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The paper investigates the resilience of an agriculture supply chain through the lens of complex network perspective. Given the susceptibility of these supply chains to bothrandom events (rainfall and yield uncertainty), and targeted events (income tax raids on millers, strikes, and lockouts), as well as spillover effects of disruptions; we propose a supply chain architecture that helps in achieving a balanced performance against these disruptions. For this, we propose a new attachment rule—'price/cost-based attachment rule', which we use along with degree-based and distance-based attachment rules in generating a resilient supply chain topology. We call the proposed supply chain network—'Balanced Supply Network' whose performance is compared with a scale-free network (BA Network) and a random network (ER Network). The comparison is based on critical performance indicators such as availability (demand and supply availability rate) and connectivity (size of largest all-role connected component). The findings, on expected lines, reveal that our proposed network exhibits a performance trade-off between BA Network and ER Network when subjected to targeted disruptions and disruption propagation scenarios. However, in case of random disruptions, it ensures maximum resilience and even outperforms BA Network due to its construction properties. Further, to optimize resilience, we introduce weights to the attachment rules of our proposed network. These weight assignments enable us to identify the most effective configuration among the three attachment rules for enhancing the network's ability to withstand disruptions. [ABSTRACT FROM AUTHOR]

In this study, we develop a graph-theoretic network model for genealogical data. It is based on the naming system used by the Galo tribe in the Indian state of Arunachal Pradesh. P-graphs are used to visually represent the genealogy. According to the analysis of the network on social network metrics, the genealogical network is a sparsely connected, scale-free network with an average path length of 11.615 and a graph density of 0.002. Only a small portion of its nodes have high centrality values. The network has three communities, twenty authority nodes, two hub nodes, and observed no relinking marriages. [ABSTRACT FROM AUTHOR]

The purpose of this work is to examine the nature of the historically observed and empirically described by the Pareto law inequality in the distribution of wealth and income in an economic system. This inequality is presumed to be the result of unequal opportunity by its members. An analytical model of the economic system consisting of a large number of actors, all having equal access to its total wealth (or income) has been developed that is formally represented by a scale-free network comprised of nodes (actors) and links (states of wealth or income). The dynamic evolution of the complex network can be mapped in turn, as is known, into a system of quantum particles (links) distributed among various energy levels (nodes) in thermodynamic equilibrium. The distribution of quantum particles (photons) at different energy levels in the physical system is then derived based on statistical thermodynamics with the attainment of maximal entropy for the system to be in a dynamic equilibrium. The resulting Planck-type distribution of the physical system mapped into a scale-free network leads naturally into the Pareto law distribution of the economic system. The conclusions of the scale-free complex network model leading to the analytical derivation of the empirical Pareto law are multifold. First, any complex economic system behaves akin to a scale-free complex network. Second, equal access or opportunity leads to unequal outcomes. Third, the optimal value for the Pareto index is obtained that ensures the optimal, albeit unequal, outcome of wealth and income distribution. Fourth, the optimal value for the Gini coefficient can then be calculated and be compared to the empirical values of that coefficient for wealth and income to ascertain how close an economic system is to its optimal distribution of income and wealth among its members. Fifth, in an economic system with equal opportunity for all its members there should be no difference between the resulting income and wealth distributions. Examination of the wealth and income distributions described by the Gini coefficient of national economies suggests that income and particularly wealth are far off from their optimal value. We conclude that the equality of opportunity should be the fundamental guiding principle of any economic system for the optimal distribution of wealth and income. The practical application of this conclusion is that societies ought to shift focus from policies such as taxation and payment transfers purporting to produce equal outcomes for all, a goal which is unattainable and wasteful, to policies advancing among others education, health care, and affordable housing for all as well as the re-evaluation of rules and institutions such that all members in the economic system have equal opportunity for the optimal utilization of resources and the distribution of wealth and income. Future research efforts should develop the scale-free complex network model of the economy as a complement to the current standard models. [ABSTRACT FROM AUTHOR]

