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Numerical discretization of a regularized inverse source problem leads to a non-symmetric saddle point linear system. Interestingly, the Schur complement of the non-symmetric saddle point system is Hermitian positive definite (HPD). Then, we propose a preconditioner matching the Schur complement (MSC). Theoretically, we show that the preconditioned conjugate gradient (PCG) method for a linear system with the preconditioned Schur complement as coefficient has a linear convergence rate independent of the matrix size and value of the regularization parameter involved in the inverse problem. Fast implementations are proposed for the matrix-vector multiplication of the preconditioned Schur complement so that the PCG solver requires only quasi-linear operations. To the best of our knowledge, this is the first solver with guarantee of linear convergence for the inversion of Schur complement arising from the discrete inverse problem. Combining the PCG solver for inversion of the Schur complement and the fast solvers for the forward problem in the literature, the discrete inverse problem (the saddle point system) is solved within a quasi-linear complexity. Numerical results are reported to show the performance of the proposed matching Schur complement (MSC) preconditioning technique. • A fast solver for a regularized inverse problem. • The solver is robust w.r.t. regularization parameters and discretization parameters. • The complexity of the solver is nearly linear (optimal). [ABSTRACT FROM AUTHOR]

We develop and study incremental algorithms for truncated higher-order singular value decompositions. By combining the SVD updating and different truncated higher-order singular value decompositions, two incremental algorithms are proposed. Not only the factor matrices but also the core tensor are updated in an incremental style. The costs of these algorithms are compared and the approximation errors are analyzed. Numerical results demonstrate that the proposed incremental algorithms have advantages in online computation. [ABSTRACT FROM AUTHOR]

Using declassified colonial and British records in Hong Kong and London, as well as memoirs of former leftists and newspapers, this article explores the strategies the Hong Kong colonial government employed in a propaganda campaign to garner political support of the rural population in the New Territories, a porous land frontier during the Cold War. It also analyses the varying political orientations of migrant farmers, who often had received economic benefits from both the colonial government and the leftist organizations. This article reveals that the colonial government established the Vegetable Marketing Organization (VMO), a state-owned enterprise, to first nationalize the vegetable wholesale market in the immediate post-war period, and subsequently used it to combat increasing political influence and anti-government activities of the communist-controlled Society of Plantations. Despite the improvement of the livelihood of immigrant farmers, the VMO Scheme failed to out-compete the Society economically, which was ultimately eliminated by draconian measures. Through studying the agrarian politics and economic contestations in Hong Kong's rural area, this article provides a lens on how the Cold War was played out at a village level in East Asia. [ABSTRACT FROM AUTHOR]

Florence Mok's book, "Covert Colonialism: Governance, Surveillance and Political Culture in British Hong Kong, c. 1966–97," challenges the prevailing belief in Hong Kong that foreign governments manipulated the massive rallies in the city. Mok argues that politics in colonial Hong Kong were not characterized by a lack of political activism, but rather by a complex interaction between political activists and the colonial government. The book reveals how the colonial government employed a secretive polling mechanism to monitor and respond to growing political activism and changing public opinion, a mechanism Mok terms "covert colonialism." The book also explores various protest movements in colonial Hong Kong and their impact on political culture. Overall, "Covert Colonialism" provides a nuanced understanding of Hong Kong's political history and challenges the myth of political apathy and stability in the city. [Extracted from the article]

This paper studies deep neural networks for solving extremely large linear systems arising from high-dimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such extremely large linear systems. Our idea is to employ a neural network to characterize the solution with many fewer parameters than the size of the solution under a matrix-free setting. We present an error analysis of the proposed method, indicating that the solution error is bounded by the condition number of the matrix and the neural network approximation error. Several numerical examples from partial differential equations, queueing problems, and probabilistic Boolean networks are presented to demonstrate that the solutions of linear systems can be learned quite accurately. [ABSTRACT FROM AUTHOR]

