Hyperbolic Alexandrov-Fenchel quermassintegral inequalities I

In this paper we prove the following geometric inequality in the hyperbolic space \H^n ($n\ge 5)$, which is a hyperbolic Alexandrov-Fenchel inequality, \begin{array}{rcl} \ds \int_\Sigma \s_4 d \mu\ge \ds\vs C_{n-1}^4\omega_{n-1}\left\{\left(\frac{|\Sigma|}{\omega_{n-1}} \right)^\frac 12 + \left(\frac{|\Sigma|}{\omega_{n-1}} \right)^{\frac 12\frac {n-5}{n-1}} \right\}^2, \end{array} provided that $\Sigma$ is a horospherical convex hypersurface. Equality holds if and only if $\Sigma$ is a geodesic sphere in \H^n.Comment: 18page

A new mass for asymptotically flat manifolds

In this paper we introduce a mass for asymptotically flat manifolds by using the Gauss-Bonnet curvature. We first prove that the mass is well-defined and is a geometric invariant, if the Gauss-Bonnet curvature is integrable and the decay order $\tau$ satisfies $\tau > \frac {n-4}{3}.$ Then we show a positive mass theorem for asymptotically flat graphs over ${\mathbb R}^n$. Moreover we obtain also Penrose type inequalities in this case.Comment: 32 pages. arXiv:1211.7305 was integrated into this new version as an applicatio

The Gauss-Bonnet-Chern mass of conformally flat manifolds

In this paper we show positive mass theorems and Penrose type inequalities for the Gauss-Bonnet-Chern mass, which was introduced recently in \cite{GWW}, for asymptotically flat CF manifolds and its rigidity.Comment: 17 pages, references added, the statement of Prop. 4.6 correcte

On Volume Growth of Gradient Steady Ricci Solitons

In this paper we study volume growth of gradient steady Ricci solitons. We show that if the potential function satisfies a uniform condition, then the soliton has at most Euclidean volume growth.Comment: 8 page

Anti-inflammatory Effects of α7-nicotinic ACh Receptors are Exerted Through Interactions with Adenylyl Cyclase-6

Background and purpose Alpha 7 nicotinic acetylcholine receptors (CHRNA7) suppress inflammation through diverse pathways in immune cells, so is potentially involved in a number of inflammatory diseases. However, the detailed mechanisms underlying CHRNA7’s anti‐inflammatory effects remain elusive. Experimental approach The anti‐inflammatory effects of CHRNA7 agonists in both murine macrophages (RAW 264.7) and bone marrow‐derived macrophages (BMDM) stimulated with LPS were examined. The role of adenylyl cyclase 6 (AC6) in Toll‐like Receptor 4 (TLR4) degradation was explored via overexpression and knockdown. A mouse model of chronic obstructive pulmonary disease was used to confirm key findings. Results Anti‐inflammatory effects of CHRNA7 were largely dependent on AC6 activation, as knockdown of AC6 considerably abnegated the effects of CHRNA7 agonists while AC6 overexpression promoted them. We found that CHRNA7 and AC6 are co‐localized in lipid rafts of macrophages and directly interact. Activation of AC6 led to the promotion of TLR4 degradation. Administration of CHRNA7 agonist PNU‐282987 attenuated pathological and inflammatory end points in a mouse model of chronic obstructive pulmonary disease (COPD). Conclusion and implications CHRNA7 inhibits inflammation through activating AC6 and promoting degradation of TLR4. The use of CHRNA7 agonists may represent a novel therapeutic approach for treating COPD and likely other inflammatory diseases

Acupuncture as adjunctive treatment for linezolid-induced peripheral neuropathy: a case series report

BackgroundThe treatment of multidrug-resistant tuberculosis (MDR-TB) and pre-extensively drug-resistant tuberculosis (pre-XDR-TB) remains challenging due to the limited availability of effective drugs. Linezolid has emerged as a promising therapeutic option for these cases. However, its long-term use can lead to complications such as peripheral and optic neuropathies. Acupuncture, a cornerstone of traditional Chinese medicine, has been shown to be effective in the treatment of peripheral neuropathy (PN). This study examines the potential benefits of acupuncture in the treatment of linezolid-induced peripheral neuropathy (LIPN).MethodsFour patients, aged 27 to 60 years, diagnosed with LIPN, underwent daily acupuncture treatments. The main endpoint was to assess the efficacy of acupuncture in reducing neuropathic pain associated with LIPN in patients. This was primarily measured using changes in the Short Form McGill Pain Questionnaire (SF-MPQ) scores before and after acupuncture treatment.ResultsThree of the patients experienced significant symptom remission, while one experienced marginal improvement. Treatments ranged from 7 to 18 sessions. Specifically, the first patient reported substantial relief with a score reduction from 33 to 13; the second patient observed minimal change; the third patient’s score decreased dramatically from 10 to 2 after eight sessions; the last patient had a score reduction from 21 to 12 after five sessions, but did not continue treatment for a second assessment.ConclusionAcupuncture is a promising therapeutic approach for LIPN. However, larger and more thorough studies are needed to determine its full potential

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