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A striking discovery in the field of network science is that the majority of real networked systems have some universal structural properties. In general, they are simultaneously sparse, scale-free, small-world, and loopy. In this article, we investigate the second-order consensus of dynamic networks with such universal structures subject to white noise at vertices. We focus on the network coherence HSO characterized in terms of the $\mathcal {H}_{2}$ -norm of the vertex systems, which measures the mean deviation of vertex states from their average value. We first study numerically the coherence of some representative real-world networks. We find that their coherence HSO scales sublinearly with the vertex number $N$. We then study analytically HSO for a class of iteratively growing networks—pseudofractal scale-free webs (PSFWs), and obtain an exact solution to HSO, which also increases sublinearly in $N$ , with an exponent much smaller than 1. To explain the reasons for this sublinear behavior, we finally study HSO for Sierpinśki gaskets, for which HSO grows superlinearly in $N$ , with a power exponent much larger than 1. Sierpinśki gaskets have the same number of vertices and edges as the PSFWs but do not display the scale-free and small-world properties. We thus conclude that the scale-free, small-world, and loopy topologies are jointly responsible for the observed sublinear scaling of HSO. [ABSTRACT FROM AUTHOR]

Estimating dynamic effective connectivity (dEC) networks is crucial to understand the time-varying directional interconnections among brain regions. It is now widely understood that brain networks have the property of being scale-free. However, this property has seldom been considered and is often inadequately preserved using conventional dEC estimation methods. As a result, important hubs and network graphical characteristics cannot be accurately obtained. In this work, we develop a new method to use a group-wise penalty together with spatial sparsity and temporal smoothness regularizations (namely Group-wise Spatial–Temporal Regularizations, GSTR) for the inference of scale-free dEC networks from functional magnetic resonance imaging (fMRI). The method employs a time-varying vector autoregressive (VAR) model, where the model coefficients can be formed as adjacency matrices of the dEC networks. Meanwhile, the proposed group-wise regularization is able to preserve the connectivities of potential hubs in scale-free networks by grouping them as an entire set. To deal with the complexity of optimization with multiple regularizations, we propose an effective algorithm based on the augmented Lagrangian multiplier. The accuracy of the GSTR method is validated using a variety of synthetic datasets with the scale-free property. Furthermore, we apply the GSTR method to an open fMRI dataset recorded from a block design visual task-related experiment containing 255 healthy participants to estimate visual-induced dEC networks and find GSTR can achieve reasonable and interpretable dEC estimates. Results from both synthetic and real-world datasets suggest that the proposed GSTR method could serve as a powerful analytical tool to accurately infer scale-free dEC patterns. [ABSTRACT FROM AUTHOR]

Evolutionary computation algorithms allow solving optimization problems through defined iterations and stages. One of the most commonly employed techniques for this type of problem is differential evolution, which contains properties of small-world complex networks, whose study is important because of the results they generate for optimization problems. Considering the results obtained in previous works, which propose an evolutionary algorithm guided by complex small-world networks, a proposal is defined which contains complex scale-free networks, with the purpose of validating the averages generated by complex networks against the results obtained by the traditional evolutionary algorithm. An experiment was defined which allows evaluating the performance of the proposed model and that of the evolutionary algorithm by means of statistic indicators. Four optimization problems (Ackley, Beale, Camel, and Sphere) were also used to evaluate the hypothesis in the proposed model, its convergence, and the reduction of execution times compared to the base model. It was observed that the scale-free complex networks generated better averages than the traditional evolutionary algorithm and the small-world networks because they use a connection preferential mechanism between their nodes and guide the combination of individuals (solutions), thus improving the convergence rate and the performance of the evolutionary algorithm in general. [ABSTRACT FROM AUTHOR]

In genome-wide association studies, epistasis detection is of great significance for the occurrence and diagnosis of complex human diseases, but it also faces challenges such as high dimensionality and a small data sample size. In order to cope with these challenges, several swarm intelligence methods have been introduced to identify epistasis in recent years. However, the existing methods still have some limitations, such as high-consumption and premature convergence. In this study, we proposed a multi-objective artificial bee colony (ABC) algorithm based on the scale-free network (SFMOABC). The SFMOABC incorporates the scale-free network into the ABC algorithm to guide the update and selection of solutions. In addition, the SFMOABC uses mutual information and the K2-Score of the Bayesian network as objective functions, and the opposition-based learning strategy is used to improve the search ability. Experiments were performed on both simulation datasets and a real dataset of age-related macular degeneration (AMD). The results of the simulation experiments showed that the SFMOABC has better detection power and efficiency than seven other epistasis detection methods. In the real AMD data experiment, most of the single nucleotide polymorphism combinations detected by the SFMOABC have been shown to be associated with AMD disease. Therefore, SFMOABC is a promising method for epistasis detection. [ABSTRACT FROM AUTHOR]

