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Place-based short-term crime prediction models leverage the spatio-temporal patterns of historical crimes to predict aggregate volumes of crime incidents at specific locations over time. Under the umbrella of thecrime opportunity theory, that suggests that human mobility can play a role in crime generation, increasing attention has been paid to the predictive power of human mobility in place-based short-term crime models. Researchers have used call detail records (CDR), data from location-based services such as Foursquare or from social media to characterize human mobility; and have shown that mobility metrics, together with historical crime data, can improve short-term crime prediction accuracy. In this paper, we propose to use a publicly available fine-grained human mobility dataset from a location intelligence company to explore the effects of human mobility features on short-term crime prediction. For that purpose, we conduct a comprehensive evaluation across multiple cities with diverse demographic characteristics, different types of crimes and various deep learning models; and we show that adding human mobility flow features to historical crimes can improve the F1 scores for a variety of neural crime prediction models across cities and types of crimes, with improvements ranging from 2% to 7%. Our analysis also shows that some neural architectures can slightly improve the crime prediction performance when compared to non-neural regression models by at most 2%.