Ear decomposition of 3-regular polyhedral links with applications.

In this paper, we introduce a notion of ear decomposition of 3-regular polyhedral links based on the ear decomposition of the 3-regular polyhedral graphs. As a result, we obtain an upper bound for the braid index of 3-regular polyhedral links. Our results may be used to characterize and analyze the structure and complexity of protein polyhedra and entanglement in biopolymers.

Three-dimensional mandibular motion trajectory-tracking system based on BP neural network.

The aim of this study was to develop a prototype three-dimensional optical motion capture system based on binocular stereo vision, Back-propagation (BP) Neural Network and 3D compen-sation method for accurate and real-time recording of mandibular movement. A specialized 3D method of compensation to eliminate the involuntary vibration motions by human heart beating and respiration. A kind of binocular visual 3D measurement method based on projection line and a calibration method based on BP neural network is proposed to solve the problem of the high complexity of camera calibration process and the low accuracy of 3D measurement. The accuracy of the proposed system is systematically evaluated by means of electric platform and clinical trials, and the root-mean-square is 0.0773 mm. Finally, comparisons with state-of-the-art methods demonstrate that our system has higher reliability and accuracy. Meanwhile, the motion trajectory-tracking system is expected to be used in the diagnosis of clinical oral diseases and digital design of restoration.