Local well-posedness for incompressible neo-Hookean Elastic equations in almost critical Sobolev spaces

Inspired by a pineeor work of Andersson-Kapitanski \cite{AK}, we prove the local well-posedness of Cauchy problem of incompressible neo-Hookean equations if the initial deformation and velocity belong to $H^{\frac{n+2}{2}+}(\mathbb{R}^n) \times H^{\frac{n}{2}+}(\mathbb{R}^n)$ ($n=2,3$), where $\frac{n+2}{2}$ and $\frac{n}{2}$ is respectively a scaling-invariant exponent for deformation and velocity in Sobolev spaces. Our new observation relies on two folds: a reduction to a second-order wave-elliptic system of deformation and velocity; a "wave-map type" null form intrinsic in this coupled system. In particular the wave nature with "wave-map type" null form allows us to prove a bilinear estimate of Klainerman-Machedon type for nonlinear terms. So we can lower $\frac12$-order regularity in 3D and $\frac34$-order regularity in 2D for well-posedness compared with \cite{AK}. Moreover, as an application, we also prove a new local well-posedness result for the ideal incompressible magnetohydrodynamic (MHD) system in the presence of a strong magnetic field.Comment: 21pages.Welcome all comment

SNR-Based Teachers-Student Technique for Speech Enhancement

It is very challenging for speech enhancement methods to achieves robust performance under both high signal-to-noise ratio (SNR) and low SNR simultaneously. In this paper, we propose a method that integrates an SNR-based teachers-student technique and time-domain U-Net to deal with this problem. Specifically, this method consists of multiple teacher models and a student model. We first train the teacher models under multiple small-range SNRs that do not coincide with each other so that they can perform speech enhancement well within the specific SNR range. Then, we choose different teacher models to supervise the training of the student model according to the SNR of the training data. Eventually, the student model can perform speech enhancement under both high SNR and low SNR. To evaluate the proposed method, we constructed a dataset with an SNR ranging from -20dB to 20dB based on the public dataset. We experimentally analyzed the effectiveness of the SNR-based teachers-student technique and compared the proposed method with several state-of-the-art methods.Comment: Published in 2020 IEEE International Conference on Multimedia and Expo (ICME 2020

Prevalence of Neuropsychiatric Symptoms across the Declining Memory Continuum: An Observational Study in a Memory Clinic Setting

Aims: The study aimed to compare the frequency of neuropsychiatric symptoms (NPS) across the declining memory continuum, from normal aging, subjective cognitive impairment (SCI), and mild cognitive impairment (MCI) to Alzheimer’s disease (AD), and to explore the clinical correlates of NPS. Method: In a memory clinic, 157 subjects (46 mild AD patients, 38 MCI individuals, 24 SCI subjects, and 49 normal controls) completed the neurobehavioral assessments with the Neuropsychiatric Inventory (NPI). The clinical significance of each NPI domain was defined as an item score ≥4. Result: Clinically significant depression was more common in the SCI than in the normal control group (p Conclusion: Across the declining memory continuum, the frequency of NPS was highest among mild AD patients. Depression, apathy, and aberrant motor behavior deserve more attention. Presence of apathy might be an independent determinant for mild AD