A study of monitor functions for two dimensional adaptive mesh generation

This is the published version, also available here: http://dx.doi.org/10.1137/S1064827597327656.In this paper we study the problem of two-dimensional adaptive mesh generation using a variational approach and, specifically, the effect that the monitor function has on the resulting mesh behavior. The basic theoretical tools employed are Green's function for elliptic problems and the eigendecomposition of symmetric positive definite matrices. Based upon this study, a general strategy is suggested for how to choose the monitor function, and numerical results are presented for illustrative purposes.The three-dimensional case is also briefly discussed. It is noted that the strategy used here can be applied to other elliptic mesh generation techniques as well

A Moving Mesh Method Based on the Geometric Conservation Law

This is the published version, also available here: http://dx.doi.org/10.1137/S1064827501384925.A new adaptive mesh movement strategy is presented, which, unlike many existing moving mesh methods, targets the mesh velocities rather than the mesh coordinates. The mesh velocities are determined in a least squares framework by using the geometric conservation law, specifying a form for the Jacobian determinant of the coordinate transformation defining the mesh, and employing a curl condition. By relating the Jacobian to a monitor function, one is able to directly control the mesh concentration. The geometric conservation law, an identity satisfied by any nonsingular coordinate transformation, is an important tool which has been used for many years in the engineering community to develop cell-volume-preserving finite-volume schemes. It is used here to transform the algebraic expression specifying the Jacobian into an equivalent differential relation which is the key formula for the new mesh movement strategy. It is shown that the resulting method bears a close relation with the Lagrangian method. Advantages of the new approach include the ease of controlling the cell volumes (and therefore mesh adaption) and a theoretical guarantee for existence and nonsingularity of the coordinate transformation. It is shown that the method may suffer from the mesh skewness, a consequence resulting from its close relation with the Lagrangian method. Numerical results are presented to demonstrate various features of the new method

Variational Mesh Adaptation Methods for Axisymmetrical Problems

This is the published version, also available here: http://dx.doi.org/10.1137/S0036142902401591.We study variational mesh adaptation for axially symmetric solutions to two-dimensional problems. The study is focused on the relationship between the mesh density distribution and the monitor function and is carried out for a traditional functional that includes several widely used variational methods as special cases and a recently proposed functional that allows for a weighting between mesh isotropy (or regularity) and global equidistribution of the monitor function. The main results are stated in Theorems \ref{thm4.1} and \ref{thm4.2}. For axially symmetric problems, it is natural to choose axially symmetric mesh adaptation. To this end, it is reasonable to use the monitor function in the form G = \lambda_1(r) {\mbox{\boldmath {e}}}_r {\mbox{\boldmath {e}}}_r^T + \lambda_2(r) {\mbox{\boldmath {e}}} _\theta {\mbox{\boldmath {e}}}_\theta^T , where {\mbox{\boldmath {e}}}_r and {\mbox{\boldmath {e}}}_\theta are the radial and angular unit vectors. It is shown that when higher mesh concentration at the origin is desired, a choice of $\lambda_1$ and $\lambda_2$ satisfying $\lambda_1(0) 0$ by choosing $\lambda_1$ and $\lambda_2$. In contrast, numerical results show that the new functional provides better control of the mesh concentration through the monitor function. Two-dimensional numerical results are presented to support the analysis

2nd Place Winning Solution for the CVPR2023 Visual Anomaly and Novelty Detection Challenge: Multimodal Prompting for Data-centric Anomaly Detection

This technical report introduces the winning solution of the team Segment Any Anomaly for the CVPR2023 Visual Anomaly and Novelty Detection (VAND) challenge. Going beyond uni-modal prompt, e.g., language prompt, we present a novel framework, i.e., Segment Any Anomaly + (SAA$+$), for zero-shot anomaly segmentation with multi-modal prompts for the regularization of cascaded modern foundation models. Inspired by the great zero-shot generalization ability of foundation models like Segment Anything, we first explore their assembly (SAA) to leverage diverse multi-modal prior knowledge for anomaly localization. Subsequently, we further introduce multimodal prompts (SAA$+$) derived from domain expert knowledge and target image context to enable the non-parameter adaptation of foundation models to anomaly segmentation. The proposed SAA$+$ model achieves state-of-the-art performance on several anomaly segmentation benchmarks, including VisA and MVTec-AD, in the zero-shot setting. We will release the code of our winning solution for the CVPR2023 VAN.Comment: The first two author contribute equally. CVPR workshop challenge report. arXiv admin note: substantial text overlap with arXiv:2305.1072

Cross-Architecture Knowledge Distillation

Transformer attracts much attention because of its ability to learn global relations and superior performance. In order to achieve higher performance, it is natural to distill complementary knowledge from Transformer to convolutional neural network (CNN). However, most existing knowledge distillation methods only consider homologous-architecture distillation, such as distilling knowledge from CNN to CNN. They may not be suitable when applying to cross-architecture scenarios, such as from Transformer to CNN. To deal with this problem, a novel cross-architecture knowledge distillation method is proposed. Specifically, instead of directly mimicking output/intermediate features of the teacher, a partially cross attention projector and a group-wise linear projector are introduced to align the student features with the teacher's in two projected feature spaces. And a multi-view robust training scheme is further presented to improve the robustness and stability of the framework. Extensive experiments show that the proposed method outperforms 14 state-of-the-arts on both small-scale and large-scale datasets

Two-dimensional grid optimization for sedimentation velocity analysis in the analytical ultracentrifuge

