Abstract. We prove that for any s, t ≥ 0 with s + t = 1 and any θ ∈ R with inf q∈N q 1 s qθ > 0, the set of y ∈ R for which (θ, y) is (s, t)-badly approximable is 1 2 -winning for Schmidt's game. As a consequence, we remove a technical assumption in a recent theorem of Badziahin-Pollington-Velani on simultaneous Diophantine approximation.
Staphylococcus aureus (S. aureus) is problematic for lactating mammals and public health. Understanding of mechanisms by which the hosts respond to severe invasion of S. aureus remains elusive. In this study, the genome-wide expression of mRNAs and miRNAs in bovine mammary gland cells were interrogated at 24 h after intra-mammary infection (IMI) with high or low concentrations of S. aureus. Compared to the negative control quarters, 194 highly-confident responsive genes were identified in the quarters with high concentration (109 cfu/mL) of S. aureus, which were predominantly implicated in pathways and biological processes pertaining to innate immune system, such as cytokine-cytokine receptor interaction and inflammatory response. In contrast, only 21 highly-confident genes were significantly differentially expressed in face of low concentration (106 cfu/mL) of S. aureus, which slightly perturbed the cell signaling and invoked corresponding responses like vasoconstriction, indicating limited perturbations and immunological evading. Additionally, the significant up-regulations of bta-mir-223 and bta-mir-21-3p were observed in the quarters infected by high concentration of S. aureus. Network analysis suggested that the two miRNAs' pivotal roles in defending hosts against bacterial infection probably through inhibiting CXCL14 and KIT. The significant down-regulation of CXCL14 was also observed in bovine mammary epithelial cells at 24 h post-infection of S. aureus (108 cfu/mL) in vitro. Integrated analysis with QTL database further suggested 28 genes (e.g., CXCL14, KIT, and SLC4A11) as candidates of bovine mastitis. This study first systematically revealed transcriptional and post-transcriptional responses of bovine mammary gland cells to invading S. aureus in a dosage-dependent pattern, and highlighted a complicated responsive mechanism in a network of miRNA-gene-pathway interplay.
Under the government of China's environmental program known as Returning Farmland To Forests (RFTF), about 28 million hectares of farmland have been converted to tree plantation. This has led to a large accumulation of biomass carbon, but less is known about underground carbon-related processes. One permanent plot (25 years of observation) and four chronosequence plot series comprising 159 plots of larch (Larix gmelinii) plantations in northeastern China were studied. Both methods found significant soil organic carbon (SOC) accumulation (96.4 g C m À2 yr À1 ) and bulk density decrease (5.7 mg cm À3 yr À1 ) in the surface soil layer (0-20 cm), but no consistent changes in deeper layers, indicating that larch planting under the RFTF program can increase SOC storage and improve the physical properties of surface soil. Nitrogen depletion (4.1-4.3 g m À2 yr À1 ), soil acidification (0.007-0.022 pH units yr À1 ) and carbon/ nitrogen (C/N) ratio increase (0.16-0.46 per year) were observed in lessive soil, whereas no significant changes were found in typical dark-brown forest soil. This SOC accumulation rate (96.4 g m À2 yr À1 ) can take 39% of the total carbon sink capacity [net ecosystem exchange (NEE)] of larch forests in this region and the total soil carbon sequestration could be 87 Tg carbon within 20 years of plantation by approximating all larch plantations in northeastern China (4.5 Mha), showing the importance of soil carbon accumulation in the ecosystem carbon balance. By comparison with the rates of these processes in agricultural use, the RFTF program of reversing land use for agriculture will rehabilitate SOC, soil fertility and bulk density slowly (o69% of the depletion rate in agricultural use), so that a much longer duration is needed to rehabilitate the underground function of soil via the RFTF program. Global forest plantations on abandoned farmland or function to protecting farmland are of steady growth and our findings may be important for understanding their underground carbon processes.
Abstract. We prove that for any pair (s, t) of nonnegative numbers with s + t = 1, the set of two-dimensional (s, t)-badly approximable vectors is winning for Schmidt's game. As a consequence, we give a direct proof of Schmidt's conjecture using his game.
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