The use of nanomaterials for strain sensors has attracted attention due to their unique electromechanical properties. However, nanomaterials have yet to overcome many technological obstacles and thus are not yet the preferred material for strain sensors. In this work, we investigated graphene woven fabrics (GWFs) for strain sensing. Different than graphene films, GWFs undergo significant changes in their polycrystalline structures along with high-density crack formation and propagation mechanically deformed. The electrical resistance of GWFs increases exponentially with tensile strain with gauge factors of ~103 under 2~6% strains and ~106 under higher strains that are the highest thus far reported, due to its woven mesh configuration and fracture behavior, making it an ideal structure for sensing tensile deformation by changes in strain. The main mechanism is investigated, resulting in a theoretical model that predicts very well the observed behavior.

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Randomized algorithms for low-rank matrix approximation are investigated, with the emphasis on the fixed-precision problem and computational efficiency for handling large matrices. The algorithms are based on the so-called QB factorization, where Q is an orthonormal matrix. Firstly, a mechanism for calculating the approximation error in Frobenius norm is proposed, which enables efficient adaptive rank determination for large and/or sparse matrix. It can be combined with any QB-form factorization algorithm in which B's rows are incrementally generated. Based on the blocked randQB algorithm by P.-G. Martinsson and S. Voronin, this results in an algorithm called randQB EI. Then, we further revise the algorithm to obtain a pass-efficient algorithm, randQB FP, which is mathematically equivalent to the existing randQB algorithms and also suitable for the fixed-precision problem. Especially, randQB FP can serve as a single-pass algorithm for calculating leading singular values, under certain condition. With large and/or sparse test matrices, we have empirically validated the merits of the proposed techniques, which exhibit remarkable speedup and memory saving over the blocked randQB algorithm. We have also demonstrated that the single-pass algorithm derived by randQB FP is much more accurate than an existing single-pass algorithm. And with data from a scenic image and an information retrieval application, we have shown the advantages of the proposed algorithms over the adaptive range finder algorithm for solving the fixed-precision problem.

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Principal component analysis (PCA) is a fundamental dimension reduction tool in statistics and machine learning. For large and high-dimensional data, computing the PCA (i.e., the top singular vectors of the data matrix) becomes a challenging task. In this work, a single-pass randomized algorithm is proposed to compute PCA with only one pass over the data. It is suitable for processing extremely large and high-dimensional data stored in slow memory (hard disk) or the data generated in a streaming fashion. Experiments with synthetic and real data validate the algorithm's accuracy, which has orders of magnitude smaller error than an existing single-pass algorithm. For a set of highdimensional data stored as a 150 GB file, the algorithm is able to compute the first 50 principal components in just 24 minutes on a typical 24-core computer, with less than 1 GB memory cost.