Triticum urartu (diploid, AA) is the progenitor of the A subgenome of tetraploid (Triticum turgidum, AABB) and hexaploid (Triticum aestivum, AABBDD) wheat. Genomic studies of T. urartu have been useful for investigating the structure, function and evolution of polyploid wheat genomes. Here we report the generation of a high-quality genome sequence of T. urartu by combining bacterial artificial chromosome (BAC)-by-BAC sequencing, single molecule real-time whole-genome shotgun sequencing , linked reads and optical mapping. We assembled seven chromosome-scale pseudomolecules and identified protein-coding genes, and we suggest a model for the evolution of T. urartu chromosomes. Comparative analyses with genomes of other grasses showed gene loss and amplification in the numbers of transposable elements in the T. urartu genome. Population genomics analysis of 147 T. urartu accessions from across the Fertile Crescent showed clustering of three groups, with differences in altitude and biostress, such as powdery mildew disease. The T. urartu genome assembly provides a valuable resource for studying genetic variation in wheat and related grasses, and promises to facilitate the discovery of genes that could be useful for wheat improvement.
We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly using the weak form of master equation for probability evolution. In the small step size regime and the presence of omnidirectional noise, our weak approximating diffusion process suggests the following dynamics for the SGD iteration starting from a local minimizer (resp. saddle point): it escapes in a number of iterations exponentially (resp. almost linearly) dependent on the inverse stepsize. The results are obtained using the theory for random perturbations of dynamical systems (theory of large deviations for local minimizers and theory of exiting for unstable stationary points). In addition, we discuss the effects of batch size for the deep neural networks, and we find that small batch size is helpful for SGD algorithms to escape unstable stationary points and sharp minimizers.Our theory indicates that one should increase the batch size at later stage for the SGD to be trapped in flat minimizers for better generalization.
This piece of the submission is being sent via mail. Leaf senescence is essential for the nutrient economy of crops and is executed by so-called senescence-associated genes (SAGs). Here we explored the monocot C model crop Sorghum bicolor for a holistic picture of SAG profiles by RNA-seq. Leaf samples were collected at four stages during developmental senescence, and in total, 3396 SAGs were identified, predominantly enriched in GO categories of metabolic processes and catalytic activities. These genes were enriched in 13 KEGG pathways, wherein flavonoid and phenylpropanoid biosynthesis and phenylalanine metabolism were overrepresented. Seven regions on Chromosomes 1, 4, 5 and 7 contained SAG 'hotspots' of duplicated genes or members of cupin superfamily involved in manganese ion binding and nutrient reservoir activity. Forty-eight expression clusters were identified, and the candidate orthologues of the known important senescence transcription factors such as ORE1, EIN3 and WRKY53 showed "SAG" expression patterns, implicating their possible roles in regulating sorghum leaf senescence. Comparison of developmental senescence with salt- and dark- induced senescence allowed for the identification of 507 common SAGs, 1996 developmental specific SAGs as well as 176 potential markers for monitoring senescence in sorghum. Taken together, these data provide valuable resources for comparative genomics analyses of leaf senescence and potential targets for the manipulation of genetic improvement of Sorghum bicolor.
A new sorbent has been prepared by coating alkyl quaternized poly(4-vinylpyridine) (PVP) on the high surface area of silica gel. The resulting granular sorbent was used to remove Cr(VI) from water. Batch experiments were conducted to determine the kinetics and sorption rate. The research demonstrated that the modified PVP coated silica gel (referred to as coated gel) could successfully remove chromium(VI) from solution and that the sorbent provided fast kinetics. A finite-bath diffusion-control model with changing bulk concentration was derived analytically for application to the coated gel sorption of Cr(VI). This model fitted the experimental data well. The sorption kinetics on modified PVP coated gel was found to be diffusion-controlled with a value of 5.8 × 10 -7 cm 2 /s for the product of the distribution coefficient and the effective diffusivity in the sorption of Cr(VI) on the coated silica gel.
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