Synchronizability of dynamical scale-free networks subject to random errors

In this paper the robustness of network synchronizability against random deletion of nodes, i.e. errors, in dynamical scale-free networks was studied. To this end, two measures of network synchronizability, namely, the eigenratio of the Laplacian and the order parameter quantifying the degree of phase synchrony were adopted, and the synchronizability robustness on preferential attachment scale-free graphs was investigated. The findings revealed that as the network size decreases, the robustness of its synchronizability against random removal of nodes declines, i.e. the more the number of randomly removed nodes from the network, the worse its synchronizability. We also showed that this dependence of the synchronizability on the network size is different with that in the growing scale-free networks. The profile of a number of network properties such as clustering coefficient, efficiency, assortativity, and eccentricity, as a function of the network size was investigated in these two cases, growing scale-free networks and those with randomly removed nodes. The results showed that these processes are also different in terms of these metrics.     

An optimal control approach to probabilistic Boolean networks

External control of some genes in a genetic regulatory network is useful for avoiding undesirable states associated with some diseases. For this purpose, a number of stochastic optimal control approaches have been proposed. Probabilistic Boolean networks (PBNs) as powerful tools for modeling gene regulatory systems have attracted considerable attention in systems biology. In this paper, we deal with a problem of optimal intervention in a PBN with the help of the theory of discrete time Markov decision process. Specifically, we first formulate a control model for a PBN as a first passage model for discrete time Markov decision processes and then find, using a value iteration algorithm, optimal effective treatments with the minimal expected first passage time over the space of all possible treatments. In order to demonstrate the feasibility of our approach, an example is also displayed.     

Structure, scaling, and phase transition in the optimal transport network

The structure and properties of optimal networks depend on the cost functional being minimized and on constraints to which the minimization is subject. We show here two different formulations that lead to identical results: minimizing the dissipation rate of an electrical network under a global constraint is equivalent to the minimization of a power-law cost function introduced by Banavar et al. [Phys. Rev. Lett. 84, 4745 (2000)10.1103/PhysRevLett.84.4745]. An explicit scaling relation between the currents and the corresponding conductances is derived, proving the potential flow nature of the latter. Varying a unique parameter, the topology of the optimized networks shows a transition from a tree topology to a very redundant structure with loops; the transition corresponds to a discontinuity in the slope of the power dissipation.     

Brownian transport in narrow channels subject to transverse periodic force

Brownian transport in two-dimensional narrow channels is extremely sensitive to the spatial modulation of the channel walls. The dependence of transport quantifiers, like the mobility and the diffusivity, on the longitudinal drive strongly varies with the sharpness of the channel corrugation. The two opposite regimes of smooth and septate channels are analyzed in the presence of a transverse periodic bias. Transverse periodic forces of appropriate frequencies enhance the particle mobility across sharp pores more effectively than across smooth bottlenecks.     

Generation of optimal persistent formations for heterogeneous multi-agent systems with a leader constraint

In this study, we consider the generation of optimal persistent formations for heterogeneous multi-agent systems,with the leader constraint that only specific agents can act as leaders. We analyze three modes to control the optimal persistent formations in two-dimensional space, thereby establishing a model for their constrained generation. Then, we propose an algorithm for generating the optimal persistent formation for heterogeneous multi-agent systems with a leader constraint(LC-HMAS-OPFGA), which is the exact solution algorithm of the model, and we theoretically prove its validity.This algorithm includes two kernel sub-algorithms, which are optimal persistent graph generating algorithm based on a minimum cost arborescence and the shortest path(MCA-SP-OPGGA), and the optimal persistent graph adjusting algorithm based on the shortest path(SP-OPGAA). Under a given agent formation shape and leader constraint, LC-HMAS-OPFGA first generates the network topology and its optimal rigid graph corresponding to this formation shape. Then, LC-HMASOPFGA uses MCA-SP-OPGGA to direct the optimal rigid graph to generate the optimal persistent graph. Finally, LCHMAS-OPFGA uses SP-OPGAA to adjust the optimal persistent graph until it satisfies the leader constraint. We also demonstrate the algorithm, LC-HMAS-OPFGA, with an example and verify its effectiveness.     

