Adaptive Finite Element Approximations for Kohn-Sham Models

The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element approximations for the Kohn-Sham model. Based on the residual type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite element approximations. Using D{\" o}rfler's marking strategy, we then get the convergence rate and quasi-optimal complexity. We also carry out several typical numerical experiments that not only support our theory,but also show the robustness and efficiency of the adaptive finite element computations in electronic structure calculations.Comment: 38pages, 7figure

Sporopollenin chemistry and its durability in the geological record: an integration of extant and fossil chemical data across the seed plants.

Sporopollenin is a highly resistant biopolymer that forms the outer wall of pollen and spores (sporomorphs). Recent research into sporopollenin chemistry has opened up a range of new avenues for palynological research, including chemotaxonomic classification of morphologically cryptic taxa. However, there have been limited attempts to directly integrate extant and fossil sporopollenin chemical data. Of particular importance is the impact of sample processing to isolate sporopollenin from fresh sporomorphs, and the extent of chemical changes that occur once sporomorphs enter the geological record. Here, we explore these issues using Fourier transform infrared (FTIR) microspectroscopy data from extant and fossil grass, Nitraria (a steppe plant), and conifer pollen. We show a 98% classification success rate at subfamily level with extant grass pollen, demonstrating a strong taxonomic signature in isolated sporopollenin. However, we also reveal substantial chemical differences between extant and fossil sporopollenin, which can be tied to both early diagenetic changes acting on the sporomorphs and chemical derivates of sample processing. Our results demonstrate that directly integrating extant and late Quaternary chemical data should be tractable as long as comparable sample processing routines are maintained. Consistent differences between extant and deeper time sporomorphs, however, suggests that classifying fossil specimens using extant training sets will be challenging. Further work is therefore required to understand and simulate the effects of diagenetic processes on sporopollenin chemistry

New Insights into the Organization, Recombination, Expression and Functional Mechanism of Low Molecular Weight Glutenin Subunit Genes in Bread Wheat

The bread-making quality of wheat is strongly influenced by multiple low molecular weight glutenin subunit (LMW-GS) proteins expressed in the seeds. However, the organization, recombination and expression of LMW-GS genes and their functional mechanism in bread-making are not well understood. Here we report a systematic molecular analysis of LMW-GS genes located at the orthologous Glu-3 loci (Glu-A3, B3 and D3) of bread wheat using complementary approaches (genome wide characterization of gene members, expression profiling, proteomic analysis). Fourteen unique LMW-GS genes were identified for Xiaoyan 54 (with superior bread-making quality). Molecular mapping and recombination analyses revealed that the three Glu-3 loci of Xiaoyan 54 harbored dissimilar numbers of LMW-GS genes and covered different genetic distances. The number of expressed LMW-GS in the seeds was higher in Xiaoyan 54 than in Jing 411 (with relatively poor bread-making quality). This correlated with the finding of higher numbers of active LMW-GS genes at the A3 and D3 loci in Xiaoyan 54. Association analysis using recombinant inbred lines suggested that positive interactions, conferred by genetic combinations of the Glu-3 locus alleles with more numerous active LMW-GS genes, were generally important for the recombinant progenies to attain high Zeleny sedimentation value (ZSV), an important indicator of bread-making quality. A higher number of active LMW-GS genes tended to lead to a more elevated ZSV, although this tendency was influenced by genetic background. This work provides substantial new insights into the genomic organization and expression of LMW-GS genes, and molecular genetic evidence suggesting that these genes contribute quantitatively to bread-making quality in hexaploid wheat. Our analysis also indicates that selection for high numbers of active LMW-GS genes can be used for improvement of bread-making quality in wheat breeding