WS Networks Research Articles

Assessing the impacts of vaccination and viral evolution in contact networks

A key lesson learned with COVID-19 is that public health measures were very different from country to country. In this study, we provide an analysis of epidemic dynamics using three well-known stochastic network models—small-world networks (Watts–Strogatz), random networks (Erdös–Rényi), and scale-free networks (Barabási–Albert)—to assess the impact of different viral strains, lockdown strategies, and vaccination campaigns. We highlight the significant role of highly connected nodes in the spread of infections, particularly within Barabási–Albert networks. These networks experienced earlier and higher peaks in infection rates, but ultimately had the lowest total number of infections, indicating their rapid transmission dynamics. We also found that intermittent lockdown strategies, particularly those with 7-day intervals, effectively reduce the total number of infections, serving as viable alternatives to prolonged continuous lockdowns. When simulating vaccination campaigns, we observed a bimodal distribution leading to two distinct outcomes: pandemic contraction and pandemic expansion. For WS and ER networks, rapid mass vaccination campaigns significantly reduced infection rates compared to slower campaigns; however, for BA networks, differences between vaccination strategies were minimal. To account for the evolution of a virus into a more transmissible strain, we modeled vaccination scenarios that varied vaccine efficacy against the wild-type virus and noted a decline in this efficacy over time against a second variant. Our results showed that vaccination coverage above 40% significantly flattened infection peaks for the wild-type virus, while at least 80% coverage was required to similarly reduce peaks for variant 2. Furthermore, the effect of vaccine efficacy on reducing the peak of variant 2 infection was minimal. Although vaccination strategies targeting hub nodes in scale-free networks did not substantially reduce the total number of infections, they were effective in increasing the probability of preventing pandemic outbreaks. These findings underscore the need to consider the network structure for effective pandemic control.

The spindle approximation of network epidemiological modeling

Understanding the dynamics of spreading and diffusion on networks is of critical importance for a variety of processes in real life. However, predicting the temporal evolution of diffusion on networks remains challenging as the process is shaped by network topology, spreading non-linearities, and heterogeneous adaptation behavior. In this study, we propose the ‘spindle vector’, a new network topological feature, which shapes nodes according to the distance from the root node. The spindle vector captures the relative order of nodes in diffusion propagation, thus allowing us to approximate the spatiotemporal evolution of diffusion dynamics on networks. The approximation simplifies the detailed connections of node pairs by only focusing on the nodal count within individual layers and the interlayer connections, seeking a compromise between efficiency and complexity. Through experiments on various networks, we show that our method outperforms the state-of-the-art on BA networks with an average improvement of 38.6% on the mean absolute error. Additionally, the predictive accuracy of our method exhibits a notable convergence with the pairwise approximation approach with the increasing presence of quadrangles and pentagons in WS networks. The new metric provides a general and computationally efficient approach to predict network diffusion problems and is of potential for a large range of network applications.

Monitoring growth and predicting crop yield through UAV-mounted spectral camera analysis of the interplay between soil compaction and vegetation index

This paper aims to introduce a prediction of crop yield based on relationship between soil compaction and vegetation index. The soil compaction increasingly with depth, which was calculated manuallyunevenly distributed in the field. The NDVI/NDRE was conducted by aerial spectral images taken by the UAV. To figure out connection, the Pearson’s correlation test was applied to analyze the correlation between factors. These research results show that the NDVI/NDRE in WS and SA crops increased and decreased steadily after reaching the maximum values (0.85 ± 0.02/ 0.38 ± 0.02 and 0.8 ± 0.02/ 0.28 ± 0.02) during the reproductive stage. The NDVI/NDRE had a high relationship with the plant height, tiller number, yield components of rice. WS and SA networks were built and tested according to the training algorithm in the Matlab software for predicting rice yield with high reliability. The developed models showcase promising results in forecasting rice yield, underscoring the potential applicability of this methodology in agricultural yield prediction.