Summary: Wireless sensor networks (WSNs) have attained a great attraction of researchers in the recent years. In these networks, many structures are considered that have different properties. This article offers a unique approach, the inter‐core based reconnection strategy (ICRS), which is intended to improve the robustness of Scale‐Free Networks (SFNs) in the setting of wireless sensor networks (WSNs), with a special emphasis on the Internet of Health Things (IoHT) network. SFNs' vulnerabilities to malicious assaults while remaining resilient to random attacks. The proposed ICRS overcomes this issue by offering a novel reconnection approach that employs separate edges between network centers. Destructive assaults that have a significant impact on network connectivity, emphasizing the importance of a robust network that can resist a variety of attacks. ICRS is positioned as a solution that optimizes the network via reconnection techniques, changing it into an onion‐like structure with increased robustness. The simulation results depict that ICRS outperforms the existing algorithms in terms of robustness enhancement. The results show that ICRS performs 48%, 29%, 22%, and 16% better than Barabasi Albert (BA), Hill Climbing (HC), Simulated Annealing (SA), Random Edge Swap Mechanism (RESM), and Robustness Strategy (ROSE), respectively. [ABSTRACT FROM AUTHOR]

Abstract Graph sampling plays an important role in data mining for large networks. Specifically, larger networks often correspond to lower sampling rates. Under the situation, traditional traversal-based samplings for large networks usually have an excessive preference for densely-connected network core nodes. Aim at this issue, this paper proposes a sampling method for unknown networks at low sampling rates, called SLSR, which first adopts a random node sampling to evaluate a degree threshold, utilized to distinguish the core from periphery, and the average degree in unknown networks, and then runs a double-layer sampling strategy on the core and periphery. SLSR is simple that results in a high time efficiency, but experiments verify that the proposed method can accurately preserve many critical structures of unknown large scale-free networks with low sampling rates and low variances.

Objective: Surveillance is critical for the rapid implementation of control measures for diseases caused by aerially dispersed plant pathogens, but such programs can be resource-intensive, especially for epidemics caused by long-distance dispersed pathogens. The current cucurbit downy mildew platform for monitoring, predicting and communicating the risk of disease spread in the United States is expensive to maintain. In this study, we focused on identifying sites critical for surveillance and treatment in an attempt to reduce disease monitoring costs and determine where control may be applied to mitigate the risk of disease spread. Methods: Static networks were constructed based on the distance between fields, while dynamic networks were constructed based on the distance between fields and wind speed and direction, using disease data collected from 2008 to 2016. Three strategies were used to identify highly connected field sites. First, the probability of pathogen transmission between nodes and the probability of node infection were modeled over a discrete weekly time step within an epidemic year. Second, nodes identified as important were selectively removed from networks and the probability of node infection was recalculated in each epidemic year. Third, the recurring patterns of node infection were analyzed across epidemic years. Results: Static networks exhibited scale-free properties where the node degree followed a power-law distribution. Betweenness centrality was the most useful metric for identifying important nodes within the networks that were associated with disease transmission and prediction. Based on betweenness centrality, field sites in Maryland, North Carolina, Ohio, South Carolina and Virginia were the most central in the disease network across epidemic years. Removing field sites identified as important limited the predicted risk of disease spread based on the dynamic network model. Conclusions: Combining the dynamic network model and centrality metrics facilitated the identification of highly connected fields in the southeastern United States and the mid-Atlantic region. These highly connected sites may be used to inform surveillance and strategies for controlling cucurbit downy mildew in the eastern United States. [ABSTRACT FROM AUTHOR]

In this study, a Cournot duopoly model describing Caputo fractional-order differential equations with piecewise constant arguments is discussed. We have obtained two-dimensional discrete dynamical system as a result of applying the discretization process to the model. By using the center manifold theory and the bifurcation theory, it is shown that the discrete dynamical system undergoes flip bifurcation about the Nash equilibrium point. Phase portraits, bifurcation diagrams, and Lyapunov exponents show the existence of many complex dynamical behaviors in the model such as the stable equilibrium point, period-2 orbit, period-4 orbit, period-8 orbit, period-16 orbit, and chaos according to changing the speed of the adjustment parameter v 1 . The discrete Cournot duopoly game model is also considered on two scale-free networks with different numbers of nodes. It is observed that the complex dynamical networks exhibit similar dynamical behaviors such as the stable equilibrium point, flip bifurcation, and chaos depending on changing the coupling strength parameter c s . Moreover, flip bifurcation and transition chaos take place earlier in more heterogeneous networks. Calculating the largest Lyapunov exponents guarantees the transition from nonchaotic to chaotic states in complex dynamical networks. [ABSTRACT FROM AUTHOR]

