On the optimal linear convergence factor of the relaxed proximal point algorithm for monotone inclusion problems

Finding a zero of a maximal monotone operator is fundamental in convex optimization and monotone operator theory, and \emph{proximal point algorithm} (PPA) is a primary method for solving this problem. PPA converges not only globally under fairly mild conditions but also asymptotically at a fast linear rate provided that the underlying inverse operator is Lipschitz continuous at the origin. These nice convergence properties are preserved by a relaxed variant of PPA. Recently, a linear convergence bound was established in [M. Tao, and X. M. Yuan, J. Sci. Comput., 74 (2018), pp. 826-850] for the relaxed PPA, and it was shown that the bound is optimal when the relaxation factor $\gamma$ lies in $[1,2)$. However, for other choices of $\gamma$, the bound obtained by Tao and Yuan is suboptimal. In this paper, we establish tight linear convergence bounds for any choice of $\gamma\in(0,2)$ and make the whole picture about optimal linear convergence bounds clear. These results sharpen our understandings to the asymptotic behavior of the relaxed PPA.Comment: 9 pages and 1 figur

Development of a New Dual-Cylinder Rotary Compressor for VI System

On the vapor compression refrigeration system, Vapor injection (VI, the phase separator type injection or the internal heat exchanger type injection) compression cycle’s superiority over non-injection cycle has been well known. VI system produces the high heating/cooling capacity, and its power consumption is less than the non-injection system. But if a VI compression cycle uses a single rotary compressor, there is the problem that refrigerant injection increases the indicated power by mixture loss. If we use a two-stage rotary compressor, indicated power also increases because of its two times exhaust process. To solve these problems, we developed a new dual-cylinder rotary compressor for VI systems, one of the cylinders is used to compress the gas from the evaporator, and the other is used to compress the gas from the phase separator (flash-tank). Its design method is discussed and its performance under different conditions is analyzed

Implications of whole-disc DSCOVR EPIC spectral observations for estimating Earth's spectral reflectivity based on low-earth-orbiting and geostationary observations

Earth’s reflectivity is among the key parameters of climate research. National Aeronautics and Space Administration (NASA)’s Earth Polychromatic Imaging Camera (EPIC) onboard National Oceanic and Atmospheric Administration (NOAA)’s Deep Space Climate Observatory (DSCOVR) spacecraft provides spectral reflectance of the entire sunlit Earth in the near backscattering direction every 65 to 110 min. Unlike EPIC, sensors onboard the Earth Orbiting Satellites (EOS) sample reflectance over swaths at a specific local solar time (LST) or over a fixed area. Such intrinsic sampling limits result in an apparent Earth’s reflectivity. We generated spectral reflectance over sampling areas using EPIC data. The difference between the EPIC and EOS estimates is an uncertainty in Earth’s reflectivity. We developed an Earth Reflector Type Index (ERTI) to discriminate between major Earth atmosphere components: clouds, cloud-free ocean, bare and vegetated land. Temporal variations in Earth’s reflectivity are mostly determined by clouds. The sampling area of EOS sensors may not be sufficient to represent cloud variability, resulting in biased estimates. Taking EPIC reflectivity as a reference, low-earth-orbiting-measurements at the sensor-specific LST tend to overestimate EPIC values by 0.8% to 8%. Biases in geostationary orbiting approximations due to a limited sampling area are between −0.7% and 12%. Analyses of ERTI-based Earth component reflectivity indicate that the disagreement between EPIC and EOS estimates depends on the sampling area, observation time and vary between −10% and 23%.The NASA/GSFC DSCOVR project is funded by NASA Earth Science Division. W. Song, G. Yan, and X. Mu were also supported by the key program of National Natural Science Foundation of China (NSFC; Grant No. 41331171). This research was conducted and completed during a 13-month research stay of the lead author in the Department of Earth and Environment, Boston University as a joint Ph.D. student, which was supported by the Chinese Scholarship Council (201606040098). DSCOVR EPIC L1B data were obtained from the NASA Langley Research Center Atmospheric Science Data Center. The authors would like to thank the editor who handled this paper and the two anonymous reviewers for providing helpful and constructive comments and suggestions that significantly helped us improve the quality of this paper. (NASA Earth Science Division; 41331171 - key program of National Natural Science Foundation of China (NSFC); 201606040098 - Chinese Scholarship Council)Accepted manuscrip

Down-regulation of microRNA-23b aggravates LPS-induced inflammatory injury in chondrogenic ATDC5 cells by targeting PDCD4

Objective(s): Osteoarthritis (OA), characterized by degradation of articular cartilage, is a leading cause of disability. As the only cell type present in cartilage, chondrocytes play curial roles in the progression of OA. In our study, we aimed to explore the roles of miR-23b in the lipopolysaccharide (LPS)-induced inflammatory injury. Materials and Methods: LPS-induced cell injury of ATDC5 cells was evaluated by the loss of cell viability, enhancement of cell apoptosis, alteration of apoptosis-associated proteins, and release of inflammatory cytokines. Then, miR-23b level after LPS treatment was assessed by qRT-PCR. Next, the effects of aberrantly expressed miR-23b on the LPS-induced inflammatory injury were explored. The possible target genes of miR-23b were virtually screened by informatics and verified by luciferase assay. Subsequently, whether miR-23b functioned through regulating the target gene was validated. The involved signaling pathways were investigated finally.Results: Cell viability was decreased but cell apoptosis, as well as release of inflammatory cytokines, was enhanced by LPS treatment. MiR-23b was down-regulated by LPS and its overexpression alleviated LPS-induced inflammatory injury. PDCD4, negatively regulated by miR-23b expression, was verified as a target gene of miR-23b. Following experiments showed miR-23b alleviated LPS-induced cell injury through down-regulating PDCD4 expression. Phosphorylated levels of key kinases in the NF-κB pathway, as well as expressions of key kinases in the Notch pathways, were increased by PDCD4 overexpression.Conclusion: MiR-23b was down-regulated after LPS treatment, and its overexpression ameliorated LPS-induced inflammatory injury in ATDC5 cells by targeting PDCD4, which could activate the NF-κB/Notch pathways

Analysis of Vegetation Vulnerability Dynamics and Driving Forces to Multiple Drought Stresses in a Changing Environment

Quantifying changes in the vulnerability of vegetation to various drought stresses in different seasons is important for rational and effective ecological conservation and restoration. However, the vulnerability of vegetation and its dynamics in a changing environment are still unknown, and quantitative attribution analysis of vulnerability changes has been rarely studied. To this end, this study explored the changes of vegetation vulnerability characteristics under various drought stresses in Xinjiang and conducted quantitative attribution analysis using the random forest method. In addition, the effects of ecological water transport and increased irrigation areas on vegetation vulnerability dynamics were examined. The standardized precipitation index (SPI), standardized precipitation-evapotranspiration index (SPEI), and standardized soil moisture index (SSMI) represent atmospheric water supply stress, water and heat supply stress, and soil water supply stress, respectively. The results showed that: (1) different vegetation types responded differently to water stress, with grasslands being more sensitive than forests and croplands in summer; (2) increased vegetation vulnerability under drought stresses dominated in Xinjiang after 2003, with vegetation growth and near-surface temperature being the main drivers, while increased soil moisture in the root zone was the main driver of decreased vegetation vulnerability; (3) vulnerability of cropland to SPI/SPEI/SSMI-related water stress increased due to the rapid expansion of irrigation areas, which led to increasing water demand in autumn that was difficult to meet; and (4) after ecological water transport of the Tarim River Basin, the vulnerability of its downstream vegetation to drought was reduced