive Social Networks

In this paper,we propose a simple model of opinion dynamics to construct social networks,based on the algorithm of link rewiring of local attachment(RLA)and global attachment(RGA).Generality,the system does reach a steady state where all individuals'opinion and the complex network structure are fixed.The RGA enhances the ability of consensus of opinion formation.Furthermore,by tuning a model parameter p,which governs the proportion of RLA and RGA,we find the formation of hierarchical structure in the social networks for p>p_(c).Here,p_(c) is related to the complex network size N and the minimal coordination number 2K.The model also reproduces many features of large social networks,including the“weak links”property.

Effect of spatial distance on search information correlation in complex systems

Spatial distance has a remarkable effect on the attended mode of a network embedded in a certain space. First, we investigate how spatial restriction leads to information-information correlation that is strong, linear and positive in real networks. We then construct a two-dimensional space, define the action radius R for nodes of networks, and propose a class of models that depend on spatial distance. Information correlation of the models is consistent with that of real networks. The spatial distance plays a leading role in generating assortative mixing by degree, while the generation of disassortative mixing relies on both the degree of preferential attachment and spatial restriction.

Modeling of epidemic spreading with white Gaussian noise

Motivated by the need to include the different characteristics of individuals and the damping effect in predictions of epidemic spreading, we build a model with variant coefficients and white Gaussian noise based on the traditional SIR model. The analytic and simulation results predicted by the model are presented and discussed. The simulations show that using the variant coefficients results in a higher percentage of susceptible individuals and a lower percentage of removed individuals. When the noise is included in the model, the percentage of infected individuals has a wider peak and more fluctuations than that predicted using the traditional SIR model.

Application of varentropy as a measure of probabilistic uncertainty for complex networks

Varentropy is used as a general measure of probabilistic uncertainty for a complex network, inspired by the first and second laws of thermodynamics, but not limited to the equilibrium system. By exploring the relationship between the varentropy of the scale free distribution and the exponent of power laws as well as network size, we get the optimal design of a scale-free network against random failures. The behaviors of varentropy and the Shannon entropy of double Pareto law degree distribution are analyzed to compare their usefulness. Our conclusion is that varentropy is suitable and reliable.