Effects of topological structure and destination selection strategies on agent dynamics in complex networks

We analyzed agent behavior in complex networks: Barabási–Albert, Erdos–Rényi, and Watts–Strogatz models under the following rules: agents (a) randomly select a destination among adjacent nodes; (b) exclude the most congested adjacent node as a potential destination and randomly select a destination among the remaining nodes; or (c) select the sparsest adjacent node as a destination. We focused on small complex networks with node degrees ranging from zero to a maximum of approximately 20 to study agent behavior in traffic and transportation networks. We measured the hunting rate, that is, the rate of change of agent amounts in each node per unit of time, and the imbalance of agent distribution among nodes. Our simulation study reveals that the topological structure of a network precisely determines agent distribution when agents perform full random walks; however, their destination selections alter the agent distribution. Notably, rule (c) makes hunting and imbalance rates significantly high compared with random walk cases (a) and (b), irrespective of network types, when the network has a high degree and high activity rate. Compared with the full random walk in (a) and (b) increases the hunting rate while decreasing the imbalance rate when activity is low; however, both increase when activity is high. These characteristics exhibit slight periodic undulations over time. Furthermore, our analysis shows that in the BA, ER, and WS network models, the hunting rate decreases and the imbalance rate increases when the system disconnects randomly selected nodes in simulations where agents follow rules (a)–(c) and the network has the ability to disconnect nodes within a certain time of all time steps. Our findings can be applied to various applications related to agent dynamics in complex networks.

Energy efficiency and coding of neural network.

Based on the Hodgkin-Huxley model, this study explored the energy efficiency of BA network, ER network, WS network, and Caenorhabditis elegans neural network, and explained the development of neural network structure in the brain from the perspective of energy efficiency using energy coding theory. The numerical simulation results showed that the BA network had higher energy efficiency, which was closer to that of the C. elegans neural network, indicating that the neural network in the brain had scale-free property because of satisfying high energy efficiency. In addition, the relationship between the energy consumption of neural networks and synchronization was established by applying energy coding. The stronger the neural network synchronization was, the less energy the network consumed.

Energy Efficient Routing Protocol in Novel Schemes for Performance Evaluation

Wireless sensor networks (WSNs) are a comparatively new revolutionary technology that has the potential to revolutionize how we live together with the present system. To enhance data archiving, WSNs are frequently used in scientific studies. Many applications have proved the value of wired sensors; however, they are prone to wire cutting or damage. While preventing wire tangles and damage, wireless sensor networks provide autonomous monitoring. The WS network suffers from a number of fundamental restrictions, including insufficient processing power, storage space, available bandwidth, and information exchange. Consequently, energy-efficient strategies are necessary for maximizing the performance and lifespan of WSNs. As a result, the special cluster head relay node and energy balancing techniques will be applied to deal with WSN energy consumptions. This extends the life of the network. In wireless sensor networks, clustering is a smart approach to reduce energy consumption. Energy scarcity and consumption are serious issues that must be addressed with effective and dependable solutions. The proposed MGSA considers the distance between each node and its corresponding CHs, as well as the residual energy and delay, as important factors in the relay node selection. The proposed approach outperforms the current methods, such as low-energy adaptive clustering hierarchy, LEACH (in terms of data delivery rate), energy efficiency, and network longevity. The next level, which will boost the efficiency of wireless sensor networks, with two fitness functions, is proposed. The cluster head (CH) is in charge of collecting and transmitting data from all other cluster nodes. The flow of the consistency of the cluster head selection process will beat the improved data delivery rate, energy efficiency, recommended fuzzy clustering performance experiments, and assessments. As a result, energy-efficient operations are necessary to maximize the WSN performance and lifespan.

Prisoner's Dilemma Game with Cooperation-Defection Dominance Strategies on Correlational Multilayer Networks.

As multilayer networks are widely applied in modern society, numerous studies have shown the impact of a multilayer network structure and the network nature on the proportion of cooperators in the network. In this paper, we use Barabási–Albert scale-free networks (BA) and Watts and Strogatz networks (WS) to build a multilayer network structure, and we propose a new strategy-updating rule called “cooperation-defection dominance”, which can be likened to dominant and recessive traits in biogenetics. With the newly constructed multilayer network structure and the strategy-updating rules, based on the simulation results, we find that in the BA-BA network, the cooperation dominance strategy can make the networks with different rs show a cooperative trend, while the defection dominance strategy only has an obvious effect on the network cooperation with a larger r. When the BA network is connected to the WS network, we find that the effect of strategy on the proportion of cooperators in the network decreases, and the main influencing factor is the structure of the network. In the three-layer network, the cooperation dominance strategy has a greater impact on the BA network, and the proportion of the cooperators is enhanced more than under the natural evolution strategy, but the promotion effect is still smaller than that of the two-layer BA network because of the WS network. Under the defection dominance strategy, the WS layer appears different from the first two strategies, and we conclude through simulation that when the payoff parameter is at the middle level, its cooperator proportion will be suppressed, and we deduce that the proportion of cooperators and defectors, as well as the payoff, play an important role.

