Scale-free Networks Research Articles

Multipopulation GA/IWO with Coupled Scale-Free Networks for Solving Flexible Job-Shop Scheduling Problems

In recent years, an increasing number of population-based metaheuristic algorithms have been proposed to solve the flexible job-shop scheduling problem (FJSP) according to its practicality and complexity. Most of these algorithms are single-population-based and hence are very susceptible to becoming trapped in local optimal values. Thus, multipopulation methods are widely used to improve these algorithms, resulting in multipopulation algorithms. These multipopulation algorithms have been widely studied in the context of single-layer complex networks recently. However, coupled networks used to control two (or more) algorithms simultaneously to get a better algorithm are always ignored in literature. Therefore, in this paper, using coupled scale-free networks (with different scaling exponents) to control the genetic algorithm (GA) and the invasive weed optimization (IWO) simultaneously, a multipopulation GA/IWO with coupled scale-free networks (MPGAIWO-SF) is proposed to solve FJSP. Then, we study how some parameters (e.g., subpopulation size, subpopulation number, and scaling exponent) of MPGAIWO-SF affect its performance, which is also ignored in literature. The simulation results illustrate that (1) the performance of MPGAIWO-SF is significantly improved compared with that of GA and IWO; (2) as the subpopulation size increases, the performance of MPGAIWO-SF first becomes better and then remains almost unchanged; (3) as the subpopulation number increases, the performance of MPGAIWO-SF first becomes better and then decreases rapidly; and (4) the performance of MPGAIWO-SF becomes worse slightly as the scaling exponent decreases. Finally, solving more FJSP instances, the MPGAIWO-SF with optimized parameters is compared with other related algorithms to verify its effectiveness.

Optimal routing strategy based on sine function for scale-free networks

The escalation of network traffic drives it imperative to enhance network traffic capacity and alleviate congestion. We propose a novel routing strategy in accordance with the properties of sine function. In simulation experiments, our strategy is compared with the efficient routing (ER) strategy. The phase change point of network from free state to congestion state can accurately define network traffic capacity. By using the optimal parameter of our strategy, the traffic capacity of network can be enhanced and the average path length can be reduced under each network size. What’s more, load variance and total load under our strategy are lower, which indicates that the total load is smaller and the load distribution is more uniform when compared to the case of ER strategy.

Assessing Graph Robustness through Modified Zagreb Index

Graph robustness or network robustness is the ability that a graph or a network preserves its connectivity or other properties after the loss of vertices and edges, which has been a central problem in the research of complex networks. In this paper, we introduce the Modified Zagreb index and Modified Zagreb index centrality as novel measures to study graph robustness. We theoretically find some relationships between these novel measures and some other graph measures. Then, we use Modified Zagreb index centrality to analyze the robustness of BA scale-free networks, ER random graphs and WS small world networks under deliberate or random vertex attacks. We also study the correlations between this new measure and some other existed measures. Finally, we use Modified Zagreb index centrality to study the robustness of two real world networks. All these results demonstrate the efficiency of Modified Zagreb index centrality for assessing the graph robustness.

Resilience enhancement of renewable cyber–physical power system against malware attacks

The widespread application of cyber technologies and Renewable Energy Sources (RESs) has gradually transformed traditional power systems into renewable Cyber–Physical Power Systems (CPPSs), which are increasingly threatened by malware attacks. In this paper, we develop an original and novel simulation framework with consideration of both malware attack process and the uncertainty of RESs to quantitatively analyze the resilience of renewable CPPS. Based on the framework, we consider different stages of the resilience process and propose corresponding prevention and restoration methods to enhance the resilience of the system. The efficacy and applicability of our proposed methods are demonstrated in a test renewable CPPS formed by coupling the IEEE 39 Bus System with a scale-free communication network. Experimental results reveal that accurate RES output forecast and a disassortative communication network can improve the resilience of renewable CPPS against malware attacks.

On the effect of memory on the Prisoner’s Dilemma game in correlated networks

Game theory is fundamental to understanding cooperation between agents. The Prisoner’s Dilemma is a well-known model extensively studied in complex networks. However, previous works ignore players’ memory, and the decisions about the strategies are based only on the latest games. At the same time, in real-world games, players generally consider the current situation and previous experiences when deciding their strategy. In this paper, we study how memory influences cooperation in correlated networks. We consider the evolutionary Prisoner’s Dilemma game on random and scale-free networks presenting degree–degree correlation. Through extensive simulations, we show that assortativity can improve cooperation when the temptation to defect increases. Moreover, our results suggest that including memory decreases the network structure’s influence on cooperation. Our study contributes to understanding the role of the network topology and the player’s memory on cooperation.