Many real-world networks have scale-free characteristics and can be abstracted into scale-free networks. Aiming at the problem that scale-free networks have low fault tolerance in the face of malicious attacks, we focus on the selective forwarding attack behavior that exists widely in the networks, and build a selective forwarding attack model based on node importance. Moreover, according to the neighbor node’s malicious and non-malicious behavior, a load redistribution strategy for failed node is proposed. Then, the network’s damage degree is given to evaluate the comprehensive impact of cascading failure phenomenon on network connectivity and information integrity under selective forwarding attack. Finally, a cascading failure model of scale-free networks considering selective forwarding attack behavior is obtained. Based on this model, the propagation condition without triggering network cascading failure, the selective forwarding attack intensity threshold and the load loss ratio are obtained. By simulation on the classical BA scale-free network model, the results show that multiple nodes’ random failure occurs in scale-free networks, selective forwarding attack behavior is helpful to improve the connectivity of the network. Besides, the network exists selective forwarding attack intensity threshold, when attack intensity is greater than the intensity threshold, the malicious nodes will not fail because of the failure of the neighbor nodes. But, selective forwarding attack behavior can destroy the information integrity, and there is a negative correlation between the attack intensity and the information integrity. These results have certain guiding significance for cascade failure analysis and prevention method research and design in real life.

In order to study the impact of random environments during the spread of the disease, we propose a novel stochastic SIQS model on scale-free networks, which introduces stochastic perturbations to the infected rates. We first obtain the existence of global positive solutions. Moreover, by constructing appropriate stochastic Lyapunov functions, we prove sufficient conditions for extinction and persistence of the disease. Finally, we verify the analysis results through numerical simulations. In addition, the results of previous studies are also improved in our research. [ABSTRACT FROM AUTHOR]

Given they are two critical infrastructure areas, the security of electricity and gas networks is highly important due to potential multifaceted social and economic impacts. Unexpected errors or sabotage can lead to blackouts, causing a significant loss for the public, businesses, and governments. Climate change and an increasing number of consequent natural disasters (e.g., bushfires and floods) are other emerging network resilience challenges. In this paper, we used network science to examine the topological resilience of national energy networks with two case studies of Australian gas and electricity networks. To measure the fragility and resilience of these energy networks, we assessed various topological features and theories of percolation. We found that both networks follow the degree distribution of power-law and the characteristics of a scale-free network. Then, using these models, we conducted node and edge removal experiments. The analysis identified the most critical nodes that can trigger cascading failure within the network upon a fault. The analysis results can be used by the network operators to improve network resilience through various mitigation strategies implemented on the identified critical nodes. [ABSTRACT FROM AUTHOR]

Abstract Background The coronavirus disease 2019 (COVID-19) epidemic met coincidentally with massive migration before Lunar New Year in China in early 2020. This study is to investigate the relationship between the massive migration and the coronavirus disease 2019 (COVID-19) epidemic in China. Methods The epidemic data between January 25th and February 15th and migration data between Jan 1st and Jan 24th were collected from the official websites. Using the R package WGCNA, we established a scale-free network of the selected cities. Correlation analysis was applied to describe the correlation between the Spring Migration and COVID-19 epidemic. Results The epidemic seriousness in Hubei (except the city of Wuhan) was closely correlated with the migration from Wuhan between January 10 and January 24, 2020. The epidemic seriousness in the other provinces, municipalities and autonomous regions was largely affected by the immigration from Wuhan. By establishing a scale-free network of the regions, we divided the regions into two modules. The regions in the brown module consisted of three municipalities, nine provincial capitals and other 12 cities. The COVID-19 epidemics in these regions were more likely to be aggravated by migration. Conclusions The migration from Wuhan could partly explain the epidemic seriousness in Hubei Province and other regions. The scale-free network we have established can better evaluate the epidemic. Three municipalities (Beijing, Shanghai and Tianjin), eight provincial capitals (including Nanjing, Changsha et al.) and 12 other cities (including Qingdao, Zhongshan, Shenzhen et al.) were hub cities in the spread of COVID-19 in China.

Recently, [T. M. Gwizdałła, The swarm-like update scheme for opinion formation, in Computational Collective Intelligence, eds. N. T. Nguyen, G. A. Papadopoulos, P. Jedrzejowciz, B. Trawinski and G. Vossen (Springer International Publishing, Cham, 2017), pp. 66–75.] we have proposed the scheme of performing the opinion formation simulation based on popular global optimization mechanism — the Particle Swarm Optimization (PSO). The basic idea was to use the interaction between two potential directions of agents’ heading: those forced by the global opinion and those forced by the opinion of neighbors/colleagues. In the proposed paper, some enhancement of the proposed model is shown. We assume that, when performing the binary PSO-like update of system, we use the generalized version of logistic function. The results are promising in the sense that the introduced change increases explicitly, the number of possible solutions.