The transport of electricity in superconductors subject to gravitational or inertial forces

In a superconductor subject to gravitational or inertial forces the flow of current is not limited to the penetration depth, but occurs also in the interior.     

The semigroup approach to transport processes in networks

We explain how operator semigroups can be used to study transport processes in networks. This method is applied to a linear Boltzmann equation on a finite as well as on an infinite network and yields well-posedness and information on the long term behavior of the solutions to the presented problems.     

A decentralised topology control to regulate global properties of complex networks

In the last decade much research effort has been devoted to the investigation of the interplay between properties (i.e. synchronization, clustering, resilience to node fault) and topology of complex networks. Many algorithms have been proposed to construct a network topology with a given properties or to optimize them. These algorithms are static, off-line implemented and may require global network knowledge. In this paper we propose a simple decentralized topology control algorithm that by local actions carried out at the node allows to regulate network global properties. Additionally the algorithm is dynamic coping with both node and link faults and can be on-line implemented.     

Robustness of optimal synchronization in real networks

Experimental studies can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection topology on synchronization in fiber-optic networks of chaotic optoelectronic oscillators. We find that the recently predicted nonmonotonic, cusplike synchronization landscape manifests itself in the rate of convergence to the synchronous state. We also observe that networks with the same number of nodes, same number of links, and identical eigenvalues of the coupling matrix can exhibit fundamentally different approaches to synchronization. This previously unnoticed difference is determined by the degeneracy of associated eigenvectors in the presence of noise and mismatches encountered in real-world conditions.     

Adaptive approach to global synchronization of directed networks with fast switching topologies

Global synchronization of directed networks with switching topologies is investigated. It is found that if there exists at least one directed spanning tree in the network with the fixed time-average topology and the time-average topology is achieved sufficiently fast, the network will reach global synchronization for appreciate coupling strength. Furthermore, this appreciate coupling strength may be obtained by local adaptive approach. A sufficient condition about the global synchronization is given. Numerical simulations verify the effectiveness of the adaptive strategy.     

Comparison of cascading failures in small-world and scale-free networks subject to vertex and edge attacks

Complex networks may undergo a global cascade of overload failures when a single highly loaded vertex or edge is intentionally attacked. Here we use the recent load model of cascading failures to investigate the performance of the small-world (SW) and scale-free (SF) networks subject to deliberate attacks on vertex and edge. Simulation results suggest that compared with the SW network, the SF network is more vulnerable to deliberate vertex attacks and more robust to deliberate edge attacks. In the SF network, deliberate vertex attacks can result in larger cascading failures than deliberate edge attacks; however, in the SW network the situation is opposite. Furthermore, with the increase of the rewiring probability the SW network becomes more and more robust to deliberate vertex and edge attacks.     

一种全局同质化相依网络耦合模式

相依网络的相依模式(耦合模式)是影响其鲁棒性的重要因素之一.本文针对具有无标度特性的两个子网络提出一种全局同质化相依网络耦合模式.该模式以子网络的总度分布均匀化为原则建立相依网络的相依边,一方面压缩度分布宽度,提高其对随机失效的抗毁性,另一方面避开对度大节点(关键节点)的相依,提高其对蓄意攻击的抗毁性.论文将其与常见的节点一对一的同配、异配及随机相依模式以及一对多随机相依模式作了对比分析,仿真研究其在随机失效和蓄意攻击下的鲁棒性能.研究结果表明,本文所提全局同质化相依网络耦合模式能大大提高无标度子网络所构成的相依网络抗级联失效能力.本文研究成果能够为相依网络的安全设计等提供指导意义.     

Analysis of global exponential stability for a class of bi—directional associative memory networks

In real-time applications of bi-directional associative memory (BAM) networks.a global exponentially stable equilibrium is highly desired.The existence,uniqueness and global exponential stability for a class of BAM networks are studied in this paper,the signal function of neurons is assumed to be piece-wise linear from the engineering point of view.A very concise condition for the equilbrium of such a network being globally exponentially stable is derived.which makes the pactical design of this kind of networks an easy job.     