Information dimension based on [formula omitted] entropy

Information dimension is applied to quantify fractal, and the current methods are improved on the basis of information entropy. Although information entropy is always used to measure the information volume, it fails when dealing with complex and uncertain information. To solve this problem, in this paper, the information dimension is defined by using Deng entropy, due to the reason that Deng entropy as the extension of information entropy has the characteristic of being able to measure uncertain information better. In our method, Deng entropy is considered to measure the information volume in the information dimension. Besides, box coverage is also combined in the process of the box covering to define box coverage Deng entropy information dimension. In addition, the classical information dimension and box dimension of BA scale-free networks, WS and NW small-world networks and four real networks are calculated to compare with the proposed information dimension. The results show that the values of Deng entropy information dimension and box coverage Deng entropy information dimension are bigger than the classical information dimension and box dimension for the same network. Moreover, the information dimension of the networks does not increase linearly with the increase of nodes.

Cascading failure analysis and critical node identification in complex networks

Cascading failures in complex networks have attracted widespread attention in recent years. In this paper, a cascade model is proposed to analyze the potential overloads of nodes and edges simultaneously. First, some theoretical results for regular networks are detailed by the cascade model. The results show that in ring networks, as long as the capacity of each node or edge exceeds twice its initial load, the networks still work normally when an arbitrary node or edge breaks down, and in regular networks the failure of the farthest edges is most likely to induce cascades and the robustness of regular networks becomes stronger with the increase in the number of edges. Furthermore, an indicator evaluating the damage of the cascades is introduced. The analysis on the robustness of some typical networks indicates that WS networks can resist cascading failures more effectively and the robustness performance of WS networks can be improved by increasing rewiring probabilities. In BA networks, the failure of a critical node may pull down the whole networks, while the networks still function normally even if any edge breaks down. Finally, a forecasting indicator, called modified betweenness centrality, is proposed to identify critical nodes and experimental results show that the proposed indicator outperforms other typical indicators in identifying critical nodes.

Turing instability induced by complex networks in a reaction–diffusion information propagation model

The dynamics of rumor spreading in the information environment is a valuable way to study information management and public opinion monitoring. In this paper, the spreading of rumors and the behavior of crowd diffusion on network structure are studied by establishing a Suspicious-Infected (SI) reaction–diffusion model of rumor spreading with Allee effect. Especially, the necessary conditions for Turing pattern to appear in space are studied. Then, Monte Carlo simulation was used to prove the validity of the model. Furthermore, extensive numerical evaluation of the system is carried out under different networks, whose results show that the diffusion coefficient can change the patterns significantly. Then, on the lattice network and the cellular network, the spatial instability will cause the same pattern type, while the density distributions of S and I are no longer consistent on WS networks and BA networks. In addition, the change of the network structure and the introduction of the periodicity of diffusion coefficient will make the instability of the original system disappear in space. These works have certain guiding value to the prediction of rumor spreading scope.

On Improving the Robustness of MEC with Big Data Analysis for Mobile Video Communication

Mobile video communication and Internet of Things are playing a more and more important role in our daily life. Mobile Edge Computing (MEC), as the essential network architecture for the Internet, can significantly improve the quality of video streaming applications. The mobile devices transferring video flow are often exposed to hostile environment, where they would be damaged by different attackers. Accordingly, Mobile Edge Computing Network is often vulnerable under disruptions, against either natural disasters or human intentional attacks. Therefore, research on secure hub location in MEC, which could obviously enhance the robustness of the network, is highly invaluable. At present, most of the attacks encountered by edge nodes in MEC in the IoT are random attacks or random failures. According to network science, scale-free networks are more robust than the other types of network under the random failures. In this paper, an optimization algorithm is proposed to reorganize the structure of the network according to the amount of information transmitted between edge nodes. BA networks are more robust under random attacks, while WS networks behave better under human intentional attacks. Therefore, we change the structure of the network accordingly, when the attack type is different. Besides, in the MEC networks for mobile video communication, the capacity of each device and the size of the video data influence the structure significantly. The algorithm sufficiently takes the capability of edge nodes and the amount of the information between them into consideration. In robustness test, we set the number of network nodes to be 200 and 500 and increase the attack scale from 0% to 100% to observe the behaviours of the size of the giant component and the robustness calculated for each attack method. Evaluation results show that the proposed algorithm can significantly improve the robustness of the MEC networks and has good potential to be applied in real-world MEC systems.