One of the key problems in tensor completion is the number of uniformly random sample entries required for recovery guarantee. The main aim of this paper is to study n 1 × n 2 × n 3 third-order tensor completion based on transformed tensor singular value decomposition, and provide a bound on the number of required sample entries. Our approach is to make use of the multi-rank of the underlying tensor instead of its tubal rank in the bound. In numerical experiments on synthetic and imaging data sets, we demonstrate the effectiveness of our proposed bound for the number of sample entries. Moreover, our theoretical results are valid to any unitary transformation applied to n 3 -dimension under transformed tensor singular value decomposition. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. The aim is to find a low rank approximation for nonnegative matrix M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to solve while it can be solved efficiently under a separability assumption, which requires that the columns of the factor matrix are some columns of the input matrix M. In this paper, we generalize the separability assumption based on 3-factor NMF (M = P1SP2), and require that S is a submatrix of the input matrix M. We refer to this NMF as a Coseparable NMF (CoS-NMF). In the paper, we discuss and study mathematical properties of CoS-NMF, and present its relationships with other matrix factorizations such as generalized separable NMF, tri-symNMF, biorthogonal trifactorization and CUR decomposition. An optimization method for CoS-NMF is proposed, and an alternating fast gradient method is employed to determine the rows and the columns of M for the submatrix S. Numerical experiments on synthetic data sets, document data sets, and facial data sets are conducted to verify the effectiveness of the proposed CoS-NMF model. By comparison with state-of-the-art methods, the CoS-NMF model performs very well in a coclustering task by finding useful features, and keeps a good approximation to the input data matrix as well. [ABSTRACT FROM AUTHOR]

This paper studies the phase-only reconstruction problem of recovering a complexvalued signal x in Cd from the phase of Ax where A is a given measurement matrix in Cmxd. The reconstruction, if possible, should be up to a positive scaling factor. By using the rank of discriminant matrices, uniqueness conditions are derived to characterize whether the underlying signal can be uniquely reconstructed. We are also interested in the problem of minimal measurement number. We show that at least 2d but no more than 4d - 2 measurements are needed for the reconstruction of all x ∈ Cd, whereas the minimal measurement number is exactly 2d - 1 if we pursue the recovery of almost all signals. Moreover, when adapted to the phase-only reconstruction of x ∈ Rd, our uniqueness conditions are more practical and general than existing ones. Our theoretical results can be straightforwardly extended to affine phase-only reconstruction where the phase of Ax + b is observed for some b ∈ Cm. [ABSTRACT FROM AUTHOR]

Graph Convolution Networks (GCNs) have been shown to be very effective in utilizing pair-wise relationships across samples. They have been successfully applied to solve various machine learning problems in practice. In many applications, the construction of GCNs involves more than one layer. However, their generalization and stability analysis are limited. The main aim of this paper is to analyze GCNs with two layers. The formulation is based on transductive semi-supervised learning and the filtering is done in the eigen-domain. We show the uniform stability of the neural network and the convergence of the generalization gap to zero. The analysis of two-layer GCN is more involved than the single-layer case and requires some new estimates of the neural network's quantities. The analysis confirms the usefulness of GCNs. It also sheds light on the design of the neural network, for instance, how the data should be scaled to achieve the uniform stability of the learning process. Some experimental results on benchmark datasets are presented to illustrate the theory. [ABSTRACT FROM AUTHOR]

The class of multi-relational graph convolutional networks (MRGCNs) is a recent extension of standard graph convolutional networks (GCNs) to handle heterogenous graphs with multiple types of relationships. MRGCNs have been shown to yield results superior than traditional GCNs in various machine learning tasks. The key idea is to introduce a new kind of convolution operated on tensors that can effectively exploit correlations exhibited in multiple relationships. The main objective of this paper is to analyze the algorithmic stability and generalization guarantees of MRGCNs to confirm the usefulness of MRGCNs. Our contributions are of three folds. First, we develop a matrix representation of various tensor operations underneath MRGCNs to simplify the analysis significantly. Next, we prove the uniform stability of MRGCNs and deduce the convergence of the generalization gap to support the usefulness of MRGCNs. The analysis sheds lights on the design of MRGCNs, for instance, how the data should be scaled to achieve the uniform stability of the learning process. Finally, we provide experimental results to demonstrate the stability results. [ABSTRACT FROM AUTHOR]