Temperature-controlled propagation of spikes in neuronal networks

Temperature plays a vital role in the functioning of biological organisms and there often exists an optimal temperature for their best performance. In this work, we investigate the role of temperature on spike propagation in scale-free and small-world neuronal networks, where a single neuron is chosen randomly for receiving a stimulus current. Upon exploiting the dominant phase-advanced driving (DPAD) method, the complex neuronal network is seen as a regular feed-forward multilayer neuronal network. The propagation route is then clearly identified, and many traveling-like waves are formed along the propagation route. Interestingly, we find that temperature not only controls the shortest path of propagation but also regulates the response time of a single neuron. The propagation speed is also maximized for an optimal choice of temperature at which the spike rapidly propagates through the entire neuronal network. Our findings extend the current understanding of the neuronal networks functioning and provide new insights into the existence of an optimal temperature as seen in our experiments on several living biological systems.

Resilience Assessment of an Urban Metro Complex Network: A Case Study of the Zhengzhou Metro

An urban metro network is susceptible to becoming vulnerable and difficult to recover quickly in the face of an unexpected attack on account of the system’s complexity and the threat of various emergencies. Therefore, it is necessary to assess the resilience of urban metro networks. However, the research on resilience assessment of urban metro networks is still in the development stage, and it is better to conduct said research using a technique which combines many attributes, multiple methods, and several cases. Therefore, based on the complex network modeling and topological characteristics analysis of metro systems, a metro network’s robustness and vulnerability measurement method under node interruption and edge failure is proposed for the first time in this study. Then, considering the three cases of general station interruption, interchange station interruption, and traffic tunnel failure, a quantitative resilience assessment model of metro networks is put forward, and the corresponding recovery strategies are discussed. Finally, a case study of the Zhengzhou Metro Network (ZZMN) under an extreme rainstorm is conducted to demonstrate the viability of the proposed model. The results show that ZZMN possesses scale-free and small-world network properties, and it is robust to random interruptions but vulnerable to deliberate attacks. ZZMN still needs to improve its effectiveness in information transmission. The centrality distribution for each node in the ZZMN network differs significantly, and each node’s failure has a unique impact on the network. The larger the DC, BC, and PR of a node is, the lower the network’s robustness after its removal is, and the stronger the vulnerability is. Compared with the three cases of general station interruption, interchange station interruption, and traffic tunnel failure, the network loss caused by tunnel failure was the lowest, followed by general station interruption, and the interruption at interchange stations was the most costly. Given the failures under various cases, the metro management department should prioritize selecting the optimal recovery strategy to improve the resilience of the metro network system. This study’s findings can assist in making urban metro systems less vulnerable to emergencies and more resilient for a quick recovery, which can provide scientific theoretical guidance and decision support for the safety and resilient, sustainable development of urban metro systems.

The regulatory network of potential transcription factors and MiRNAs of mitochondria-related genes for sarcopenia.

Background: Mitochondrial dysfunction is a significant contributor to sarcopenia, but the mechanism remains unclear. Methods: In the present study, we downloaded GSE117525 and GSE8479 datasets from Gene Expression Omnibus (GEO), then the weighted correlation network analysis (WGCNA) was used to construct scale-free co-expression networks respectively. The key genes of aging muscle were obtained by overlapping key modules of two networks. Receiver operating characteristic (ROC) curve was drawn to explore the diagnostic efficacy of key genes. Finally, a transcription factor-key gene network was constructed based on ChEA3 platform and hTFtarget database, and a miRNA-key gene network was constructed using starBase and the multimiR R package. Results: The most positively or negatively correlated modules of the two datasets were identified, and genes related to oxidative phosphorylation and mitochondrial ribosomal proteins were identified as key genes. The diagnostic values were confirmed with ROC curves by self-verification (GSE117525 and GSE8479) and external verification (GSE47881). Then, Yin Yang 1 (YY1) was identified as the most important transcription factor of the transcription factor-key gene network. In addition, miRNAs related to key genes were also predicted. Conclusion: The findings of the present study provide a novel insight into the pathological mechanism of sarcopenia.

Root and shoot biology of Arabidopsis halleri dissected by WGCNA: an insight into the organ pivotal pathways and genes of an hyperaccumulator.