Stock Network Stability After Crashes Based on Entropy Method

This paper studies the stability of stock network after crashes based on the entropy method. By measuring the network stability using the entropy calculated with the degree distribution, we find that the entropy of stock network is close to the ER and WS networks. We further introduce the government rescue policies as a natural experiment and apply the measurement of entropy to study the influence of rescue polices after crashes on the network stability, and find that rescue policies only have short-term influence. Analysis of relation between stock degrees and government purchasing behaviors further verifies the influences of rescue policies on the stock network stability.

Research on network robustness based on different deliberate attack methods

Many real-world networks can be abstracted into complex networks, which nodes are correlated with each other, once these functional nodes suffer from external or internal attack, they may lead to malfunction of the rest part of networks. In order to explore the impact of different attack methods on network robustness against cascading failures, we propose three attack methods and compare them with HD and LD which had been researched. By simulation on ER, BA and WS networks, the results show that, no matter what value α is, for BA and WS networks, attacking networks in GHS is the most difficult to cause cascading failures, and now, the networks show the strongest robustness. In α<1, attacking networks by GLS is the most likely to trigger cascading failures and robustness against cascading failures is the worst. In α>1, it is the easiest to make networks cascading failures when attacked networks by HD. In α=1, attacking networks by MD and LD,respectively, is the easiest to lead networks to cascading failures and the networks show the worst robustness. However, for ER network, no matter what value α is, there is the same effectiveness of attacking network by five attack methods and has stronger robustness than BA and WS networks. This work provides a good reference value for maintaining network security and enabling the network to operate normally and stably. It is possible to make effective preventive measures against these different attacks in advance and save costs for maintaining the network.

WSBP/NWBP small-world neural network and its performance for wind power forecasting

A small-world neural network has stronger generalization ability with high transfer efficiency than that of the regular neural networks. This paper presents two novel small-world neural networks, the Watts-Strogatz small-world based on a BP neural network (WSBP) and a Newman-Watts small-world neural network based on a BP neural network (NWBP), related to previous research of complex networks. The algorithms are developed separately by adopting WS and NW small-world networks as their topological structures, and their derivation and convergence criterion are progressively discussed. After that, the proposed models are subsequently tested by two typical nonlinear functions which confirm their significant improvement over the regular BP networks and other algorithms. Finally, a wind power prediction system is advanced to verify their generalization abilities, and show that the models are practically feasible and effective with improved accuracy and acceptable forecasting errors caused by wind fluctuation and randomness with a time scale up to 24 h.

Robustness of complex networks: Cascading failure mechanism by considering the characteristics of time delay and recovery strategy

To study the robustness of complex networks while encountering random failures or deliberate attacks, the cascading failure model is constructed by considering failure propagation with probability, which can depict the dynamic failure process. In particular, the characteristics of time delay and repetitive failure are taken into account in our model, and the network comprehensive robustness index (RI) is further designed according to valid survival edges and nodes. Additionally, the probability recovery strategy is proposed as well, and it is implemented in four typical networks, including the BA network, WS network, NC network and ER network. Different parameters in our model, including α, f, R, and β, are applied in simulation experiments to reveal their effects on RI in the cascading failure process. The simulation results show that nodes’ recovery abilities increase with R, which reduce the impacts of cascading failures and produce good network robustness. Meanwhile, the time delay increases with parameter α, and the size of the cascading failure decreases accordingly, which indicates that the larger that the time delay is, the stronger the RI. Additionally, the speed of the cascading failure process and the size of the cascading failure both present an increasing trend when parameter f increases gradually in the cascading failure. This indicates that the failure probability apparently impacts the RI. We also analyze the turning point t for RI(t) during the cascading failure process.

ILSR rumor spreading model with degree in complex network

Most rumors in social networks are extremely harmful and have a significant negative impact on social welfare. Therefore, exploring the laws of rumor propagation has been one of the hot topics in current researches. Most traditional rumor spreading models are based on infectious disease transmission models, such as SIR. Since the influence of individual differences and the network structure on rumor spreading are not considered, the rumor propagation process in complex networks can only be described in a coarse-grained manner. In this paper, we consider the role of different users in rumor propagation. Based on the degree of different nodes in the network, we design a new state transition function for each node and proposed a new rumor propagation ILSR model. Firstly, we analyze the model, calculate the equilibrium point and the basic reproductive number to prove the rationality of the model. Then experiments are performed in WS networks, BA scale-free networks and a real Facebook network to investigate the relationship between various nodes with time and the impact of network structure on rumor propagation, and the experimental results show the correctness and effectiveness of the model. It provides a reference for exploring the propagation law of rumors in complex networks and guiding and controlling the propagation of rumors.

