BA Model Research Articles

Information cascade on networks and phase transitions

Herein, we consider a voting model for information cascades on several types of networks – a random graph, the Barabási–Albert(BA) model, and lattice networks – by using one parameter ω; ω=1,0,−1 respectively correspond to these networks. Our objective is to study the relation between the phase transitions and networks using the parameter, ω which is related to the size of hubs. We discuss the differences between the phases in which the networks depend. In ω≠−1, without a lattice, the following two types of phase transitions can be observed: information cascade transition and super-normal transition. The first is the transition between a state where most voters make correct choices and a state where most of them are wrong. This is an absorption transition that belongs to the non-equilibrium transition. In the symmetric case, the phase transition is continuous and the universality class is the same as nonlinear Pólya model. In contrast, in the asymmetric case, there is a discontinuous phase transition, where the gap depends on the network. As ω increases, the size of the hub and the gap increase. Therefore, a network that has hubs has a greater effect through this phase transition. The critical point of information cascade transition does not depend on ω. The super-normal transition is the transition of the convergence speed, and the critical point of the convergence speed transition depends on ω. At ω=1, in the BA model, this transition disappears, and the range where we can observe the phase transition is the same as that in the percolation model on the network. Both phase transitions disappear at ω=−1 in the lattice case. In conclusion, as the performance near the lattice case, ω∼−1 exhibits the best performance of the voting in all networks. As the hub size decreases, the performance improves. Finally, we show the relation between the voting model and the elephant walk model.

Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

To investigate the relationship between histological properties and thermal conductivities of binary self-assembled/self-organized fractal materials fabricated by the mixed diffusion of filler particles, the particle group distribution of the filler particles was analyzed. Unlike conventional research on particle size distribution, we performed an analysis that focuses on interactions and connectivity between particles from the perspective of the Barabasi-Albert model. In three complex network systems of β-Si3N4 (SN)/austenitic stainless steel (SUS), SN/piezoelectric polyvinylidene fluoride (PVDF), and BaTiO3 (BT)/PVDF, the size distribution of secondary particles was a power-law distribution until the particle group grew relatively large. In the SN/SUS and SN/PVDF systems, a crossover phenomenon was observed in which the order distribution exhibited a power-law in the region where the particle group area was small, and as the particle group became larger, the order distribution became exponential distribution. On the other hand, the BT/PVDF system deviated from the power law distribution as the particle group area increased but did not exhibit an exponential distribution. The characteristics of the particle group distribution of these filler particles were closely related to thermal conductivity, indicating that the connection of particle groups was important. Furthermore, the relationship between the multifractal capacitance dimension, which is strongly correlated with the distance between the particle groups, and the total number of filler particle groups suggests that the texture of these composite material systems may have both small-world and scale-free properties. We also focused on the relationship between the multifractal and complex network properties of the three particle groups. As a result, a correlation was found between the slope γ, which reflects the characteristics of the power distribution, and the thermodynamic parameter α (corresponding to internal energy change) obtained from multifractals. In particular, the smaller the change in γ relative to the change in α, the more pronounced the bonding of particles and particle groups, while the larger change in γ suggested the dispersion of particle groups.

An innovative approach for predicting groundwater TDS using optimized ensemble machine learning algorithms at two levels of modeling strategy

