我们考察了Watts、Dodds和Newman（D. J. Watts等人，Science 296（2002）1302）作为组的层级，每个组有5个个体。同质性参数$α$控制相对于距离$x$选择邻居的概率，该概率与$\exp(-αx)$成比例。网络节点被赋予自旋类变量$s_i = \pm 1$，具有伊辛相互作用$J>0$。用Glauber动力学研究了有序-无序转变。对于$α< 0.0$，转变温度$T_c$接近3.8，并且在高于该值时下降至零。结果提供了一个数学说明的社会能力的集体行动{ \it通过}弱关系，讨论了由格兰米特在1973年。
英文摘要：
We investigate the network model of community by Watts, Dodds and Newman (D. J. Watts et al., Science 296 (2002) 1302) as a hierarchy of groups, each of 5 individuals. A homophily parameter $α$ controls the probability proportional to $\exp(-αx)$ of selection of neighbours against distance $x$. The network nodes are endowed with spin-like variables $s_i = \pm 1$, with Ising interaction $J>0$. The Glauber dynamics is used to investigate the order-disorder transition. The transition temperature $T_c$ is close to 3.8 for $α< 0.0$ and it falls down to zero above this value. The result provides a mathematical illustration of the social ability to a collective action {\it via} weak ties, as discussed by Granovetter in 1973.
线图是群集的和独立的。它们与某些社交网络共享这些拓扑特征。我们认为，这种相似性揭示了社交网络的小团体性质。在这里提出的模型中，社会网络是由家庭、社区、利益集团、学校班级和小公司组成的初始网络的线图。这些群体扮演节点的角色，个体由这些节点之间的链接表示。这张图片得到了LiveJournal网络上大约8 x 10^6人的数据的支持。特别地，聚类系数C（k）的度依赖性的观测数据的尖锐最大值与社交网络中的集团相关联。
Discontinuous phase transitions occurs to be particularly interesting from a social point of view because of their relationship to social hysteresis and critical mass. In this paper, we show that the replacement of a time-varying (annealed, situation-based) disorder by a static (quenched, personality-based) one can lead to a change from a continuous to a discontinuous phase transition. This is a result beyond the state of art, because so far numerous studies on various complex systems (physical, biological and social) have indicated that the quenched disorder can round or destroy the existence…
The frequent emergence of diseases with the potential to become threats at local and global scales, such as influenza A(H1N1), SARS, MERS, and recently COVID-19 disease, makes it crucial to keep designing models of disease propagation and strategies to prevent or mitigate their effects in populations. Since isolated systems are exceptionally rare to find in any context, especially in human contact networks, here we examine the susceptible-infected-recovered model of disease spreading in a multiplex network formed by two distinct networks or layers, interconnected through a fraction $q$ of shar…
Entropic analysis of a scenario at a traffic intersection is attempted in detail. The model is utilized to define Conflict Entropy. It is shown that with the use of strategies (policies) like installing traffic lights and construction of flyovers the Entropy is reduced thereby making the traffic ordered. It is shown that these policies help in reducing the Entropy and eliminating the Conflict Entropy completely in both the cases. Such an analysis can find immense application in deciding a favorable policy and in formulation of artificial intelligence algorithms. A striking similarity of the tr…
Addiction epidemiology has been an active area of mathematical research in recent years. However, the social and mental processes involved in substance use disorders versus contraction of a pathogenic disease have presented challenges to advancing the epidemiological theory of substance abuse, especially within the context of the opioids where both prescriptions and social contagion have played a major role. In this paper, we utilize an agent-based modeling approach on social networks to further explore these dynamics. Using parameter estimation approaches, we compare our results to that of th…
We investigate the effects of long-range social interactions in flocking dynamics by studying the dynamics of a scalar model of collective motion embedded in a complex network representing a pattern of social interactions, as observed in several social species. In this scalar model we find a phenomenology analogous to that observed in the classic Vicsek model: In networks with low heterogeneity, a phase transition separates an ordered from a disordered phase. At high levels of heterogeneity, instead, the transition is suppressed and the system is always ordered. This observation is backed up a…
We consider a first neighbor interaction where agents are spread through a uni-dimensional network. Some agents are also connected to a hub, or master node, who has preferential values (or orientation). The role of master node is to persuade some individuals to follow a specific orientation, subject to a probability of successful persuasion. The connections between master node and the network society are quenched in disorder. Despite its simplicity, we found a phase transition from disorder to order for three different control parameters. We also discuss how this model may be useful as a frame…
We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal and ordered bimodal distribution states, characterized by an increase in the vote-share variability of the equilibrium distributions. The random heterogeneities in the external perturbations are shown to affect the critical behavior of the network relative to networks without disorder. The size of the shift in the critical behavior essentially depends on th…
Epstein's model for a civil disorder is an agent-based model that simulates a social protest process where the central authority uses the police force to dissuade it. The interactions of police officers and citizens produce dynamics that do not yet have any analysis from the sociophysics approach. We present numerical simulations to characterize the properties of the one-dimensional civil disorder model on stationary-state. To do this, we consider interactions on a Moore neighborhood and a random neighborhood with two different visions. We introduce a Potts-like energy function and construct t…
Many theoretical studies of the voter model (or variations thereupon) involve order parameters that are population-averaged. While enlightening, such quantities may obscure important statistical features that are only apparent on the level of the individual. In this work, we ask which factors contribute to a single voter maintaining a long-term statistical bias for one opinion over the other in the face of social influence. To this end, a modified version of the network voter model is proposed, which also incorporates quenched disorder in the interaction strengths between individuals and the p…
In this work we study the critical behavior of a three-state opinion model in the presence of noise. This noise represents the independent behavior, that plays the role of social temperature. Each agent on a regular D-dimensional lattice has a probability $q$ to act as independent, i.e., he can choose his opinion independent of the opinions of his neighbors. Furthermore, with the complementary probability $1-q$ the agent interacts with a randomly chosen nearest neighbor through a kinetic exchange. Our numerical results suggest that the model undergoes nonequilibrium phase transitions at critic…
We analyze Axelrod's model of social interactions on coevolving complex networks. We introduce four extensions with different mechanisms of edge rewiring. The models are intended to catch two kinds of interactions - preferential attachment, which can be observed in scientists or actors collaborations, and local rewiring, which can be observed in friendship formation in everyday relations. Numerical simulations show that proposed dynamics can lead to the power-law distribution of nodes' degree and high value of the clustering coefficient, while still retaining the small-world effect in three mo…