Introduction: Acute respiratory distress syndrome (ARDS) presents a significant clinical challenge, with ventilator-induced lung injury (VILI) being a critical complication arising from life-saving mechanical ventilation. Understanding the spatial and temporal dynamics of VILI can inform therapeutic strategies to mitigate lung damage and improve outcomes. Methods: Histological sections from initially healthy mice and pulmonary lavageinjured mice subjected to a second hit of VILI were segmented with Ilastik to define regions of lung injury. A scale-free network approach was applied to assess the correlation between injury regions, with regions of injury represented as 'nodes' in the network and 'edges' quantifying the degree of correlation between nodes. A simulated time series analysis was conducted to emulate the temporal sequence of injury events. Results: Automated segmentation identified different lung regions in good agreement with manual scoring, achieving a sensitivity of 78% and a specificity of 85% across 'injury' pixels. Overall accuracy across 'injury', 'air', and 'other' pixels was 81%. The size of injured regions followed a power-law distribution, suggesting a 'rich-get-richer' phenomenon in the distribution of lung injury. Network analysis revealed a scale-free distribution of injury correlations, highlighting hubs of injury that could serve as focal points for therapeutic intervention. Simulated time series analysis further supported the concept of secondary injury events following an initial insult, with patterns resembling those observed in seismological studies of aftershocks. Conclusion: The size distribution of injured regions underscores the spatially heterogeneous nature of acute and ventilator-induced lung injury. The application of network theory demonstrates the emergence of injury 'hubs' that are consistent with a 'rich-get-richer' dynamic. Simulated time series analysis demonstrates that the progression of injury events in the lung could follow spatiotemporal patterns similar to the progression of aftershocks in seismology, providing new insights into the mechanisms of injury distribution and propagation. Both phenomena suggest a potential for interventions targeting these injury 'hubs' to reduce the impact of VILI in ARDS management. [ABSTRACT FROM AUTHOR]

Objective Surveillance is critical for the rapid implementation of control measures for diseases caused by aerially dispersed plant pathogens, but such programs can be resource-intensive, especially for epidemics caused by long-distance dispersed pathogens. The current cucurbit downy mildew platform for monitoring, predicting and communicating the risk of disease spread in the United States is expensive to maintain. In this study, we focused on identifying sites critical for surveillance and treatment in an attempt to reduce disease monitoring costs and determine where control may be applied to mitigate the risk of disease spread. Methods Static networks were constructed based on the distance between fields, while dynamic networks were constructed based on the distance between fields and wind speed and direction, using disease data collected from 2008 to 2016. Three strategies were used to identify highly connected field sites. First, the probability of pathogen transmission between nodes and the probability of node infection were modeled over a discrete weekly time step within an epidemic year. Second, nodes identified as important were selectively removed from networks and the probability of node infection was recalculated in each epidemic year. Third, the recurring patterns of node infection were analyzed across epidemic years. Results Static networks exhibited scale-free properties where the node degree followed a power-law distribution. Betweenness centrality was the most useful metric for identifying important nodes within the networks that were associated with disease transmission and prediction. Based on betweenness centrality, field sites in Maryland, North Carolina, Ohio, South Carolina and Virginia were the most central in the disease network across epidemic years. Removing field sites identified as important limited the predicted risk of disease spread based on the dynamic network model. Conclusions Combining the dynamic network model and centrality metrics facilitated the identification of highly connected fields in the southeastern United States and the mid-Atlantic region. These highly connected sites may be used to inform surveillance and strategies for controlling cucurbit downy mildew in the eastern United States.

IntroductionAcute respiratory distress syndrome (ARDS) presents a significant clinical challenge, with ventilator-induced lung injury (VILI) being a critical complication arising from life-saving mechanical ventilation. Understanding the spatial and temporal dynamics of VILI can inform therapeutic strategies to mitigate lung damage and improve outcomes.MethodsHistological sections from initially healthy mice and pulmonary lavage-injured mice subjected to a second hit of VILI were segmented with Ilastik to define regions of lung injury. A scale-free network approach was applied to assess the correlation between injury regions, with regions of injury represented as ‘nodes’ in the network and ‘edges’ quantifying the degree of correlation between nodes. A simulated time series analysis was conducted to emulate the temporal sequence of injury events.ResultsAutomated segmentation identified different lung regions in good agreement with manual scoring, achieving a sensitivity of 78% and a specificity of 85% across ‘injury’ pixels. Overall accuracy across ‘injury’, ‘air’, and ‘other’ pixels was 81%. The size of injured regions followed a power-law distribution, suggesting a ‘rich-get-richer’ phenomenon in the distribution of lung injury. Network analysis revealed a scale-free distribution of injury correlations, highlighting hubs of injury that could serve as focal points for therapeutic intervention. Simulated time series analysis further supported the concept of secondary injury events following an initial insult, with patterns resembling those observed in seismological studies of aftershocks.ConclusionThe size distribution of injured regions underscores the spatially heterogeneous nature of acute and ventilator-induced lung injury. The application of network theory demonstrates the emergence of injury ‘hubs’ that are consistent with a ‘rich-get-richer’ dynamic. Simulated time series analysis demonstrates that the progression of injury events in the lung could follow spatiotemporal patterns similar to the progression of aftershocks in seismology, providing new insights into the mechanisms of injury distribution and propagation. Both phenomena suggest a potential for interventions targeting these injury ‘hubs’ to reduce the impact of VILI in ARDS management.

