Some properties of the Schouten tensor and applications to conformal geometry

The note is about some nonlinear curvature conditions which arise naturally in conformal geometry.Comment: 10 page

Protective effect of ethosuximide on hearing in NOD/LtJ mice via blockage of endogenous apoptosis

Purpose: To determine the protective effect of ethosuximide on the hearing of NOD/LtJ mice, and the underlying mechanism of action. Methods: The mice were randomly assigned to control and treatment groups (20 mice per group). Mice in the treatment group were administered ethosuximide intraperitoneally at a dose of 200mg/kg body weight (bwt), while those in the control group received an equivalent dose of saline via the same route. Both groups were subjected to auditory brainstem response (ABR) and distortion product otoacoustic emissions (DPOAE) tests, as well as determination of mRNA expressions of α1G, α1H, α1I, m-calpain, μ-calpain, and caspase-3. Results: At ages of 6 and 9 weeks, ABR values were significantly lower in the treatment group than those in the control group (p < 0.05). At age 3, 6 and 9 weeks, control group DPOAE values were much lower than those in the treatment group. However, at signal frequency of 35344 Hz, DPOAE value was significantly reduced in the treatment group (p < 0.05). There was significant down-regulation in mRNA expressions of α1G, α1H, α1I, m-calpain, μ-calpain and caspase-3, in the treatment group, when compared with the control group (p < 0.05). Conclusion: Ethosuximide delays mice hearing loss and protects their hearing via a mechanism involving blockage of endogenous apoptotic pathways. This mechanism may provide guidance in the search for suitable new drugs. Keywords: Ethosuximide, Endogenous apoptosis, Hearing, Protectio

Can upscaling ground nadir SIF to eddy covariance footprint improve the relationship between SIF and GPP in croplands?

Ground solar-induced chlorophyll fluorescence (SIF) is important for the mechanistic understanding of the dynamics of vegetation gross primary production (GPP) at fine spatiotemporal scales. However, eddy covariance (EC) observations generally cover larger footprint areas than ground SIF observations (a bare fiber with nadir), and this footprint mismatch between nadir SIF and GPP could complicate the canopy SIF-GPP relationships. Here, we upscaled nadir SIF observations to EC footprint and investigated the change in SIF-GPP relationships after the upscaling in cropland. We included 13 site-years data in our study, with seven site-years corn, four siteyears soybeans, and two site-years miscanthus, all located in the US Corn Belt. All sites’ crop nadir SIF observations collected from the automated FluoSpec2 system (a hemispheric-nadir system) were upscaled to the GPP footprint-based SIF using vegetation indices (VIs) calculated from high spatiotemporal satellite reflectance data. We found that SIF-GPP relationships were not substantially changed after upscaling nadir SIF to GPP footprint at our crop sites planted with corn, soybean, and miscanthus, with R2 change after the upscaling ranging from -0.007 to 0.051 and root mean square error (RMSE) difference from -0.658 to 0.095 umol m-2 s-1 relative to original nadir SIF-GPP relationships across all the site-years. The variation of the SIF-GPP relationship within each species across different site-years was similar between the original nadir SIF and upscaled SIF. Different VIs, EC footprint models, and satellite data led to marginal differences in the SIF-GPP relationships when upscaling nadir SIF to EC footprint. Our study provided a methodological framework to correct this spatial mismatch between ground nadir SIF and GPP observations for croplands and potentially for other ecosystems. Our results also demonstrated that the spatial mismatch between ground nadir SIF and GPP might not significantly affect the SIF-GPP relationship in cropland that are largely homogeneous

Partitioning controls on Amazon forest photosynthesis between environmental and biotic factors at hourly to interannual timescales

Gross ecosystem productivity (GEP) in tropical forests varies both with the environment and with biotic changes in photosynthetic infrastructure, but our understanding of the relative effects of these factors across timescales is limited. Here, we used a statistical model to partition the variability of seven years of eddy covariance-derived GEP in a central Amazon evergreen forest into two main causes: variation in environmental drivers (solar radiation, diffuse light fraction, and vapor pressure deficit) that interact with model parameters that govern photosynthesis and biotic variation in canopy photosynthetic light-use efficiency associated with changes in the parameters themselves. Our fitted model was able to explain most of the variability in GEP at hourly (R2 = 0.77) to interannual (R2 = 0.80) timescales. At hourly timescales, we found that 75% of observed GEP variability could be attributed to environmental variability. When aggregating GEP to the longer timescales (daily, monthly, and yearly), however, environmental variation explained progressively less GEP variability: At monthly timescales, it explained only 3%, much less than biotic variation in canopy photosynthetic light-use efficiency, which accounted for 63%. These results challenge modeling approaches that assume GEP is primarily controlled by the environment at both short and long timescales. Our approach distinguishing biotic from environmental variability can help to resolve debates about environmental limitations to tropical forest photosynthesis. For example, we found that biotically regulated canopy photosynthetic light-use efficiency (associated with leaf phenology) increased with sunlight during dry seasons (consistent with light but not water limitation of canopy development) but that realized GEP was nonetheless lower relative to its potential efficiency during dry than wet seasons (consistent with water limitation of photosynthesis in given assemblages of leaves). This work highlights the importance of accounting for differential regulation of GEP at different timescales and of identifying the underlying feedbacks and adaptive mechanisms

