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To analyze long-range temporal correlations in surface growth, we study numerically the (1 + 1)-dimensional Kardar-Parisi-Zhang (KPZ) equation driven by temporally correlated noise, and obtain the scaling exponents based on two dierent numerical methods. Our simulations show that the numerical results are in good agreement with the dynamic renormalization group (DRG) predictions, and are also consistent with the simulation results of the ballistic deposition (BD) model.

With the rapid development of mobile internet and online to offline marketing model, various spatial crowdsourcing platforms, such as Gigwalk and Gmission, are getting popular. Most existing studies assume that spatial crowdsourced tasks are simple and trivial. However, many real crowdsourced tasks are complex and need to be collaboratively finished by a team of crowd workers with different skills. Therefore, an important issue of spatial crowdsourcing platforms is to recommend some suitable teams of crowd workers to satisfy the requirements of skills in a task. In this paper, to address the issue, we first propose a more practical problem, called Top-k team recommendation in spatial crowdsourcing (TopkTR) problem. We prove that the TopkTR problem is NP-hard and designs a two-level-based framework, which includes an approximation algorithm with provable approximation ratio and an exact algorithm with pruning techniques to address it. In addition, we study a variant of the TopkTR problem, called TopkTRL, where a team leader is appointed among each recommended team of crowd workers in order to coordinate different crowd workers conveniently, and the aforementioned framework can be extended to address this variant. Finally, we verify the effectiveness and efficiency of the proposed methods through extensive experiments on real and synthetic datasets.

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