The properties of a scale-free network are little known; its node degree following a power-law distribution is among its few known properties. By selecting real-field scale-free networks from a network dataset and comparing them to other networks, such as random and non-scale-free networks, the topology characteristics of scale-free networks are identified. The assortative coefficient is identified as a key metric of a scale-free network. It is also identified that most scale-free networks have negative assortative coefficients. Traditional generation models of scale-free networks are evaluated based on the identified topology characteristics. Most representative models, such as BA and Holme&Kim, are not effective in generating real-field scale-free networks. A link-rewiring method is suggested that can control the assortative coefficient while preserving the node degree sequence. Our analysis reveals that it is possible to effectively reproduce the assortative coefficients of real-field scale-free networks through link-rewiring. [ABSTRACT FROM AUTHOR]

As a fundamental research object, the minimum edge dominating set (MEDS) problem is of both theoretical and practical interest. However, determining the size of a MEDS and the number of all MEDSs in a general graph is NP-hard, and it thus makes sense to find special graphs for which the MEDS problem can be exactly solved. In this paper, we study analytically the MEDS problem in the pseudofractal scale-free web and the Sierpiński gasket with the same number of vertices and edges. For both graphs, we obtain exact expressions for the edge domination number, as well as recursive solutions to the number of distinct MEDSs. In the pseudofractal scale-free web, the edge domination number is one-ninth of the number of edges, which is three-fifths of the edge domination number of the Sierpiński gasket. Moreover, the number of all MEDSs in the pseudofractal scale-free web is also less than that corresponding to the Sierpiński gasket. We argue that the difference of the size and number of MEDSs between the two studied graphs lies in the scale-free topology. [ABSTRACT FROM AUTHOR]

This paper investigates the evolutionary public goods game on a network and studies the effect of the leaders rewiring mechanism (LRM) on the evolution of cooperation. A trust mechanism is introduced to give information to the leader about the sincerity of the group. The network dynamics is driven by the LRM, allowing leaders to change their game groups if these groups are not trusted anymore. We investigate how the emergence of the network guided by LRM affects the transformation of individuals' strategies and empowers them to cooperate. We find that LRM plays a crucial role in the emergence of cooperation, by clustering the graph into regions with high clusters of cooperators and small one of defectors. LRM enables cooperators to form compact big clusters, thus reducing exploitation by defectors. [ABSTRACT FROM AUTHOR]

We study the algorithmic problem of finding the most "scale-free-like" spanning tree of a connected graph. This problem is motivated by the fundamental problem of genomic epidemiology: given viral genomes sampled from infected individuals, reconstruct the transmission network ("who infected whom"). We use two possible objective functions for this problem and introduce the corresponding algorithmic problems termedm-SF (-scale free) ands-SF Spanning Tree problems. We prove that those problems are APX- and NP-hard, respectively, even in the classes of cubic and bipartite graphs. We propose two integer linear programming (ILP) formulations for thes-SF Spanning Tree problem, and experimentally assess its performance using simulated and experimental data. In particular, we demonstrate that the ILP-based approach allows for accurate reconstruction of transmission histories of several hepatitis C outbreaks. [ABSTRACT FROM AUTHOR]

How did cooperation emerge and persist while betrayal was beneficial for individuals? Previous studies suggested that network reciprocity was a promising explanation. However, these studies usually analyzed cooperation performances of different types of networks separately and/or statically, thus failing to fully capture the co-evolution and interaction features in our history. We proposed a mechanism that analyzed the cooperation level of different types of networks under co-evolutionary circumstances of cooperation and heterogeneous networks. The paper adopted the prisoner's dilemma game and analyzed Erdos-Renyi (ER) random networks, Watts Strogatz (WS) small-world networks, and Barabasi-Albert (BA) scale-free networks. In this study, these networks were interconnected and continuously grew after gaming evolutions were stable. And the growth versions of WS and ER respectively were proposed that maintained their topology features. Comprehensive experimental results showed that high-level cooperation emerged and was maintained in scale-free networks. This advantage was strengthened with networks grew from a small scale to a middle scale. Moreover, once most nodes of a scale-free network evolved to be cooperators, the group cooperation they formed were able to survive in betrayer-prevailing and high betrayal temptation environments. These findings may deepen our understanding of the relationship between how cooperation evolved and why many social networks exhibited scale-free properties. [ABSTRACT FROM AUTHOR]

Most individuals opt for vaccination to acquire immunity protection and prevent disease transmission. However, individuals cannot obtain perfect immunity protection after vaccination, due to various factors such as the limitation of vaccine itself, storage and transportation. Failed vaccination experiences can alter individuals' perception of vaccination behavior. To analyze the influence of vaccine efficacy on vaccination behavior with adaptive perception, we propose a novel vaccination game model. The results demonstrate that for the moderate vaccination cost, the introduction of adaptive perception can promote vaccination behavior, and the promoting effect becomes more pronounced in the population with smaller perception fluctuation. Nonetheless, vaccination behavior is still constrained by a significant number of free-riders when vaccine effectiveness is high. Analyzing the distribution of strategies among individuals with different degrees, it is revealed that the reduction in vaccinated individuals influenced by free-riders predominantly occurs in individuals with low-degree. Furthermore, we examine the coupled effects of vaccination cost and vaccine efficacy on vaccination behavior, considering various levels of perception fluctuations. The results indicate the crucial role of vaccination cost in enhancing vaccination behavior, and previous findings also are consistent across scenarios with diverse vaccination cost. Our work contributes to an improved comprehension of vaccination behavior considering vaccine efficacy and perception. • Propose a novel vaccination game model with the vaccine efficacy and the adaptive perceived vaccination cost. • For the moderate vaccination cost, the introduction of adaptive perception can promote vaccination behavior. • The population with a smaller perception fluctuation has a more pronounced improvement in vaccination behavior. • Vaccination behavior is constrained by a significant number of free-riders when vaccine effectiveness is high. • The free-riders are mainly individuals with low-degree, when vaccine effectiveness is high. [ABSTRACT FROM AUTHOR]

