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  1. Accurate traffic speed prediction is critical to many applications, from routing and urban planning to infrastructure management. With sufficient training data where all spatio-temporal patterns are well- represented, machine learning models such as Spatial-Temporal Graph Convolutional Networks (STGCN), can make reasonably accurate predictions. However, existing methods fail when the training data distribution (e.g., traffic patterns on regular days) is different from test distribution (e.g., traffic patterns on special days). We address this challenge by proposing a traffic-law-informed network called Reaction-Diffusion Graph Ordinary Differential Equation (RDGODE) network, which incorporates a physical model of traffic speed evolution based on a reliable and interpretable reaction- diffusion equation that allows the RDGODE to adapt to unseen traffic patterns. We show that with mismatched training data, RDGODE is more robust than the state-of-the-art machine learning methods in the following cases. (1) When the test dataset exhibits spatio-temporal patterns not represented in the training dataset, the performance of RDGODE is more consistent and reliable. (2) When the test dataset has missing data, RDGODE can maintain its accuracy by intrinsically imputing the missing values. 
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  2. We consider a game in which one player (the principal) seeks to incentivize another player (the agent) to exert effort that is costly to the agent. Any effort exerted leads to an outcome that is a stochastic function of the effort. The amount of effort exerted by the agent is private information for the agent and the principal observes only the outcome; thus, the agent can misreport his effort to gain higher payment. Further, the cost function of the agent is also unknown to the principal and the agent can also misreport a higher cost function to gain higher payment for the same effort. We pose the problem as one of contract design when both adverse selection and moral hazard are present. We show that if the principal and agent interact only finitely many times, it is always possible for the agent to lie due to the asymmetric information pattern and claim a higher payment than if he were unable to lie. However, if the principal and agent interact infinitely many times, then the principal can utilize the observed outcomes to update the contract in a manner that reveals the private cost function of the agent and hence leads to the agent not being able to derive any rent. The result can also be interpreted as saying that the agent is unable to keep his information private if he interacts with the principal sufficiently often. 
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