Objective: To consolidate the evidence on the effect of physical exercise on fear of falling in individuals with stroke. Data Sources: PubMed, CINAHL, Cochrane Database and MEDLINE Methods: An extensive database search was conducted to identify the randomised controlled trials that examined the effect of physical exercise on fear of falling post-stroke. Grading of Recommendation, Assessment, Development and Evaluation (GRADE) was used to assess the quality of evidence for each meta-analysis. Results: Fourteen trials totalling 1211 participants were included in this review. Thirteen of these (1180 participants) were included in the meta-analyses. In the primary analysis, very low-quality evidence suggested that exercise reduced fear of falling post-stroke (standardized mean difference (SMD) 0.48; 95% confidence interval (CI) 0.23 to 0.72). The effect was diminished at three- to six-month follow-up after exercise training ended (SMD −0.09; 95% CI −0.27 to 0.10; high-quality evidence). In the sensitivity analyses, the treatment effect was more pronounced in individuals with a lower baseline Berg balance score (BBS ≤45; SMD 0.53; 95%CI 0.17 to 0.88) and for those trials with exercise frequency of ≥3 sessions per week (SMD 0.70; 95%CI 0.39 to 1.01). Compared with circuit-based training consisting of a combination of walking, balance and strengthening exercises (SMD 0.27; 95% CI −0.09 to 0.63), walking programmes seemed to generate a larger effect on fear of falling (SMD 1.06; 95%CI 0.43 to 1.70). Conclusion: Physical exercise was beneficial for reducing fear of falling in individuals with stroke, particularly those with poorer balance ability. [ABSTRACT FROM AUTHOR]

Semiconductor nanorods have often been observed to emit polarized light. This property can be useful for emission applications such as displays, optical communications, and biological labeling. Recently, many researchers have tried to replace nanocrystals containing toxic metals, such as Cd or Pb, with alternatives that can also demonstrate polarized emission. Here a low temperature injection (LTI) method with a relatively short chain octylammonium bromide ligand precursor is used to slow down the nanorod formation reaction and the controlled anisotropic growth of Cs3Cu2Br5 nanorods is realized, producing more uniform samples of nanorods with higher aspect ratios than those previously reported. Such nanorods exhibit a very high degree of polarization (DOP) of 0.88 ± 0.04 for single rods, and a corresponding polarization anisotropy of 0.26 for the sample population, both the highest yet reported for any perovskite‐like material. Further this method can be extended to produce Cs3Cu2Cl5 nanorods as well, allowing for broad tuning of their optical properties. [ABSTRACT FROM AUTHOR]

In this paper, we study deep neural networks (DNNs) for solving high-dimensional evolution equations with oscillatory solutions. Different from deep least-squares methods that deal with time and space variables simultaneously, we propose a deep adaptive basis Galerkin (DABG) method which employs the spectral-Galerkin method for time variable by a tensor-product basis for oscillatory solutions and the deep neural network method for high-dimensional space variables. The proposed method can lead to a linear system of differential equations having unknown DNNs that can be trained via the loss function. We establish a posteriori estimates of the solution error which is bounded by the minimal loss function and the term O(N-m), where N is the number of basis functions and m characterizes the regularity of the equation, and show that if the true solution is a Barron-type function, the error bound converges to zero as M = O(Np) approaches to infinity where M is the width of the used networks and p is a positive constant. Numerical examples, including high-dimensional linear parabolic and hyperbolic equations, and a nonlinear Allen--Cahn equation are presented to demonstrate that the performance of the proposed DABG method is better than that of existing DNNs. [ABSTRACT FROM AUTHOR]

Poisson observations for videos are important models in video processing and computer vision. In this paper, we study the third-order tensor completion problem with Poisson observations. The main aim is to recover a tensor based on a small number of its Poisson observation entries. A existing matrix-based method may be applied to this problem via the matricized version of the tensor. However, this method does not leverage on the global low-rankness of a tensor and may be substantially suboptimal. Our approach is to consider the maximum likelihood estimate of the Poisson distribution, and utilize the Kullback-Leibler divergence for the data-fitting term to measure the observations and the underlying tensor. Moreover, we propose to employ a transformed tensor nuclear norm ball constraint and a bounded constraint of each entry, where the transformed tensor nuclear norm is used to get a lower transformed multi-rank tensor with suitable unitary transformation matrices. We show that the upper bound of the error of the estimator of the proposed model is less than that of the existing matrix-based method. Also an information theoretic lower error bound is established. An alternating direction method of multipliers is developed to solve the resulting convex optimization model. Extensive numerical experiments on synthetic data and real-world datasets are presented to demonstrate the effectiveness of our proposed model compared with existing tensor completion methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel method for solving high-dimensional spectral fractional Laplacian equations. Using the Caffarelli--Silvestre extension, the d-dimensional spectral fractional equation is reformulated as a regular partial differential equation of dimension d+1. We transform the extended equation as a minimal Ritz energy functional problem and search for its minimizer in a special class of deep neural networks. Moreover, based on the approximation property of networks, we establish estimates on the error made by the deep Ritz method. Numerical results are reported to demonstrate the effectiveness of the proposed method for solving fractional Laplacian equations up to 10 dimensions. Technically, in this method, we design a special network-based structure to adapt to the singularity and exponential decaying of the true solution. Also, a hybrid integration technique combining the Monte Carlo method and sinc quadrature is developed to compute the loss function with higher accuracy. [ABSTRACT FROM AUTHOR]

