Scale-free Networks Research Articles

Influence of subsidy policies against insurances on controlling the propagation of epidemic security risks in networks

Subsidies are used to further control the propagation of epidemic security risks as they offer users incentives to practice security investment behaviors. However, previously proposed subsidy policies have typically been studied without insurance, and it is still challenging to build effective subsidy strategies when users can transfer some of the infection loss to the insurer by purchasing insurance, because these external incentives may alter users' decisions to purchase insurance. To this end, we designed three subsidy policies in a scenario where purchasing insurance is one of the available strategies to users: under SPIns and SPInsp, the subsidies are used as the insurance funds and the risk precaution aspect of the insurance funds, respectively, and under SPInsd, a fraction of the subsidies are used to support some free-riding users with high node importance in their purchase of insurance, and the remaining subsidies are used as the precaution aspect of the insurance funds. The subsidy policies are studied with a formulated security investment game model on scale-free networks from the perspectives of the public and insurer. The results show that SPInsd can always work effectively and outperforms others in limiting the extent of an epidemic outbreak with similar or lower social costs, and without a reduction in profit for the insurer. More importantly, an interesting phenomenon emerges in the SPInsp scenario: under specific insurance parameters, the increase in subsidy funding has a negative impact on preventing the risk spread, leading to larger final epidemic sizes. In addition, the effectiveness of SPInsd on scale-free networks with larger average degree or network size and random networks are also studied. We anticipate this work can provide useful insights for policy makers with respect to design and implementation of optimal subsidy policies related to the control of epidemic security risks under an insurance scenario.

Analysis of professional competency awareness based on visible network graphs

Introduction: With the advancement of society and technology, the importance of professional competency has been increasingly emphasized. This study aims to provide an in-depth analysis of the Baidu search index for “professional competency” from July 3, 2017, to October 6, 2023, across 34 provincial-level administrative regions in China.Methods: The study begins with a literature review to establish a theoretical framework. Subsequently, it delves into the fundamental concepts of complex networks, their parameters, and the principles of visible network graph algorithms. The application of system clustering and community detection algorithms is explored within this framework.Results: The empirical analysis starts with a provincial-level examination, involving the construction of visible network graphs, the exploration of scale-free networks, and discussions on regional system clustering. Following this, a nationwide analysis is conducted, focusing on the construction of visible network graphs to visualize the awareness of professional competency and studying community structures.Discussion: The findings provide insights into the awareness of professional competency across different regions. These insights are valuable for informing policy formulation and corporate decision-making, contributing to a deeper understanding of professional competency awareness and its implications.

A scale-free model of acute and ventilator-induced lung injury: a network theory approach inspired by seismology.

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. Histological 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. 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. 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.

The impact of relationship stickiness and memory on the evolution of individual behavior

This study investigates the dynamics of individual behavior and decision-making processes shaped by changes in personal relationships and preferences, using the prisoner’s dilemma game as a framework. The research focuses on the effects of relationship stickiness and memory on behavior evolution and network structural changes, considering two types of initial relationship networks. The findings indicate that as the number of games increases, there is a general trend of gradual increases in the average relationship stickiness, topological changes, and network heterogeneity. Notably, networks with greater initial heterogeneity, such as scale-free networks, better facilitate individual cooperation. Contrary to previous studies, the stable density of cooperators does not consistently increase with higher temptation gains. This suggests that individuals’ adaptive strategies, which include changing neighbors, can foster cooperation even under greater temptations. Additionally, an increase in the sensitivity coefficient correlates with increases in the final cooperator density, network heterogeneity, and topological changes. As individual memory and temptation gain rise, network heterogeneity measures tend to increase, while measures of topological change generally decrease. A sharp decline in the stable density of cooperators coincides almost synchronously with a rapid increase in network heterogeneity and a decrease in topological changes. This research reveals how relationship stickiness and memory impact individual cooperation, enhancing our understanding of the underlying mechanisms driving cooperative behaviors in complex networks.

Dynamic modulation of external excitation enhance synchronization in complex neuronal network

Understanding and controlling neural network synchronization is crucial for neuroscience in revealing brain functions and addressing neurological disorders. This study explores the innovative use of dynamic learning of synchronization (DLS) technology to enhance synchronization within neuronal networks. Using the Hodgkin-Huxley model across various network topologies, including Erdős-Rényi random graphs, small-world, and scale-free networks, it dynamically adjusts external electrical excitation to study its effects on network synchrony. To further demonstrate the universality of DLS technology, this study also validates the main results using larger-scale networks and the Izhikevich and FitzHugh-Nagumo models. The research quantifies the enhancement of synchrony through DLS, using root-mean-square error (RMSE) and synchronization factors as metrics. Findings show that DLS effectively boosts network synchrony by dynamically adjusting external excitation in response to node differences, significantly in both small-world and scale-free networks, irrespective of synaptic connections. Furthermore, DLS demonstrates potential for targeted synchronization enhancement in specific region of network. This paper highlights DLS technology's effectiveness in modulating external excitation to improve complex neural network synchrony, providing new insights into neural synchronization and information transmission.

