Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correcte

Convex domains of Finsler and Riemannian manifolds

A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the Riemannian case. Ours not only can be extended to the Finsler setting but it also reduces the typical requirements of differentiability for the metric and it yields consequences on the multiplicity of connecting geodesics in the convex domain defined by the hypersurface.Comment: 22 pages, AMSLaTex. Typos corrected, references update

SA‐BiSeNet: Swap attention bilateral segmentation network for real‐time inland waterways segmentation

Abstract The technology for autonomous navigation on inland waterways is worth investigating, and navigable water surface segmentation is a key part of this technology. Semantic segmentation methods based on deep learning are able to distinguish between water surface areas and non‐water surface areas. However, existing semantic segmentation methods cannot meet the requirements of the water surface segmentation task in terms of both segmentation precision and real‐time performance. In this study, a Swap Attention Bilateral Segmentation Network (SA‐BiSeNet) is proposed to improve segmentation performance while ensuring model inference speed by better fusing the two features of the dual‐branch down‐sampling network using the attention mechanism. Specifically, an innovative Swap Attention Module is designed to model the dependency between the features of the spatial detail branch and the features of the semantic branches, thus expanding the receptive fields of the spatial detail and semantic branches to each other's global contexts. This design can effectively fuse features and thus enhance feature representation. Experiments were conducted on the inland waterway dataset USVInland to verify the performance of SA‐BiSeNet in terms of segmentation precision and inference speed, and SA‐BiSeNet achieved 93.65% Mean IoU and maintained the same level of fps as the baseline

Use of fluorescence quantitative polymerase chain reaction (PCR) for the detection of Escherichia coli adhesion to pig intestinal epithelial cells

An efficient and accurate method to test Escherichia coli (E. coli) adhesion to intestinal epithelial cells will contribute to the study of bacterial pathogenesis and the function of genes that encode receptors related to adhesion. This study used the quantitative real-time polymerase chain reaction (qPCR) method. qPCR primers were designed from the PILIN gene of E. coli F18ab, F18ac, and K88ac, and the pig β-ACTIN gene. Total deoxyribonucleic acid (DNA) from E. coli and intestinal epithelial cells (IPEC-J2 cells) were used as templates for qPCR. The 2−ΔΔCt formula was used to calculate the relative number of bacteria in cultures of different areas. We found that the relative numbers of F18ab, F18ac, and K88ac that adhered to IPEC-J2 cells did not differ significantly in 6-, 12-, and 24-well culture plates. This finding indicated that there was no relationship between the relative adhesion number of E. coli and the area of cells, so the method of qPCR could accurately test the relative number of E. coli. This study provided a convenient and reliable testing method for experiments involving E. coli adhesion, and also provided innovative ideas for similar detection methods