Narrow Results

About 45000 years ago, symbolic and technological complexity of human artefacts increased drastically. Computer simulations of Powell, Shennan and Thomas (2009) explained it through an increase of the population density, facilitating the spread of information about useful innovations. We simplify this demographic model and make it more similar to standard physics models. For this purpose, we assume that bands (extended families) of stone-age humans were distributed randomly on a square lattice such that each lattice site is randomly occupied with probability p and empty with probability 1 - p. Information spreads randomly from an occupied site to one of its occupied neighbors. If we wait long enough, information spreads from one side of the lattice to the opposite site if and only if p is larger than the percolation threshold; this process was called "ant in the labyrinth" by de Gennes 1976. We modify it by giving the diffusing information a finite lifetime, which shifts the threshold upwards.

In the Name-Your-Own-Price (NYOP) auction, the spread of bidding information among buyers is incredibly important for both buyers and sellers. However, the impact of hub nodes on the spread of bidding information is less investigated. In this research, we proposed a directed distance index, and used it to explore the roles of hub nodes during an NYOP auction. The results showed significant impacts of hub nodes on buyers’ behaviors and seller profits, but the impacts highly depend on the fading speed of information. When information fades fast, the hub nodes should be more valued to increase buyers’ bidding intention and make them bid more wisely. Seller’s profits will also be increased. While information fades slow, the hub nodes and the regular nodes should be approximately valued. Moreover, we explored the case of sharing failed bids, and found that the roles of hub nodes become more salient when buyers are more willing to share the failed bids.

In this paper, a two-layer network on various immunization strategies in the post-epidemic era is constructed and an improved symbiotic evolutionary model of COVID-19 and information collaboration is proposed. The dynamic transformation probability is introduced to influence the virus information transmission coevolutionary process. The dynamic transformation probability is influenced by the immunization strategies and vertex characteristics. We quantify the effects of immunization strategy, node properties, global temperature, and collaborative information dissemination on new crown outbreaks. We simulated our model in a scale-free network to analyze the propagation. The evolutionary phenomenon of the network during propagation was investigated. We simulated the proven epidemic information coevolutionary model in a two-layer network, validated it with real data comparisons by proving that our proposed model fits the real situation.

In this paper, we construct and analyze a mathematically reasonable and simplest population dynamics model based on Mark Granovetter’s idea for the spread of a matter (rumor, innovation, psychological state, etc.) in a population. The model is described by a one-dimensional difference equation. Individual threshold values with respect to the decision-making on the acceptance of a spreading matter are distributed throughout the population ranging from low (easily accepts it) to high (hardly accepts). Mathematical analysis on our model with some general threshold distributions (uniform; monotonically decreasing/increasing; unimodal) shows that a critical value necessarily exists for the initial frequency of acceptors. Only when the initial frequency of acceptors is beyond the critical, the matter eventually spreads over the population. Further, we give the mathematical results on how the equilibrium acceptor frequency depends on the nature of threshold distribution.