Recently, deep-learning-based denoising methods for hyperspectral images (HSIs) have been comprehensively studied and achieved impressive performance because they can effectively extract complex and nonlinear image features. Compared with deep-learning-based methods, the nonlocal similarity-based denoising methods are more suitable for images containing edges or regular textures. We propose a powerful HSI denoising method, termed non-local 3-D convolutional neural network (NL-3DCNN), combining traditional machine learning and deep learning techniques. NL-3DCNN exploits the high spectral correlation of an HSI using subspace representation, and the corresponding representation coefficients are termed eigenimages. The high spatial correlation in eigenimages is exploited by grouping nonlocal similar patches, which are denoised by a 3-D convolutional neural network. The numerical and graphical denoising results of the simulated and real data show that the proposed method is superior to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The coronavirus disease 2019 (COVID‐19) pandemic has brought about many changes in the relationships between high‐income countries and partner organisations in low‐ or low–middle‐income countries, such as predominate in sub‐Saharan Africa. Medicine, surgery and in particular urology is no exception to the changes that COVID‐19 has demanded. Urolink represents the British Association of Urological Surgeons (BAUS) on the global urology stage and has been deleteriously impacted by the pandemic. Education, one of the pillars of Urolink's founding philosophies, has conventionally been delivered by face‐to face teaching, training, or mentoring by UK urologists at their host's site outside of the UK. As a consequence of the inability to travel due to the pandemic, BAUS Urolink has evolved a virtual on‐line webinar package evolved by, and delivered between, urologists in Lusaka, Zambia, and various centres in the UK. The aim was to deliver curricular‐based educational topics to trainees in both countries. This programme has generated a number of live webinars and archived recordings during the pandemic that has proven accessible and educationally acceptable to trainees in the UK and Zambia. This webinar series has also generated relationships between young urologists on different continents, given each a different view of healthcare delivery outside of their country of origin at no appreciable cost, and would appear to be an educational mechanism that is durable for, and applicable to, a wider participation in the post‐pandemic world. [ABSTRACT FROM AUTHOR]

In this paper, we first give new model formulations for computing arbitrary generalized singular value of a Grassmann matrix pair or a real matrix pair. In these new formulations, we need to solve matrix optimization problems with unitary constraints or orthogonal constraints. We propose a geometric inexact Newton--conjugate gradient (Newton-CG) method for solving the resulting matrix optimization problems. Under some mild assumptions, we establish the global and quadratic convergence of the proposed method for the complex case. Some numerical examples are given to illustrate the effectiveness and high accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Primary choroidal lymphoma is a rare, slowly progressive intraocular malignancy. Most are low grade B cell lymphomas, often involving tissues adjacent to the choroid such as the subconjunctival space, lacrimal gland or orbit. Ideally, these lesions are biopsied to establish histopathological diagnosis. The most accessible ocular structure is biopsied. Obtaining tissue by transvitreal choroidal biopsy imparts a small but significant risk of ocular morbidity, including the need for multiple surgeries, retinal detachment and vision loss. External beam radiotherapy (EBRT) is a common and effective treatment of low-grade lymphomas. EBRT has been found to very successfully treat primary marginal zone lymphomas of the ocular adnexa, which are typically of the same cell type as most primary choroid lymphomas. Ultra-low dose EBRT, most commonly using a total dose of 4 Gy, has been shown to be as effective as higher doses of radiotherapy for follicular or marginal zone lymphomas. The use of this low dose regimen for conjunctival lymphomas has been recently explored. The role of EBRT, and especially ultra-low dose EBRT, for treatment of primary choroidal lymphoma has been confined to case reports. We describe a case of presumed primary choroidal lymphoma diagnosed on clinical findings alone as the risks of ocular biopsy were deemed too high, and report outcome following treatment with ultra-low dose EBRT. [ABSTRACT FROM AUTHOR]

