Abstract. Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. Limiting cases are characterized by the existence of real Killing spinors and the minimality of the boundary.

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Background: Cardiovascular disease is the leading cause of death in China. The aim of this study was to evaluate the levels of cardiovascular health among Chinese adults and to understand the geographic pattern of cardiovascular health. Methods:In 2015, a total of 74,726 respondents aged ≥ 20 years with no history of cardiovascular disease were randomly sampled from 298 counties/districts of 31 provinces in mainland China and were interviewed. Seven metrics, including smoking, body mass index, physical activity, diet, total cholesterol, blood pressure, and fasting glucose, were determined. Ideal cardiovascular health was defined as the simultaneous presence of all metrics at the ideal level. A score ranging from 0 to 14 was calculated as the sum of all seven metrics for each province. Scores for cardiovascular health behaviors (smoking, body mass index, physical activity and diet) and those for cardiovascular health factors (smoking, total cholesterol, blood pressure, and fasting glucose) were also calculated. Findings:The mean age was 44.4 ± 15.9 years, and 49.3% were women. The age-sex-standardized prevalence of ideal cardiovascular health was universally poor, ranging from 0.02% [95% confidence interval (CI): 0%, 0.05%] in Tibet to 2.76% (95% CI: 0.45%, 5.07%) in Heilongjiang. Ideal diet (7.1%) was the least common factor of the seven metrics in each province and varied considerably across provinces. Other component metrics of ideal cardiovascular health were also spatially patterned. In all provinces, women had higher scores than men for cardiovascular health, health behaviors and health factors. Differences in cardiovascular health and health behavior scores between urban and rural areas were associated with levels of socio-economic development.Interpretation: Strategies for addressing poor cardiovascular health require geographic targeting and localized consideration.

In plants, long non-coding RNAs regulate disease resistance against fungi and other pathogens. However, the specific mechanism behind this regulation remains unclear. In this study, we identified disease resistance-related lncRNAs as well as their regulating genes and assessed their functions by infection of cotton (Gossypium) chromosome segment substitution lines with Verticillium dahliae. Our results demonstrated that lncRNA7 and its regulating gene Pectin methylesterase inhibitor 13 (GbPMEI13) positively regulated disease resistance via the silencing approach, while ectopic overexpression of GbPMEI13 in Arabidopsis (Arabidopsis thaliana) promoted growth and enhanced resistance to V. dahliae. In contrast, lncRNA2 and its regulating gene Polygalacturonase 12 (GbPG12) negatively regulated resistance to V. dahliae. We further found that fungal disease-related agents, including the pectin-derived oligogalacturonide (OG), could down-regulate the expression of lncRNA2 and GbPG12, leading to pectin accumulation. Conversely, OG up-regulated the expression of lncRNA7, which encodes a plant peptide phytosulfokine (PSK-α), which was confirmed by lncRNA7 overexpression and UPLC-MS experiments. We showed that PSK-α promoted IAA accumulation and activated GbPMEI13 expression through Auxin Response Factor 5 (ARF5). Since it is an inhibitor of pectin methylesterase (PME), GbPMEI13 promotes pectin methylation and therefore increases the resistance to V. dahliae. Consistently, we also demonstrated that GbPMEI13 inhibits the mycelial growth and spore germination of V. dahliae in vitro. In this study, we demonstrated that lncRNA7, lncRNA2, and their regulating genes modulate cell wall defense against V. dahliae via auxin-mediated signaling, providing a strategy for cotton breeding.

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