SELF-ORGANIZED CRITICALITY IN ONE-DIMENSIONAL PACKET FLOW MODEL

Packet flow affects the behavior of Internet routers, which in return regulates the flow. Even a non-correlated uniform packet flow from a terminal will be modulated to show correlated fluctuations by going through the network nodes. In this paper, we study a simple model in an abstract level to describe intuitively the self-organized criticality in packet level, the emergence of collective behavior of packets, which causes the long-range dependence of congestion in computer networks. We find that the character of the jam lifetime is consistent with the measurement results, the packet delivery time appears the feature of 1/f noise, and the intervals between the packet arrivals are power-law distributed.     

Jamming in complex networks with degree correlation

We study the effects of the degree-degree correlations on the pressure congestion J when we apply a dynamical process on scale free complex networks using the gradient network approach. We find that the pressure congestion for disassortative (assortative) networks is lower (bigger) than the one for uncorrelated networks which allow us to affirm that disassortative networks enhance transport through them. This result agree with the fact that many real world transportation networks naturally evolve to this kind of correlation. We explain our results showing that for the disassortative case the clusters in the gradient network turn out to be as much elongated as possible, reducing the pressure congestion J and observing the opposite behavior for the assortative case. Finally we apply our model to real world networks, and the results agree with our theoretical model.     

Self-organized criticality in a computer network model

We study the collective behavior of computer network nodes by using a cellular automaton model. The results show that when the load of network is constant, the throughputs and buffer contents of nodes are power-law distributed in both space and time. Also the feature of 1/f noise appears in the power spectrum of the change of the number of nodes that bear a fixed part of the system load. It can be seen as yet another example of self-organized criticality. Power-law decay in the distribution of buffer contents implies that heavy network congestion occurs with small probability. The temporal power-law distribution for throughput might be a reasonable explanation for the observed self-similarity in computer network traffic.     

Spontaneous pattern formation with incoherent white light

We present the first experimental observation of modulation instability and spontaneous pattern formation with incoherent white light emitted from an incandescent light bulb. We show experimentally that modulation instability of white light propagating in a noninstantaneous self-focusing medium is a collective effect, where the entire temporal spectrum of the light beam becomes unstable at the same threshold value and collectively forms a pattern with a single periodicity. We experimentally demonstrate that the temporal spectrum of the evolving perturbation self-adjusts to match the collective pattern formation phenomenon.     

Influence of a network structure on the network effect in the communication service market

In this study, we analyze the network effect in a model of a personal communication market, by using a multi-agent based simulation approach. We introduce into the simulation model complex network structures as the interaction patterns of agents. With complex network models, we investigate the dynamics of a market in which two providers are competing. We also examine the structure of networks that affect the complex behavior of the market. By a series of simulations, we show that the structural properties of complex networks, such as the clustering coefficient and degree correlation, have a major influence on the dynamics of the market. We find that the network effect is increased if the interaction pattern of agents is characterized by a high clustering coefficient, or a positive degree correlation. We also discuss a suitable model of the interaction pattern for reproducing market dynamics in the real world, by performing simulations using real data of a social network.     

计算机网络的长程相关特性

针对一种计算机网络模型，利用节点排队长度累计量的均方涨落函数，研究了网络节点在时间上的长程相关特性.结果表明，随着负载的增加，网络节点数据包排队长度在时间上由自由流状态的不相关或短程相关逐渐演变为临界和拥塞时的长程相关，关联范围逐渐增大，长程关联特性开始显现.在自由流状态时，节点的不相关或短程相关，并且有一致的数值为0.5的幂指数这一典型特征.而在临界状态时，节点数据包排队长度长程相关，有大于0.5的幂指数为特征.并且随网络规模的增大，节点间的群体作用逐渐显著，幂指数呈下降趋势. 关键词： 计算机网络 相变 长程相关 幂律     

The structure and resilience of financial market networks

Financial markets can be viewed as a highly complex evolving system that is very sensitive to economic instabilities. The complex organization of the market can be represented in a suitable fashion in terms of complex networks, which can be constructed from stock prices such that each pair of stocks is connected by a weighted edge that encodes the distance between them. In this work, we propose an approach to analyze the topological and dynamic evolution of financial networks based on the stock correlation matrices. An entropy-related measurement is adopted to quantify the robustness of the evolving financial market organization. It is verified that the network topological organization suffers strong variation during financial instabilities and the networks in such periods become less robust. A statistical robust regression model is proposed to quantity the relationship between the network structure and resilience. The obtained coefficients of such model indicate that the average shortest path length is the measurement most related to network resilience coefficient. This result indicates that a collective behavior is observed between stocks during financial crisis. More specifically, stocks tend to synchronize their price evolution, leading to a high correlation between pair of stock prices, which contributes to the increase in distance between them and, consequently, decrease the network resilience.     