Arabidopsis halleri is a hyperaccumulating pseudo-metallophyte and an emerging model to explore molecular basis of metal tolerance and hyperaccumulation. In this regard, understanding of interacting genes can be a crucial aspect as these interactions regulate several biological functions at molecular level in response to multiple signals. In this current study, we applied a weighted gene co-expression network analysis (WGCNA) on root and shoot RNA-seq data of A. halleri to predict the related scale-free organ specific co-expression networks, for the first time. A total of 19,653 genes of root and 18,081 genes of shoot were grouped into 14 modules and subjected to GO and KEGG enrichment analysis. "Photosynthesis" and "photosynthesis-antenna proteins" were identified as the most enriched and common pathway to both root and shoot. Whereas "glucosinolate biosynthesis," "autophagy," and "SNARE interactions in vesicular transport" were specific to root, and "circadian rhythm" was found to be enriched only in shoot. Later, hub and bottleneck genes were identified in each module by using cytoHubba plugin based on Cytoscape and scoring the relevance of each gene to the topology of the network. The modules with the most significant differential expression pattern across control and treatment (Cd-Zn treatment) were selected and their hub and bottleneck genes were screened to validate their possible involvement in heavy metal stress. Moreover, we combined the analysis of co-expression modules together with protein-protein interactions (PPIs), confirming some genes as potential candidates in plantheavy metal stress and as biomarkers. The results from this analysis shed the light on the pivotal functions to the hyperaccumulative trait of A. halleri,giving perspective to new paths for future research on this species.

Stochastic resonance: The response to envelope modulation signal for neural networks with different topologies

Neurons receive complex multiple signals from different regions in the biology system, and the neuron information carried by the multi-frequency signals can be detected by the neural system. Noise can induce stochastic resonance and promote the response of the neural network to a weak signal. The responses to weak envelope modulation signals for the neural networks with different topologies are investigated under electromagnetic induction and Gaussian white noise. We analyze and compare the stochastic resonance with tuning system parameters. The results show that in the three different networks, network systems exhibit double resonance with the variation of noise and beat frequency. Appropriate noise and electromagnetic induction can promote the generation of stochastic resonance and affect the response of envelope modulation signal in the neural network. The difference is that the three different networks differ in the noise intensity required to induce stochastic resonance and the effective range of the electrical coupling strength. Unlike the other two networks, the Fourier coefficient in scale-free network increases with the electromagnetic induction, and the number of neurons has no affect on stochastic resonance. Our results are conducive to understanding the mechanism of stochastic resonance in envelope modulation signals and electromagnetic induction.

Accelerate minimum cut calculation by tree-cut mapping with local pruning

As a fundamental problem in graph theory, the minimum cut (min-cut) problem and solutions have many applications in networking related researches. A new approximation algorithm for the problem in undirected graph is proposed that can accelerate existing method by up to 6 orders of magnitude, while the preprocessing overhead is just a limited number of depth-first traversing. In the algorithm, after checking and recording the cut values of various types of traversal trees, the good upper bound on the min-cut value between any node pair can be approximated using the minimal cut value of all related traversal trees, and the upper bound is very likely to be the exact value. The independence between different traversal passes makes it ready for further acceleration using parallelization. The traversal tree-cut mapping algorithm with local pruning (TCLP) is compared with other methods using random, scale-free and real-world graphs, the results show that even the serial implementation of TCLP can achieve far larger acceleration ratio than existing methods while obtaining exact min-cut value of 99.9% node pairs. The results also indicate that TCLP is general enough to not rely on any special local graph structure and is seldom affected by graph types, thus can be used as an effective supplement to the existing methods.

Percolation transitions in interdependent networks with reinforced dependency links.

Dependence can highly increase the vulnerability of interdependent networks under cascading failure. Recent studies have shown that a constant density of reinforced nodes can prevent catastrophic network collapses. However, the effect of reinforcing dependency links in interdependent networks has rarely been addressed. Here, we develop a percolation model for studying interdependent networks by introducing a fraction of reinforced dependency links. We find that there is a minimum fraction of dependency links that need to be reinforced to prevent the network from abrupt transition, and it can serve as the boundary value to distinguish between the first- and second-order phase transitions of the network. We give both analytical and numerical solutions to the minimum fraction of reinforced dependency links for random and scale-free networks. Interestingly, it is found that the upper bound of this fraction is a constant 0.088 01 for two interdependent random networks regardless of the average degree. In particular, we find that the proposed method has higher reinforcement efficiency compared to the node-reinforced method, and its superiority in scale-free networks becomes more obvious as the coupling strength increases. Moreover, the heterogeneity of the network structure profoundly affects the reinforcement efficiency. These findings may provide several useful suggestions for designing more resilient interdependent networks.

