Transient dynamics increasing network vulnerability to cascading failures

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws. It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. The robustness of networks showing cascading failures is generally given by a complex interplay between the network topology and flow dynamics.     

Preservation of network degree distributions from non-uniform failures

There has been a considerable amount of interest in recent years on the robustness of networks to failures. Many previous studies have concentrated on the effects of node and edge removals on the connectivity structure of a static network; the networks are considered to be static in the sense that no compensatory measures are allowed for recovery of the original structure. Real world networks such as the world wide web, however, are not static and experience a considerable amount of turnover, where nodes and edges are both added and deleted. Considering degree-based node removals, we examine the possibility of preserving networks from these types of disruptions. We recover the original degree distribution by allowing the network to react to the attack by introducing new nodes and attaching their edges via specially tailored schemes. We focus particularly on the case of non-uniform failures, a subject that has received little attention in the context of evolving networks. Using a combination of analytical techniques and numerical simulations, we demonstrate how to preserve the exact degree distribution of the studied networks from various forms of attack.     

Degree distribution of random birth-and-death network with network size decline

In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-death network(RBDN) with network size decline.First,by stochastic process rules,the steady state transformation equations and steady state degree distribution equations are given in the case of m ≥ 3 and 0 p 1/2,then the average degree of network with n nodes is introduced to calculate the degree distributions.Specifically,taking m = 3 for example,we explain the detailed solving process,in which computer simulation is used to verify our degree distribution solutions.In addition,the tail characteristics of the degree distribution are discussed.Our findings suggest that the degree distributions will exhibit Poisson tail property for the declining RBDN.     

Critical behavior of a random diode network

We study the percolation properties of a random diode network (RDN) which contains two kinds of directed bonds on a square lattice. This network is a special case of the random insulation-resistor-diode network. Both Monte Carlo simulations and series expansion for the percolation probability show that an estimated critical exponent, beta=0.1794+/-0.008, is different from known values for a conventional insulation-resistor-diode network. RDN belongs to neither the isotropic percolation universality class nor to the directed percolation universality, which we attribute to a difference of symmetry breakdown around the critical point.     

Agile protection based on network coding against key link failures

In order to provide cost-efficient and rapid protection against the key link failures dynamically, an intelligent p-cycle protection strategy based on network coding is proposed. Data units are combined from different links using network coding method at the on-cycle nodes, and then they are transmitted downstream for recovering data units lost due to failures. Under static traffic, an integer linear program (ILP) is formulated to provision the optimal p-cycles. Furthermore, according to the dynamic variation of the link importance degree, a heuristic cycle construction algorithm for generating, extending and contracting p-cycle is introduced to achieve intelligent and self-adaptive protection. The key of the proposed protection strategy is how to set the key link as a straddling link of the p-cycle as possible. The experiments demonstrate that the proposed strategy can guarantee instantaneous recovery of data units upon the failure of a key link with a low blocking rate and resource cost.     

Properties of a growing random directed network

We study a number of properties of a simple random growing directed network which can be used to model real directed networks such as the world-wide web and call graphs. We confirm numerically that the distributions of in- and out-degree are consistent with a power law, in agreement with previous analytical results and with empirical measurements from real graphs. We study the distribution and mean of the minimum path length, the high degree nodes, the appearance and size of the giant component and the topology of the nodes outside the giant component. These properties are compared with empirical studies of the world-wide web. Received 15 June 2001 and Received in final form 12 July 2001     

Band structure from random interactions

The anharmonic vibrator and rotor regions in nuclei are investigated in the framework of the interacting boson model using an ensemble of random one- and two-body interactions. We find a predominance of L(P) = 0(+) ground states, as well as strong evidence for the occurrence of both vibrational and rotational band structures. This remarkable result suggests that such band structures represent a far more general (robust) property of the collective model space than is generally thought.     

Band structure of one-dimensional random alloys

A one-dimensional random alloy with an original tight-binding model is considered. Impurities are represented by δ-type attractive potentials. An analytical expression for the density of states is obtained.     

Phase transition in a self-repairing random network

We consider a network the bonds of which are being sequentially removed; this is done at random but conditioned on the system remaining connected (self-repairing bond percolation, SRBP). This model is the simplest representative of a class of random systems for which the formation of isolated clusters is forbidden. It qualitatively describes the process of fabrication of artificial porous materials and degradation of strained polymers. We find a phase transition at a finite concentration of bonds p=p _c , at which the backbone of the system vanishes; for all p< p _c , the network is a dense fractal.     

