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In this paper, we first establish an $L^2$-type Dolbeault isomorphism for logarithmic differential forms by H\"{o}rmander's $L^2$-estimates. By using this isomorphism and the construction of smooth Hermitian metrics, we obtain a number of new %Akizuki-Kodaira-Nakano type vanishing theorems for sheaves of logarithmic differential forms on compact K\"ahler manifolds with simple normal crossing divisors, which generalize several classical vanishing theorems, including Norimatsu's vanishing theorem, Gibrau's vanishing theorem, Le Potier's vanishing theorem and a version of the Kawamata-Viehweg vanishing theorem.

Next-generation sequencing technology enables the routine detection of bacterial pathogens for clinical diagnostics and genetic research. Whole-genome sequencing has been of importance in the epidemiologic analysis of bacterial pathogens. However, few whole-genome sequencing-based genotyping pipelines are available for practical applications. Here, we present the whole-genome sequencing-based single nucleotide polymorphism(SNP) genotyping method and apply to the evolutionary analysis of methicillin-resistant Staphylococcus aureus. The SNP genotyping method calls genome variants using next-generation sequencing reads of whole genomes and calculates the pair-wise Jaccard distances of the genome variants. The method may reveal the high-resolution whole-genome SNP profiles and the structural variants of different isolates of methicillin-resistant S. aureus(MRSA) and methicillin-susceptible S. aureus(MSSA) strains. The phylogenetic analysis of whole genomes and particular regions may monitor and track the evolution and the transmission dynamic of bacterial pathogens. The computer pro- grams of the whole genome sequencing-based SNP genotyping methods are available to the public at https://github. com/ cyinbox/NGS.

A multilevel quality-guided phase unwrapping algorithm for real-time 3D shape measurement is presented. The quality map is generated from the gradient of the phase map. Multilevel thresholds are used to unwrap the phase level by level. Within the data points in each level, a fast scan-line algorithm is employed. The processing time of this algorithm is approximately 18.3 ms for an image size of 640480 pixels in an ordinary computer. We demonstrate that this algorithm can be implemented into our real-time 3D shape measurement system for real-time 3D reconstruction. Experiments show that this algorithm improves the previous scan-line phase unwrapping algorithm significantly although it reduces its processing speed slightly.

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