A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ , we derive an explicit form for the distribution functions by regulating λ , and then explore the nontrivial relationship between these functions and energy nonextensivity, as well other system parameters such as system size. A variational entropy function is also derived from these distribution functions.
Spatial distance has a remarkable effect on the attended mode of a network embedded in a certain space. First, we investigate how spatial restriction leads to information-information correlation that is strong, linear and positive in real networks. We then construct a two-dimensional space, define the action radius R for nodes of networks, and propose a class of models that depend on spatial distance. Information correlation of the models is consistent with that of real networks. The spatial distance plays a leading role in generating assortative mixing by degree, while the generation of disassortative mixing relies on both the degree of preferential attachment and spatial restriction.
Varentropy is used as a general measure of probabilistic uncertainty for a complex network, inspired by the first and second laws of thermodynamics, but not limited to the equilibrium system. By exploring the relationship between the varentropy of the scale free distribution and the exponent of power laws as well as network size, we get the optimal design of a scale-free network against random failures. The behaviors of varentropy and the Shannon entropy of double Pareto law degree distribution are analyzed to compare their usefulness. Our conclusion is that varentropy is suitable and reliable.
Motivated by the need to include the different characteristics of individuals and the damping effect in predictions of epidemic spreading, we build a model with variant coefficients and white Gaussian noise based on the traditional SIR model. The analytic and simulation results predicted by the model are presented and discussed. The simulations show that using the variant coefficients results in a higher percentage of susceptible individuals and a lower percentage of removed individuals. When the noise is included in the model, the percentage of infected individuals has a wider peak and more fluctuations than that predicted using the traditional SIR model.
We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship parameter to measure the collaboration between scientists. The collaboration relationship parameter of two scientists depends not only on the connection weights between the nodes, but also on the network's structure. The stability of the network's structure in terms of different edge removal strategies is also studied. According to the parameter, we find that a community structure exists in this type of network.
English and Chinese language frequency time series (LFTS) were constructed based on an English and two Chinese novels. Methods of statistical hypothesis testing were adopted to test the nonlinear properties of the LFTS. Results suggest the series exhibited non-normal, auto-correlative, and stationary characteristics. Moreover, we found that LFTS follow the power law distributions, and thereby we investigated the fractal structure, long range correlation, and intermittency, which indicated the self-similarity features of LFTS, and also provided hints that human societies are likely to share some universal properties.
DENG WeiBingWANG DuJuanLI WeiWANG Qiuping Alexandre
In this paper,we propose a simple model of opinion dynamics to construct social networks,based on the algorithm of link rewiring of local attachment(RLA)and global attachment(RGA).Generality,the system does reach a steady state where all individuals'opinion and the complex network structure are fixed.The RGA enhances the ability of consensus of opinion formation.Furthermore,by tuning a model parameter p,which governs the proportion of RLA and RGA,we find the formation of hierarchical structure in the social networks for p>p_(c).Here,p_(c) is related to the complex network size N and the minimal coordination number 2K.The model also reproduces many features of large social networks,including the“weak links”property.
We propose a mean-field Bak-Sneppen (MFBS) model with varying interaction strength. The interaction strength, here denoted by α, specifies the degree of interaction, and varies smoothly between 0 for no interaction and 1 for full interaction (restoring the original BS model). Our simulations of the MFBS model reveal some interesting features. When α is non-zero, the MFBS model can evolve to a self-organized critical (SOC) state. The critical exponent of the avalanche size distribution, α, is insensitive to changes in α. The critical exponent of average avalanche size, α, and the avalanche dimension exponent, D, both increase slightly with α < 0.5 but remain constant if α > 0.5. The critical threshold fc decreases almost linearly with α.