The contact process on scale-free geometric random graphs

We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on Rd. This class includes the age-dependent random connection model and the soft Boolean model. In the ultrasmall regime of these random graphs we provide exact asymptotics for the non-extinction probability when the rate of infection spread is small and show for a finite version of these graphs that the extinction time is of exponential order in the size of the graph.

Integration of multi-omics data for survival prediction of lung adenocarcinoma

Background and ObjectiveThe morbidity of lung adenocarcinoma (LUAD) has been increasing year by year and the prognosis is poor. This has prompted researchers to study the survival of LUAD patients to ensure that patients can be cured in time or survive after appropriate treatment. There is still no fully valid model that can be applied to clinical practice. MethodsWe introduced struc2vec-based multi-omics data integration (SBMOI), which could integrate gene expression, somatic mutations and clinical data to construct mutation gene vectors representing LUAD patient features. Based on the patient features, the random survival forest (RSF) model was used to predict the long- and short-term survival of LUAD patients. To further demonstrate the superiority of SBMOI, we simultaneously replaced scale-free gene co-expression network (FCN) with a protein-protein interaction (PPI) network and a significant co-expression network (SCN) to compare accuracy in predicting LUAD patient survival under the same conditions. ResultsOur results suggested that compared with SCN and PPI network, the FCN based SBMOI combined with RSF model had better performance in long- and short-term survival prediction tasks for LUAD patients. The AUC of 1-year, 5-year, and 10-year survival in the validation dataset were 0.791, 0.825, and 0.917, respectively. ConclusionsThis study provided a powerful network-based method to multi-omics data integration. SBMOI combined with RSF successfully predicted long- and short-term survival of LUAD patients, especially with high accuracy on long-term survival. Besides, SBMOI algorithm has the potential to combine with other machine learning models to complete clustering or stratificational tasks, and being applied to other diseases.

Hyperbolic multichannel graph convolutional network for social recommendation

Social recommendations enhance the quality of recommendations by integrating social network information. Existing methods predominantly rely on pairwise relationships to uncover potential user preferences. However, they usually overlook the exploration of higher-order user relations. Moreover, because social relation graphs often exhibit scale-free graph structures, directly embedding them in Euclidean space will lead to significant distortion. To this end, we propose a novel graph neural network framework with hypergraph and hyperbolic embedding learning, namely HMGCN. Specifically, we first construct hypergraphs over user-item interactions and social networks, and then perform graph convolution on the hypergraphs. At the same time, a multi-channel setting is employed in the convolutional network, with each channel encoding its corresponding hypergraph to capture different high-order user relation patterns. In addition, we feed the item embeddings and the obtained high-order user embeddings into a hyperbolic graph convolutional network to extract user and item representations, enabling the model to better capture the hierarchical structure of their complex relationships. Experimental results on three public datasets, namely FilmTrust, LastFM, and Yelp, demonstrate that the model achieves more comprehensive user and item representations, more accurate fitting and processing of graph data, and effectively addresses the issues of insufficient user relationship extraction and data embedding distortion in social recommendation models.

Towards a robust scale‐free network in internet of health things against multiple attacks using an inter‐core based reconnection strategy

SummaryWireless 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.

Reflection modulation generated by scale-free network resonator periodic structure

The pattern of resonator in a periodical array is decisive for its response under impinging electromagnetic wave. A scale-free network resonator is proposed by connecting sub-units in the form of scale free network. Scale-free network resonator array’s reflectivity near resonant frequency could be modulated at arbitrary value between zero and unity, which is different from known resonator array or frequency selective surface. Reflection amplitude modulation could generate rich behaviors, as effective medium property in wide band could be maintained near zero constant, which means zero phase shift and is favorable in radar radome structure. S-parameter analysis indicates amplitude modulation is owing to polarization conversion generated by network links. Scale-free network resonator array has application potentials in future radar radomes, electromagnetic wave lens and microwave antenna panels.