Solving N-body problems with neural networks

We show a new approach for solving the N-body problems based on neural networks. Without loss of generality, we derived a network solution for the time-dependent positions of N bodies in self-gravitating systems. The simulation is limited to a system of collisionless disks-a case for determining the spatial distributions of dark matter and in reproducing global effects such as formation of spiral galaxies. Our approach yields a solution that is analytic with time-reversed path-tracing capabilities that could lead to new findings in the study of the collective behavior of N-body systems.     

Collective firing regularity of a scale-free Hodgkin–Huxley neuronal network in response to a subthreshold signal

We consider a scale-free network of stochastic HH neurons driven by a subthreshold periodic stimulus and investigate how the collective spiking regularity or the collective temporal coherence changes with the stimulus frequency, the intrinsic noise (or the cell size), the network average degree and the coupling strength. We show that the best temporal coherence is obtained for a certain level of the intrinsic noise when the frequencies of the external stimulus and the subthreshold oscillations of the network elements match. We also find that the collective regularity exhibits a resonance-like behavior depending on both the coupling strength and the network average degree at the optimal values of the stimulus frequency and the cell size, indicating that the best temporal coherence also requires an optimal coupling strength and an optimal average degree of the connectivity.     

Transitions in spatial networks

Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the Erdös–Rényi graph, and spatial networks display a large variety of behaviors. We will discuss here some (mostly recent) results about topological transitions, ‘localization’ transitions seen in the shortest paths pattern, and also about the effect of congestion and fluctuations on the structure of optimal networks. The importance of spatial networks in real-world applications makes these transitions very relevant, and this review is meant as a step towards a deeper understanding of the effect of space on network structures.     

Self-Organized Criticality in a Simple Neuron Model Based on Scale-Free Networks

A simple model for a set of interacting idealized neurons in scale-free networks is introduced. The basic elements of the model are endowed with the main features of a neuron function. We find that our model displays powerlaw behavior of avalanche sizes and generates long-range temporal correlation. More importantly, we find different dynamical behavior for nodes with different connectivity in the scale-free networks.     

Self-Organized Criticality in a Simple Neuron Model Based on Scale-Free Networks

A simple model for a set of interacting idealized neurons in scale-free networks is introduced. The basic elements of the model are endowed with the main features of a neuron function. We find that our model displays powerlaw behavior of avalanche sizes and generates long-range temporal correlation. More importantly, we find different dynamical behavior for nodes with different connectivity in the scale-free networks.     

Optimal structure of complex networks for minimizing traffic congestion

To design complex networks to minimize traffic congestion, it is necessary to understand how traffic flow depends on network structure. We study data packet flow on complex networks, where the packet delivery capacity of each node is not fixed. The optimal configuration of capacities to minimize traffic congestion is derived and the critical packet generating rate is determined, below which the network is at a free flow state but above which congestion occurs. Our analysis reveals a direct relation between network topology and traffic flow. Optimal network structure, free of traffic congestion, should have two features: uniform distribution of load over all nodes and small network diameter. This finding is confirmed by numerical simulations. Our analysis also makes it possible to theoretically compare the congestion conditions for different types of complex networks. In particular, we find that network with low critical generating rate is more susceptible to congestion. The comparison has been made on the following complex-network topologies: random, scale-free, and regular.     

Traffic dynamics on layered complex networks

To minimize traffic congestion, understanding how traffic dynamics depend on network structure is necessary. Many real-world complex systems can be described as multilayer structures. In this paper, we introduce the idea of layers to establish a traffic model of two-layer complex networks. By comparing different two-layer complex networks based on random and scale-free networks, we find that the physical layer is much more important to the network capacity of two-layer complex networks than the logical layer. Two-layer complex networks with a homogeneous physical topology are found to be more tolerant to congestion. Moreover, simulation results show that the heterogeneity of logical and physical topologies makes the packet-delivery process of two-layer networks more efficient in the free-flow state, without the occurrence of traffic congestion.     