Critical fluctuations in a random network model

Individual threshold behaviors generate large endogenous fluctuations in a globally interactive network. In a version of NK models, the bonds are allowed to be allocated randomly across nodes in each period. It is shown that the aggregate output asymptotically follows a branching process with martingale property on a unique globally stable state.     

无规电阻网络的等效电阻

以Y←→△、串联、并联变换为基础，介绍一种计算二维无规电阻网络的等效电阻的普适计算方法。     

Morphometry and structure of natural random tilings

A vast range of both living and inanimate planar cellular partitions obeys universal empirical laws describing their structure. To better understand this observation, we analyze the morphometric parameters of a sizeable set of experimental data that includes animal and plant tissues, patterns in desiccated starch slurry, suprafroth in type-I superconductors, soap froths, and geological formations. We characterize the tilings by the distributions of polygon reduced area, a scale-free measure of the roundedness of polygons. These distributions are fairly sharp and seem to belong to the same family. We show that the experimental tilings can be mapped onto the model tilings of equal-area, equal-perimeter polygons obtained by numerical simulations. This suggests that the random two-dimensional patterns can be parametrized by their median reduced area alone.     

Phase structure function of random wave fields

The phase properties of a complex Gaussian field, which can arise following scattering from random phase screens and through extended random media, are investigated. It is shown that the unwrapped phase of a complex Gaussian field constitutes a non-stationary process, such that the phase autocorrelation function does not exist. However, the phase structure function remains finite, allowing analytical results to be obtained for various field correlations. Methods for numerical simulation are discussed and their results found to be in excellent agreement with analytical predictions. More general considerations reveal that the phase structure function of a complex Gaussian field increases linearly with large separation distance. The results are relevant to phase-sensitive detection in fields undergoing strong intensity fluctuations.     

Impact of core-periphery structure on cascading failures in interdependent scale-free networks

Core-periphery structure is a typical meso-scale structure in networks. Previous studies on core-periphery structure mainly focus on the improvement of detection methods, while the research on the impact of core-periphery structure on cascading failures in interdependent networks is still missing. Therefore, we investigate the cascading failures of interdependent scale-free networks with different core-periphery structures and coupling preferences in the paper. First, we introduce an evaluation index to calculate the goodness of core-periphery structure. Second, we propose a new scale-free network evolution model, which can generate tunable core-periphery structures, and its degree distribution is analyzed mathematically. Finally, based on a degree-load-based cascading failure model, we mainly investigate the impact of goodness of core-periphery structure on cascading failures in both symmetrical and asymmetrical interdependent networks. Through numerical simulations, we find that with the same average degree, the networks with weak core-periphery structure will be more robust, while the initial load on node will influence the improvement of robustness. In addition, we also find that the inter-similarity coupling performs better than random coupling. These findings may be helpful for building resilient interdependent networks.     

Cascading failures of overload behaviors using a new coupled network model between edges

With the development of network science,the coupling between networks has become the focus of complex network research.However,previous studies mainly focused on the coupling between nodes,while ignored the coupling between edges.We propose a novel cascading failure model of two-layer networks.The model considers the different loads and capacities of edges,as well as the elastic and coupling relationship between edges.In addition,a more flexible load-capacity strategy is adopted to verify the model.The simulation results show that the model is feasible.Different networks have different behaviors for the same parameters.By changing the load parameters,capacity parameters,overload parameters,and distribution parameters reasonably,the robustness of the model can be significantly improved.     

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.     

Image quantization and its relation to network structure processes

The relation between image quantization and network structure is described. HalLtoning methods are interpreted as special network types and a learning algorithm for halftoning is presented.     

Optimal network structure to induce the maximal small-world effect

In this paper, the general efficiency, which is the average of the global efficiency and the local efficiency, is defined to measure the communication efficiency of a network. The increasing ratio of the general efficiency of a small-world network relative to that of the corresponding regular network is used to measure the small-world effect quantitatively. The more considerable the small-world effect, the higher the general efficiency of a network with a certain cost is. It is shown that the small-world effect increases monotonically with the increase of the vertex number. The optimal rewiring probability to induce the best small-world effect is approximately 0.02 and the optimal average connection probability decreases monotonically with the increase of the vertex number. Therefore, the optimal network structure to induce the maximal small-world effect is the structure with the large vertex number （〉 500）, the small rewiring probability （≈0.02） and the small average connection probability （〈 0.1）. Many previous research results support our results.