Groundwater salinization in coastal aquifers is a major socioeconomic challenge in Oman and many other regions worldwide due to several anthropogenic activities and natural drivers. Therefore, assessing the salinization of groundwater resources is crucial to ensure the protection of water resources and sustainable management. The aim of this study is to apply a novel approach using predictive optimized ensemble trees-based (ETB) machine learning models, namely Catboost regression (CBR), Extra trees regression (ETR), and Bagging regression (BA), at two levels of modeling strategy for predicting groundwater TDS as an indicator for seawater intrusion in a coastal aquifer, Oman. At level 1, ETR and CBR models were used as base models or inputs for BA in level 2. The results show that the models at level 1 (i.e., ETR and CBR) yielded satisfactory results using a limited number of inputs (Cl, K, and Sr) from a few sets of 40 groundwater wells. The BA model at level 2 improved the overall performance of the modeling by extracting more information from ETR and CBR models at level 1 models. At level 2, the BA model achieved a significant improvement in accuracy (MSE = 0.0002, RSR = 0.062, R2 = 0.995 and NSE = 0.996) compared to each individual model of ETR (MSE = 0.0007, RSR = 0.245, R2 = 0.98 and NSE = 0.94), and CBR (MSE = 0.0035, RSR = 0.258, R2 = 0.933 and NSE = 0.934) at level 1 models in the testing dataset. BA model at level 2 outperformed all models regarding predictive accuracy, best generalization of new data, and matching the locations of the polluted and unpolluted wells. Our approach predicts groundwater TDS with high accuracy and thus provides early warnings of water quality deterioration along coastal aquifers which will improve water resources sustainability.

BAT: Barabasi–Albert With Topsis Scale-Free Topology Evolution for Load-Balanced WSNs

Recent advancements in sensor technology have made Wireless Sensor Networks (WSNs) a preferable choice for several applications. As sensor nodes rely on limited batteries in order to operate, clustering techniques are proven to be energy efficient and effective in the case of WSNs. Avoiding premature death of sensor nodes by load balancing and prolonging network lifetime is an essential aspect that needs to be addressed. Hence there is always a need for protocol that can uniformly evolve energy consumption among all the nodes by load balancing the network with respect to energy. This work presents a clustering framework, named as BAT, that uses Barabasi-Albert (BA) model and Topsis (T) technique to effectively balance the load on all the sensor nodes present in the network. In the proposed BAT approach, network backbone topology is initially constructed, and later topology evolution happens according to the BA model. After network evolution, the best possible attachments are retained in order to form the final network. Best possible Cluster Heads (CHs) are determined by the weighted-objective function. The outcome of the proposed BAT protocol is evenly consumed energy among nodes over the whole network to avoid the energy hole. The simulation results reveal that the proposed approach has attained a better stable region and balanced energy efficient consumption when compared to other simulated protocols.

Butterfly Algorithm for Sustainable Lot Size Optimization

The challenges faced by classical supply chain management affect efficiency with regard to business. Classical supply chain management is associated with high risks due to a lack of accountability and transparency. The use of optimization algorithms is considered decision-making support to improve the operations and processes in green manufacturing. This paper suggests a solution to the green lot size optimization problem using bio-inspired algorithms, specifically, the butterfly algorithm. For this, our methodology consisted of first collecting the real data, then the data were expressed with a simple function with several constraints to optimize the total costs while reducing the CO2 emission, serving as input for the butterfly algorithm BA model. The BA model was then used to find the optimal lot size that balances cost-effectiveness and sustainability. Through extensive experiments, we compared the results of BA with those of other bio-inspired algorithms, showing that BA consistently outperformed the alternatives. The contribution of this work is to provide an efficient solution to the sustainable lot-size optimization problem, thereby reducing the environmental impact and optimizing the supply chain well. Conclusions: BA has shown that it can achieve the best results compared to other existing optimization methods. It is also a valuable chainsaw tool.

Land subsidence susceptibility mapping: comparative assessment of the efficacy of the five models.

Land subsidence (LS) as a major geological and hydrological hazard poses a major threat to safety and security. The various triggers of LS include intense extraction of aquifer bodies. In this study, we present an LS inventory map of the Daumeghan plain of Iran using 123 LS and 123 non-LS locations which were identified through field survey. Fourteen LS causative factors related to topography, geology, hydrology, and anthropogenic characteristics were selected based on multi-collinearity test. Based on the results, five susceptibility maps were generated employing models and input data. The LS susceptibility models were evaluated and validated using the receiver operating characteristic (ROC) curve and statistical indices. The results indicate that the LS susceptibility maps produced have good accuracy in predicting the spatial distribution of LS in the study area. The result showed that the optimization models BA and GWO were better than the other machine learning algorithm (MLA). In addition, The BA model has 96.6% area under of ROC (AUROC) followed by GWO (95.8%), BART (94.5%), BRT (93.1%), and SVR (92.7%). The LS susceptibility maps formulated in our study can serve as a useful tool for formulating mitigation strategies and for better land-use planning.

Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties

Networks are prevalent in real life, and the study of network evolution models is very important for understanding the nature and laws of real networks. The distribution of the initial degree of nodes in existing classical models is constant or uniform. The model we proposed shows binomial distribution, and it is consistent with real network data. The theoretical analysis shows that the proposed model is scale-free at different probability values and its clustering coefficients are adjustable, and the Barabasi-Albert model is a special case of p = 0 in our model. In addition, the analytical results of the clustering coefficients can be estimated using mean-field theory. The mean clustering coefficients calculated from the simulated data and the analytical results tend to be stable. The model also exhibits small-world characteristics and has good reproducibility for short distances of real networks. Our model combines three network characteristics, scale-free, high clustering coefficients, and small-world characteristics, which is a significant improvement over traditional models with only a single or two characteristics. The theoretical analysis procedure can be used as a theoretical reference for various network models to study the estimation of clustering coefficients. The existence of stable equilibrium points of the model explains the controversy of whether scale-free is universal or not, and this explanation provides a new way of thinking to understand the problem.

Real-time updating of dynamic social networks for COVID-19 vaccination strategies

Vaccination strategy is crucial in fighting the COVID-19 pandemic. Since the supply is still limited in many countries, contact network-based interventions can be most powerful to set an efficient strategy by identifying high-risk individuals or communities. However, due to the high dimension, only partial and noisy network information can be available in practice, especially for dynamic systems where contact networks are highly time-variant. Furthermore, the numerous mutations of SARS-CoV-2 have a significant impact on the infectious probability, requiring real-time network updating algorithms. In this study, we propose a sequential network updating approach based on data assimilation techniques to combine different sources of temporal information. We then prioritise the individuals with high-degree or high-centrality, obtained from assimilated networks, for vaccination. The assimilation-based approach is compared with the standard method (based on partially observed networks) and a random selection strategy in terms of vaccination effectiveness in a SIR model. The numerical comparison is first carried out using real-world face-to-face dynamic networks collected in a high school, followed by sequential multi-layer networks generated relying on the Barabasi-Albert model emulating large-scale social networks with several communities.

Phase Transitions in Ising Model Defined on Complex Networks

In this work, we consider an Ising model which allows spin-spin interaction in the systems. We assume that two-level quantum systems are randomly located in N nodes of a complex annealed scale-free network described by the Barabasi-Albert model. It is defined by the power-law degree distribution of nodes. We consider the mean-field approach to the system described by the Ising Hamiltonian. At a certain level, the system is totally characterized by the order parameter Sz. It contains a critical inverse temperature β, which depends on parameter ζ2 as the ratio of the second to the first moment of the degree distribution. We have found that for ζ2, that exceeds its critical value ζ2,c, high temperature phase transition occurs that can be explained by the hubs and clusters which appear in scale-free networks.

An extended scale-free network evolution model based on star-like coupling motif embedding

