Abstract. There are two scalings for the convergence analysis of tau-leaping methods in the literature. This paper attempts to resolve this debate in the paper. We point out the shortcomings of both scalings. We systematically develop the weak Ito-Taylor expansion based on the infinitesimal generator of the chemical kinetic system and generalize the rooted tree theory for ODEs and SDEs driven by Brownian motion to rooted directed graph theory for the jump processes. We formulate the local truncation error analysis based on the large volume scaling. We find that even in this framework the midpoint tau-leaping does not improve the weak local order for the covariance compared with the explicit tau-leaping. We propose a procedure to explain the numerical order behavior by abandoning the dependence on the volume constant V from the leading error term. The numerical examples validate our arguments. We also give a general global weak convergence analysis for the explicit tau-leaping type methods in the large volume scaling.

The positioning error of ball screw feed systems is mainly caused by thermal elongation of the screw shaft in machine tools. In this article, an adaptive on-line compensation method of positioning error for the ball screw shaft is established. In order to explore the thermal–solid mechanism of ball screw feed drive systems, the experiments were carried out. An exponential fitting equation is presented to obtain the temperature relationship between the temperature sensitive point and its center of each heat source based on the finite element method of the feed drive system. Consequently, based on time and position exponential distribution functions, a variable separation model of heat transfer is established. Furthermore, based on the heat transfer model of multiple varying and moving heat sources, an adaptive on-line analytical compensation model of positioning error is presented. Finally, the effect of the adaptive on-line analytical compensation model of positioning error is verified through the experiments. And, this model has self-adaptive ability and robustness. Therefore, this adaptive on-line analytical compensation model based on the heat transfer theory can be applied in real-time compensation of positioning error.

Gesture is a natural form of human communication, and it is of great significance in human–computer interaction. In the dynamic gesture recognition method based on deep learning, the key is to obtain comprehensive gesture feature information. Aiming at the problem of inadequate extraction of spatiotemporal features or loss of feature information in current dynamic gesture recognition, a new gesture recognition architecture is proposed, which combines feature fusion network with variant convolutional long short‐term memory (ConvLSTM). The architecture extracts spatiotemporal feature information from local, global and deep aspects, and combines feature fusion to alleviate the loss of feature information. Firstly, local spatiotemporal feature information is extracted from video sequence by 3D residual network based on channel feature fusion. Then the authors use the variant ConvLSTM to learn the global spatiotemporal information of dynamic gesture, and introduce the attention mechanism to change the gate structure of ConvLSTM. Finally, a multi‐feature fusion depthwise separable network is used to learn higher‐level features including depth feature information. The proposed approach obtains very competitive performance on the Jester dataset with the classification accuracies of 95.59%, achieving state‐of‐the‐art performance with 99.65% accuracy on the SKIG (Sheffifield Kinect Gesture) dataset.

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