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Heat conduction analogous process has ever been introduced into information filtering named standard heat conduction (SHC) method, resulting in a highly personalized but less accurate recommendation. In order to improve the recommendation accuracy, different algorithms have been proposed, with typical examples to be the highly accurate mass diffusion (MD) method, and a both highly accurate and highly diverse biased heat-conduction method (BHC). These previous algorithms have not considered the rating effect, where ratings essentially depict how users like objects. In this article, we propose a heterogeneous heat conduction method (HHC), by taking the ratings as the weight of heat conduction, which thus generates a heterogeneous heat diffusion pattern. Experimental results obtained from the Movie Lens dataset show that, the HHC greatly enhances the recommendation accuracy against the SHC, with the improvement percentage to be 46.32%, and also elevates the recommendation accuracy against the MD as well as the BHC. Moreover, the HHC simultaneously outperforms the MD, and even the BHC in recommendation diversity.

Initial configuration effect is investigated for a both highly accurate and highly diverse biased heat conduction method. According to the individual object degree, we assign a heterogeneous initial resource for each object. Experimental results obtained from the MovieLens dataset show that, the proposed method outperforms the standard heat conduction method by 47.33%, and also outperforms an accurate mass diffusion method by 24.04% in recommendation accuracy. Especially, even compared with an excellent hybrid method of heat conduction and mass diffusion, and the original biased heat conduction method, the manifested method further enhances both the recommendation accuracy and the diversity.

In a competitive environment, the formation of network structures is not only related to the preferential linking but also the multiple state of interacting agents. With an adjustable parameter controlling the growth of networks, we study the correlations between the commonly observed topological properties of networks and the configuration of individual states. Numerical simulations show that a cooperative environment promotes the formation of scalefree networks. In an uncooperative environment, a large number of benefit-pursuing agents make equally distributed connections and the topological property of the network exhibits exponential node degree sequences. The mean field theory is applied to predict the growth of networks and analytical calculations are in accordance with simulation results.

Incorporating unequal allocation into the original public goods game, we study the effects of spatial structures on the extent of the emergence of cooperation. By playing the game on random regular networks with a fixed degree 2 K, we find that the cooperator frequencies are not only related to the average degree of the network but also the rewiring process. Randomizing a regular network will lead to the decrease of the average path length and the clustering coefficient of the network, which furtherly shortens the relaxation time for the system to reach the final steady state and suppresses the frequencies of cooperation. A linear relationship between the cooperator frequencies and the clustering coefficient is found.