This paper proposes a novel deep learning (DL) based source reconstruction method (SRM). The proposed DL-based SRM employs the deep convolutional asymmetric encoder–decoder structure (DCAEDS), which only demands one-time single-frequency far-field measurement on EM scattered field as its input and further predicts the equivalent source on target scatterers. During the offline training, an EM scattering simulator is designed to compute EM scattered field originated from the predicted equivalent source on target scatterers. The DCAEDS is combined with the EM scattering simulator to optimize the loss function, including two parts: (1) Data-induced loss, which directly evaluates the difference between the prediction of the proposed DCAEDS and the true-labelled equivalent source of target scatterers; (2) Physics-induced loss, which evaluates the difference between received EM scattered field and the computed EM scattered field originated from the prediction of DCAEDS. Moreover, the proposed DL-based SRM can overcome the limitation of conventional methods, involving high computation cost and strong ill-conditions. Consequently, the proposed DL-based SRM can realize the reconstruction of the equivalent current source with higher accuracy and lower computation complexity. Numerical examples illustrate the feasibility of the proposed DL-based SRM, which opens the new path for DL-based EM computation approaches. [ABSTRACT FROM AUTHOR]

We study a class of spectral learning methods with dependent observations, including popular ridge regression, Landweber iteration, spectral cut-off and so on. We derive an explicit risk bound in terms of the correlation of the observations, regularity of the regression function, and effective dimension of the reproducing kernel Hilbert space. By appropriately choosing regularization parameter according to the sample size, the risk bound yields a nearly optimal learning rate with a logarithmic term for strongly mixing sequences. We thus extend the applicable range of spectral algorithm to non-i.i.d. sampling process. Particularly, it is shown that the learning rates for i.i.d. samples in the literature refer to our special case, i.e., the mixing condition parameter tends to zero. [ABSTRACT FROM AUTHOR]

Summary: Robust Principal Component Analysis plays a key role in various fields such as image and video processing, data mining, and hyperspectral data analysis. In this paper, we study the problem of robust tensor train (TT) principal component analysis from partial observations, which aims to decompose a given tensor into the low TT rank and sparse components. The decomposition of the proposed model is used to find the hidden factors and help alleviate the curse of dimensionality via a set of connected low‐rank tensors. A relaxation model is to minimize a weighted combination of the sum of nuclear norms of unfolding matrices of core tensors and the tensor ℓ1 norm. A proximal alternating direction method of multipliers is developed to solve the resulting model. Furthermore, we show that any cluster point of the convergent subsequence is a Karush‐Kuhn‐Tucker point of the proposed model under some conditions. Extensive numerical examples on both synthetic data and real‐world datasets are presented to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

• Making use of the nonnegativity and the support constraints as well as the dictionary learning approach. • Establishing a blind deconvolution model to determine the inverse filter and the deblurred image. • Using sparse and redundant representations of the objective deblurred image over learned dictionaries. • The objective image can be represented with more details by the dictionary basis. In this paper, we study a novel inverse filtering method by using a dictionary approach. The main idea is to combine a learned dictionary for the representation of the deconvoluted image and an inverse filter based on nonnegativity and support constraints, to deconvolute the observed image with an unknown point spread function. The advantage of this approach is that the target image can be represented with more details by learned basis in the dictionary. We also employ the alternating direction method of multipliers to solve the resulting optimization problem. Experimental results are presented to show that the performance of the proposed methods are better than other testing methods for several testing images. [ABSTRACT FROM AUTHOR]

In [McDonald, Pestana, and Wathen, SIAM J. Sci. Comput., 40 (2018), pp. A1012--A1033], a block circulant preconditioner is proposed for all-at-once linear systems arising from evolutionary partial differential equations, in which the preconditioned matrix is proven to be diagonalizable and to have identity-plus-low-rank decomposition in the case of the heat equation. In this paper, we generalize the block circulant preconditioner by introducing a small parameter ϵ>0 into the top-right block of the block circulant preconditioner. The implementation of the generalized preconditioner requires the same computational complexity as that of the block circulant one. Theoretically, we prove that (i) the generalization preserves the diagonalizability and the identity-plus-low-rank decomposition; (ii) all eigenvalues of the new preconditioned matrix are clustered at 1 for sufficiently small\epsilon; (iii) GMRES method for the preconditioned system has a linear convergence rate independent of size of the linear system when\epsilon is taken to be smaller than or comparable to square root of time-step size. Numerical results are reported to confirm the efficiency of the proposed preconditioner and to show that the generalization improves the performance of block circulant preconditioner. [ABSTRACT FROM AUTHOR]

