The evolution of donations on scale-free networks during a COVID-19 breakout

Having a large number of timely donations during the early stages of a COVID-19 breakout would normally be considered rare. Donation is a special public goods game with zero yield, and it has the characteristics of prisoners’ dilemma. This paper discusses why timely donations in the early stages of COVID-19 occur. Based on the idea that donation is a strategy adopted by interconnected players on account of their understanding of the environment, donation-related populations are placed in social networks and the inter-correlation structure in the population is described by scale-free networks. Players in donation-related groups are of four types: donors, illegal beneficiaries, legal beneficiaries, and inactive people. We model the evolutionary game of donation on a scale-free network. Donors, illegal beneficiaries and inactive people learn and update strategies under the Fermi Update Rule, whereas the conversion between the legal beneficiaries and the other three strategies is determined by the environment surrounding the players. We study the evolution of cooperative action when the agglomeration coefficient, the parameters in the utility function, the selection strength parameter, the utility discount coefficient, the public goods discount coefficient and the initial state of the population in the scale-free network change. For population sizes of 50,100,150 and 200, we give the utility functions and the agglomeration coefficients for promoting cooperation. And we study the corresponding steady state and structural characteristics of the population. We identify the best ranges of selection strength K, the public goods discount coefficient α and the utility discount coefficient β for promoting cooperation at different population sizes. Furthermore, with an increase of the population size, the Donor Trap are found. At the same time, it is discovered that the initial state of the population has a great impact on the steady state; thus the Upper and Lower Triangle Phenomena are proposed. We also find that population size itself is also an important factor for promoting donation, pointing out the direction of efforts to further promote donation and achieve better social homeostasis under the donation model.

Air Quality Estimation Using Dendritic Neural Regression with Scale-Free Network-Based Differential Evolution

With the rapid development of the global economy, air pollution, which restricts sustainable development and threatens human health, has become an important focus of environmental governance worldwide. The modeling and reliable prediction of air quality remain substantial challenges because uncertainties residing in emissions data are unknown and the dynamic processes are not well understood. A number of machine learning approaches have been used to predict air quality to help alleviate air pollution, since accurate air quality estimation may result in significant social-economic development. From this perspective, a novel air quality estimation approach is proposed, which consists of two components: newly-designed dendritic neural regression (DNR) and customized scale-free network-based differential evolution (SFDE). The DNR can adaptively utilize spatio-temporal information to capture the nonlinear correlation between observations and air pollutant concentrations. Since the landscape of the weight space in DNR is vast and multimodal, SFDE is used as the optimization algorithm due to its powerful search ability. Extensive experimental results demonstrate that the proposed approach can provide stable and reliable performances in the estimation of both PM2.5 and PM10 concentrations, being significantly better than several commonly-used machine learning algorithms, such as support vector regression and long short-term memory.

Emergency of Tsallis statistics in fractal networks

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network’s properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks, and here we discuss a mechanism based on the way information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed.

Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes.

Evolving complex networks with logistic property: Global versus local growth

Considering the retarding effect of natural resources, environmental conditions, and other factors on network growth, the capacity of network nodes to connect to new edges is generally limited. Inspired by this hindered growth of many real-world networks, two types of evolving network models are suggested with different logistic growth schemes. In the global and local logistic network, the total number of network edges and the number of edges added into the network at each step are in line with the Logistic growth, respectively. The most exciting feature of the Logistic growth network is that the growth rule of network edges is first fast, then slow and finally reaches the saturation value [Formula: see text]. Theoretical analysis and numerical simulation reveal that the node degrees of two new networks converge to the same results of the BA scale-free network, [Formula: see text], as the growth rate [Formula: see text] approaches to 0. The local logistic network follows a bilateral power-law degree distribution with a given value of [Formula: see text]. Meanwhile, for these two networks, it is found that the greater [Formula: see text] and [Formula: see text], the smaller the average shortest paths, the greater the clustering coefficients, and the weaker the disassortativity. Additionally, compared to the local logistic growth network, the clustering feature of the global logistic network is more obvious.