The convergence of the alternating direction method of multipliers (ADMMs) algorithm to convex/nonconvex combinational optimization has been well established in the literature. Due to the extensive applications of a weakly convex function in signal processing and machine learning, in this paper, we investigate the convergence of an ADMM algorithm to the strongly and weakly convex combinational optimization (SWCCO) problem. Specifically, we firstly show the convergence of the iterative sequences of the SWCCO-ADMM under a mild regularity condition; then we establish the o(1/k) sublinear convergence rate of the SWCCO-ADMM algorithm using the same conditions and the linear convergence rate by imposing the gradient Lipschitz continuity condition on the objective function. The techniques used for the convergence analysis in this paper are fundamental, and we accomplish the global convergence without using the Kurdyka-Łojasiewicz (KL) inequality, which is common but complex in the proof of nonconvex ADMM.

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In this paper, the stabilization analysis problem of a bi‐directional coupled ODE‐PDE system is proposed. The spatially varying coefficient and the intermediate point interaction between the subsystems makes the coupled system more representative. An invertible infinite‐dimensional backstepping transformation is introducted to bring the original system into an exponentially stable target system. By employing the backstepping method, the kernel functions in the transformations are worked out under some assumptions of the spatially varying coefficient. Then, an explicit state‐feedback law is designed and the exponential stability of the transformed closed‐loop system has been also discussed. Finally, numerical simulation is provided to illustrate the effectiveness of the proposed design.

Cell cytotoxicity assays include cell activity assays and morphological identification assays. Currently, all frequently used cytotoxicity assays belong to cell activity assays but suffer from detection limitations. Morphological identification of cell death remains as the gold standard, although the method is difficult to scale up. At present there is no generally accepted morphological identification based cell cytotoxicity assay. In this study, we applied previous developed cell cytoplasm-localized fluorescent probe (CLFP) to display cell morphologies. Under fluorescence microscopy, the fluorescence morphology and intensity of living cells are distinct from dead cells. Based on these characters we extracted the images of living cells from series of samples via computational analysis. Thus, a novel cell morphological identification cytotoxicity assay (CLFP assay) is developed. The performance of the CLFP assay was similar to cell activity assay (MTT assay), but the accuracy of the CLFP assay was superior when measuring the cytotoxicity of active compounds.

A composite analysis‐based model for image restoration by utilising the image edge's well preserving property of the total variation (TV) and the sparsely representation capability of the wavelet frame‐based image restoration model is proposed. This model is an analysis‐based approach that the wavelet frame coefficient is quite often able to be linked with the smoothness of the image and is more in accord with the model's essence of TV model. This model is solved using the alternating direction method of multipliers fast iterative shrinkage‐thresholding algorithm and a faster alternating minimisation algorithm, and numerical experiments show that the proposed method is more suitable for image restoration.