As the only brand-new basic model that can study networks with scale change characteristics at present, the Barabási–Albert scale-free network evolution model (BA model) can well describe the entry phenomenon of a single subject. However, for many evolutionary networks in the real world, the entry of the subject is more realized in a team way. Therefore, the BA model’s assumption concerning one new node entering alone per unit of time can only be used as a particular case of a team entry. This deficiency makes it difficult for the BA model to analyze how the team entry mechanism affects the network’s performance and thus leads to the BA model’s certain limitations. To make up for this shortcoming, with the help of the motif’s concept, an extended BA model with a star-like coupling motif embedding (SCME-BA model) is constructed, where the motif’s scale obeys an arbitrary discrete probability distribution. The exact explicit expression of the network’s steady-state degree distribution of the SCME-BA model is first obtained by the Markov chain analytic method, and its numerical characteristics are explored. Then, the correctness of the analytic expression is verified by numerical simulation. The study results show that, compared with the BA model, the left tail of the SCME-BA model’s steady-state degree distribution can reflect the distribution law of the embedded motif scale well while the right one still has power-law attenuation characteristics whose power-law exponent is adjustable. Specifically, the power-law exponent is positively and negatively correlated with the expectation of the motif’s scale and the initial number of existing nodes connected to the new embedded motif, respectively. Moreover, the SCME-BA model can degenerate into the BA model when the motif’s scale is subject to the one-point distribution with parameter 1. Finally, the rationality of the SCME-BA model is verified through a case study.

Random processes with high variance produce scale free networks

Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms leading to these networks and are incorporated in the Barabási–Albert (BA) model (Barabási, 2009 [1]). We provide an alternative model using a randomly stopped linking process inspired by a generalized Central Limit Theorem (CLT) for geometric distributions with widely varying parameters. The common characteristic of both the BA model and our randomly stopped linking model is the mixture of widely varying geometric distributions, suggesting the critical characteristic of scale free networks is high variance, not growth or preferential attachment. The limitation of classical random graph models is low variance in parameters, while scale free networks are the natural, expected result of real-world variance.

Geometric Nodal Degree Distributions Arise in Barabási-Albert Graphs!

In random graphs, node degrees are random variables that can have different statistical properties in comparison to the (empirical) degree distribution of the entire network. In the present work, we analyze the degree distribution of individual nodes in Barabási-Albert graphs, and observe them to be geometrically distributed with parameter dependent on the node's age. This result directly shows an “old-get-rich” phenomenon in the BA model, i.e., older nodes are more likely to have a higher degree than more recent nodes. We also conclude that old nodes tend to have a flatter degree distribution, while later nodes have a more pronounced exponential tail. The result provides an approach for estimating nodal degree distribution in a finite BA graph. Finally, we reconcile with the well known result that the degree distribution of the entire network is power law (heavy-tailed) in spite of the individual nodes being geometrically distributed (light-tailed). In fact, we show that an infinitesimally small fraction of early nodes in the network make the degree distribution power-law. This suggests that in heterogeneous models, e.g., network growth models, the degree distribution of the node can be very different in comparison to the network-wide empirical distribution, possibly of a different class altogether.

An Adaptive Designer Network Model and Its Robustness Research

The designer network is the carrier for designers to carry out product design tasks, and the study of its evolution helps to accurately identify the designer team. The uncertainty of whether the designer chooses to keep in touch with other members of the network, its nonlinearity on the overall performance of the network and the external interference of the network, etc., increase the complexity of the designer network, which is not conducive to the development of product design tasks. Therefore, it is very interesting and important to study the co-evolution mechanism of the designer’s network structure and the designer’s opinion. This paper analyzes the Deffuant opinion dynamics model, considers the asymmetry of nodes in the network caused by the designer’s unequal relationship (the number of node links is different), and the difference in the degree of acceptance of other people’s opinions by different individuals, and improves the Deffuant model. Then combining the improved Deffuant model with the BA (Barabasi–Albert) model, a DBA (Deffuant and BA Adaptive) model was proposed that integrates opinion update, broken edge and reconnection, and opinion changes. On this basis, this paper designs a virtual network through the crowdsourcing of a certain product. The adjacency matrix of this network is symmetric, and corresponding comparative experiments are carried out on this network. The analysis of test results shows that under six different deliberate attacks, the DBA model is more robust than the BA model. In addition, the average shortest path of the DBA network will vary with the parameters. The proposed integrated DBA model has important guiding significance for building a robust designer network.