The purpose of this work is to examine the nature of the historically observed and empirically described by the Pareto law inequality in the distribution of wealth and income in an economic system. This inequality is presumed to be the result of unequal opportunity by its members. An analytical model of the economic system consisting of a large number of actors, all having equal access to its total wealth (or income) has been developed that is formally represented by a scale-free network comprised of nodes (actors) and links (states of wealth or income). The dynamic evolution of the complex network can be mapped in turn, as is known, into a system of quantum particles (links) distributed among various energy levels (nodes) in thermodynamic equilibrium. The distribution of quantum particles (photons) at different energy levels in the physical system is then derived based on statistical thermodynamics with the attainment of maximal entropy for the system to be in a dynamic equilibrium. The resulting Planck-type distribution of the physical system mapped into a scale-free network leads naturally into the Pareto law distribution of the economic system. The conclusions of the scale-free complex network model leading to the analytical derivation of the empirical Pareto law are multifold. First, any complex economic system behaves akin to a scale-free complex network. Second, equal access or opportunity leads to unequal outcomes. Third, the optimal value for the Pareto index is obtained that ensures the optimal, albeit unequal, outcome of wealth and income distribution. Fourth, the optimal value for the Gini coefficient can then be calculated and be compared to the empirical values of that coefficient for wealth and income to ascertain how close an economic system is to its optimal distribution of income and wealth among its members. Fifth, in an economic system with equal opportunity for all its members there should be no difference between the resulting income and wealth distributions. Examination of the wealth and income distributions described by the Gini coefficient of national economies suggests that income and particularly wealth are far off from their optimal value. We conclude that the equality of opportunity should be the fundamental guiding principle of any economic system for the optimal distribution of wealth and income. The practical application of this conclusion is that societies ought to shift focus from policies such as taxation and payment transfers purporting to produce equal outcomes for all, a goal which is unattainable and wasteful, to policies advancing among others education, health care, and affordable housing for all as well as the re-evaluation of rules and institutions such that all members in the economic system have equal opportunity for the optimal utilization of resources and the distribution of wealth and income. Future research efforts should develop the scale-free complex network model of the economy as a complement to the current standard models.

How to accurately model and effectively suppress the spread of network viruses has been a major concern in the field of complex networks and cybersecurity. Most existing work often considers the transmission between the infected and uninfected nodes (i.e., horizontal transmission) and assumes that all new nodes connected to the Internet are susceptible, but the nodes might have been implanted with a backdoor or virus by attackers or infected nodes before connecting to the Internet. This vertical transmission also provides an important route for virus propagation. In this paper, we investigate the propagation of network viruses under the combined influence of network topology and hybrid transmission (i.e., horizontal and vertical transmissions). Through rigorous qualitative analysis, we identify the propagation threshold R 0 which determines whether viruses in the network tend to become extinct or persist, and explore the impacts of vertical transmission on the viral spread. Furthermore, we consider the problem of how to dynamically contain the hybrid spread of network viruses with limited resources. By utilizing optimal control theory, we prove the existence of an optimal control strategy. Finally, a group of representative simulation experiments verify the validity of the theoretical findings. Specifically, the simulation results show that the optimal control strategy proposed in this paper reduces the value of the target generic function J by 67.69% compared with no control. [ABSTRACT FROM AUTHOR]

This paper analyses the characteristics and laws of information dissemination in social networks, proposes a propensity index based on the propensity of individuals in the network to spread information about events, and studies the influence of the propensity index on information spreading. This study is based on a scale-free network and takes the SI model as the base model and improves it. The experimental results show that the propagation process and infection density of information is affected by the propensity index, and the stronger the individual's propensity for information spreading, the larger the propensity index owned, which promotes the propagation of information. Moreover, the information spreading model based on propensity index is more in line with the reality of information spreading. [ABSTRACT FROM AUTHOR]

