Discrete schemes for Gaussian curvature and their convergence

In this paper, several discrete schemes for Gaussian curvature are surveyed. The convergence property of a modified discrete scheme for the Gaussian curvature is considered. Furthermore, a new discrete scheme for Gaussian curvature is resented. We prove that the new scheme converges at the regular vertex with valence not less than 5. By constructing a counterexample, we also show that it is impossible for building a discrete scheme for Gaussian curvature which converges over the regular vertex with valence 4. Finally, asymptotic errors of several discrete scheme for Gaussian curvature are compared

Triangular surface mesh fairing via Gaussian curvature flow

AbstractSurface mesh fairing by the mean curvature flow and its various modifications have become a popular topic. However, very few researches have been attempted on using the Gaussian curvature flow in surface fairing. The aim of this paper is to investigate such a problem. We find that Gaussian curvature flow can only be used to smooth convex meshes. Hence, it cannot be used to smooth noisy surface meshes because a noisy surface mesh is not convex. To overcome this difficulty, we design a new diffusion equation whose evolution direction depends on the mean curvature normal and the magnitude is a properly defined function of the Gaussian curvature. Experimental results show that the designed fairing scheme can effectively remove the noise and simultaneously preserve the sharp features, such as corners and edges

MLP-AIR: An Efficient MLP-Based Method for Actor Interaction Relation Learning in Group Activity Recognition

The task of Group Activity Recognition (GAR) aims to predict the activity category of the group by learning the actor spatial-temporal interaction relation in the group. Therefore, an effective actor relation learning method is crucial for the GAR task. The previous works mainly learn the interaction relation by the well-designed GCNs or Transformers. For example, to infer the actor interaction relation, GCNs need a learnable adjacency, and Transformers need to calculate the self-attention. Although the above methods can model the interaction relation effectively, they also increase the complexity of the model (the number of parameters and computations). In this paper, we design a novel MLP-based method for Actor Interaction Relation learning (MLP-AIR) in GAR. Compared with GCNs and Transformers, our method has a competitive but conceptually and technically simple alternative, significantly reducing the complexity. Specifically, MLP-AIR includes three sub-modules: MLP-based Spatial relation modeling module (MLP-S), MLP-based Temporal relation modeling module (MLP-T), and MLP-based Relation refining module (MLP-R). MLP-S is used to model the spatial relation between different actors in each frame. MLP-T is used to model the temporal relation between different frames for each actor. MLP-R is used further to refine the relation between different dimensions of relation features to improve the feature's expression ability. To evaluate the MLP-AIR, we conduct extensive experiments on two widely used benchmarks, including the Volleyball and Collective Activity datasets. Experimental results demonstrate that MLP-AIR can get competitive results but with low complexity.Comment: Submit to Neurocomputin

Estimate haplotype frequencies in pedigrees

BACKGROUND: Haplotype analysis has gained increasing attention in the context of association studies of disease genes and drug responsivities over the last years. The potential use of haplotypes has led to the initiation of the HapMap project which is to investigate haplotype patterns in the human genome in different populations. Haplotype inference and frequency estimation are essential components of this endeavour. RESULTS: We present a two-stage method to estimate haplotype frequencies in pedigrees, which includes haplotyping stage and estimation stage. In the haplotyping stage, we propose a linear time algorithm to determine all zero-recombinant haplotype configurations for each pedigree. In the estimation stage, we use the expectation-maximization (EM) algorithm to estimate haplotype frequencies based on these haplotype configurations. The experiments demonstrate that our method runs much faster and gives more credible estimates than other popular haplotype analysis software that discards the pedigree information. CONCLUSION: Our method suggests that pedigree information is of great importance in haplotype analysis. It can be used to speedup estimation process, and to improve estimation accuracy as well. The result also demonstrates that the whole haplotype configuration space can be substituted by the space of zero-recombinant haplotype configurations in haplotype frequency estimation, especially when the considered haplotype block is relatively short

Eupatilin attenuates diabetic nephropathy by upregulating matrix metalloproteinase-9 expression in diabetic rat kidney

Purpose: To evaluate the nephro-protective effect of eupatilin in diabetic nephropathic (DN) rats.Method: Diabetes was induced by intraperitoneal administration of streptozotocin (STZ, 55 mg/kg) and confirmed by fasting blood glucose results, while DN was determined by measuring serum urea and creatinine levels on day 40 after STZ administration. The eupatilin-treated group received eupatilin at 50 and 100 mg/kg, p.o. for 20 days, after which blood levels of some biochemical parameters, glomerulosclerosis index, eosinophilic cast index, and expression of MMP-9 were determined using standard procedures.Results: Treatment with eupatilin significantly decreased serum levels of glucose, creatinine and urea, and increased creatinine clearance, compared to the negative control group. Moreover, eupatilin attenuated changes in kidney histopathology, and significantly enhanced the expression of MMP-9 in the kidney tissues of the DN rats, relative to negative control group.Conclusion: These results indicate that eupatilin attenuates renal failure in STZ-induced DN rats by upregulating the expression of MMP-9.Keywords: Eupatilin, Streptozotocin, Diabetic nephropathy, MMP-