On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data

In this paper, we analyze the uniqueness of the sparse time frequency decomposition and investigate the efficiency of the nonlinear matching pursuit method. Under the assumption of scale separation, we show that the sparse time frequency decomposition is unique up to an error that is determined by the scale separation property of the signal. We further show that the unique decomposition can be obtained approximately by the sparse time frequency decomposition using nonlinear matching pursuit

Low-Multi-Rank High-Order Bayesian Robust Tensor Factorization

The recently proposed tensor robust principal component analysis (TRPCA) methods based on tensor singular value decomposition (t-SVD) have achieved numerous successes in many fields. However, most of these methods are only applicable to third-order tensors, whereas the data obtained in practice are often of higher order, such as fourth-order color videos, fourth-order hyperspectral videos, and fifth-order light-field images. Additionally, in the t-SVD framework, the multi-rank of a tensor can describe more fine-grained low-rank structure in the tensor compared with the tubal rank. However, determining the multi-rank of a tensor is a much more difficult problem than determining the tubal rank. Moreover, most of the existing TRPCA methods do not explicitly model the noises except the sparse noise, which may compromise the accuracy of estimating the low-rank tensor. In this work, we propose a novel high-order TRPCA method, named as Low-Multi-rank High-order Bayesian Robust Tensor Factorization (LMH-BRTF), within the Bayesian framework. Specifically, we decompose the observed corrupted tensor into three parts, i.e., the low-rank component, the sparse component, and the noise component. By constructing a low-rank model for the low-rank component based on the order-$d$ t-SVD and introducing a proper prior for the model, LMH-BRTF can automatically determine the tensor multi-rank. Meanwhile, benefiting from the explicit modeling of both the sparse and noise components, the proposed method can leverage information from the noises more effectivly, leading to an improved performance of TRPCA. Then, an efficient variational inference algorithm is established for parameters estimation. Empirical studies on synthetic and real-world datasets demonstrate the effectiveness of the proposed method in terms of both qualitative and quantitative results

Constructivist learning method of ordinary differential equations in college mathematics teaching

The article uses ordinary differential to solve inhomogeneous equations by the constructivist learning concept. We use the equivalent equations to study the n-Th order non-homogeneous linear ordinary differential equations with constant coefficients and get the method of solving this equation. Then we use the Filippov transformation and comparison theorem to prove the boundedness of all system trajectories. Numerical results show that the calculation formula is effective for solving stiff ordinary differential equations

Is hydrogen diffusion in amorphous metals non-Arrhenian?

Hydrogen diffusion is critical to the performance of metals for hydrogen storage as well as other important applications. As compared to its crystalline counterpart which follows the Arrhenius relation, hydrogen diffusion in amorphous metals sometimes are experimentally found to be non-Arrhenian. In this work we studied the diffusion of hydrogen in amorphous Pd-H and Zr-Cu-H alloys based on molecular dynamics simulations. Our simulations confirm Arrhenian diffusion behaviour for hydrogen in amorphous alloys, in contrast to previous theoretical studies which predict non-Arrhenian behaviour. We show that the simulated non-Arrhenian diffusion based on molecular dynamics could result from a systematic error related to too short simulation time. We also discussed the experimental non-Arrhenian behaviour of hydrogen diffusion within the framework of quantum tunneling and amorphous-amorphous phase transformations

Ultrasonic Tomography of Immersion Circular Array by Hyperbola Algorithm

This paper presents a development and research of a non-invasive ultrasonic tomography for imaging gas/liquid two-phase flow. Ultrasonic transmitting and receiving are implemented using a circular array model that consists of 36 transducers. COMSOL Multiphysics® software is adopted for the simulation of the ultrasonic propagation in the detecting zone. Various two-phase flows with different gas distributions are radiated by ultrasonic waves and the reflection mode approach is utilized for detecting the scattering waves after the generation of fan-shaped beam. Ultrasonic attenuation and sound speed are both taken into consideration while reconstructing the two-phase flow images under the inhomogeneous medium conditions. The inversion procedure of the image reconstruction is realized using the hyperbola algorithm, which in return demonstrates the feasibility and validity of the proposed circular array model

Natural liquid organic hydrogen carrier with low dehydrogenation energy: A first principles study

Liquid organic hydrogen carriers (LOHCs) represent a promising approach for hydrogen storage due to their favorable properties including stability and compatibility with the existing infrastructure. However, fossil-based LOHC molecules are not green or sustainable. Here we examined the possibility of using norbelladine and trisphaeridine, two typical structures of Amaryllidaceae alkaloids, as the LOHCs from the sustainable and renewable sources of natural products. Our first principles thermodynamics calculations reveal low reversibility for the reaction of norbelladine to/from perhydro-norbelladine because of the existence of stabler isomers of perhydro-norbelladine. On the other hand, trisphaeridine is found promising due to its high hydrogen storage capacity ($\sim$5.9 wt\%) and favorable energetics. Dehydrogenation of perhydro-trisphaeridine has an average standard enthalpy change of $\sim$54 KJ/mol-H$_2$, similar to that of perhydro-\textit{N}-ethylcarbazole, a typical LOHC known for its low dehydrogenation enthalpy. This work is a first exploration of Amaryllidaceae alkaloids for hydrogen storage and the results demonstrate, more generally, the potential of bio-based molecules as a new sustainable resource for future large-scale hydrogen storage

Coexistence and different determinants of posttraumatic stress disorder and posttraumatic growth among Chinese survivors after earthquake: role of resilience and rumination

Posttraumatic stress disorder (PTSD) and posttraumatic growth (PIG) are two different outcomes that may occur after experiencing traumatic events. Resilience and rumination are two important factors that determine the development of these outcomes after trauma. We investigated the association between these two factors, PTSD and PIG, among Chinese survivors in an earthquake. With a convenience sample of 318 survivors from earthquake, we measured trauma exposure, PTSD, PIG, resilience, and rumination (Impact of Event Scale-Revised, Posttraumatic Growth Inventory, 10 item Connor-Davidson Resilience Scale, Ruminative Response Scale). Then we used bivariate correlation and structural equation modeling to examine the structure of relations among these factors. Results showed that resilience and reflective rumination have a positive effect on PIG (beta = 0.32, p &lt; 0.001; = 0.17, p = 0.049). Earthquake exposure, brooding rumination and depressed-related rumination are related with higher level of PTSD = 0.10, p = 0.021; = 0.33, p &lt; 0.001; beta = 0.36, p &lt; 0.001). The findings suggest distinct determinants of the negative and positive outcomes, and this may provide better understanding about the risk and protective factors for traumatic reactions.</p