This paper firstly coordinates the relationship between the internal elements of university innovation and entrepreneurship incubation systems through positive and negative feedback regulation so that the system reaches equilibrium or rises to a higher level of equilibrium. Secondly, based on the whole process of innovation and entrepreneurship, the diffusion model of the university innovation and entrepreneurship system is constructed, setting university students’ innovation and entrepreneurship ability as the expected benefit and cognitive bias as the cost and exploring the benefit curve of innovation and entrepreneurship ability and cognitive bias. Finally, we initialize the parameters of the simulation system for incubating innovation and entrepreneurship among college students and simulate the constructed scale-free network model using Matlab simulation. The results show that in the simulation Corporation1, when tick=5, the maximum value of the Y coordinate appears to be 27.5, which responds to the growing process of college students’ innovation and entrepreneurship incubation objects. The simulation of college students’ innovation and entrepreneurship proposed in this paper complements the short board of college students’ inability to practice innovation and entrepreneurship and provides a practical reference for the cultivation of innovation and entrepreneurship talent ability in college education.

The construction of a professional learning development community for foreign language teachers is related to the personal development and group development of college teachers and is a guarantee for the improvement of the quality of foreign language teaching in colleges and universities. Starting from the model of professional learning networks and network learning communities, this paper establishes a teacher development community using the mean drift clustering algorithm optimized by the Gaussian kernel function. The scale-free network BA algorithm is utilized to construct a network alliance of foreign language teachers’ development community and establish indicators related to network metrics. The data of foreign language teachers’ communication platforms is used as an example to analyze the network structure of the community network alliance, and a comparison experiment is designed to analyze the application effect of the community network alliance. When the clustering cluster of foreign language teachers’ community is defined as 5, the clustering sum of squares is 79.45%, and the clustering effect is the greatest. The average interaction degree number of network members was only 1.853, and only six foreign language teachers had mediated centrality above 0.5. The teaching abilities of ordinary and excellent teachers improved between 0.36 and 0.66 points after implementing the network alliance of foreign language teachers’ development community. Making full use of intelligent technology to carry out the establishment of foreign language teacher development community network alliance helps to improve the teaching ability of foreign language teachers and realize the improvement of foreign language teaching quality.

• We present a new model based on the fractal structure of social groups to describe the epidemic spread of diseases. • The model gives the number of contacts among those individuals infecting the population. • The q -exponential function is the basic mathematical tool to describe the transmission of the virus. • The SIR model is a special case of the fractal model, recovered when the number of contacts is sufficiently large. • We demonstrated the model's self-consistency. The model reproduces the data more accurately than the SIR model. A common basis to address the dynamics of directly transmitted infectious diseases, such as COVID-19, are compartmental (or SIR) models. SIR models typically assume homogenous population mixing, a simplification that is convenient but unrealistic. Here we validate an existing model of a scale-free fractal infection process using high-resolution data on COVID-19 spread in São Caetano, Brazil. We find that transmission can be described by a network in which each infectious individual has a small number of susceptible contacts, of the order of 2–5. This model parameter correlated tightly with physical distancing measured by mobile phone data, such that in periods of greater distancing the model recovered a lower average number of contacts, and vice versa. We show that the SIR model is a special case of our scale-free fractal process model in which the parameter that reflects population structure is set at unity, indicating homogeneous mixing. Our more general framework better explained the dynamics of COVID-19 in São Caetano, used fewer parameters than a standard SIR model and accounted for geographically localized clusters of disease. Our model requires further validation in other locations and with other directly transmitted infectious agents. [ABSTRACT FROM AUTHOR]

This study takes diffusion capacity, absorptive capacity, and relationship strength as the main influencing factors, constructs models of knowledge flow in small‐world networks and scale‐free networks, and uses numerical simulation to observe the flow characteristics of explicit knowledge and tacit knowledge in different networks. The knowledge of explicit flow in different networks exhibits the phenomenon of knowledge emergence, but this phenomenon is more obvious in a small‐world network. The flow of tacit knowledge in a small‐world network has a better effect. In a scale‐free network, the quantity and frequency of knowledge flow are significantly higher than those in a small‐world network. The reason for this phenomenon is the differences in the response, connection and structure of different networks. The quantity and frequency of the flow of explicit knowledge in the same network are significantly higher than those of tacit knowledge. The reason for this phenomenon is the different types of knowledge flow in different modes, with different levels of flow difficulty and flow sustainability. First, this study visually compares the differences in flow between the two types of knowledge. Second, flow models of the two types of knowledge are constructed, and the flow characteristics of the two types of knowledge in different networks are simulated. Finally, the reasons for the differences in flow between the two types of knowledge are explained by using loosely coupled theory. [ABSTRACT FROM AUTHOR]