Quasi-Synchronization of Delayed Stochastic Multiplex Networks via Impulsive Pinning Control

The quasi-synchronization problems of the delayed multiplex networks with stochastic perturbations are investigated in this article. Different from previous studies on complete synchronization for the delayed multiplex networks, quasi-synchronization, which is more practical and more challenging than complete synchronization, is discussed. To adopt a better cost-saving control, an impulsive pinning scheme is designed. That is, the key nodes in the multiplex networks are pinned and controlled at impulsive instants. At the same time, a virtual leader is introduced. Based on the theory of stochastic impulsive differential equations and the Lyapunov–Krasovskii functional method, the sufficient conditions are derived for the error systems to converge into a bounded region in the sense of the mean square. Therefore, stochastic quasi-synchronization is guaranteed. Finally, the two-layer Newman–Watts (NW) small-world networks and two-layer Barabási–Albert (BA) scale-free networks are provided to illustrate the effectiveness of the theoretical results.

The role of syntax in the formation of scale-free language networks

The overall structure of a network is determined by its micro features, which are different in both syntactic and non-syntactic networks. However, the fact that most language networks are small-world and scale-free raises the question: does syntax play a role in forming the scale-free feature? To answer this question, we build syntactic networks and co-occurrence networks to compare the generation mechanisms of nodes, and to investigate whether syntactic and non-syntactic factors have distinct roles. The results show that frequency is the foundation of the scale-free feature, while syntax is beneficial to enhance this feature. This research introduces a microscopic approach, which may shed light on the scale-free feature of language networks.

Characterization of a Class of Generalised Core-satellite Graphs Using Average Degree

Network equilibrium models are significantly distinct in supply chain networks, traffic networks, and e-waste flow networks. The idea of network equilibrium is strongly perceived while determining the tuner sets of a graph (network). Tuner sets are subsets of vertices of the graph G whose degrees are lower than the average degree of G, d(G) that can compensate or balance the presence of vertices whose degrees are greater than d(G). Generalised core-satellite graph <img src=image/13428150_01.gif> comprises <img src=image/13428150_02.gif> copies of <img src=image/13428150_03.gif> (the satellites) meeting in K_c (the core) and it belongs to the family of graphs of diameter two. It has a central core of vertices connected to a few satellites, where all satellite cliques need not be identical and can be of different sizes. Properties like hierarchical structure of large real-world networks, are competently modeled using core-satellite graphs [1, 2, 5]. This family of graphs exhibits the properties similar to scale-free network as they possess anomalous vertex connectivity, where a small fraction of vertices (the core) are densely connected. Since these graphs possess such a structural property, interesting results are obtained for these graphs when tuner sets are determined. In this paper, we have considered the graph <img src=image/13428150_04.gif>, with p > q, a subclass of the generalized core-satellite graph which is a join of η copies of the clique K_q and γ copies of the clique K_p with the core K₁. We have obtained the tuner set for this subclass and established the relation between the Top T(G) and the cardinality of the tuner set <img src=image/13428150_05.gif> through necessary and sufficient conditions. We analyze and characterize these graphs and obtain some interesting results while simultaneously examining the existence of tuner sets.

An Adversarial Dynamic Game to Controlling Information Diffusion under Typical Strategies on Online Social Networks

The diffusion of negative information, such as rumours, misinformation and computer viruses on Online Social Networks (OSNs), may lead to serious losses and consequences. And there are always some rational malicious spreaders, who strategically spread negative information. Therefore, how to control the information diffusion of the malicious spreader is a great challenge. In recent years, some studies have analyzed the controlling problem which belongs to the issue of influence blocking maximization (IBM) from the perspective of the large-scale strategy set on the game theory. However, the aforementioned methods cannot timely solve the controlling diffusion problem on high-speed OSNs. In this study, we achieve the purpose of effectively controlling diffusion on OSNs by blocking information under typical strategies. Based on the existing two-player Stackelberg zero-sum game model and evaluation methods of node’s importance on the network, we analyze the typical strategic dynamic game in which the blocker moves first and the spreader moves later on scale-free networks with different power exponent. Experimental results show that the absolute dominance strategy of the blocker is Leader Rank with 90.16% probability. And using Leader Rank can be relatively effective against malicious spreaders with 98.33% probability. When the power exponent of the network is smaller, it is more conducive to blocking information dissemination with fewer seed nodes.