Modeling Internet graphs at the autonomous-system (AS) level is helpful for recognizing and predicting the development trend of evolving Internet topology from a macro perspective. In contrast to the global statistical models such as the power-law distribution of node degrees, the structural decomposition models can more effectively represent the local connection. In this paper, we propose a structure-based model. Starting with the classification of links among the AS nodes, the proposed model partitions the core and periphery of Internet graphs into 16 atomic-level solid and dotted components. Additionally, the model captures the stable evolving features of these components based on the UCLA dataset that continuously explore Internet graphs over a long historic period from 2001 to 2015. Finally, according to the structure-based model, we design a new Internet-topology generator. Compared with the recently proposed generators, the advantages of our generator are as follows: (1) it accurately captures the structure decomposition property studied in this work, (2) it performs best on three statistical properties of the distance, assortativity coefficient, and maximum degree, and (3) it exhibits the best comprehensive performance in terms of runtime and multiple graph properties.

Understanding individual decisions in a world where communications and information move instantly via cell phones and the internet, contributes to the development and implementation of policies aimed at stopping or ameliorating the spread of diseases. In this manuscript, the role of official social network perturbations generated by public health officials to slow down or stop a disease outbreak are studied over distinct classes of static social networks. The dynamics are stochastic in nature with individuals (nodes) being assigned fixed levels of education or wealth. Nodes may change their epidemiological status from susceptible, to infected and to recovered. Most importantly, it is assumed that when the prevalence reaches a pre-determined threshold level, P*, information, called awareness in our framework, starts to spread, a process triggered by public health authorities. Information is assumed to spread over the same static network and whether or not one becomes a temporary informer, is a function of his/her level of education or wealth and epidemiological status. Stochastic simulations show that threshold selection P* and the value of the average basic reproduction number impact the final epidemic size differentially. For the Erdős-Rényi and Small-world networks, an optimal choice for P* that minimize the final epidemic size can be identified under some conditions while for Scale-free networks this is not case.

In this paper, we discuss the average path length for a class of scale-free modular networks with deterministic growth. To facilitate the analysis, we define the sum of distances from all nodes to the nearest hub nodes and the nearest peripheral nodes. For the unweighted network, we find that whether the scale-free modular network is single-hub or multiple-hub, the average path length grows logarithmically with the increase of nodes number. For the weighted network, we deduce that when the network iteration t tends to infinity, the average weighted shortest path length is bounded, and the result is independent of the connection method of network. [ABSTRACT FROM AUTHOR]

Semantic knowledge has been investigated using both online and offline methods. One common online method is category recall, in which members of a semantic category like "animals" are retrieved in a given period of time. The order, timing, and number of retrievals are used as assays of semantic memory processes. One common offline method is corpus analysis, in which the structure of semantic knowledge is extracted from texts using co-occurrence or encyclopedic methods. Online measures of semantic processing, as well as offline measures of semantic structure, have yielded data resembling inverse power law distributions. The aim of the present study is to investigate whether these patterns in data might be related. A semantic network model of animal knowledge is formulated on the basis of Wikipedia pages and their overlap in word probability distributions. The network is scale-free, in that node degree is related to node frequency as an inverse power law. A random walk over this network is shown to simulate a number of results from a category recall experiment, including power law-like distributions of inter-response intervals. Results are discussed in terms of theories of semantic structure and processing.

The development of the wireless sensor networks (WSNs) in the recent years is mainly due to the readily obtainable low-cost and short-range sensors. The objective of the WSN system is to both sense and transmit the real-time sense contents belonging to a particular monitoring environment for the back-end system for performing the necessary processing and analysis tasks. One of the most significant tasks of prime consideration is to ensure the safety and privacy aspects of the WSN in a wireless channel. The ultimate idea of the wireless sensor network is to preserve the limited node energy and thereby process the huge volume of data without affecting the robustness. The main objective of this work is to strengthen the robustness of the wireless sensor network that particularly relies on a scale-free type of network. The ability of the Scale-free WSNs in tolerating the random attacks efficiently have made them appear significant; on the other hand, they may be vulnerable to certain malicious attacks, that specifically targets the significant nodes in the system. This limitation has been addressed in this work by means of introducing a new modelling strategy called sequential probability ratio test (SPRT) that assists in the generation of scale-free network topologies. SPRT, a unique robustness improvising algorithm for the scale free type of WSNs, has been designed in this work and also the proposed SPRT is compared with the existing EROSE technique. The wide range of experimental results thus ensure that the introduced SPRT modelling methodology can achieves robustness and enhances the security of WSN. [ABSTRACT FROM AUTHOR]