It is well known that in many real networks, such as brain networks and scientific collaboration networks, there exist higher order nonpairwise relations among nodes, i.e. interactions between more than two nodes at a time. This simplicial structure can be described by simplicial complexes and has an important effect on topological and dynamical properties of networks involving such group interactions. In this paper, we study analytically resistance distances in iteratively growing networks with higher order interactions characterized by the simplicial structure that is controlled by a parameter |$q$|⁠. We derive exact formulas for interesting quantities about resistance distances, including Kirchhoff index, additive degree-Kirchhoff index, multiplicative degree-Kirchhoff index, as well as average resistance distance, which have found applications in various areas elsewhere. We show that the average resistance distance tends to a |$q$| -dependent constant, indicating the impact of simplicial organization on the structural robustness measured by average resistance distance. [ABSTRACT FROM AUTHOR]

A reasonable definition of nodes load and capacity is essential for improving the robustness of scale-free networks against cascading failure, which has gained significant attention over recent years. This paper presents two methods for defining the load-capacity model: a degree-based method and a betweenness-based method. In these methods, the initial load and capacity of nodes were determined by considering the degrees and betweenness centrality of nodes and their neighbors. These values could be adjusted using both global and local parameters. This paper achieved load redistribution during cascading failures through targeted attacks on network nodes. In addition, this study applied load redistribution to cascading failure processes in networks by targeting network nodes. In order to evaluate the effectiveness of the proposed approach, this paper examines the impact of adjusting two parameters on the minimum critical tolerance coefficient and network robustness. Computer-generated scale-free networks and a real network were used for evaluation purposes. The findings indicated that higher global parameters resulted in a lower average robustness index. Moreover, our degree-based method demonstrated a smaller minimum critical tolerance coefficient and average robustness index compared to existing load definition methods. Therefore, the proposed methods enhanced the robustness and integrity of scale-free networks against attacks. [ABSTRACT FROM AUTHOR]

Enterprises in the prefabricated building supply chain (PBSC) only share information according to their interests, which is bound to cause conflicts of interest and reduce the efficiency of supply chain operations. To promote information sharing (IS) in PBSC, it is necessary to construct an evolutionary game model that fits the realistic network. In this paper, based on the integration of existing research, 13 influencing factors of IS in PBSC are analyzed comprehensively from the perspective of information ecology theory. In addition, due to the complexity and uncertainty of the PBSC, enterprise interaction and supply chain network structure affect the IS decision. Therefore, this paper builds an evolutionary game model of IS in PBSC under a scale-free network, and conducts numerical simulation analysis with MATLAB 2017 software to analyze the evolution law of enterprise IS under different situations. The results show that (1) when the network scale is large, the density of information sharers generally increases, and the speed of network evolution to a steady state generally slows down; (2) eight factors can promote the increase in information sharers' density, and five factors can inhibit it, but factors have no significant effect on the speed of network evolution to reach the steady state. Based on the simulation results, this paper proposes countermeasures and suggestions such as strengthening the support of the policy environment and social environment, setting up the demonstration benchmark of leading construction enterprises, establishing a directional information resource database, and improving information technologies and risk management systems to provide the scientific basis for government supervision and enterprise decision making. [ABSTRACT FROM AUTHOR]

The bio-brain presents robustness function to external stimulus through its self-adaptive regulation and neural information processing. Drawing from the advantages of the bio-brain to investigate the robustness function of a spiking neural network (SNN) is conducive to the advance of brain-like intelligence. However, the current brain-like model is insufficient in biological rationality. In addition, its evaluation method for anti-disturbance performance is inadequate. To explore the self-adaptive regulation performance of a brain-like model with more biological rationality under external noise, a scale-free spiking neural network(SFSNN) is constructed in this study. Then, the anti-disturbance ability of the SFSNN against impulse noise is investigated, and the anti-disturbance mechanism is further discussed. Our simulation results indicate that: (i) our SFSNN has anti-disturbance ability against impulse noise, and the high-clustering SFSNN outperforms the low-clustering SFSNN in terms of anti-disturbance performance. (ii) The neural information processing in the SFSNN under external noise is clarified, which is a dynamic chain effect of the neuron firing, the synaptic weight, and the topological characteristic. (iii) Our discussion hints that an intrinsic factor of the anti-disturbance ability is the synaptic plasticity, and the network topology is a factor that affects the anti-disturbance ability at the level of performance. [ABSTRACT FROM AUTHOR]

