Temporal human contact networks have their own dynamical properties, which can be depicted by defining appropriate topological and temporal characteristic. On the other hand, the inherent structural features of temporal networks affect the dynamical processes occurring on the network significantly, such as epidemic spreading. The research progress is reviewed in this paper, covering the types and representations of human interactions, temporal network structure (network topology, temporal features and time scales), temporal network models as well as the spreading dynamics on temporal network. Then we analyze the current research situation and put forward several future research directions of this field.

The signed network is a network with both of positive and negative attributes on the edges, and has important effects on the function of the system. By changing the proportion of negative edges in the network, the relationship between the ratio of negative edges and the proportion of balanced structures is obtained. Subsequently, a dynamic evolution model based on nodes and edges was established in the signed network. Then its dynamics and final steady states are investigated by computer simulation. It is found that the increase in the proportion of negative edges can expand the scope of changing nodes, and at the same time it will affect the evolution behaviour. In the coupling evolution of edges and states, adding the adjustment probability of the interaction and the influence of the time scale, it will produce a richer cycle change pattern. During the research process, we found a method to construct a fully-balanced network, and found that it can accelerate the system to reach a steady state during the evolution, and can finally divide the network into two communities.

Social public opinions transfer from the real society to the network space, resulting in the emergence of network public opinion events. Online public opinion diffusion reverses the contrast between the support and opposition of public opinions, and finally changes the initial decision of interest groups, which is called the structure reversal of online public opinion. In order to explore the complex systems mechanism underlying this phenomenon, we established a network public opinion structure reversal model based on the Deffuant model. The Deffuant model is modified from two aspects: one is to transform the individual′s own opinion value into the perception opinion value in the interaction; the other is to introduce the influence of social transformation from a macro perspective. The simulation results show that social transformation factors positively influence the diffusion of online public opinion. The higher the degree of social transformation, the higher diffusion of public opinion in structure reversal. Heterogeneity level positively delays the public opinion structure reversal. The larger the size of interest groups, the more difficult it is to complete public opinion structure reversal. The model proposed in this paper can explain the structural reversal phenomenon of public opinion diffusion to a certain extent and can provide certain theoretical reference and decision support for the control of network public opinion in practice.

The structural characteristics of real networks usually have a very important impact on spread speed. In order to explore which structural features have a crucial impact on the speed of spreading, we collect the data of a SMS social network, and perform simulation experiments on the original network and its corresponding null-model networks. Simulation results show that the average shortest path length of the network is the key factor affecting the propagation speed, and the network distribution is the key factor affecting the propagation range. This study systematically proposes a method to test and quantify the influencing factors of real-life network spreading by referring to null model theory, which can also be extended to other researches of network dynamics, such as synchronization, game, cascading failures.

In view of the difference of users′ resistance to rumors and the different intimacy between users in social networks, the dissemination rate of inconsistent contact reflecting network structure characteristics is defined by introducing a rumor reliability function and an individual intimacy function. Considering the different degree and intensity of rumors, a new dynamic model of network rumor propagation is established based on the mean field theory. The correctness of theoretical analysis is verified by numerical simulation in BA scale-free networks. The results show that rumors spread faster and wider in nodes with large degree; high rumor reliability and user intimacy will make rumors spread faster and wider; and further explore the impact of forgetting rate, rumor denial rate and other related parameters on rumor propagation in the model. Based on the sensitivity analysis of the basic reproduction number, some suggestions are put forward to control the spread of rumors, and the effects of two common immunization strategies, random immunization and target immunization, are compared and analyzed. The influence of network structure on rumor propagation is analyzed in simulation network and real network.

This paper investigated the evolution of cooperation in three typical social network topologies: regular lattice network, scale-free network and small-world network, using NetLogo simulation platform and ABM method to design simulation experiment. We also studied which network is more conducive to the occurrence of cooperation. By introducing factors such as network scale, initial cooperation probability, betrayal benefit, selection mode of neighbor node, interaction rules and so on, this paper measured how the above variables affect the occurrence and continuity of cooperation. Then we compared the different evolution results and discussed how to design effective incentive mechanism to maintain and to promote cooperation. Experimental results show that regular lattice network and small-world network have more commonality, while scale-free network is more conducive to the evolution of cooperation. In order to develop an effective incentive mechanism to promote the occurrence and continuity of cooperation, the design of incentive mechanism should take full account of the influence of social network structure of groups.

More and more evidences show that different ensembles can be not equivalent. Especially in the systems with long-range interactions, the ensemble inequivalence is more obvious. We believed that the long-range interaction system corresponds to the power-law distribution, and proved that the power-law distributions are not applicable to the near-independent systems and the extensive systems with the short-range interactions. Therefore, it is imperative to perfect or enrich various ensembles of the power-law distribution. Based on the principle of maximum entropy and Rényi entropy, we obtained the power-law distributions of a completely open system, grand canonical system, isothermal-isobaric system and various other systems, and gave a variety of formulas for calculating thermodynamic quantities.

Based on the HFMD reported cases in 31 provinces, autonomous regions and municipalities of China, this paper estimated the transmission rate of HFMD and its seasonality, then analyzed possible related factors. The Time Series Susceptible Infected Recovered (TSIR) model was established to examine the HFMD transmission rate, and the parameters in the TSIR model were estimated by Markov chain Monte Carlo (MCMC). We also established a linear regression model to analyze the effects of climate factors, school terms and the spring festival travel rush on the transmission rate of HFMD. The results show that the HFMD transmission rate in all provinces of China has obvious seasonality. According to the peak time of HFMD transmission rate, the provinces can be divided into four regions: the peak period of HFMD transmission rate in the southeast region is from February to March, which is affected by the spring festival travel rush; the peak time in the northwest region is April and its seasonality is mainly affected by relative humidity and spring Festival travel rush; in the northern region, the peak period happens in May, which is associated with average temperature, summer vacation and spring festival travel rush; the peak of Tibet Autonomous Region is in August. The seasonality of its isn’t affected by climate or the contact rate.

An optimal weighted stochastic pooling network is used as the basic framework for analog-to-digital converter (ADC) with multilevel quantizers. This paper, for a fixed number of network nodes, divides the threshold uniformly for easily implement and low costs. Based on the output distribution of the networks, the expressions of the optimal weight vector and the minimum mean square error are derived theoretically. For a sufficiently large size of networks, the Fisher information of the network output is also obtained. The results show that, as the network size increases, the minimum mean square error becomes smaller and smaller, and the noise benefit gradually disappears. However, the minimum mean square error at the optimal noise level approaches the bound denoted by the Fisher information. These theoretical and experimental results of multilevel networks are significant for adaptive signal estimation.