Collective temporal coherence for subthreshold signal encoding on a stochastic small-world Hodgkin-Huxley neuronal network

We study the collective temporal coherence of a small-world network of coupled stochastic Hodgkin-Huxley neurons. Previous reports have shown that network coherence in response to a subthreshold periodic stimulus, thus subthreshold signal encoding, is maximal for a specific range of the fraction of randomly added shortcuts relative to all possible shortcuts, p, added to an initially locally connected network. We investigated this behavior further as a function of channel noise, stimulus frequency and coupling strength. We show that temporal coherence peaks when the frequency of the external stimulus matches that of the intrinsic subthreshold oscillations. We also find that large values of the channel noise, corresponding to small cell sizes, increases coherence for optimal values of the stimulus frequency and the topology parameter p. For smaller values of the channel noise, thus larger cell sizes, network coherence becomes insensitive to these parameters. Finally, the degree of coupling between neurons in the network modulates the sensitivity of coherence to topology, such that for stronger coupling the peak coherence is achieved with fewer added short cuts.     

虚拟网络行为对互联网整体特性的影响

虚拟网络是一种依赖Internet基础设施所提供的传输能力，但又具有独立拓扑结构和信息传递规则的应用层网络行为逻辑网络.提出了耦合虚拟网络行为与物理节点的抽象模型，对一类典型的虚拟网络逻辑拓扑给互联网整体特性带来的影响进行了分析.研究表明在虚拟网络作用下，节点数据包排队长度存在相变特性，但相变临界点比对规则网络发生了明显左移，网络性能相对恶化.当数据包注入速率小于相变临界速率时，节点数据包排队长度不相关或短程相关；在接近临界速率处，节点数据包排队长度长程相关，幂指数H增大，网络获得更强的长程相关性.同时，在注入速率大于或等于临界速率时，虚拟网络行为使网络呈现出一致的长程相关特性.     

Avalanche dynamics of idealized neuron function in the brain on an uncorrelated random scale-free network

We study a simple model for a neuron function in a collective brain system. The neural network is composed of an uncorrelated configuration model (UCM) for eliminating the degree correlation of dynamical processes. The interaction of neurons is assumed to be isotropic and idealized. These neuron dynamics are similar to biological evolution in extremal dynamics with locally isotropic interaction but has a different time scale. The functioning of neurons takes place as punctuated patterns based on avalanche dynamics. In our model, the avalanche dynamics of neurons exhibit self-organized criticality which shows power-law behavior of the avalanche sizes. For a given network, the avalanche dynamic behavior is not changed with different degree exponents of networks, γ≥2.4 and various refractory periods referred to the memory effect, T_r. Furthermore, the avalanche size distributions exhibit power-law behavior in a single scaling region in contrast to other networks. However, return time distributions displaying spatiotemporal complexity have three characteristic time scaling regimes Thus, we find that UCM may be inefficient for holding a memory.     

Affinity driven social networks

In this work we present a model for evolving networks, where the driven force is related to the social affinity between individuals of a population. In the model, a set of individuals initially arranged on a regular ordered network and thus linked with their closest neighbors are allowed to rearrange their connections according to a dynamics closely related to that of the stable marriage problem. We show that the behavior of some topological properties of the resulting networks follows a non trivial pattern.     

有倾向性重连产生的反匹配网络

在具有网络结构的系统中度关联属性对于动力学行为具有重要的影响, 所以产生适当度关联网络的方法对于大量网络系统的研究具有重要的作用. 尽管产生正匹配网络的方法已经得到很好的验证, 但是产生反匹配网络的方法还没有被系统的讨论过. 重新连接网络中的边是产生度关联网络的一个常用方法. 这里我们研究使用重连方法产生反匹配无标度网络的有效性. 我们的研究表明, 有倾向的重连可以增强网络的反匹配属性. 但是有倾向重连不能使皮尔森度相关系数下降到-1, 而是存在一个依赖于网络参数的最小值. 我们研究了网络的主要参数对于网络度相关系数的影响, 包括网络尺寸, 网络的连接密度和网络节点的度差异程度. 研究表明在网络尺寸大的情况下和节点度差异性强的情况下, 重连的效果较差. 我们研究了真实Internet网络, 发现模型产生的网络经过重连不能达到真实网络的度关联系数.