• Superspreading events are commonly observed since the individual variance of contact patterns is heterogeneous. • Heterogeneity of contact patterns should be incorporated as a key factor assessing the severity of the COVID-19 outbreaks. • An agent-based model is developed to propose an alternative measurement, the degree-specific basic reproduction number. • The degree-specific basic reproduction number can capture more accurate and realistic transmission probability. Assessing the transmission potential of emerging infectious diseases, such as COVID-19, is crucial for implementing prompt and effective intervention policies. The basic reproduction number is widely used to measure the severity of the early stages of disease outbreaks. The basic reproduction number of standard ordinary differential equation models is computed for homogeneous contact patterns; however, realistic contact patterns are far from homogeneous, specifically during the early stages of disease transmission. Heterogeneity of contact patterns can lead to superspreading events that show a significantly high level of heterogeneity in generating secondary infections. This is primarily due to the large variance in the contact patterns of complex human behaviours. Hence, in this work, we investigate the impacts of heterogeneity in contact patterns on the basic reproduction number by developing two distinct model frameworks: 1) an SEIR-Erlang ordinary differential equation model and 2) an SEIR stochastic agent-based model. Furthermore, we estimated the transmission probability of both models in the context of COVID-19 in South Korea. Our results highlighted the importance of heterogeneity in contact patterns and indicated that there should be more information than one quantity (the basic reproduction number as the mean quantity), such as a degree-specific basic reproduction number in the distributional sense when the contact pattern is highly heterogeneous. [ABSTRACT FROM AUTHOR]

BackgroundEmerging infectious diseases are a class of diseases that are spreading rapidly and are highly contagious. It seriously affects social stability and poses a significant threat to human health, requiring urgent measures to deal with them. Its outbreak will very easily lead to the large-scale spread of the virus, causing social problems such as work stoppages and traffic control, thereby causing social panic and psychological unrest, affecting human activities and social stability, and even endangering lives. It is essential to prevent and control the spread of infectious diseases effectively.PurposeWe aim to propose an effective method to classify the risk level of a new epidemic region by using graph theory and risk classification methods to provide a theoretical reference for the comprehensive evaluation and determination of epidemic prevention and control, as well as risk level classification.MethodsUsing the graph theory method, we first define the network structure of social groups and construct the risk transmission network of the new epidemic region. Then, combined with the risk classification method, the classification of high, medium, and low risk levels of the new epidemic region is discussed from two cases with common and looped graph nodes, respectively. Finally, the reasonableness of the classification method is verified by simulation data.ResultsThe directed weighted scale-free network can better describe the transmission law of an epidemic. Moreover, the proposed method of classifying the risk level of a region by using the correlation function between two regions and the risk value of the regional nodes can effectively evaluate the risk level of different regions in the new epidemic region. The experiments show that the number of medium and high risk nodes shows no increasing trend. The number of high-risk regions is relatively small compared to medium-risk regions, and the number of low-risk regions is the largest.ConclusionsIt is necessary to distinguish scientifically between the risk level of the epidemic area and the neighboring regions so that the constructed social network model of the epidemic region's spread risk can better describe the spread of the epidemic risk in the social network relations.

The physical reality can be partially mapped with network theory, showing the edging links between connected nodes, and their spatial and intertemporal dynamic interaction. The Internet is a network of networks representing a global system of interconnected computer networks. The metaverse is a network of 3D virtual worlds focused on social connection. There is so an evident Ariadne’s thread between these ecosystems, interpreted with multilayer network theory that examines the connectivity and interdependency between nodes positioned in the physical world, the web, or the metaverse.This pioneering study illustrates a new research avenue, analyzing the application of some of the most evident properties of network theory to the case, showing for instance how replica nodes can link through an avatar the physical world with the metaverse. A valuation methodology of the metaverse ecosystems will be proposed, using a with-and-without approach or multilayer network metrics.

