Translating Solutions of a Generalized Mean Curvature Flow in a Cylinder: I. Constant Boundary Angles

We study a generalized mean curvature flow involving a positive power of the mean curvature and a driving force. In this paper, we first construct all kinds of radially symmetric translating solutions, and then select one of them to satisfy a prescribed boundary angle in a cylinder. We then consider the flow starting at an initial hypersurface: showing the a priori estimates (especially the uniform-in-time bounds for the mean curvature which guarantee the uniform parabolicity of the corresponding fully nonlinear equation), giving the global existence for the solution of the initial boundary value problem, and proving its convergence to the corresponding translating solution. Our study provides a complete exposition on the influence of the dimension, the power of the mean curvature, the driving force and the boundary angles on the existence and stability of radially symmetric translating solutions.Comment: 29 page

A Mean Curvature Flow Propagating in a Cylinder at Exponential Speed

In this paper, we study the long time behaviour of mean curvature flow in a cylinder with Robin boundary conditions. Such a boundary condition can force the solution to have a singular behaviour at the boundary when $t\to \infty$. The planar version of this problem has been investigated in an existing literature, where the curve shortening flow in $2$-dimensional band with Robin boundary conditions is shown to converge to a translating Grim Reaper with finite speed and fixed profile. By considering a radially symmetric mean curvature flow, denoted by $u(|x|,t)$, in $(N+1)$-dimensional cylinder ($N\geq 2$), we find in the present paper a new feature of the flow: both the interior gradients and the propagating speed of the flow increase to infinity exponentially, $Du/u\sim x$ and $u\sim C_0 e^{(N-1)t}e^{\frac{|x|^2}{2}}$ as $t\to \infty$ for some $C_0>0$, which is completely different from the 2-dimensional case

Convergence to the Grim Reaper for a Curvature Flow with Unbounded Boundary Slopes

We consider a curvature flow $V=H$ in the band domain $\Omega :=[-1,1]\times \R$, where, for a graphic curve $\Gamma_t$, $V$ denotes its normal velocity and $H$ denotes its curvature. If $\Gamma_t$ contacts the two boundaries $\partial_\pm \Omega$ of $\Omega$ with constant slopes, in 1993, Altschular and Wu \cite{AW1} proved that $\Gamma_t$ converges to a {\it grim reaper} contacting $\partial_\pm \Omega$ with the same prescribed slopes. In this paper we consider the case where $\Gamma_t$ contacts $\partial_\pm \Omega$ with slopes equaling to $\pm 1$ times of its height. When the curve moves to infinity, the global gradient estimate is impossible due to the unbounded boundary slopes. We first consider a special symmetric curve and derive its uniform interior gradient estimates by using the zero number argument, and then use these estimates to present uniform interior gradient estimates for general non-symmetric curves, which lead to the convergence of the curve in $C^{2,1}_{loc} ((-1,1)\times \R)$ topology to the {\it grim reaper} with span $(-1,1)$

G2PTL: A Pre-trained Model for Delivery Address and its Applications in Logistics System

Text-based delivery addresses, as the data foundation for logistics systems, contain abundant and crucial location information. How to effectively encode the delivery address is a core task to boost the performance of downstream tasks in the logistics system. Pre-trained Models (PTMs) designed for Natural Language Process (NLP) have emerged as the dominant tools for encoding semantic information in text. Though promising, those NLP-based PTMs fall short of encoding geographic knowledge in the delivery address, which considerably trims down the performance of delivery-related tasks in logistic systems such as Cainiao. To tackle the above problem, we propose a domain-specific pre-trained model, named G2PTL, a Geography-Graph Pre-trained model for delivery address in Logistics field. G2PTL combines the semantic learning capabilities of text pre-training with the geographical-relationship encoding abilities of graph modeling. Specifically, we first utilize real-world logistics delivery data to construct a large-scale heterogeneous graph of delivery addresses, which contains abundant geographic knowledge and delivery information. Then, G2PTL is pre-trained with subgraphs sampled from the heterogeneous graph. Comprehensive experiments are conducted to demonstrate the effectiveness of G2PTL through four downstream tasks in logistics systems on real-world datasets. G2PTL has been deployed in production in Cainiao's logistics system, which significantly improves the performance of delivery-related tasks

Global research of artificial intelligence in strabismus: a bibliometric analysis

PurposeTo analyze the global publications on artificial intelligence (AI) in strabismus using a bibliometric approach.MethodsThe Web of Science Core Collection (WoSCC) database was used to retrieve all of the publications on AI in strabismus from 2002 to 2023. We analyzed the publication and citation trend and identified highly-cited articles, prolific countries, institutions, authors and journals, relevant research domains and keywords. VOSviewer (software) and Bibliometrix (package) were used for data analysis and visualization.ResultsBy analyzing a total of 146 relevant publications, this study found an overall increasing trend in the number of annual publications and citations in the last decade. USA was the most productive country with the closest international cooperation. The top 3 research domains were Ophthalmology, Engineering Biomedical and Optics. Journal of AAPOS was the most productive journal in this field. The keywords analysis showed that “deep learning” and “machine learning” may be the hotspots in the future.ConclusionIn recent years, research on the application of AI in strabismus has made remarkable progress. The future trends will be toward optimized technology and algorithms. Our findings help researchers better understand the development of this field and provide valuable clues for future research directions

The Correlation between High-Sensitivity C-Reactive Protein, Matrix Metallopeptidase 9, and Traditional Chinese Medicine Syndrome in Patients with Hypertension