In practical applications, incremental tensors are very common: only a portion of tensor data is available, and new data are arriving in the next time step or continuously over time. To handle this type of tensors time-saving algorithms are required for online computation. In this paper, we consider incremental CP ( CANDECOMP/PARAFAC ) decomposition, which requires one to update the CP decomposition after new tensor data, together with the exiting tensor, are ready for analysis. There exist several incremental CP decomposition algorithms, but almost all of these algorithms assume that the number of CP decomposition components remains fixed in the incremental process. The main contribution of this paper is the study of how to add components in the incremental CP decomposition. We derive the coordinate representation of the incremental CP decomposition with respect to a special basis and show related properties of tensor rank and the uniqueness of such incremental CP decomposition. Under the framework of this representation, the proposed method can be solved by using an alternating minimization algorithm. Numerical examples are presented to show the good performance of the proposed algorithms in terms of computational time and data fitting compared with existing methods. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to develop the quaternion generalized minimal residual method (QGMRES) for solving quaternion linear systems. Quaternion linear systems arise fromthree-dimensional or color imaging filtering problems. The proposed quaternion Arnoldi procedure can preserve quaternion Hessenberg form during the iterations. The main advantage is that the storage of the proposed iterative method can be reduced by comparing with the Hessenberg form constructed by the classical GMRES iterations for the real representation of quaternion linear systems. The convergence of the proposed QGMRES is also established. Numerical examples are presented to demonstrate the effectiveness of the proposed QGMRES compared with the traditional GMRES in terms of storage and computing time [ABSTRACT FROM AUTHOR]

Multiple graph clustering is an important tool in data integration and data mining for graph-based data. The prediction and classification accuracy can be significantly improved by integrating information from multiple sources and data sets. The aim of multiple graph clustering is to partition objects into several clusters such that clusters in each graph are well-separated and clusters across different graphs are consistent. Existing methods assume that the degrees of association among different graphs are the same. However, some graphs may be strongly or weakly associated with the other graphs due to high or low correlation of their associated cluster structures. When their cluster structures are (or are not) similar, their degree of association should be high (or low). Accurate clustering results can be obtained by integrating such association information in multiple graphs. The main aim of this paper is to study multiple graph semi-supervised clustering by considering a large amount of multiple graph data and a small amount of labeled data. We propose a constrained optimization problem that can determine cluster structures and degrees of association simultaneously in multiple graph clustering. In our formulation, we make use of orthogonality for cluster structure indicator and cosine correlation for degree of association. With orthogonality constraint in the clustering process, we develop a gradient flow method to solve the resulting optimization problem. And the convergence of the proposed iterative method is also shown. Numerical examples including synthetic data and real data sets with few known labels are tested, and are presented to show the efficiency and effectiveness of our proposed method compared with the testing methods in the literature. [ABSTRACT FROM AUTHOR]

• Previously we identified a causal association of Dupuytren's Disease (DD) with a non-synonymous SNP variant (rs1042704, p.D273N) of MT1-MMP. • We discovered that this SNP variant MT1-MMP (MT1-N 273) exhibits only 17% of cell surface collagenolytic activity compared to the ancestral form of MT1-MMP (MT1-D 273). • DD patients myofibroblasts with heterozygous (G/A) and homozygous (A/A) SNP genotypes exhibited around 30% of collagen degrading activities in comparison to cells with wild-type (G/G) genotype. • Low collagenolytic activity of the SNP would contribute to the fibrotic phenotype of DD. Dupuytren's Disease (DD) is a common fibroproliferative disease of the palmar fascia. We previously identified a causal association with a non-synonymous variant (rs1042704, p.D273N) in MMP14 (encoding MT1-MMP). In this study, we investigated the functional consequences of this variant, and demonstrated that the variant MT1-MMP (MT1-N 273) exhibits only 17% of cell surface collagenolytic activity compared to the ancestral enzyme (MT1-D 273). Cells expressing both MT1-D 273 and MT1-N 273 in a 1:1 ratio, mimicking the heterozygous state, possess 38% of the collagenolytic activity compared to the cells expressing MT1-D 273 , suggesting that MT1-N 273 acts in a dominant negative manner. Consistent with the above observation, patient-derived DD myofibroblasts with the alternate allele demonstrated around 30% of full collagenolytic activity detected in ancestral G/G genotype cells, regardless of the heterozygous (G/A) or homozygous (A/A) state. Small angle X-ray scattering analysis of purified soluble Fc-fusion enzymes allowed us to construct a 3D-molecular envelope of MT1-D 273 and MT1-N 273 , and demonstrate altered flexibility and conformation of the ectodomains due to D 273 to N substitution. Taking together, rs1042704 significantly reduces collagen catabolism in tissue, which tips the balance of homeostasis of collagen in tissue, contributing to the fibrotic phenotype of DD. Since around 30% of the worldwide population have at least one copy of the low collagenolytic alternate allele, further investigation of rs1042704 across multiple pathologies is needed. [ABSTRACT FROM AUTHOR]