Simultaneous use of data repeated levelling measurements and continuous GNSS observations allows increasing the spatial resolution of geodynamics models. For this purpose, it is necessary to create a single network, a so-called hybrid network. This paper aims at examining the possibility of using scale-free network theory to determine the most relevant common points in hybrid networks using the distance criterion. Used on European network points: UELN (United European Levelling Network) and EPN (European Permanent GPS Network) and the regional network. In the hybrid network (UELN + EPN), 18 pseudo-nodal points with the highest number of links were identified. The accepted distance criterion shows that about 90 % of the EPN points can be used as common points. The application of the scale-free network theory allows determining the significance of points in a hybrid network. [ABSTRACT FROM AUTHOR]

The complexity and changeability of electromagnetic environment make the deficiency of traditional methods of electromagnetic protection increasingly prominent. The organisms with the regulation of nervous system have advantages of self-adaptive, self-organizing, and self-repairing. Therefore, it is necessary to explore a new thought on electromagnetic protection by drawing from the biological self-adaptive advantage. In this study, two kinds of scale-free spiking neural networks (sfSNNs) with different clustering coefficients are constructed. Then, the antiinterference function of the sfSNNs under the ac magnetic field stimulation is evaluated and compared. Finally, the antiinterference mechanism is analyzed. The experimental results show that both sfSNNs have a certain antiinterference function, and the performance of the sfSNN with high clustering coefficient is better than that with low clustering coefficient in the antiinterference function; the dynamic evolution of neural information processing in the sfSNN is clarified; and the dynamic regulation of synaptic plasticity is the intrinsic factor of the antiinterference function of the sfSNNs. This study lays a theoretical foundation for the electromagnetic protection of electronic system based on adaptive bionic mechanism. [ABSTRACT FROM AUTHOR]

Knowledge about the molecular basis of SARS-CoV-2 infection is incipient. However, recent experimental results about the virus interactome have shown that this single-positive stranded RNA virus produces a set of about 28 specific proteins grouped into 16 non-structural proteins (Nsp1 to Nsp16), four structural proteins (E, M, N, and S), and eight accessory proteins (orf3a, orf6, orf7a, orf7b, orf8, orf9b, orf9c, and orf10). In this brief communication, the network model of the interactome of these viral proteins with the host proteins is analyzed. The statistical analysis of this network shows that it has a modular scale-free topology in which the virus proteins orf8, M, and Nsp7 are the three nodes with the most connections (links). This result suggests the possibility that a simultaneous pharmacological attack on these hubs could assure the destruction of the network and the elimination of the virus.

Many complex systems are abstractly regarded as complex networks in the study of complicated problems. The research field of information spreading in complex networks has attracted extensive interest. Many spreading strategies have been proposed for improving the spreading efficiency in complex networks. However, the strategies differ in terms of performance in various complex networks. In this paper, a hybrid and effective method for improving the spreading efficiency in small-world networks and assortative scale-free networks is proposed. The proposed method can be applied to solve the essential problem of low spreading efficiency due to spreading to small-degree vertices. The proposed method combines two strategies: 1) a set of top small-degree vertices are specified as the initial spreaders and 2) vertices preferentially spread information to large-degree neighbors. Sixty-eight groups of Monte Carlo experiments are conducted in three real complex networks and seventeen synthetic complex networks. According to the experimental results and theoretical analysis, the proposed method is efficient for improving the spreading efficiency in small-world networks and assortative scale-free networks. Moreover, in assortative scale-free networks, the improvement in the spreading efficiency that is realized via the proposed method increases with the assortativity coefficient.

Complex networks are extensively applied to study the dynamics of real systems, such as how information spreads in social networks. Most existing spreading strategies are studied based on simple information spreading model, such as the optimized compartmental models in epidemics. However, for information spreading in social networks, more complex social factors should be considered. In this paper, we build an information spreading model that involves information decays and partial interactions based on multi-agent modeling in scale-free networks. The positive effects of a set of vertices on the spreading efficiency are discovered based on the proposed information spreading model. On the basis of the positive effects of those vertices, we propose an efficient spreading strategy for extending the spreading in scale-free networks. Ten groups of Monte Carlo experiments are conducted to verify the effectiveness of the proposed strategy. The experimental results demonstrated the effectiveness and validity of the proposed strategy. The proposed strategy can be exploited to extend the spread of warnings or control the spread of rumors in social networks.

