Zika virus (ZIKV) is a mosquito-borne flavivirus. It was first isolated from Uganda in 1947 and has become an emergent event since 2007. However, because of the inconsistency of alignment methods, the evolution of ZIKV remains poorly understood. In this study, we first use the complete protein and an alignment-free method to build a phylogenetic tree of 87 Zika strains in which Asian, East African, and West African lineages are characterized. We also use the NS5 protein to construct the genetic relationship among 44 Zika strains. For the first time, these strains are divided into two clades: African 1 and African 2. This result suggests that ZIKV originates from Africa, then spread to Asia, Pacific islands, and throughout the Americas. We also perform the phylogeny analysis for 53 viruses in genus Flavivirus to which ZIKV belongs using complete proteins. Our conclusion is consistent with the classification by the hosts and transmission vectors.

In the research of computer vision and machine perception, 3D objects are usually represented by 2-manifold triangular meshes M. In this paper, we present practical and efficient algorithms to construct iso-contours, bisectors, and Voronoi diagrams of point sites onM, based on an exact geodesic metric. Compared to euclidean metric spaces, the Voronoi diagrams onMexhibit many special properties that fail all of the existing euclidean Voronoi algorithms. To provide practical algorithms for constructing geodesicmetric- based Voronoi diagrams onM, this paper studies the analytic structure of iso-contours, bisectors, and Voronoi diagrams onM. After a necessary preprocessing of model M, practical algorithms are proposed for quickly obtaining full information about iso-contours, bisectors, and Voronoi diagrams on M. The complexity of the construction algorithms is also analyzed. Finally, three interesting applications—surface sampling and reconstruction, 3D skeleton extraction, and point pattern analysis—are presented that show the potential power of the proposed algorithms in pattern analysis.

In this paper, we propose and analyze a new stabilized finite element method using continuous piecewise linear (or bilinear) elements for solving 2D reaction-convection-diffusion equations. The equation under consideration involves a small diffusivity $\varepsilon$ and a large reaction coefficient $\sigma$, leading to high P\'eclet number and high Damk\"{o}hler number. In addition to giving error estimates of the approximations in $L^2$ and $H^1$ norms, we explicitly establish the dependence of error bounds on the diffusivity, the $L^{\infty}$ norm of convection field, the reaction coefficient and the mesh size. Our analysis shows that the proposed method is particularly suitable for problems with a small diffusivity and a large reaction coefficient, or more precisely, with a large mesh P\'eclet number and a large mesh Damk\"{o}hler number. Several numerical examples exhibiting boundary or interior layers are given to illustrate the high accuracy and stability of the proposed method. The results obtained are also compared with those of existing stabilization methods.

No abstract uploaded!

We develop a method searching for quasi-conformal maps from point-cloud surfaces to Euclidean plane. The maps can be got by directly solving Beltrami equation with proper boundary condition or solving optimization problem of the variational formu- lation. The point integral methd (PIM) is used for discretization on point clouds. Numerical experiments suggest that the method converges as the density of points in- creases.