DYNAMICS OF AN SIRS EPIDEMIC MODEL WITH PERIODIC INFECTION RATE ON A SCALE-FREE NETWORK

Influenced by seasonal changes, the infection rate of many infectious diseases fluctuates in cycles. In this paper, we propose and investigate an SIRS model on a scale-free network. To model seasonality, we assume that the infection rate is periodic. The existence and positivity of solutions of the proposed model are proved and the basic reproduction number [Formula: see text] is defined. The global stability of steady states is determined by rigorous mathematical analysis. When [Formula: see text], the disease-free equilibrium [Formula: see text] is globally asymptotically stable. When [Formula: see text], the system has a unique positive periodic solution [Formula: see text], and [Formula: see text] is globally asymptotically stable. Numerical simulations are performed to support our theoretic results, and the effects of various parameters on the amplitude and mean of infected individuals are studied. The sensitivity of parameters of the basic reproduction number [Formula: see text] is solved by the Sobol global sensitivity analysis method, and the results show that the effects of the parameters [Formula: see text] and [Formula: see text] on [Formula: see text] are remarkable.

Dynamics of semiflexible generalized scale-free polymer networks

We study the relaxation dynamics of a new type of hyperbranched polymer networks, which are constructed using a degree distribution specific to scale-free networks. The topology of the constructed networks is controlled through three parameters: γ, which measures the density of links in the network, the minimum allowed degree Kmin and the maximum allowed degree Kmax. The static properties of the polymers are investigated through the mean square radius of gyration. We study the dynamics in the framework of the generalized Gaussian structures model by monitoring in detail the influence of networks’ construction parameters, namely γ, Kmin, and Kmax, and the stiffness parameter q on the relaxation quantities: averaged monomer displacement, storage modulus and loss modulus. In the intermediate (time or frequency) regions of the dynamical quantities we encounter a scaling behavior for γ=2.5 and usually a non-scaling behavior for other values of γ. Switching on the stiffness parameter q one is able to destroy, create or enlarge some scaling regions for other combinations of the parameters. Another way to widen a scaling region is to slightly increase Kmin.

Investigation on the Distribution Characteristics of Chinese Continuing Education Based on the Community Detection Algorithm in Complex Networks.

In order to closely fit the characteristics of continuing education, the development of continuing education teaching activities under the network background should not only be combined with the characteristics of professional adult education but also make reasonable use of modern teaching models in the actual teaching process. Based on the community detection algorithm in complex networks, this article makes thorough research and analysis on the complexity of Chinese continuing education by using complex network technology. By establishing the characteristics of vertex degree distribution, average path length, and clustering coefficient of complex networks, it is confirmed that Chinese continuing education has scale-free network characteristics and small-world network characteristics. The three aspects of relationship strength comprehensively analyze the information dissemination speed, scope, interpretation, and application; through the combination of the ant colony algorithm and complex network technology, multiple information dissemination paths are abstracted in Chinese continuing education. The research shows that the application of complex network algorithms can effectively improve the speed and quality of continuing education in China. It is found that the government should increase the number of adult education projects and improve the level of project categories, form key adult education research basis to promote the diversification of research subjects, expand the space for adult education projects to balance regional and provincial differences and attach importance to basic research on adult education, and integrate applied research.

Control capacity and bimodality in target control

Controlling large networks is a fundamental problem and a great challenge in network science. Typically, full control is not necessary and infeasible. In many cases, only a preselected subset of nodes is required to be controlled, which is the target control problem. Each node does not participate in controlling the target set with equal probability, prompting us to quantify their contributions for target control. Here we develop a random sampling method to estimate the likelihood of each node participating as a driver node in target control configurations and demonstrate the unbiasedness of sampling. Each node is assigned with a role of critical, intermittent or redundant as it appears in all, some and none of the minimum driver node sets accordingly. We apply the method to Erdős-Rényi (ER) and scale-free (SF) networks and find that the fractions of critical and intermittent nodes increase as the scale of the target set increases. Furthermore, when the size of target node is fixed in SF networks, the fraction of redundant nodes may show a bimodal behavior as the networks become denser, leading to two control modes: centralized control and distributed control. The findings help understand the dynamics of control and offer tools for target control in complex systems.