The evolutionary game of emotions considering the influence of reputation

The influence of reputation and emotions on the evolution of cooperation is acknowledged, but current research predominantly focuses on one aspect. This paper integrates both reputation and emotions to examine their collective impacts on the evolution of cooperation. Initially, we define the expression of individual emotional profiles and emotional reputation. Subsequently, we consider the combined effects of the emotional reputation of an individual's neighbors and their interactive individuals on emotional responses. Further, an emotional transfer activation parameter is introduced. Lastly, we construct an algorithm for the evolutionary game of emotions. Simulation results demonstrate that considering emotional reputation is more conducive to the cooperation. The emotional reputation of interacting individuals has a greater influence on the development of positive emotions and the establishment of collaboration within groups than that of neighboring environments. In heterogeneous networks, considering the emotional reputation of neighbors increases the probability of “free-riding” by unfriendly people. When game parameters are set in favor of betrayal and negative emotions, the system evolves to produce “cautious and friendly people”. Individuals with stable emotions, high sympathy for the weak, and high respect for the strong dominate the group. Furthermore, the individuals' emotional expression towards both the weak and the strong exhibits an evolutionary synchronicity. Compared to other network structures, scale-free networks are more conducive to the evolutionary dominance of emotions of high respect for the strong.

On Low-Rank Directed Acyclic Graphs and Causal Structure Learning.

Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high-dimensional settings when the graphs to be learned are not sparse. In this article, we propose to exploit a low-rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low-rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low-rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free (SF) networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low-rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.

Evolution of cooperation on reinforcement-learning driven-adaptive networks.

Complex networks are widespread in real-world environments across diverse domains. Real-world networks tend to form spontaneously through interactions between individual agents. Inspired by this, we design an evolutionary game model in which agents participate in a prisoner's dilemma game (PDG) with their neighboring agents. Agents can autonomously modify their connections with neighbors using reinforcement learning to avoid unfavorable environments. Interestingly, our findings reveal some remarkable results. Exploiting reinforcement learning-based adaptive networks improves cooperation when juxtaposed with existing PDGs performed on homogeneous networks. At the same time, the network's topology evolves from homogeneous to heterogeneous states. This change occurs as players gain experience from past games and become more astute in deciding whether to join PDGs with their current neighbors or disconnect from the least profitable neighbors. Instead, they seek out more favorable environments by establishing connections with second-order neighbors with higher rewards. By calculating the degree distribution and modularity of the adaptive network in a steady state, we confirm that the adaptive network follows a power law and has a clear community structure, indicating that the adaptive network is similar to networks in the real world. Our study reports a new phenomenon in evolutionary game theory on networks. It proposes a new perspective to generate scale-free networks, which is generating scale-free networks by the evolution of homogeneous networks rather than typical ways of network growth and preferential connection. Our results provide new aspects to understanding the network structure, the emergence of cooperation, and the behavior of actors in nature and society.

Cooperation emerged and survived in scale-free networks in co-evolution and betrayer-prevailing circumstances

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.

Goldilocks Fluctuations: Dynamic Constraints on Loop Formation in Scale-Free Transport Networks.

Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a complete stability analysis of the dynamical behavior of any loop formed by fluctuating flows. We find a threshold for loop stability that involves an interplay of geometric constraints and hydrodynamic forcing mapped to constant and fluctuating components. Loops require fluctuation in the relative size of the flux between nodes, not just a temporal variation in the flux at a given node. Hence, there is both a minimum and a maximum amount of fluctuation relative to the constant-flux component where loops are supported.

Granting leaders priority exit options promotes and jeopardizes cooperation in social dilemmas

Cooperation in human interactions often involves voluntary participation rather than obligatory requirements. This paper investigates the impact of voluntary exit strategies on cooperation within scale-free networks, employing spatial prisoner’s dilemma games as the framework. We analyze three distinct exit strategies: leader priority exit, fringe priority exit, and random exit, across varying dilemma strengths. Our findings reveal that in scenarios of weak dilemma strength, leader priority exit significantly diminishes cooperation, particularly when only a small subset of players is granted exit rights. In contrast, under strong dilemma strength conditions, both leader priority and random exits serve to unexpectedly bolster cooperation. This enhancement is primarily facilitated by high-degree nodes opting out, thereby enabling low-degree nodes to establish stable cooperation. Furthermore, our study underscores the pivotal role of network structure. In assortative networks, random exit emerges as the most effective strategy in promoting cooperation. On the other hand, disassortative networks exhibit a substantial increase in cooperation levels when employing leader priority exit. These results highlight the intricate interplay between exit strategies, dilemma strength, and network topology, offering critical insights for promoting cooperation in varied social contexts.

Propagation and control of congestion risk in scale-free networks based on information entropy.

