Decoupling process for better synchronizability on scale-free networks

DLS: A Link Prediction Method Based on Network Local Structure for Predicting Drug-Protein Interactions

The studies on drug-protein interactions (DPIs) had significant for drug repositioning, drug discovery, and clinical medicine. The biochemical experimentation (in vitro) requires a long time and high cost to be confirmed because it is difficult to estimate. Therefore, a feasible solution is to predict DPIs efficiently with computers. We propose a link prediction method based on drug-protein interaction (DPI) local structural similarity (DLS) for predicting the DPIs. The DLS method combines link prediction and binary network structure to predict DPIs. The ten-fold cross-validation method was applied in the experiment. After comparing the predictive capability of DLS with the improved similarity-based network prediction method, the results of DLS on the test set are significantly better. Moreover, several candidate proteins were predicted for three approved drugs, namely captopril, desferrioxamine and losartan, and these predictions are further validated by the literature. In addition, the combination of the Common Neighborhood (CN) method and the DLS method provides a new idea for the integrated application of the link prediction method.

Enhancing network synchronizability by strengthening a single node

In improving the stability of complex dynamical systems, an outstanding problem is how to achieve the desired performance at a low cost. For engineering and biological complex systems whose performance and functionality rely on the synchronous motion of their units, an important question related to the performance-cost-balance problem is how to improve efficiently the system synchronizability when a small amount of additional coupling resource is available. Here, employing a complex network of coupled chaotic oscillators as the model, we address this question by introducing a small amount of coupling intensity to only a single oscillator and investigate how the improvement of the network synchronizability is dependent on the location of the target oscillator. Theoretical analysis shows that, to achieve the maximum network synchronizability, the target oscillator to be strengthened should be chosen according to the eigenvector of the most unstable mode. Based on the theoretical finding, we further propose a single-node-based scheme for improving synchronization: the eigenvector-centrality-based strengthening scheme. We describe in detail how to apply this scheme under different synchronization scenarios and justify its efficiency in various network models by numerical simulations. The performance of the new scheme is compared with the conventional ones based on betweenness, closeness, and degree centralities, and it is shown that the new scheme has a clear advantage over the conventional ones. Furthermore, by a brute-force search of the target oscillator over the network, it is verified numerically that the oscillator identified by the new scheme indeed gives the best synchronization performance.

Perturbation analysis and comparison of network synchronization methods

In many networked systems, synchronization is important and useful, and how to enhance synchronizability is an interesting problem. Based on the matrix perturbation theory, we analyze five methods of network synchronization enhancement, including the link removal, node removal, dividing hub node, pull control, and pinning control methods, and obtain explicit expressions for eigenvalue changes. By these comparisons, we find that, among all these methods, the pull control method is remarkable, as it can extend the synchronization (coupling strength) region from both the left and right sides, for any controlled node. Extensive simulation results are given to support the accuracy of the perturbation-based analysis.

Control for a synchronization-desynchronization switch

How to freely enhance or suppress synchronization of networked dynamical systems is of great importance in many disciplines. A unified precise control method for a synchronization-desynchronization switch, called the pull-push control method, is suggested. Namely, synchronization can be achieved when the original systems are desynchronous by pulling (or protecting) one node or a certain subset of nodes, whereas desynchronization can be accomplished when the systems are already synchronous by pushing (or kicking) one node or a certain subset of nodes. With this method, the controlled nodes should be chosen by the generalized eigenvector centrality of the critical synchronization mode of the Laplacian matrix. Compared with existing control methods for synchronization, it displays high efficiency, flexibility, and precision as well.

Suppressing traffic-driven epidemic spreading by edge-removal strategies

The interplay between traffic dynamics and epidemic spreading on complex networks has received increasing attention in recent years. However, the control of traffic-driven epidemic spreading remains to be a challenging problem. In this Brief Report, we propose a method to suppress traffic-driven epidemic outbreak by properly removing some edges in a network. We find that the epidemic threshold can be enhanced by the targeted cutting of links among large-degree nodes or edges with the largest algorithmic betweenness. In contrast, the epidemic threshold will be reduced by the random edge removal. These findings are robust with respect to traffic-flow conditions, network structures, and routing strategies. Moreover, we find that the shutdown of targeted edges can effectively release traffic load passing through large-degree nodes, rendering a relatively low probability of infection to these nodes.

Local MEG networks: the missing link between protein expression and epilepsy in glioma patients?

