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Osteoarthritis (OA) is a prevalent degenerative joint disease whose pathogenesis remains unclear. The research aims to investigate the roles of Circ_0136474/miR‐127‐5p/MMP‐13 axis in OA. Differentially expressed circRNAs and miRNAs in OA cartilage tissue were screened out and visualized by R project based on RNA‐seq data and microarray data respectively. qRT‐PCR was carried out for detection of relative expression levels of Circ_0136474, miR‐127‐5p, MMP‐13 and other inflammatory factors and Western blot analysis was conducted to detect the protein expression level of MMP‐13. CCK‐8 assay and flow cytometry were conducted to determine cell proliferation and cell apoptotic ability respectively. RNA‐fluorescence in situ hybridization (RNA‐FISH) experiments were conducted to confirm the immune‐localization of the Circ_0136474 and MMP‐13 in human tissues. Targeted relationships were predicted by bioinformatic analysis and verified by dual‐luciferase reporter assay. Our findings revealed that the expression levels of both Circ_0136474 and MMP‐13 in OA cartilage tissue were significantly higher than that in normal cartilage tissue. Circ_0136474 could suppress cell proliferation by facilitating MMP‐13 expression and suppressing miR‐127‐5p expression in OA. Overexpression of miR‐127‐5p negatively regulated MMP‐13 expression to enhance cell proliferation. Our study demonstrated that Circ_0136474 and MMP‐13 suppressed cell proliferation, while enhanced cell apoptosis by competitive binding to miR‐127‐5p in OA, which may well provide us with a new therapeutic strategy for osteoarthritis.

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A novel formulation of gradient-enhanced surrogate model, called weighted gradient-enhanced kriging, is proposed and used in combination with the cheap gradients obtained by the adjoint method to ameliorate the "curse of dimensionality". The core idea is to build a series of submodels with much smaller correlation matrices and then sum them up with appropriate weight coefficients, aiming to avoid the prohibitive cost associated with decomposing the large correlation matrix of a gradient-enhanced kriging. A self-contained derivation of the proposed method is presented, and then it is verified by surrogate modeling test cases. The present method is integrated into a surrogatebased optimizer and tested for design optimizations. It is further demonstrated for inverse design of a transonic wing, parameterized with a number of design variables in the range from 36 to 108, using Reynolds-averaged Navier-Stokes flow and adjoint solvers. It is observed that, for the wing design with 36 and 54 variables, the weighted and conventional gradient-enhanced kriging are comparable, and both are much more efficient than kriging without using any gradient. For the wing design with 72 and 108 variables, the cost of training a gradient-enhanced kriging increases rapidly and becomes prohibitive. In contrast, the cost of training a weighted gradient-enhanced kriging is kept in an acceptable level, which makes it more practical for higher-dimensional problems.