Traffic accident has become a significant health and development threat with rapid urbanizations. An accurate urban accident forecasting enables higher-quality police force pre-allocation and safe route planning for both traffic administrations and travelers, maximumly reducing injuries and damages. Off-the-shelf short-term accident forecasting methods, which focus on modeling static region-wise correlations with existing neural networks, mostly performed on hour levels and with single step. However, given the dynamic nature of road networks and expanding urban areas, it is challenging when the spatiotemporal granularity of forecasting improves as the rareness of accident records and complexity of long-term future dependencies. To address these challenges, we propose a unified framework RiskSeq, to foresee sparse urban accidents with finer granularities and multiple steps in spatiotemporal perspective. In particular, we design region-wise proximity measurements and temporal feature differential operations, and embed them into a novel Differential Time-varying Graph Convolution Network to dynamically capture traffic variations. Considering the hierarchical spatial dependencies and obvious context influences, a hierarchical sequence learning structure is devised by introducing contextual factors into a step-wise decoder. The multi-scale spatial risks are learned jointly to boost the risk predictions based on risk-gather and risk-assign networks. Extensive experiments demonstrate our RiskSeq can increase 5 to 15 percent performances on two datasets.

We present criteria on the existence of telescopers for trivariate rational functions in four mixed cases, in which discrete and continuous variables appear simultaneously. We reduce the existence problem in the trivariate case to the exactness testing problem, the separation problem and the existence problem in the bivariate case. The existence criteria help us to determine the termination of Zeilberger's algorithm for the input functions studied in this paper.