Modelling Underload Cascading Failure and Mitigation Strategy of Supply Chain Complex Network in COVID-19

The outbreak of COVID-19 has caused problems such as shortage of workforce, cost increase, cash flow tension, and uncertainty of supply chain. It has a specific negative impact on the raw material supply, procurement management, production resumption, logistics, and market of the supply chain, which can trigger cascading failures in supply chain networks. Aiming at the failure of upstream/downstream firms in supply chain networks due to the decreased product demand/material supply under the COVID-19, the present study adopted an underload cascading failure model for the supply chain networks. In this model, the hierarchical supply chain networks were constructed based on the Erdos Renyi (ER) model and Barabasi Albert (BA) model. The validity of the model was verified under random attack and target attack. In the random attack mode, the influences of model parameters were studied, and in the target attack mode, the influence of target protection and random protection measures on enhancing network invulnerability was also studied. Simulation results showed that the initial load and capacity lower bound of nodes impact cascading failure size. The former has a positive correlation with cascading failure size, while the latter negatively correlates with cascading failure size. Furthermore, random protection measures are more practical to prevent cascading failures.

Can Lightning Network’s Autopilot Function Use BA Model as the Underlying Network?

By extending micropayment channel technology and building a transaction network, the Lightning Network solves inefficient bitcoin transactions. Currently, more than 1,000 Bitcoins have been deposited in the Lightning Network. In designing the Lightning Network routing protocol, simulating its transactions, and evaluating the network robustness, researchers have almost always used the Barabasi Albert Model as a substrate network. In particular, as the network grows in size, it becomes particularly important to automatically establish links for the network of joined nodes—the autopilot function—and it becomes a crucial question whether the Barabasi Albert Model as the underlying network for the autopilot function conforms to the real topology of the Lightning Network. In this paper, we construct the temporal network of Lightning Network and compare the topological properties of Lightning Network with those of Barabasi Albert Model of the same scale in detail. Lightning Network has a large gap with Barabasi Albert Model in terms of assortativity and network diameter. We found that nodes tend to connect to nodes with greater Closeness Centrality in terms of node preference connectivity. Our findings suggest that using the Barabasi Albert Model as the underlying network for the autopilot function is not a reasonable choice.

Understanding the Dynamics of Knowledge Building Process in Online Knowledge‐Sharing Platform: A Structural Analysis of Zhihu Tag Network

Through structural analysis of 8‐year tag networks from online knowledge‐sharing platforms, this study finds that, with the scale of tag networks growing quickly, the growth trend of number edges indicates that tag network follows densification law. The clustering coefficient and the average shortest path of the network show that the rapid growth of network size does not bring about the compartmentalization of the knowledge network, and the degree distribution of tag networks shows a truncated power‐law distribution. According to the structural characteristics of the tag network, this study proposes a tag network model based on the BA model. Based on the preference attachment, the triadic closure mechanism is employed to construct the edges between the old nodes, which revises the limitation that the BA model only connects edges between old and new nodes. The results show that the simulation model matches the actual tag network structure well. The generation mechanism of the tag network model provides a reference for understanding the knowledge construction process of the online knowledge‐sharing platform to a certain extent.

Characteristics of Water Supplying Network on Leaf

The purpose of this study is to analyze the leaf network, understand the characteristics and structure of the network. The leaves remain lush even when insects eat, tear and leave holes. We thought that the structure of the leaf network was responsible for the plant's ability to remain lush despite damage. The veins are used to supply nutrients to the leaf and are the lifeblood of the leaf, but other studies have observed leaf water supply even when only leaf cells are present. Our study will analyze the leaf network, focusing on the network of leaf cells, that could be applied to lifelines. We believe that by applying a network of attack-resistant leaves, it is possible to realize a lifeline that is not affected by natural disasters. This study examines the structure of the leaf net- work by comparing to the Watts-Strogatz model (WS model), and Barabasi-Albert model (BA mod- el). By comparing the average path lengths and cluster coefficients of each network, the leaf net- work was found to be a small network. Smaller size may facilitate water supply. The water supply- ing inside the node needs to realize with the diffusion of water. This diffusion is a phenomenon, so that small substantial network as leaf is suitable for the leaf network.

