The social network is a main tunnel of rumor spreading. Previous studies concentrated on a static rumor spreading. The content of the rumor is invariable during the whole spreading process. Indeed, the rumor evolves constantly in its spreading process, which grows shorter, more concise, more easily grasped, and told. In an early psychological experiment, researchers found about $70\%$ of details in a rumor were lost in the first six mouth-to-mouth transmissions. Based on these observations, we investigate rumor spreading on social networks, where the content of the rumor is modified by the individuals with a certain probability. In the scenario, they have two choices, to forward or to modify. As a forwarder, an individual disseminates the rumor directly to their neighbors. As a modifier, conversely, an individual revises the rumor before spreading it out. When the rumor spreads on the social networks, for instance, scale-free networks and small-world networks, the majority of individuals actually are infected by the multirevised version of the rumor, if the modifiers dominate the networks. The individuals with more social connections have a higher probability to receive the original rumor. Our observation indicates that the original rumor may lose its influence in the spreading process. Similarly, a true information may turn out to be a rumor as well. Our result suggests the rumor evolution should not be a negligible question, which may provide a better understanding of the generation and destruction of a rumor. DOI: http://dx.doi.org/10.1103/PhysRevE.87.032133 ©2013 American Physical Society

Temporal causal discovery is a crucial task aimed at uncovering the causal relations within time series data. The latest temporal causal discovery methods usually train deep learning models on prediction tasks to uncover the causality between time series. They capture causal relations by analyzing the parameters of some components of the trained models, e.g., attention weights and convolution weights. However, this is an incomplete mapping process from the model parameters to the causality and fails to investigate the other components, e.g., fully connected layers and activation functions, that are also significant for causal discovery. To facilitate the utilization of the whole deep learning models in temporal causal discovery, we proposed an interpretable transformer-based causal discovery model termed CausalFormer, which consists of the causality-aware transformer and the decomposition-based causality detector. The causality-aware transformer learns the causal representation of time series data using a prediction task with the designed multi-kernel causal convolution which aggregates each input time series along the temporal dimension under the temporal priority constraint. Then, the decomposition-based causality detector interprets the global structure of the trained causality-aware transformer with the proposed regression relevance propagation to identify potential causal relations and finally construct the causal graph. Experiments on synthetic, simulated, and real datasets demonstrate the state-of-the-art performance of CausalFormer on discovering temporal causality.

Temporal networks are obtained from time-dependent interactions among individuals, whereas the interactions can be emails, phone calls, face-to-face meetings, or work collaboration. In this article, a temporal game framework is established, in which interactions among rational individuals are embedded into two-player games in a time-dependent manner. This allows studying the time-dependent complexity and variability of interactions, and the way they affect prosocial behaviors. Based on this simple mathematical model, it is found that the level of cooperation is promoted when the time of collaboration is equally limited for every individual. This observation is confirmed by a series of systematic human experiments on over 1,400 subjects, forming a foundation for comprehensively describing human temporal interactions in collaboration. The research results reveal an important incentive for human cooperation, leading to a better understanding of a fascinating aspect of human nature in society.

With the increasing traffic congestion problems in metropolises, traffic prediction plays an essential role in intelligent traffic systems. Notably, various deep learning models, especially graph neural networks (GNNs), achieve state-of-the-art performance in traffic prediction tasks but still lack interpretability. To interpret the critical information abstracted by traffic prediction models, we proposed a flexible framework termed Traffexplainer towards GNN-based interpretable traffic prediction. Traffexplainer is applicable to a wide range of GNNs without making any modifications to the original model structure. The framework consists of the GNN-based traffic prediction model and the perturbation-based hierarchical interpretation generator. Specifically, the hierarchical spatial mask and temporal mask are introduced to perturb the prediction model by modulating the values of input data. Then the prediction losses are backward propagated to the masks, which can identify the most critical features for traffic prediction, and further improve the prediction performance. We deploy the framework with five representative GNN-based traffic prediction models and analyse their prediction and interpretation performance on three real-world traffic flow datasets. The experiment results demonstrate that our framework can generate effective and faithful interpretations for GNN-based traffic prediction models, and also improve the prediction performance. The code will be publicly available at https://github.com/lingbai-kong/Traffexplainer .

The mining missing links and predicting upcoming links are two important topics in the link prediction. In the past decades, a variety of algorithms have been developed, the majority of which apply similarity measures to estimate the bonding probability between nodes. And for these algorithms, it is still difficult to achieve a satisfactory tradeoff among precision, computational complexity, robustness to network types, and scalability to network size. In this article, we propose a chaotic ant colony optimized (CACO) link prediction algorithm, which integrates the chaotic perturbation model and ant colony optimization. The extensive experiments on a wide variety of unweighted and weighted networks show that the proposed algorithm CACO achieves significantly higher prediction accuracy and robustness than most of the state-of-the-art algorithms. The results demonstrate that the chaotic ant colony effectively takes advantage of the fact that most real networks possess the transmission capacity and provides a new perspective for future link prediction research.