Abstract Background The majority of cancer-related deaths are due to lung cancer, and there is a need for reliable diagnostic biomarkers to predict stages in non-small cell lung cancer cases. Recently, microRNAs were found to have potential as both biomarkers and therapeutic targets for lung cancer. However, some of the microRNA’s functions are unknown, and their roles in cancer stage progression have been mostly undiscovered in this clinically and genetically heterogeneous disease. As evidence suggests that microRNA dysregulations are implicated in many diseases, it is essential to consider the changes in microRNA-target regulation across different lung cancer subtypes. Results We proposed a pipeline to identify microRNA synergistic modules with similar dysregulation patterns across multiple subtypes by constructing the MicroRNA Dysregulational Synergistic Network. From the network, we extracted microRNA modules and incorporated them as prior knowledge to the Sparse Group Lasso classifier. This leads to a more relevant selection of microRNA biomarkers, thereby improving the cancer stage classification accuracy. We applied our method to the TCGA Lung Adenocarcinoma and the Lung Squamous Cell Carcinoma datasets. In cross-validation tests, the area under ROC curve rate for the cancer stages prediction has increased considerably when incorporating the learned microRNA dysregulation modules. The extracted modules from multiple independent subtypes differential analyses were found to have high agreement with microRNA family annotations, and they can also be used to identify mutual biomarkers between different subtypes. Among the top-ranked candidate microRNAs selected by the model, 87% were reported to be related to Lung Adenocarcinoma. The overall result demonstrates that clustering microRNAs from the dysregulation pattern between microRNAs and their targets leads to biomarkers with high precision and recall rate to known differentially expressed disease-associated microRNAs. Conclusions The results indicated that our method improves microRNA biomarker selection by detecting similar microRNA dysregulational synergistic patterns across the multiple subtypes. Since microRNA-target dysregulations are implicated in many cancers, we believe this tool can have broad applications for discovery of novel microRNA biomarkers in heterogeneous cancer diseases.

With the rapid development of the internet,the network bearer content is gradually transformed from a service based on connection-based information interaction to a service based on content sharing (video).The network transmits a large amount of redundant information,resulting in abnormal large-scale investment.And the quality of the service is difficult to guarantee,and it is urgent to study and construct a network that matches the business development.The content sharing connection relationship and the communication network architecture connection relationship were studied,and the two-dimensional poor time distribution or three-dimensional distribution and other implementation methods were explored.CDN was constructed to construct the content edge node,and the core network,wireless network,bearer network architecture and network element deployment were optimized.And space-based network such as satellite was considered to introduce to build a scale-free small hop network on the existing communication network to achieve matching of network architecture and content distribution.

Power information systems are important for the operation of power systems. When part of the power information system fails, the loads will be redistributed. Due to network congestions, cascading failures may occur, and additional devices or sub-systems would fail. In this paper, power information system was abstracted to a complex network. The traditional load-capacity model was improved to satisfy the characteristics of power information systems. The improved model also reflects the distribution of power information system nodes. Moreover, two vulnerability indices were established from the perspective of both topological structure and network properties, and the vulnerability assessment process was proposed. Finally, cascading failure process and the impact of redundancy factor were analyzed in case study. The effectiveness and rationality of this method was verified by the results.

Strategic emerging industrial cluster network as an important form of the current industrial development, with an intensive technological innovation, prominent economies of scale and knowledge spillovers, and other characteristics, is a symbol of strategic emerging industry formation and an effective model for its development. In this paper, the Logistic model is used to characterize the strategic emerging industry cluster's life cycle. Then, the scale-free evolution model being optimized based on the growth rate of strategic emerging industrial clusters and gray number being introduced, an evolution model of the strategic emerging industrial network is constructed considering the growth of innovators flow, the evolution process, and the stability state of the strategic emerging industrial cluster network are analyzed. Finally, an example is given to simulate and comparatively analyze the characteristics of the inflection point with the change of relevant parameters in the evolution process of the cluster network. The research results can provide some theoretical reference and guidance for the cultivation of strategic emerging industries. [ABSTRACT FROM AUTHOR]

• In this work a non-autonomous SIS network model is developed and analyzed. • The transmission rate is periodic to study impacts of the heterogeneity networks and seasonal diseases. • There exists a unique periodic solution which is globally asymptotically stable. • The heterogeneity is important in accelerating disease spreading and increasing the amplitude of solution. Seasonal forcing and contact patterns are two key features of many disease dynamics that generate periodic patterns. Both features have not been ascertained deeply in the previous works. In this work, we develop and analyze a non-autonomous degree-based mean field network model within a Susceptible-Infected-Susceptible (SIS) framework. We assume that the disease transmission rate being periodic to study synergistic impacts of the periodic transmission and the heterogeneity of the contact network on the infection threshold and dynamics for seasonal diseases. We demonstrate both analytically and numerically that (1) the disease free equilibrium point is globally asymptotically stable if the basic reproduction number is less than one; and (2) there exists a unique global periodic solution that both susceptible and infected individuals coexist if the basic reproduction number is larger than one. We apply our framework to Scale-free contact networks for the simulation. Our results show that heterogeneity in the contact networks plays an important role in accelerating disease spreading and increasing the amplitude of the periodic steady state solution. These results confirm the need to address factors that create periodic patterns and contact patterns in seasonal disease when making policies to control an outbreak. [ABSTRACT FROM AUTHOR]