Connectivity and network analysis in neuroscience has been applied to multiple spatial scales, but the links between these different scales have rarely been investigated. In tumor-related epilepsy, altered network topology is related to behavior, but the molecular basis of these observations is unknown. We elucidate the associations between microscopic features of brain tumors, local network topology, and functional patient status. We hypothesize that expression of proteins related to tumor-related epilepsy is directly correlated with network characteristics of the tumor area. Glioma patients underwent magnetoencephalography, and functional network topology of the tumor area was used to predict tissue protein expression patterns of tumor tissue collected during neurosurgery. Protein expression and network topology were interdependent; in particular between-module connectivity was selectively associated with two epilepsy-related proteins. Total number of seizures was related to both the role of the tumor area in the functional network and to protein expression. Importantly, classification of protein expression was predicted by between-module connectivity with up to 100% accuracy. Thus, network topology may serve as an intermediate level between molecular features of tumor tissue and symptomatology in brain tumor patients, and can potentially be used as a non-invasive marker for microscopic tissue characteristics.

Interplay between collective behavior and spreading dynamics on complex networks

There are certain correlations between collective behavior and spreading dynamics on some real complex networks. Based on the dynamical characteristics and traditional physical models, we construct several new bidirectional network models of spreading phenomena. By theoretical and numerical analysis of these models, we find that the collective behavior can inhibit spreading behavior, but, conversely, this spreading behavior can accelerate collective behavior. The spread threshold of spreading network is obtained by using the Lyapunov function method. The results show that an effective spreading control method is to enhance the individual awareness to collective behavior. Many real-world complex networks can be thought of in terms of both collective behavior and spreading dynamics and therefore to better understand and control such complex networks systems, our work may provide a basic framework.

Induced synchronization of a mobile agent network by phase locking

We investigate synchronization issues of a set of mobile agents in plane, where each agent carries an identical chaotic oscillator and interacts with its neighbors through a blinking coupling mechanism. We discuss the effect of blinking pattern on synchronization of the related network. In particular, we show that phase locking of the blinking behavior can dramatically enhance synchronizability of the mobile agent network, while the random blinking pattern works little. Also, we show that by assessing the convergence time, the mobile agent networks with different blinking periods and duty ratios share a common idle duration which is independent of both the blinking period and the corresponding duty ratio.

Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions

Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by the network has resisted comprehensive characterization within the prevailing paradigm that interactions facilitating pairwise synchronization also facilitate collective synchronization. Here we challenge this paradigm and show that networks with best complete synchronization, least coupling cost, and maximum dynamical robustness, have arbitrary complexity but quantized total interaction strength, which constrains the allowed number of connections. It stems from this characterization that negative interactions as well as link removals can be used to systematically improve and optimize synchronization properties in both directed and undirected networks. These results extend the recently discovered compensatory perturbations in metabolic networks to the realm of oscillator networks and demonstrate why "less can be more" in network synchronization.

Synchronization performance of complex oscillator networks

Recently, synchronization of complex networks has attracted increasing attention from various research fields. However, most previous works focused on the stability of synchronization manifold. In this paper, we analyze the time-delay tolerance and converging speed of synchronization. Our theoretical analysis and extensive simulations show that the critical value of time delay for network synchronization is inversely proportional to the largest Laplacian eigenvalue, the converging speed without time delay is proportional to the second least Laplacian eigenvalue, and the time delay could increase the converging speed linearly for heterogeneous networks and significantly for homogeneous networks.

Three structural properties reflecting the synchronizability of complex networks

During the process of adding links, we find that the synchronizability of the classical Barabási-Albert (BA) scale-free or Watts-Strogatz (WS) small-world networks can be statistically quantified by three essentially structural quantities of these networks, i.e., the eccentricity, variance of the degree distribution, and clustering coefficients. The results indicate that both the eccentricity and clustering coefficient are positively linearly correlated with synchronizability, while the variance is negatively linearly correlated. Moreover, the efficiency of some particular strategies of adding links to change the synchronizability is also investigated. This information can be used to guide us to design corresponding strategies of structure-evolving processes to manipulate the synchronizability of a given network.

Entraining the topology and the dynamics of a network of phase oscillators

We show that the topology and dynamics of a network of unsynchronized Kuramoto oscillators can be simultaneously controlled by means of a forcing mechanism which yields a phase locking of the oscillators to that of an external pacemaker in connection with the reshaping of the network's degree distribution. The entrainment mechanism is based on the addition, at regular time intervals, of unidirectional links from oscillators that follow the dynamics of a pacemaker to oscillators in the pristine graph whose phases hold a prescribed phase relationship. Such a dynamically based rule in the attachment process leads to the emergence of a power-law shape in the final degree distribution of the graph whenever the network is entrained to the dynamics of the pacemaker. We show that the arousal of a scale-free distribution in connection with the success of the entrainment process is a robust feature, characterizing different networks' initial configurations and parameters.