Research on the Model of Industrial Interconnection Intelligent Manufacturing Supply and Demand Network and Its Robustness

The industrial interconnection intelligent manufacturing supply and demand network is the carrier for the cooperation of related enterprises, and research on its evolution helps to optimize the cooperation between enterprises. This paper considers the factors that affect enterprise cooperation, applies consensus, disconnection, reconnection, and change of opinion into one model, and constructs two models of industrial interconnection intelligent manufacturing supply and demand networks. Because the industrial interconnection intelligent manufacturing supply and demand network is affected by certain factors, the network will be subject to fluctuations and the functions of the network will change. The smaller the function change, the higher the robustness of the model. The related topological structure statistics (such as clustering coefficient, average path length, and degree distribution) of the two models are analyzed, and the analysis results indicate that the network structure of the two models has changed. In addition, different attack algorithms are used to verify the robustness of the model. The experimental results show that under the four different attack algorithms, compared with the BA model, the two models proposed in this paper have stronger robustness. Research on the industrial interconnection of intelligent manufacturing supply and demand networks and its robustness optimization has certain guiding significance.

Modularity affects the robustness of scale-free model and real-world social networks under betweenness and degree-based node attack

In this paper we investigate how the modularity of model and real-world social networks affect their robustness and the efficacy of node attack (removal) strategies based on node degree (ID) and node betweenness (IB). We build Barabasi–Albert model networks with different modularity by a new ad hoc algorithm that rewire links forming networks with community structure. We traced the network robustness using the largest connected component (LCC). We find that when model networks present absent or low modular structure ID strategy is more effective than IB to decrease the LCC. Conversely, in the case the model network present higher modularity, the IB strategy becomes the most effective to fragment the LCC. In addition, networks with higher modularity present a signature of a 1st order percolation transition and a decrease of the LCC with one or several abrupt changes when nodes are removed, for both strategies; differently, networks with non-modular structure or low modularity show a 2nd order percolation transition networks when nodes are removed. Last, we investigated how the modularity of the network structure evaluated by the modularity indicator (Q) affect the network robustness and the efficacy of the attack strategies in 12 real-world social networks. We found that the modularity Q is negatively correlated with the robustness of the real-world social networks for both the node attack strategies, especially for the IB strategy (p-value < 0.001). This result indicates how real-world networks with higher modularity (i.e. with higher community structure) may be more fragile to node attack. The results presented in this paper unveil the role of modularity and community structure for the robustness of networks and may be useful to select the best node attack strategies in network.

Making intelligent topology design choices: understanding structural and physical property performance implications in optical networks [Invited

The key goal in optical network design is to introduce intelligence in the network and deliver capacity when and where it is needed. It is critical to understand the dependencies between network topology properties and the achievable network throughput. Real topology data of optical networks are scarce, and often large sets of synthetic graphs are used to evaluate their performance including proposed routing algorithms. These synthetic graphs are typically generated via the Erdos–Renyi (ER) and Barabasi–Albert (BA) models. Both models lead to distinct structural properties of the synthetic graphs, including degree and diameter distributions. In this paper, we show that these two commonly used approaches are not adequate for the modeling of real optical networks. The structural properties of optical core networks are strongly influenced by internodal distances. These, in turn, impact the signal-to-noise ratio, which is distance dependent. The analysis of optical network performance must, therefore, include spatial awareness to better reflect the graph properties of optical core network topologies. In this work, a new variant of the BA model, taking into account the internodal signal-to-noise ratio, is proposed. It is shown that this approach captures both the effects of graph structure and physical properties to generate better networks than traditional methods. The proposed model is compared to spatially agnostic approaches, in terms of the wavelength requirements and total information throughput, and highlights how intelligent choices can significantly increase network throughputs while saving fiber.