Existence theorems for a crystal surface model involving the p-Laplace operator

The manufacturing of crystal films lies at the heart of modern nanotechnology. How to accurately predict the motion of a crystal surface is of fundamental importance. Many continuum models have been developed for this purpose, including a number of PDE models, which are often obtained as the continuum limit of a family of kinetic Monte Carlo models of crystal surface relaxation that includes both the solid-on-solid and discrete Gaussian models. In this paper we offer an analytical perspective into some of these models. To be specific, we study the existence of a weak solution to the boundary value problem for the equation - \Delta e^{-\mbox{div}\left(|\nabla u|^{p-2}\nabla u\right)}+au=f, where $p>1, a>0$ are given numbers and $f$ is a given function. This problem is derived from a crystal surface model proposed by J.L.~Marzuola and J.~Weare (2013 Physical Review, E 88, 032403). The mathematical challenge is due to the fact that the principal term in our equation is an exponential function of a p-Laplacian. Existence of a suitably-defined weak solution is established under the assumptions that $p\in(1,2], \ N\leq 4$, and $f\in W^{1,p}$. Our investigations reveal that the key to our existence assertion is how to control the set where -\mbox{div}\left(|\nabla u|^{p-2}\nabla u\right) is $\pm\infty$

Vitamin D level regulates serum lipids discrepantly in adults with and without dyslipidemia

Vitamin D deficiency is associated with hyperlipidemia, but it r emains unclear whether vitamin D supplementation reduces serum lipid levels. The aims of this study were to investigate the associations between increased serum 25-hydroxyvitamin D (25(OH)D) concentrations and lipid levels and identify the characteristics of people with or without lipid reduction associated with increased 25(OH)D levels. The medical records of 118 individuals (53 men; mean age, 54.4 ± 10.6 years) whose serum 25(OH)D levels increased between 2 consecutive measurements were retrospectively reviewed. People with increased 25(OH)D levels (from 22.7 (17.6–29.2) to 32.1 (25.6–36.8) mg/dL; P < 0.01) had a significant reduction in serum levels of triglycerides (TG s) (from 111.0 (80–164) to 104.5 (73–142) mg/dL; P < 0.01) and total cholesterol (TC) (from 187.5 (155–213) to 181.0 (150–210) mg/dL; P < 0.05). The individuals who responded to vitamin D (≥10% reduction in TG or TC levels) exhibited significantly higher baseline TG a nd TC levels than those who did not. Only patients with hyperlipidemia (not those without hyperlipidemia) at baseline exhibited significantly reduced TG and TC levels at fol low-up. However, increasing serum 25(OH)D concentrations were significantly correlated with decreasing lipid levels in individuals with baseline 25(OH)D levels less than 30 ng/mL and in individuals aged 50–65 years (not in patients younger than 50 years or older than 65 years). In conclusion, increasing serum 25(OH)D concentrations may be potentially helpful for the treatment of hyperlipidemia in people with vitamin D deficiency

Learning Fine-Grained Visual Understanding for Video Question Answering via Decoupling Spatial-Temporal Modeling

While recent large-scale video-language pre-training made great progress in video question answering, the design of spatial modeling of video-language models is less fine-grained than that of image-language models; existing practices of temporal modeling also suffer from weak and noisy alignment between modalities. To learn fine-grained visual understanding, we decouple spatial-temporal modeling and propose a hybrid pipeline, Decoupled Spatial-Temporal Encoders, integrating an image- and a video-language encoder. The former encodes spatial semantics from larger but sparsely sampled frames independently of time, while the latter models temporal dynamics at lower spatial but higher temporal resolution. To help the video-language model learn temporal relations for video QA, we propose a novel pre-training objective, Temporal Referring Modeling, which requires the model to identify temporal positions of events in video sequences. Extensive experiments demonstrate that our model outperforms previous work pre-trained on orders of magnitude larger datasets.Comment: BMVC 2022. Code is available at https://github.com/shinying/des

Investigation of a Photoelectrochemical Passivated ZnO-Based Glucose Biosensor

A vapor cooling condensation system was used to deposit high quality intrinsic ZnO thin films and intrinsic ZnO nanorods as the sensing membrane of extended-gate field-effect-transistor (EGFET) glucose biosensors. The sensing sensitivity of the resulting glucose biosensors operated in the linear range was 13.4 μA mM−1 cm−2. To improve the sensing sensitivity of the ZnO-based glucose biosensors, the photoelectrochemical method was utilized to passivate the sidewall surfaces of the ZnO nanorods. The sensing sensitivity of the ZnO-based glucose biosensors with passivated ZnO nanorods was significantly improved to 20.33 μA mM−1 cm−2 under the same measurement conditions. The experimental results verified that the sensing sensitivity improvement was the result of the mitigation of the Fermi level pinning effect caused by the dangling bonds and the surface states induced on the sidewall surface of the ZnO nanorods