Pointwise Convergence of Double Trigonometric Series

AbstractThe pointwise convergence problem of the rectangular partial sums of a certain type of double trigonometric series is considered, This type of series obeys certain conditions on the finite-order differences of its coefficients. We prove that if the Césaro sums of the double series converge unrestrictedly, then so do its partial sums, It is pointed out that the converse of the last statement may not hold for the same kind of double trigonometric series. As a corollary, it is shown that the double Fourier series of the mentioned type converges unrestrictedly almost everywhere. Generalizations of the above results to the restricted case are also established. These results generalize the theorems of Chen

Metabolic engineering of rice endosperm towards higher vitamin B1 accumulation

Rice is a major food crop to approximately half of the human population. Unfortunately, the starchy endosperm, which is the remaining portion of the seed after polishing, contains limited amounts of micronutrients. Here, it is shown that this is particularly the case for thiamin (vitamin B1). Therefore, a tissue-specific metabolic engineering approach was conducted, aimed at enhancing the level of thiamin specifically in the endosperm. To achieve this, three major thiamin biosynthesis genes, THIC, THI1 and TH1, controlled by strong endosperm-specific promoters, were employed to obtain engineered rice lines. The metabolic engineering approaches included ectopic expression of THIC alone, in combination with THI1 (bigenic) or combined with both THI1 and TH1 (trigenic). Determination of thiamin and thiamin biosynthesis intermediates reveals the impact of the engineering approaches on endosperm thiamin biosynthesis. The results show an increase of thiamin in polished rice up to threefold compared to WT, and stable upon cooking. These findings confirm the potential of metabolic engineering to enhance de novo thiamin biosynthesis in rice endosperm tissue and aid in steering future biofortification endeavours

Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson lattice Dirac operator

A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac operator does not possess any topological zero modes in topologically-nontrivial gauge backgrounds, it can reproduce correct axial anomaly for sufficiently smooth gauge configurations, provided that it is exponentially-local, doublers-free, and has correct continuum behavior. In this paper, we calculate the axial anomaly of this lattice Dirac operator in weak coupling perturbation theory, and show that it recovers the topological charge density in the continuum limit.Comment: 25 pages, v2: calculation up to O(g^4) for nonabelian gauge backgroun

Quenched chiral logarithms in lattice QCD with exact chiral symmetry

We examine quenched chiral logarithms in lattice QCD with overlap Dirac quark. For 100 gauge configurations generated with the Wilson gauge action at $\beta = 5.8$ on the $8^3 \times 24$ lattice, we compute quenched quark propagators for 12 bare quark masses. The pion decay constant is extracted from the pion propagator, and from which the lattice spacing is determined to be 0.147 fm. The presence of quenched chiral logarithm in the pion mass is confirmed, and its coefficient is determined to be $\delta = 0.203 \pm 0.014$, in agreement with the theoretical estimate in quenched chiral perturbation theory. Further, we obtain the topological susceptibility of these 100 gauge configurations by measuring the index of the overlap Dirac operator. Using a formula due to exact chiral symmetry, we obtain the $\eta'$ mass in quenched chiral perturbation theory, $m_{\eta'} = (901 \pm 64)$ Mev, and an estimate of $\delta = 0.197 \pm 0.027$, which is in good agreement with that determined from the pion mass.Comment: 24 pages, 6 EPS figures; v2: some clarifications added, to appear in Physical Review

The Plasma Environment of Comets

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138863/1/rog199129s2976.pd

Recurrent inversion polymorphisms in humans associate with genetic instability and genomic disorders

Unlike copy number variants (CNVs), inversions remain an underexplored genetic variation class. By integrating multiple genomic technologies, we discover 729 inversions in 41 human genomes. Approximately 85% of inversions <2 kbp form by twin-priming during L1 retrotransposition; 80% of the larger inversions are balanced and affect twice as many nucleotides as CNVs. Balanced inversions show an excess of common variants, and 72% are flanked by segmental duplications (SDs) or retrotransposons. Since flanking repeats promote non-allelic homologous recombination, we developed complementary approaches to identify recurrent inversion formation. We describe 40 recurrent inversions encompassing 0.6% of the genome, showing inversion rates up to 2.7 × 10(-4) per locus per generation. Recurrent inversions exhibit a sex-chromosomal bias and co-localize with genomic disorder critical regions. We propose that inversion recurrence results in an elevated number of heterozygous carriers and structural SD diversity, which increases mutability in the population and predisposes specific haplotypes to disease-causing CNVs

Integrating sequence and array data to create an improved 1000 Genomes Project haplotype reference panel

A major use of the 1000 Genomes Project (1000GP) data is genotype imputation in genome-wide association studies (GWAS). Here we develop a method to estimate haplotypes from low-coverage sequencing data that can take advantage of single-nucleotide polymorphism (SNP) microarray genotypes on the same samples. First the SNP array data are phased to build a backbone (or 'scaffold') of haplotypes across each chromosome. We then phase the sequence data 'onto' this haplotype scaffold. This approach can take advantage of relatedness between sequenced and non-sequenced samples to improve accuracy. We use this method to create a new 1000GP haplotype reference set for use by the human genetic community. Using a set of validation genotypes at SNP and bi-allelic indels we show that these haplotypes have lower genotype discordance and improved imputation performance into downstream GWAS samples, especially at low-frequency variants. © 2014 Macmillan Publishers Limited. All rights reserved

The Cancer Genome Atlas Comprehensive Molecular Characterization of Renal Cell Carcinoma

Renal cell carcinoma(RCC) is not a single disease, but several histologically defined cancers with different genetic drivers, clinical courses, and therapeutic responses. The current study evaluated 843 RCC from the three major histologic subtypes, including 488 clear cell RCC, 274 papillary RCC, and 81 chromophobe RCC. Comprehensive genomic and phenotypic analysis of the RCC subtypes reveals distinctive features of each subtype that provide the foundation for the development of subtype-specific therapeutic and management strategies for patients affected with these cancers. Somatic alteration of BAP1, PBRM1, and PTEN and altered metabolic pathways correlated with subtype-specific decreased survival, while CDKN2A alteration, increased DNA hypermethylation, and increases in the immune-related Th2 gene expression signature correlated with decreased survival within all major histologic subtypes. CIMP-RCC demonstrated an increased immune signature, and a uniform and distinct metabolic expression pattern identified a subset of metabolically divergent (MD) ChRCC that associated with extremely poor survival