Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descent

This paper considers the problem of recovering a tensor with an underlying low-tubal-rank structure from a small number of corrupted linear measurements. Traditional approaches tackling such a problem require the computation of tensor Singular Value Decomposition (t-SVD), that is a computationally intensive process, rendering them impractical for dealing with large-scale tensors. Aim to address this challenge, we propose an efficient and effective low-tubal-rank tensor recovery method based on a factorization procedure akin to the Burer-Monteiro (BM) method. Precisely, our fundamental approach involves decomposing a large tensor into two smaller factor tensors, followed by solving the problem through factorized gradient descent (FGD). This strategy eliminates the need for t-SVD computation, thereby reducing computational costs and storage requirements. We provide rigorous theoretical analysis to ensure the convergence of FGD under both noise-free and noisy situations. Additionally, it is worth noting that our method does not require the precise estimation of the tensor tubal-rank. Even in cases where the tubal-rank is slightly overestimated, our approach continues to demonstrate robust performance. A series of experiments have been carried out to demonstrate that, as compared to other popular ones, our approach exhibits superior performance in multiple scenarios, in terms of the faster computational speed and the smaller convergence error.Comment: 13 pages, 4 figure

RMT: Rule-based Metamorphic Testing for Autonomous Driving Models

Deep neural network models are widely used for perception and control in autonomous driving. Recent work uses metamorphic testing but is limited to using equality-based metamorphic relations and does not provide expressiveness for defining inequality-based metamorphic relations. To encode real world traffic rules, domain experts must be able to express higher order relations e.g., a vehicle should decrease speed in certain ratio, when there is a vehicle x meters ahead and compositionality e.g., a vehicle must have a larger deceleration, when there is a vehicle ahead and when the weather is rainy and proportional compounding effect to the test outcome. We design RMT, a declarative rule-based metamorphic testing framework. It provides three components that work in concert:(1) a domain specific language that enables an expert to express higher-order, compositional metamorphic relations, (2) pluggable transformation engines built on a variety of image and graphics processing techniques, and (3) automated test generation that translates a human-written rule to a corresponding executable, metamorphic relation and synthesizes meaningful inputs.Our evaluation using three driving models shows that RMT can generate meaningful test cases on which 89% of erroneous predictions are found by enabling higher-order metamorphic relations. Compositionality provides further aids for generating meaningful, synthesized inputs-3012 new images are generated by compositional rules. These detected erroneous predictions are manually examined and confirmed by six human judges as meaningful traffic rule violations. RMT is the first to expand automated testing capability for autonomous vehicles by enabling easy mapping of traffic regulations to executable metamorphic relations and to demonstrate the benefits of expressivity, customization, and pluggability

Tanshinone IIA suppresses fibrosis induced by high glucose conditions in HK-2 cells via inhibition of extracellular matrix deposition, reduction of oxidative stress, and inhibition of epithelial to mesenchymal transition

Purpose: To investigate the anti-fibrotic effects of tanshinone IIA (TS) on renal tubular epithelial cells (HK-2 cells) under high glucose conditions and their related molecular mechanism(s) of action.Methods: After treatment with TS (6 μg/mL) for 24 h, the morphology of HK-2 cells stimulated by high glucose was observed under the microscope. Additionally, potential mechanisms related to the antifibrosis effects of TS were evaluated using western blotting assay and quantitative real time PCR (qRTPCR), including transforming growth factor (TGF) β1, α-smooth muscle actin (α-SMA), heme oxygenase 1 (HO-1), laminin (LN), fibronectin (FN), and E-cadherin (E-cad).Results: A high-glucose culture environment induced fibrosis of HK-2 cells, as indicated by changes in cell morphology. The anti-fibrotic effects of TS were mainly associated with a decrease in the expression levels of TGF-β1, α-SMA and LN, while the expression of E-cad increased. These resultsalso revealed that TS increased the expressions of HO-1.Conclusion: The findings suggest that TS suppresses fibrosis caused by high glucose in HK-2 cells by inhibiting extracellular matrix deposition and epithelial-mesenchymal transition and by reducing oxidative stress. Further investigations are needed to evaluate the clinical application of this compound in diabetic nephropathy. Keywords: Tanshinone IIA, Diabetic nephropathy, HK-2 cells, Fibrosi

Representation and measurement of the beam health based on one-dimensional model

This paper proposes a method for online structural health evaluation, and analyzes the correlation between online monitoring data and structural health status. On the basis of this analysis, the structural health can be evaluated by using the deviation of the current status from the initially designed status. The health degree index, representation and measurement models are also defined for structural health evaluation in this work. A numerical case study is conducted to validate the related concept and health evaluation model using a beam under pressure loads. The results indicate that the proposed method can effectively represent the structural health status