It has been recently shown that weak signal response of a neuron can be amplified with the help of chaotic fluctuations at an optimal intensity. This phenomenon is referred to as chaotic resonance (CR). Here, we numerically investigate the signal detection ability of nervous system via CR using hybrid coupled scale-free networks of Hodgkin-Huxley (H-H) neurons. Firstly, we find that chaotic internal fluctuations are prone to enhance signal response of neuron population, even with a weak connectivity, more than that of single isolated cell's. We show that gap junctions can satisfy the stability against such variability and the quality of perception due to synchronizability. We also show that intense hybrid network interaction with strong chemical coupling can induce the similar degree of stability and decent quality of CR performance. Our results imply that a balanced connectivity may respond to weak signals efficiently in the presence of optimal chaotic fluctuations and exhibit frequency selectivity. • CR performance is enhanced in the presence of network interaction. • Gap junctions in hybrid coupled population promote more pronounced perception. • Strongly coupled network increases sensitivity and precision on frequency modulation. [ABSTRACT FROM AUTHOR]

Vertex cover of complex networks is essentially a major combinatorial optimization problem in network science, which has wide application potentials in engineering. To optimally cover the vertices of complex networks, this paper employs a potential game for the vertex cover problem, designs a novel cost function for network vertices, and proves that the solutions to the minimum value of the potential function are the minimum vertex covering (MVC) states of a general complex network. To achieve the optimal (minimum) covering states, we propose a novel distributed time-variant binary log-linear learning algorithm, and prove that the MVC state of a general complex network is attained under the proposed optimization algorithm. Furthermore, we estimate the upper bound of the convergence rate of the proposed algorithm, and show its effectiveness and superiority using numerical examples with representative complex networks and optimization algorithms. [ABSTRACT FROM AUTHOR]

In this article, we study the mechanism of generating a scale-free network using strong dependency between nodes. It is found that dependency should be aided by two key factors, namely, the reduced structure of network connections and small zero inflation. Our finding provides key conditions bridging the gap between the two groups having different opinions on scale-free networks. These groups include a camp of network scientists that consider scale-free networks as ideal objects in the large-size limit and the others that consider them as concrete objects in the real world. [ABSTRACT FROM AUTHOR]

The spread of rumors in the era of new media poses a serious challenge to sustaining social order. Models regarding rumor propagation should be proposed in order to prevent them. Taking the cooling-off period into account in this paper, a modified ISCR model with saturated incidence and time delay on a scale-free network is introduced. The basic reproduction number R 0 , which does not depend on time delay τ , is given by simple calculation. The stability of the rumor-free and rumor-endemic equilibrium points is proved by constructing proper Lyapunov functions. The study of the ISCR rumor-spreading process acquires an understanding of the impact of many factors on the prevalence of rumors. Then, the optimal control strategy for restraining rumors is studied. Numerous sensitivity studies and numerical simulations are carried out. Based on the saturated incidence and time delay, results indicate that the effect of time delay plays a significant part in rumor propagation on a scale-free network. [ABSTRACT FROM AUTHOR]

Surrogate-assisted meta-heuristic algorithms (SAMAs) have been increasingly popular in recent years for solving challenging optimization problems. However, the majority of recent studies concentrate on low-dimensional problems. In this paper, a scale-free network based multi-surrogate-assisted stochastic fractal search (SF-MSASFS) algorithm is proposed. Specifically, based on the stochastic fractal search (SFS) algorithm, multiple surrogate models, namely RBF and Kriging models, are used to enhance the robustness of the algorithm. The scale-free network is used to build the topology structure of the SFS algorithm, and the offspring particles are generated by means of the connection relationship between the parent particles. In addition, to further enhance adaptability, an adaptive mechanism is implemented, tailoring three distinct update mechanisms based on their corresponding reward values. Finally, the performance of the proposed algorithm is demonstrated by comparing the proposed algorithm with a number of state-of-the-art SAMAs on several well-known benchmark functions, in particular in solving high-dimensional expensive problems (HEOPs). The results underscore the SF-MSASFS algorithm's commendable optimization performance. (The MATLAB code can be found at the authors github: https://github.com/xiaodi-Cheng/SF-MSASFS) [ABSTRACT FROM AUTHOR]

The interaction and diversification of different behavior patterns of individual communication sources in cyberspace make the crisis evolution increasingly complex. Based on the activity and attitude of individual communication sources, a nonlinear dynamic system is obtained, and numerical simulation is carried out in combination with model threshold, and a co performance model of strong relationship and weak relationship social platform is constructed. The theoretical analysis is verified by numerical simulation on scale-free networks, and the propagation and evolution characteristics of strong and weak social platforms under different settings are discussed from the aspects of the heterogeneity of positive information dissemination sources' propagation ability, information dissemination sources' enthusiasm, information dissemination sources' heterogeneity and inter layer activity heterogeneity. [ABSTRACT FROM AUTHOR]

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]

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]