To study the propagation pattern of congestion risk in the traffic network and enhance risk control capabilities, a model has been developed. This model takes into account the probabilities of five threats (the risk occurrence probability; the risk of loss; the unpredictability of risk; the uncontrollability of risk; the transferability of risk) in the traffic network to define the risk entropy and determine the risk capacity, analyze the mechanism of congestion risk propagation, and explore the impact of risk resistance, the average degree of risk capacity at intersections, and the degree of correlation on congestion risk propagation. Further, a control method model for risk propagation is proposed. Numerical simulation results demonstrate that the risk resistance parameter θ can inhibit the propagation of congestion risk during traffic congestion. The highest efficiency in controlling risk propagation is achieved when θ reaches a threshold value θ*. Furthermore, the average degree of intersection risk capacity α shows a positive correlation with θ* and a negative correlation with control efficiency. However, the degree of association ω has a negative effect on risk propagation control, decreasing the degree of association between nodes aids in risk propagation control.

Characterization of Skeletal Muscle Regeneration Revealed a Novel Growth Network Induced by Molecular Acupuncture-like Transfection.

The low efficiency of in vivo transfection of a few fibres revealed a novel tissue network that temporally amplified growth stimulation in the entire regenerating rat soleus muscle. This acupuncture-like effect was demonstrated when the fibres began to grow after complete fibre degradation, synchronous inflammation, myoblast and myotube formation. Neonatal sarcoplasmic/endoplasmic reticulum ATPase (SERCA1b) was first detected in this system. The neonatal, fast and slow SERCA isoforms displayed consequent changes with innervation and differentiation, recapitulating events in muscle development. In vivo transfection of myotubes with plasmids expressing dominant negative Ras or a calcineurin inhibitor peptide (Cain/cabin) proved that expression of the slow myosin heavy chain and the slow muscle type SERCA2a are differentially regulated. In vivo transfection of a few nuclei of myotubes with dnRas or SERCA1b shRNA stimulated fibre size growth in the whole regenerating muscle but only until the full size had been reached. Growth stimulation by Ras and SERCA1b antisense was abolished by co-transfection of Cain or with perimuscular injection of IL4 antibody. This revealed a novel signalling network resembling scale-free networks which, starting from transfected fibre myonuclei as "hubs", can amplify growth stimulation uniformly in the entire regenerating muscle.

Complexity in road freight transport outsourcing networks. TRANSOPE: An agent-based dynamic model

This paper proposes a dynamic agent-based model (TRANSOPE) to simulate outsourcing among transport companies where, for the first time, accumulated knowledge is included as a variable to select service providers. The model consists of two main procedures. Firstly, the model simulates the decision-making of the professionals that contract transport service providers and the formation of outsourcing chains. Secondly, the model simulates the direct learning of participating companies and the transfer of knowledge towards their environment. Imperfect competition is replicated in three different scenarios, which involve the demand for transport services, regional distances and the intensity of knowledge transfer. The model is based on expert consultations and a survey conducted in an environment with a high concentration of transport companies in the Basque Country, Spain. The results indicate significant imbalances in the distribution of outsourcing, particularly in situations of low transport service demand, where 30% of transport companies do not secure any contracts. However, such situations led to strong regional interdependence. The dynamics of outsourcing reveals that over 75% of the contracted companies participate in all simulated scenarios from the first day. A strong hierarchy is also observed in the network, where certain transport companies act as connector hubs (with z-score values higher than 2.5 and participation coefficient values between 0.3 and 0.75), indicating a greater capacity for interaction and leadership in the transfer of knowledge. This feature allows the collaboration network to be identified as a scale-free network. The model has a low computational cost since the distances between agents remain constant. Finally, the formalisation of outsourcing decision-making in the model underpins its validity in forecasting the conduct of a freight transport system under shifting scenarios.

Collective dynamics of coupled Lorenz oscillators near the Hopf boundary: Intermittency and chimera states.

We study collective dynamics of networks of mutually coupled identical Lorenz oscillators near a subcritical Hopf bifurcation. Such systems exhibit induced multistable behavior with interesting spatiotemporal dynamics including synchronization, desynchronization, and chimera states. For analysis, we first consider a ring topology with nearest-neighbor coupling and find that the system may exhibit intermittent behavior due to the complex basin structures and dynamical frustration, where temporal dynamics of the oscillators in the ensemble switches between different attractors. Consequently, different oscillators may show a dynamics that is intermittently synchronized (or desynchronized), giving rise to intermittent chimera states. The behavior of the intermittent laminar phases is characterized by the characteristic time spent in the synchronization manifold, which decays as a power law. Such intermittent dynamics is quite general and is also observed in an ensemble of a large number of oscillators arranged in variety of network topologies including nonlocal, scale-free, random, and small-world networks.