Robustness of complex networks to cascading failures induced by Poisson fluctuating loads

Considering the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of complex networks against cascading overload failures in such situation. In our model, at each cascading step the fluctuating load on a network is described by the total number of walkers, which is a random number that subjects to Poisson distribution. And a node fails when its overload probability is beyond its risk tolerance. Relative size of the giant component as a function of the cascade step is used to assess the robustness of networks against cascading overload.Comparing to the cases of stationary overload probability in Kishore et al., (2011, 2012) and previous study on temporally fluctuating (the total load reduced in accordance with the reduction of the network size during a cascade process) overload probability in Mizutaka and Yakubo, (2015), we find that the total fluctuating loads that subject to random distribution at each cascade process induce remarkable difference for extreme events probability distribution. The study shows that the change in the property of the load fluctuations may drastically alter the dependence degree of the overload probability and hence the robustness of networks. Furthermore, our results obtained through intensive simulations show that scale-free networks are more fragile against cascading overload failures than ER and WS networks. This conclusion is contrary to those previous prediction without considering random fluctuating loads and endogenous risk resistance ability.

Practical k-agents search algorithm towards information retrieval in complex networks

Spanking information retrieval in large-scale Web and network has attracted increasing interest in the research community, many typical approaches have been recalled such as greedy, random-walk and high degree seeking since the search capabilities of complex networks are proved by Kleinberg in 2000. Unfortunately, the retrieval efficiency of these classic approaches is not ideal, and they are only suitable for the specific networks due to their defects. The motivation of this paper is to increase the retrieval efficiency, and we thus proposed a novel k-agents search approach for different types of networks which searches the networks with k-agents, simultaneously. Besides, to better test the efficiency of algorithms, a new evaluation method which considers search steps and query information both is put forward to measure the cost of the search algorithm. The complexity analysis also will be discussed, and the comparison with other algorithms will be displayed in detail to show its superiority. In the end, for the purpose of displaying a universe application of our algorithm, the simulations in WS (proposed by Watts and Strogatz), NW (proposed by Newman and Watts) small-world and BA (proposed by Barabai and Albert) scale-free network model are carried out to illustrate the performance of the proposed method.

An information spreading model based on online social networks

Online social platforms are very popular in recent years. In addition to spreading information, users could review or collect information on online social platforms. According to the information spreading rules of online social network, a new information spreading model, namely IRCSS model, is proposed in this paper. It includes sharing mechanism, reviewing mechanism, collecting mechanism and stifling mechanism. Mean-field equations are derived to describe the dynamics of the IRCSS model. Moreover, the steady states of reviewers, collectors and stiflers and the effects of parameters on the peak values of reviewers, collectors and sharers are analyzed. Finally, numerical simulations are performed on different networks. Results show that collecting mechanism and reviewing mechanism, as well as the connectivity of the network, make information travel wider and faster, and compared to WS network and ER network, the speed of reviewing, sharing and collecting information is fastest on BA network.

Effect of direct reciprocity and network structure on continuing prosperity of social networking services

BackgroundSocial networking services (SNSs) are widely used as communicative tools for a variety of purposes. SNSs rely on the users’ individual activities associated with some cost and effort, and thus it is not known why users voluntarily continue to participate in SNSs. Because the structures of SNSs are similar to that of the public goods (PG) game, some studies have focused on why voluntary activities emerge as an optimal strategy by modifying the PG game. However, their models do not include direct reciprocity between users, even though reciprocity is a key mechanism that evolves and sustains cooperation in human society.Proposed methodsWe developed an abstract SNS model called the reciprocity rewards and meta-rewards games that include direct reciprocity by extending the existing models. Then, we investigated how direct reciprocity in an SNS facilitates cooperation that corresponds to participation in SNS by posting articles and comments and how the structure of the networks of users exerts an influence on the strategies of users using the reciprocity rewards game.Experimental resultsWe run reciprocity rewards games on various complex networks and an instance network of Facebook and found that two types of stable cooperation emerged. First, reciprocity slightly improves the rate of cooperation in complete graphs but the improvement is insignificant because of the instability of cooperation. However, this instability can be avoided by making two assumptions: high degree of fun, i.e. articles are read with high probability, and different attitudes to reciprocal and non-reciprocal agents. We then propose the concept of half free riders to explain what strategy sustains cooperation-dominant situations. Second, we indicate that a certain WS network structure affects users’ optimal strategy and facilitates stable cooperation without any extra assumptions. We give a detailed analysis of the different characteristics of the two types of cooperation-dominant situations and the effect of the memory of reciprocal agents on cooperation.