Featured Application: The Climate conditions as factors in the equations and random values will be incorporated into the featured application for future research model. The nature and characteristics of free-burning wildland fires have significant economic, safety, and environmental impacts. Additionally, the increase in global warming has led to an increase in the number and severity of wildfires. Hence, there is an increasing need for accurately calculating the probability of wildfire propagation in certain areas. In this study, we firstly demonstrate that the landscapes of wildfire propagation can be represented as a scale-free network, where the wildfire is modeled as the scale-free network whose degree follows the power law. By establishing the state-related concepts and modifying the Binary-Addition-Tree (BAT) together with the PageRank, we propose a new methodology to serve as a reliable tool in predicting the probability of wildfire propagation in certain areas. Furthermore, we demonstrate that the proposed maximum-state PageRank used in the methodology can be implemented separately as a fast, simple, and effective tool in identifying the areas that require immediate protection. The proposed methodology and maximum-state PageRank are validated in the example generated from the Barabási-Albert model in the study. [ABSTRACT FROM AUTHOR]

In transmission problem of many complex networks, there are some restrictions on the routing path between a pair of sources and destinations, especially for the transmission process that has a segment distance limit, which has a wide range of applications in real transportation, information transmission, etc. on large real networks. In this work, we constructed a complex network transmission model, defined the transmission distance limit to L and randomly selected a part of the nodes in the scale-free network as the station. Based on the shortest path algorithm and a weighted routing algorithm, we observed the results under the transmission distance limit. The results show that the setting of L is important, which can be used to guide and control the fuel carrying capacity of vehicles on the transportation network. Finally, we selected two real road network for simulation and the results demonstrate the effectiveness of the algorithm in scale-free networks and real networks. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms (EAs) have been successfully applied to solve numerous optimization problems. Neighborhood field optimization algorithm (NFO) has been proposed to integrate the neighborhood field in EAs, which utilizes local cooperation behaviors to explore new solutions. In this paper, certain new NFO variants are proposed based on the cooperation of descendent neighbors. The competitive and cooperative behaviors of NFO variants provide a remarkable ability to accelerate information exchanges and achieve global search. Experimental results show that NFO variants perform better than basic and other state-of-the-art EAs under different benchmark functions. For NFO and other EAs, it is difficult to quantify benefits of local cooperation in the optimization process. For this purpose, the cooperation behaviors are analyzed in a new network approach in this paper. In the proposed NFO variants, population graph shows a scale-free network with power-law distribution. Network characteristics, i.e., degree distribution, cluster coefficient and average degree, are used to quantify the cooperation behaviors. Experimental results show that network characteristics can effectively indicate the optimization performance of NFO variants in terms of convergence rate and population diversity. NFO variants with large cluster coefficients and significant heterogeneous characteristics can achieve a significant performance improvement on numerous problems. [ABSTRACT FROM AUTHOR]

Background: The coronavirus disease 2019 (COVID-19) epidemic met coincidentally with massive migration before Lunar New Year in China in early 2020. This study is to investigate the relationship between the massive migration and the coronavirus disease 2019 (COVID-19) epidemic in China. Methods: The epidemic data between January 25th and February 15th and migration data between Jan 1st and Jan 24th were collected from the official websites. Using the R package WGCNA, we established a scale-free network of the selected cities. Correlation analysis was applied to describe the correlation between the Spring Migration and COVID-19 epidemic. Results: The epidemic seriousness in Hubei (except the city of Wuhan) was closely correlated with the migration from Wuhan between January 10 and January 24, 2020. The epidemic seriousness in the other provinces, municipalities and autonomous regions was largely affected by the immigration from Wuhan. By establishing a scale-free network of the regions, we divided the regions into two modules. The regions in the brown module consisted of three municipalities, nine provincial capitals and other 12 cities. The COVID-19 epidemics in these regions were more likely to be aggravated by migration. Conclusions: The migration from Wuhan could partly explain the epidemic seriousness in Hubei Province and other regions. The scale-free network we have established can better evaluate the epidemic. Three municipalities (Beijing, Shanghai and Tianjin), eight provincial capitals (including Nanjing, Changsha et al.) and 12 other cities (including Qingdao, Zhongshan, Shenzhen et al.) were hub cities in the spread of COVID-19 in China. [ABSTRACT FROM AUTHOR]

Recently, [T. M. Gwizdałła, The swarm-like update scheme for opinion formation, in Computational Collective Intelligence, eds. N. T. Nguyen, G. A. Papadopoulos, P. Jedrzejowciz, B. Trawinski and G. Vossen (Springer International Publishing, Cham, 2017), pp. 66–75.] we have proposed the scheme of performing the opinion formation simulation based on popular global optimization mechanism — the Particle Swarm Optimization (PSO). The basic idea was to use the interaction between two potential directions of agents' heading: those forced by the global opinion and those forced by the opinion of neighbors/colleagues. In the proposed paper, some enhancement of the proposed model is shown. We assume that, when performing the binary PSO-like update of system, we use the generalized version of logistic function. The results are promising in the sense that the introduced change increases explicitly, the number of possible solutions. [ABSTRACT FROM AUTHOR]