Hypertension is a common disease affecting millions of people throughout the world. Currently, there is a growing interest in the traditional Chinese medicine (TCM) for patients with hypertension mainly due to the personalized therapy of TCM in many countries. Clinical treatment of patients relies on the successful differentiation of a specific TCM syndrome for hypertension. However, it is difficult to understand that TCM syndrome classifications depend on the clinical experience of a TCM practitioner. Therefore, discovering an objective biomarker associated with TCM syndrome may be beneficial for TCM syndrome classifications. This paper focused on high sensitivity C-reactive protein (HCRP), matrix metallopeptidase 9 (MMP9), and TCM syndrome, and aimed to investigate the relationships between TCM syndrome and the two inflammatory biomarkers in patients with essential hypertension. The result showed that both HCRP and MMP9 are positively correlated with syndrome of wind and phlegm turbidity. Detection of the serum levels of HCRP and MMP9 is beneficial for TCM syndrome classification and prediction of cardiovascular and cerebrovascular risk events in hypertensive patients

Effects of Wenxin Keli on the Action Potential and L-Type Calcium Current in Rats with Transverse Aortic Constriction-Induced Heart Failure

Objective. We investigated the effects of WXKL on the action potential (AP) and the L-type calcium current (ICa-L) in normal and hypertrophied myocytes. Methods. Forty male rats were randomly divided into two groups: the control group and the transverse aortic constriction- (TAC-) induced heart failure group. Cardiac hypertrophy was induced by TAC surgery, whereas the control group underwent a sham operation. Eight weeks after surgery, single cardiac ventricular myocytes were isolated from the hearts of the rats. The APs and ICa-L were recorded using the whole-cell patch clamp technique. Results. The action potential duration (APD) of the TAC group was prolonged compared with the control group and was markedly shortened by WXKL treatment in a dose-dependent manner. The current densities of the ICa-L in the TAC group treated with 5 g/L WXKL were significantly decreased compared with the TAC group. We also determined the effect of WXKL on the gating mechanism of the ICa-L in the TAC group. We found that WXKL decreased the ICa-L by accelerating the inactivation of the channels and delaying the recovery time from inactivation. Conclusions. The results suggest that WXKL affects the AP and blocked the ICa-L, which ultimately resulted in the treatment of arrhythmias

Qingkailing Suppresses the Activation of BV2 Microglial Cells by Inhibiting Hypoxia/Reoxygenation-Induced Inflammatory Responses

Qingkailing (QKL) is a well-known composite extract used in traditional Chinese medicine. This extract has been extensively administered to treat the acute phase of cerebrovascular disease. Our previous experiments confirmed that QKL exerts an inhibitory effect on cerebral ischemia-induced inflammatory responses. However, whether QKL suppresses the activation of microglia, the primary resident immune cells in the brain, has yet to be determined. In this study, BV2 microglial cells were used to validate the protective effects of QKL treatment following ischemia-reperfusion injury simulated via hypoxia/reoxygenation in vitro. Under these conditions, high expression levels of ROS, COX-2, iNOS, and p-p38 protein were detected. Following ischemia/reperfusion injury, QKL significantly increased the activity of BV2 cells to approximately the basal level by modulating microglial activation via inhibition of inflammatory factors, including TNF-, COX-2, iNOS, and p-p38. However, QKL treatment also displayed dosedependent differences in its inhibitory effects on p38 phosphorylation and inflammatory factor expression

Qingkailing Suppresses the Activation of BV2 Microglial Cells by Inhibiting Hypoxia/Reoxygenation-Induced Inflammatory Responses

Qingkailing (QKL) is a well-known composite extract used in traditional Chinese medicine. This extract has been extensively administered to treat the acute phase of cerebrovascular disease. Our previous experiments confirmed that QKL exerts an inhibitory effect on cerebral ischemia-induced inflammatory responses. However, whether QKL suppresses the activation of microglia, the primary resident immune cells in the brain, has yet to be determined. In this study, BV2 microglial cells were used to validate the protective effects of QKL treatment following ischemia-reperfusion injury simulated via hypoxia/reoxygenation in vitro. Under these conditions, high expression levels of ROS, COX-2, iNOS, and p-p38 protein were detected. Following ischemia/reperfusion injury, QKL significantly increased the activity of BV2 cells to approximately the basal level by modulating microglial activation via inhibition of inflammatory factors, including TNF-α, COX-2, iNOS, and p-p38. However, QKL treatment also displayed dose-dependent differences in its inhibitory effects on p38 phosphorylation and inflammatory factor expression

Facile Fabrication of Ultrafine Hollow Silica and Magnetic Hollow Silica Nanoparticles by a Dual-Templating Approach

The development of synthetic process for hollow silica materials is an issue of considerable topical interest. While a number of chemical routes are available and are extensively used, the diameter of hollow silica often large than 50 nm. Here, we report on a facial route to synthesis ultrafine hollow silica nanoparticles (the diameter of ca. 24 nm) with high surface area by using cetyltrimethylammmonium bromide (CTAB) and sodium bis(2-ethylhexyl) sulfosuccinate (AOT) as co-templates and subsequent annealing treatment. When the hollow magnetite nanoparticles were introduced into the reaction, the ultrafine magnetic hollow silica nanoparticles with the diameter of ca. 32 nm were obtained correspondingly. Transmission electron microscopy studies confirm that the nanoparticles are composed of amorphous silica and that the majority of them are hollow