Accepted author manuscriptSedimentation velocity experiments performed in the analytical ultracentrifuge are modeled using finite-element solutions of the Lamm equation. During modeling, three fundamental parameters are optimized: the sedimentation coefficients, the diffusion coefficients, and the partial concentrations of all solutes present in a mixture. A general modeling approach consists of fitting the partial concentrations of solutes defined in a two-dimensional grid of sedimentation and diffusion coefficient combinations that cover the range of possible solutes for a given mixture. An increasing number of grid points increase the resolution of the model produced by the subsequent analysis, with denser grids giving rise to a very large system of equations. Here, we evaluate the efficiency and resolution of several regular grids and show that traditionally defined grids tend to provide inadequate coverage in one region of the grid, while at the same time being computationally wasteful in other sections of the grid. We describe a rapid and systematic approach for generating efficient two-dimensional analysis grids that balance optimal information content and model resolution for a given signal-to-noise ratio with improved calculation efficiency. These findings are general and apply to one- and two-dimensional grids, although they no longer represent regular grids. We provide a recipe for an improved grid-point spacing in both directions which eliminates unnecessary points, while at the same time providing a more uniform resolution that can be scaled based on the stochastic noise in the experimental data.Ye

Low-Protein Diet Supplemented with Keto Acids Is Associated with Suppression of Small-Solute Peritoneal Transport Rate in Peritoneal Dialysis Patients

Objective. We investigate whether low-protein diet would show benefits in suppressing peritoneal transport rate in peritoneal dialysis (PD) patients. Methods. This is a supplemented analysis of our previously published trial, which randomized 60 PD patients to receive low- (LP: dietary protein intake of 0.6–0.8 g/kg/d), keto-acid-supplemented low- (sLP: 0.6–0.8 g/kg/d with 0.12 g/kg/d of keto acids), or high- (HP: 1.0–1.2 g/kg/d) protein diet and lasted for one year. In this study, the variations of peritoneal transport rate were assessed. Results. While baseline D/Pcr (dialysate-to-plasma concentration ratio for creatinine at 4 hour) and D/D0glu (dialysate glucose at 4 hour to baseline dialysate glucose concentration ratio) were similar, D/Pcr in group sLP was lower, and D/D0glu was higher than those in the other two groups (P < 0.05) at 12th month. D/D0glu increased (P < 0.05), and D/Pcr tended to decrease, (P = 0.071) in group sLP. Conclusions. Low-protein diet with keto acids may benefit PD patients by maintaining peritoneum at a lower transport rate

Linking young men who have sex with men (YMSM) to STI physicians: a nationwide cross-sectional survey in China.

BACKGROUND: Many young men who have sex with men (YMSM) are reluctant to seek health services and trust local physicians. Online information seeking may encourage YMSM to identify and see trustworthy physicians, obtain sexual health services, and obtain testing for sexually transmitted infections (STIs). This study examined online STI information seeking behaviors among Chinese YMSM and its association with offline physician visits. METHODS: We conducted a nationwide online survey among YMSM through WeChat, the largest social media platform in China. We collected information on individual demographics, sexual behaviors, online STI information seeking, offline STI testing, and STI physician visits. We examined the most commonly used platforms (search engines, governmental websites, counseling websites, generic social media, gay mobile apps, and mobile medical apps) and their trustworthiness. We assessed interest and willingness to use an MSM-friendly physician finder function embedded within a gay mobile app. Logistic regression models were used to examine the correlation between online STI information searching and offline physician visits. RESULTS: A total of 503 men completed the survey. Most men (425/503, 84.5%) searched for STI information online. The most commonly used platform to obtain STI information were search engines (402/425, 94.5%), followed by gay mobile apps (201/425, 47.3%). Men reported high trustworthiness of information received from gay mobile apps. Men also reported high interest (465/503, 92.4%) and willingness (463/503, 92.0%) to use a MSM-friendly physician finder function within such apps. Both using general social media (aOR =1.14, 95%CI: 1.04-1.26) and mobile medical apps (aOR =1.16, 95%CI: 1.01-1.34) for online information seeking were associated with visiting a physician. CONCLUSION: Online STI information seeking is common and correlated with visiting a physician among YMSM. Cultivating partnerships with the emerging mobile medical apps may be useful for disseminating STI information and providing better physician services to YMSM

Laparoscopic Surgery Can Reduce Postoperative Edema Compared with Open Surgery

Aim. The study aimed to investigate the impact of laparoscopic surgery and open surgery on postoperative edema in Crohn’s disease. Methods. Patients who required enterectomy were divided into open group (Group O) and laparoscopic group (Group L). Edema was measured using bioelectrical impedance analysis preoperatively (PRE) and on postoperative day 3 (POD3) and postoperative day 5 (POD5). The postoperative edema was divided into slight edema and edema by an edema index, defined as the ratio of total extracellular water to total body water. Results. Patients who underwent laparoscopic surgery had better clinical outcomes and lower levels of inflammatory and stress markers. A total of 31 patients (26.05%) developed slight edema and 53 patients (44.54%) developed edema on POD3. More patients developed postoperative edema in Group O than in Group L on POD3 (p=0.006). The value of the edema index of Group O was higher than that of Group L on POD3 and POD5 (0.402±0.010 versus 0.397±0.008, p=0.001; 0.401±0.009 versus 0.395±0.007, p=0.039, resp.). Conclusions. Compared with open surgery, laparoscopic surgery can reduce postoperative edema, which may contribute to the better outcomes of laparoscopic surgery over open surgery