Onset of synchronization in weighted scale-free networks

We investigate Kuramoto dynamics on scale-free networks to include the effect of weights, as weighted networks are conceivably more pertinent to real-world situations than unweighted networks. We consider both symmetric and asymmetric coupling schemes. Our analysis and computations indicate that more links in weighted scale-free networks can either promote or suppress synchronization. In particular, we find that as a parameter characterizing the weighting scheme is varied, there can be two distinct regimes: a normal regime where more links can enhance synchronization and an abnormal regime where the opposite occurs. A striking phenomenon is that for dense networks for which the mean-field approximation is satisfied, the point separating the two regimes does not depend on the details of the network structure such as the average degree and the degree exponent. This implies the existence of a class of weighted scale-free networks for which the synchronization dynamics are invariant with respect to the network properties. We also perform a comparison study with respect to the onset of synchronization in Kuramoto networks and the synchronization stability of networks of identical oscillators.

Rewiring networks for synchronization

We study the synchronization of identical oscillators diffusively coupled through a network and examine how adding, removing, and moving single edges affects the ability of the network to synchronize. We present algorithms which use methods based on node degrees and based on spectral properties of the network Laplacian for choosing edges that most impact synchronization. We show that rewiring based on the network Laplacian eigenvectors is more effective at enabling synchronization than methods based on node degree for many standard network models. We find an algebraic relationship between the eigenstructure before and after adding an edge and describe an efficient algorithm for computing Laplacian eigenvalues and eigenvectors that uses the network or its complement depending on which is more sparse.

Network synchronizability analysis: a graph-theoretic approach

This paper addresses the fundamental problem of complex network synchronizability from a graph-theoretic approach. First, the existing results are briefly reviewed. Then, the relationships between the network synchronizability and network structural parameters (e.g., average distance, degree distribution, and node betweenness centrality) are discussed. The effects of the complementary graph of a given network and some graph operations on the network synchronizability are discussed. A basic theory based on subgraphs and complementary graphs for estimating the network synchronizability is established. Several examples are given to show that adding new edges to a network can either increase or decrease the network synchronizability. To that end, some new results on the estimations of the synchronizability of coalescences are reported. Moreover, a necessary and sufficient condition for a network and its complementary network to have the same synchronizability is derived. Finally, some examples on Chua circuit networks are presented for illustration.

Phase locking induces scale-free topologies in networks of coupled oscillators

An initial unsynchronized ensemble of networking phase oscillators is further subjected to a growing process where a set of forcing oscillators, each one of them following the dynamics of a frequency pacemaker, are added to the pristine graph. Linking rules based on dynamical criteria are followed in the attachment process to force phase locking of the network with the external pacemaker. We show that the eventual locking occurs in correspondence to the arousal of a scale-free degree distribution in the original graph.

Geographical effect on small-world network synchronization

We investigate the geographical effect on the synchronization of small-world oscillator networks. We construct small-world geographical networks by randomly adding links to one- and two-dimensional regular lattices, and we find that the synchronizability is a nonmonotonic function of both the coupling strength and the geographical distance of randomly added shortcuts. Our findings demonstrate that the geographical effect plays an important role in network synchronization, which may shed some light on the study of collective dynamics of complex networks.

Paths to globally generalized synchronization in scale-free networks

We apply the auxiliary-system approach to study paths to globally generalized synchronization in scale-free networks of identical chaotic oscillators, including Hénon maps, logistic maps, and Lorentz oscillators. As the coupling strength epsilon between nodes of the network is increased, transitions from partially to globally generalized synchronization and intermittent behaviors near the synchronization thresholds, are found. The generalized synchronization starts from the hubs of the network and then spreads throughout the whole network with the increase of epsilon . Our result is useful for understanding the synchronization process in complex networks.

Enhanced synchronizability via age-based coupling

In this Brief Report, we study the synchronization of growing scale-free networks. An asymmetrical age-based coupling method is proposed with only one free parameter alpha . Although the coupling matrix is asymmetric, our coupling method could guarantee that all the eigenvalues are non-negative reals. The eigenratio R will approach 1 in the large limit of alpha .