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Recently, low-rank tensor completion (LRTC) methods by exploiting the global low-rankness of the target tensor have shown great potential for traffic data imputation. However, in real-world transportation networks, traffic data usually suffer from more complicated structural missing patterns than random-missing patterns, e.g., tube-missing patterns due to disruptions in wireless connections or slice-missing mechanism caused by sensor maintenance. As the naturally low-rank structure of traffic data in several missing scenarios, the existing LRTC methods indeed refrain from desirable performance for imputing traffic data. To tackle the complicated missing scenarios, we propose a convolutional low-rank tensor representation (CLRTR). Especially, CLRTR represents each unfolding matrix of the tensor as a sum of convolutions between two-dimensional (2D) filters and the corresponding low-rank coefficients, which allows us to simultaneously reveal the local patterns and the low-rankness of traffic data. Based on the CLRTR, we introduce the corresponding low-rank metric CLRTR-rank. Based on the suggested low-rank metric, we propose a traffic data imputation model that is well-suited to the complicated missing data scenarios. To implement the resultant imputation model, we design the alternating direction method of multipliers (ADMM) based algorithm with a theoretical convergence guarantee. Extensive numerical experiments on several real-world traffic datasets for both traffic data imputation and downstream traffic data prediction highlight the superiority of our model over the existing state-of-the-art matrix/tensor models for extensive missing scenarios.

Recently, tensor singular value decomposition (t-SVD), based on the tensor-tensor product (t-product), has become a powerful tool for processing third-order tensor data. However, constrained by the fact that the basic element is the fiber (i.e., vector) in the t-product, higher-order tensor data (i.e., order $d>3$) are usually unfolded into third-order tensors to satisfy the classical t-product setting, which leads to the destroying of high-dimensional structure. By revisiting the basic element in the t-product, we suggest a generalized t-product called element-based tensor-tensor product (elt-product) as an alternative of the classic t-product, where the basic element is a $(d-2)$th-order tensor instead of a vector. The benefit of the elt-product is that it can better preserve high-dimensional structures and that it can explore more complex interactions via higher-order convolution instead of first-order convolution in classic t-product. Starting from the elt-product, we develop new tensor-SVD and low-rank tensor metrics (e.g., rank and nuclear norm). Equipped with the suggested metrics, we present a tensor completion model for high-order tensor data and prove the exact recovery guarantees. To harness the resulting nonconvex optimization problem, we apply an alternating direction method of the multiplier (ADMM) algorithm with a theoretical convergence guarantee. Extensive experimental results on the simulated and real-world data (color videos, light-field images, light-field videos, and traffic data) demonstrate the superiority of the proposed model against the state-of-the-art baseline models.

Long-term management of inflammatory skin diseases is challenging because of side effects from repeated use of systemic treatments or topical corticosteroids. This study sought to identify mechanisms and developmental therapeutics for these diseases using genetic models and pharmacological approaches. We found mice overexpressing Smad7 in keratinocytes, but not mice overexpressing the N-terminal domain of Smad7 (N-Smad7), were resistant to imiquimod (IMQ)-induced Th1/17 and Th2 type inflammation. We generated a truncated Smad7 protein encompassing C-terminal Smad7 and PY motif fused with cell-penetrating Tat peptide (Tat-PYC-Smad7). Topically applied Tat-PYC-Smad7 to inflamed skin entered cells upon contact and attenuated IMQ-, 2,4-dinitrofluorobenzene- and tape-stripping-induced inflammation. RNAseq analyses of mouse skin exposed to these insults identified that in addition to inhibiting TGFβ/NFκB, Smad7 blunted IL22/STAT3 activation and associated pathogenesis, which is due to Smad7 transcriptionally upregulating IL22 antagonist IL22RA2. Mechanistically, Smad7 facilitated nuclear translocation and DNA binding of C/EBPβ to IL22RA2promoter for IL22RA2transactivation. Consistent to the above observations in mice, transcript levels of IL22RA2were increased in human atopic dermatitis and psoriasis lesions with clinical remission. Our study identified the anti-inflammation functional domain of Smad7 and suggests mechanism and feasibility for developing Smad7-based biologics as a topical therapy for skin inflammatory disorders.