Optimization of transport protocols in complex networks

In this paper, an optimal routing strategy is proposed to enhance the traffic capacity of complex networks. In order to avoid nodes overloading, the new algorithm is derived on the basis of generalized betweenness centrality which gives an estimate of traffic handled by the node for a route set. Since the nodes with large betweenness centrality are more susceptible to traffic congestion, the traffic can be improved, as our strategy, by redistributing traffic load from nodes with large betweenness centrality to nodes with small betweenness centrality in the proceeding of computing collective routing table. Particularly, depending on a parameter that controls the optimization scale, the new routing can not only enlarge traffic capacity of networks more, but also enhance traffic efficiency with smaller average path length. Comparing results of previous routing strategies, it is shown that the present improved routing performs more effectively.     

Resilience of public transport networks against attacks

The behavior of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable to targeted attacks. In recent studies of public transport networks of fourteen major cities of the world it was shown that these systems when represented by appropriate graphs may exhibit scale-free behavior [Physica A 380, 585 (2007); Eur. Phys. J. B 68, 261 (2009)]. Our present analysis focuses on the effects that defunct or removed nodes have on the properties of public transport networks. Simulating different directed attack strategies, we derive vulnerability criteria that result in minimal strategies with high impact on these systems.     

Observation of transport in mesoscopic honeycomb-shaped networks

An electronic transport was observed in honeycomb-shaped mesoscopic (submicron) networks at liquid helium temperature. These networks were manufactured by the reactive ion etching of highly (nearly degenerated) and moderately doped n-GaAs epilayers through the initially structured, by self-organised patterning, polymer masks. The free electron transport was observed in the networks of thin, highly doped, n-GaAs epilayer. The detected multiple switching on theI–Vcharacteristics was explained in the framework of the model of a dynamic random resistor network. The existence of the patterned part of the thick, moderately doped, n-GaAs epilayer was the reason for the increase of the compensation ratio, the ionization energy and, as a result, the threshold voltage of the impact ionization of the shallow donor impurity level in the bulk of the epilayer.     

Cooling and transport of energetic ions due to the global geodesic acoustic mode

It is shown that (i) the destabilization of global Geodesic Acoustic modes (GAM or E-GAM) by passing energetic ions in tokamaks can be accompanied with a considerable energy transfer from these ions to the mode; (ii) the mode-induced slowing down of the energetic ions leads to a radial shift outwards/inwards of the ions moving in the direction counter to/of the plasma current, in spite of the fact that the canonical angular momentum of the particles is conserved during GAMs. Some practical consequences of these phenomena are discussed.     

Structure profile of complex networks by a model of precipitation

The organizational structure of a network is investigated with a simulated precipitation model which does not make use of prior knowledge about the community structure of the network. The result is presented as a structure profile through which various definitions of communities can be applied for specific applications. The simulated precipitation model performs the grouping of nodes so that nodes belonging to the same “community” automatically aggregate, thereby revealing regions of the adjacency matrix with denser interconnections. The process is analogous to massive particles precipitating towards the lower potential layer. Without loss of the infrastructure information, a community structure profile of a network can be obtained as the ground state of the Hamiltonian. The method is also applicable to directed and weighted networks.     

Detecting the optimal number of communities in complex networks

To obtain the optimal number of communities is an important problem in detecting community structures. In this paper, we use the extended measurement of community detecting algorithms to find the optimal community number. Based on the normalized mutual information index, which has been used as a measure for similarity of communities, a statistic Ω(c) is proposed to detect the optimal number of communities. In general, when Ω(c) reaches its local maximum, especially the first one, the corresponding number of communities c is likely to be optimal in community detection. Moreover, the statistic Ω(c) can also measure the significance of community structures in complex networks, which has been paid more attention recently. Numerical and empirical results show that the index Ω(c) is effective in both artificial and real world networks.     

Experimental verification of the optimal tuning of a tunable vibration neutralizer for global vibration control

A theoretical method has been previously proposed by the authors to optimize a tunable vibration neutralizer for global vibration control. However, experimental verification of the tuning method has yet to be presented. This paper aims to do this. It is shown that by using the proposed optimization method, the tunable vibration neutralizer can be as effective as an active control device in reducing global vibration of a structure. One particularly interesting finding is that although the vibration neutralizer is a passive device which is incapable of supplying energy to a system, it appears to be as effective as active control in reducing the global vibration of a structure, even in the frequency range where the control device is required to supply energy.