Knowledge about the molecular basis of SARS-CoV-2 infection is incipient. However, recent experimental results about the virus interactome have shown that this single-positive stranded RNA virus produces a set of about 28 specific proteins grouped into 16 non-structural proteins (Nsp1 to Nsp16), four structural proteins (E, M, N, and S), and eight accessory proteins (orf3a, orf6, orf7a, orf7b, orf8, orf9b, orf9c, and orf10). In this brief communication, the network model of the interactome of these viral proteins with the host proteins is analyzed. The statistical analysis of this network shows that it has a modular scale-free topology in which the virus proteins orf8, M, and Nsp7 are the three nodes with the most connections (links). This result suggests the possibility that a simultaneous pharmacological attack on these hubs could assure the destruction of the network and the elimination of the virus. [ABSTRACT FROM AUTHOR]

The investigation of earthquake recurrence networks that were constructed from two aftershock sequences in Greece, is performed, aiming to detect whether the structure of networks became distinct (non-random) before the occurrence of either the main shock or a major (strong) aftershock. The network nodes are the time series observations, which are the aftershocks magnitudes. Their binary connections are given by the arbitrary threshold ε on the recurrence matrix, which is computed with the Heaviside function. Two aftershock sequences are the 2014 Kefalonia doublet, main shocks ( M = 6.1 and M = 6.0 ), and the 2015 Lefkada main shock ( M = 6.5 ) sequence. The earthquake networks are formed for three different thresholds of ε , for monitoring eight basic network measures and non-trivial properties such as the small world and scale free, and examining their structure during the evolution of the sequences. To assess whether the values of the eight network measures are statistically significant and the network gets non-trivial properties are present, the construction of randomized networks is required and then the comparison of the randomized network values with the ones from the original recurrence networks. The monitoring of network measures reveals that their original values diverge from the statistical significance, i.e., the structure of networks is random, immediately after the main shocks and shortly before the occurrence of the strongest aftershocks. On the contrary, in the intervening time, between the occurrences of main shocks and strongest aftershocks, their original values are statistically significant, which means that reveal the distinct network structure. The small-world and scale-free properties are sought but not revealed. [ABSTRACT FROM AUTHOR]

The frequent global financial crises in recent years show that it is necessary to implement macroprudential regulation for the banking system. At present, quantitative research on the macroprudential regulation for the dynamic Chinese banking network system is lacking, while the related studies in other countries have not considered the interbank network structure. Therefore, in the present paper, we construct a dynamic banking network model with a scale-free network and a dynamic macroprudential regulation model under four risk allocation mechanisms (CVaR, Incremental VaR, Shapley value EL, and ΔCoVaR) for the dynamic Chinese banking network system. Then, we conduct empirical research to study the effect of the macroprudential regulation model on the Chinese banking network system. Our results show that the Chinese banking network system was the most unstable in 2010 and that the average default probability decreased every year after the macroprudential regulation, indicating the effectiveness of the macroprudential regulation model. From the perspective of the scale-free network structure, we find that the intrinsic mechanism of macroprudential regulation is to rewire the interbank linkages from small banks to large banks with more interbank lending to prevent contagious risk, thereby improving the stability of the entire banking system. Moreover, the regulation effects of ΔCoVaR and CVaR mechanisms are found to be better than those of the other mechanisms. The regulation effect of ΔCoVaR is the most significant. [ABSTRACT FROM AUTHOR]

This paper studied the dissemination mechanism of rumors on microblog networks. According to its propagation characteristics, the paper divided the audience users of microblog rumors into four categories: unknown, viewer, forwarder and reviewer, thus constructing a network rumor propagation model of UVFR. It used the model to analyze the influence of the main parameters on the propagation process, and proposed the corresponding control strategies. The main feature of the model redefined the rules of rumor propagation and the propagation dynamics equation, which made the propagation formula more in line with the real use habits of micro-blog users. The paper used a multi-agent simulation platform to simulate the spread of rumors in scale-free network structure, and compared the simulation results with the real data of Sina Weibo to verify the rationality and validity of the conclusions. The simulation results show that the more initial propagation nodes, the faster the rumor spread, and the greater the forwarding probability, the wider range the rumor spread. [ABSTRACT FROM AUTHOR]

We consider a simple preferential attachment graph process, which begins with a finite graph and in which a new (t + 1)st vertex is added at each subsequent time step t that is connected to each previous vertex u ≤ t with probability d u (t)/ t , where d u (t) is the degree of u at time t. We analyse the graph obtained as the infinite limit of this process, and we show that, as long as the initial finite graph is neither edgeless nor complete, with probability 1 the outcome will be a copy of the Rado graph augmented with a finite number of either isolated or universal vertices. [ABSTRACT FROM AUTHOR]