Nowadays, autonomous driving cars have become commercially available. However, the safety of a self-driving car is still a challenging problem that has not been well studied. Motion prediction is one of the core functions of an autonomous driving car. In this paper, we propose a novel scheme called GRIP which is designed to predict trajectories for traffic agents around an autonomous car efficiently. GRIP uses a graph to represent the interactions of close objects, applies several graph convolutional blocks to extract features, and subsequently uses an encoder-decoder long short-term memory (LSTM) model to make predictions. The experimental results on two wellknown public datasets show that our proposed model improves the prediction accuracy of the state-of-the-art solution by 30%. The prediction error of GRIP is one meter shorter than existing schemes. Such an improvement can help autonomous driving cars avoid many traffic accidents. In addition, the proposed GRIP runs 5x faster than the state-of-the-art schemes.

The reaction-diffusion Holling-Tanner predator-prey model with Neumann boundary condition is considered. We perform a detailed stability and Hopf bifurcation analysis and derive conditions for determining the direction of bifurcation and the stability of the bifurcating periodic solution. For partial differential equation (PDE), we consider the Turing instability of the equilibrium solutions and the bifurcating periodic solutions. Through both theoretical analysis and numerical simulations, we show the bistability of a stable equilibrium solution and a stable periodic solution for ordinary differential equation and the phenomenon that a periodic solution becomes Turing unstable for PDE.

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We collected data from Kailuan cohort study from 2006 to 2011 to examine whether short-term effects of ambient temperature on heart rate (HR) and blood pressure (BP) are non-linear or linear, and their potential modifying factors. The HR, BP and individual information, including basic characteristics, life style, socio-economic characteristics and other characteristics, were collected for each participant. Daily mean temperature and relative humidity were collected. A regression model was used to evaluate associations of temperature with HR and BP, with a non-linear function for temperature. We also stratified the analyses in different groups divided by individual characteristics. 47,591 residents were recruited. The relationships of temperature with HR and BP were “V” shaped with thresholds ranging from 22 °C to 28 °C. Both cold and hot effects were observed on HR and BP. The differences of effect estimates were observed among the strata of individual characteristics. The effect estimate of temperature was higher among older people. The cold effect estimate was higher among people with lower Body Mass Index. However, the differences of effect estimates among other groups were inconsistent. These findings suggest both cold and hot temperatures may have short-term impacts on HR and BP. The individual characteristics could modify these relationships.