Shape registration has a wide range of applications in geometric modeling, medical imaging, and computer vision. This paper focuses on the registration of the genus-3 vestibular systems and studies the geometric differences between the normal and Adolescent Idiopathic Scoliosis (AIS) groups. The non-trivial topology of the VS poses great technical challenges to the geometric analysis. To tackle these challenges, we present an effective and practical solution to register the vestibular systems. We first extract six geodesic landmarks for the VS, which are stable, intrinsic, and insensitive to the VS’s resolution and tessellation. Moreover, they are highly consistent regardless of the AIS and normal groups. The detected geodesic landmarks partition the VS into three patches, a topological annulus and two topological disks. For each pair of patches of the AIS subject and the control, we compute a bijective map using the holomorphic 1-form and harmonic map techniques. With a carefully designed boundary condition, the three individual maps can be glued in a seamless manner so that the resulting registration is a homeomorphism with exact landmark matching. Our method is robust, automatic and efficient. It takes only a few seconds on a low-end PC, which significantly outperforms the non-rigid ICP algorithm. We conducted a student’s t-test on the test data. Computational results show that using the mean curvature measure E_H, our method can distinguish the AIS subjects and the normal subjects.

The quantitative adiabatic condition (QAC), or quantitative condition, is a convenient (a priori) tool for estimating the adiabaticity of quantum evolutions. However, the range of the applicability of QAC is not well understood. It has been shown that QAC can become insufficient for guaranteeing the validity of the adiabatic approximation, but under what conditions the QAC would become necessary has become controversial. Furthermore, it is believed that the inability for the QAC to reveal quantum adiabaticity is due to induced resonant transitions. However, it is not clear how to quantify these transitions in general. Here we present a progress to this problem by finding an exact relation that can reveal how transition amplitudes are related to QAC directly. As a posteriori condition for quantum adiabaticity, our result is universally applicable to any (nondegenerate) quantum system and gives a clear picture on how QAC could become insufficient or unnecessary for the adiabatic approximation, which is a problem that has gained considerable interest in the literature in recent years

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For cable bridges, the cable tension force plays a crucial role in their construction, assessment and long-term structural health monitoring. Cable tension forces vary in real time with the change of the moving vehicle loads and environmental effects, and this continual variation in tension force may cause fatigue damage of a cable. Traditional vibration-based cable tension force estimation methods can only obtain the time-averaged cable tension force and not the instantaneous force. This paper proposes a new approach to identify the time-varying cable tension forces of bridges based on an adaptive sparse time-frequency analysis method. This is a recently developed method to estimate the instantaneous frequency by looking for the sparsest time-frequency representation of the signal within the largest possible time-frequency dictionary (i.e. set of expansion functions). In the proposed approach, first, the time-varying modal frequencies are identified from acceleration measurements on the cable, then, the time-varying cable tension is obtained from the relation between this force and the identified frequencies. By considering the integer ratios of the different modal frequencies to the fundamental frequency of the cable, the proposed algorithm is further improved to increase its robustness to measurement noise. A cable experiment is implemented to illustrate the validity of the proposed method. For comparison, the Hilbert–Huang transform is also employed to identify the time-varying frequencies, which are then used to calculate the time-varying cable-tension force. The results show that the adaptive sparse time-frequency analysis method produces more accurate estimates of the time-varying cable tension forces than the Hilbert–Huang transform method.