Attributing differences of solar-induced chlorophyll fluorescence (SIF)-gross primary production (GPP) relationships between two C4 crops: corn and miscanthus

There remains limited information to characterize the solar-induced chlorophyll fluorescence (SIF)-gross primary production (GPP) relationship in C4 cropping systems. The annual C4 crop corn and perennial C4 crop miscanthus differ in phenology, canopy structure and leaf physiology. Investigating the SIF-GPP relationships in these species could deepen our understanding of SIF-GPP relationships within C4 crops. Using in situ canopy SIF and GPP measurements for both species along with leaf-level measurements, we found considerable differences in the SIF-GPP relationships between corn and miscanthus, with a stronger SIF-GPP relationship and higher slope of SIF-GPP observed in corn compared to miscanthus. These differences were mainly caused by leaf physiology. For miscanthus, high non-photochemical quenching (NPQ) under high light, temperature and water vapor deficit (VPD) conditions caused a large decline of fluorescence yield (ΦF), which further led to a SIF midday depression and weakened the SIF-GPP relationship. The larger slope in corn than miscanthus was mainly due to its higher GPP in mid-summer, largely attributed to the higher leaf photosynthesis and less NPQ. Our results demonstrated variation of the SIF-GPP relationship within C4 crops and highlighted the importance of leaf physiology in determining canopy SIF behaviors and SIF-GPP relationships

A physiological signal derived from sun-induced chlorophyll fluorescence quantifies crop physiological response to environmental stresses in the U.S. Corn Belt

Sun-induced chlorophyll fluorescence (SIF) measurements have shown unique potential for quantifying plant physiological stress. However, recent investigations found canopy structure and radiation largely control SIF, and physiological relevance of SIF remains yet to be fully understood. This study aims to evaluate whether the SIF-derived physiological signal improves quantification of crop responses to environmental stresses, by analyzing data at three different spatial scales within the U.S. Corn Belt, i.e. experiment plot, field, and regional scales, where ground-based portable, stationary and space-borne hyperspectral sensing systems are used, respectively. We found that, when controlling for variations in incoming radiation and canopy structure, crop SIF signals can be decomposed into non-physiological (i.e. canopy structure and radiation, 60% ∼ 82%) and physiological information (i.e. physiological SIF yield, ΦF, 17% ∼ 31%), which confirms the contribution of physiological variation to SIF. We further evaluated whether ΦF indicated plant responses under high-temperature and high vapor pressure deficit (VPD) stresses. The plot-scale data showed that ΦF responded to the proxy for physiological stress (partial correlation coefficient, r p= 0.40, p\u3c 0.001) while non-physiological signals of SIF did not respond (p\u3e 0.1). The field-scale ΦF data showed water deficit stress from the comparison between irrigated and rainfed fields, and ΦF was positively correlated with canopy-scale stomatal conductance, a reliable indicator of plant physiological condition (correlation coefficient r= 0.60 and 0.56 for an irrigated and rainfed sites, respectively). The regional-scale data showed ΦF was more strongly correlated spatially with air temperature and VPD (r= 0.23 and 0.39) than SIF (r= 0.11 and 0.34) for the U.S. Corn Belt. The lines of evidence suggested that ΦF reflects crop physiological responses to environmental stresses with greater sensitivity to stress factors than SIF, and the stress quantification capability of ΦF is spatially scalable. Utilizing ΦF for physiological investigations will contribute to improve our understanding of vegetation responses to high-temperature and high-VPD stresses

A fully nonlinear conformal flow on locally conformally flat manifolds

We study a fully nonlinear flow for conformal metrics. The long-time existence and the sequential convergence of flow are established for locally conformally flat manifolds. As an application, we solve the σk-Yamabe problem for locally conformal flat manifolds when k ̸ = n/2