In this paper, we study nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ ONTD on the image data sets from the real world applications including face recognition, image representation, and hyperspectral unmixing. Numerical results are shown to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Non-Lipschitz regularization has got much attention in image restoration with additive noise removal recently, which can preserve neat edges in the restored image. In this paper, we consider a class of minimization problems with gradient compounded non-Lipschitz regularization applied to non-additive noise removal, with Poisson and multiplicative one as examples. The existence of a solution of the general model is discussed. We also extend the recent iterative support shrinkage strategy to give an algorithm to minimize it, where the subproblem at each iteration is allowed to be solved inexactly. Moreover, this paper is the first one to give the subdifferential of the gradient compounded non-Lipschitz regularization term, based on which we are able to establish the global convergence of the iterative sequence to a stationary point of the original objective function. This is, to our best knowledge, stronger than all the convergence results for gradient compounded non-Lipschitz minimization problems in the current published literature. Numerical experiments show that our proposed method performs well. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inverse problem with quasi-boundary value regularization for recovering a source term of the time fractional diffusion equations from the final observation data. In particular, a two-by-two block linear system arising from the problem is studied. We propose a fast preconditioning technique by approximating the Schur complement in the system using a product of some factors, motivated by an approximate diagonalization of one of the blocks. The eigenvalues of the preconditioned system are shown to be clustered around 1, and the fast convergence of the methods is guaranteed theoretically. We also present an approach for selecting the regularization parameter of the quasi-boundary value method. Numerical experiments are carried out to demonstrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

Although image denoising as a basic task of image restoration has been widely studied in the past decades, there are not many studies on mixed noise denoising. In this paper, we propose two structured dictionary learning models to recover images corrupted by mixed Gaussian and impulse noise. These two models can be merged as $\ell _{p}$ -norm fidelity plus $\ell _{q}$ -norm regularization. The fidelity term is used to fit image patches and the regularization term is employed for sparse coding. Particularly, we utilize proximal (and proximal linearized) alternating minimization methods as the main solvers to deal with these two models. We remove the Gaussian noise under the assumption that the uncorrupted image can be approximated with a linear representation under an appropriate orthogonal basis. We use different ways to remove impulse noise for these two models. The experimental results are reported to compare the existing methods and demonstrate the performance of the proposed denoising model is better than the other existing methods in terms of some quality assessment metrics. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to develop a framelet representation of the tensor nuclear norm for third-order tensor recovery. In the literature, the tensor nuclear norm can be computed by using tensor singular value decomposition based on the discrete Fourier transform matrix, and tensor completion can be performed by the minimization of the tensor nuclear norm which is the relaxation of the sum of matrix ranks from all Fourier transformed matrix frontal slices. These Fourier transformed matrix frontal slices are obtained by applying the discrete Fourier transform on the tubes of the original tensor. In this paper, we propose to employ the framelet representation of each tube so that a framelet transformed tensor can be constructed. Because of framelet basis redundancy, the representation of each tube is sparsely represented. When the matrix slices of the original tensor are highly correlated, we expect the corresponding sum of matrix ranks from all framelet transformed matrix frontal slices would be small, and the resulting tensor completion can be performed much better. The proposed minimization model is convex and global minimizers can be obtained. Numerical results on several types of multi-dimensional data (videos, multispectral images, and magnetic resonance imaging data) have tested and shown that the proposed method outperformed the other testing methods. [ABSTRACT FROM AUTHOR]

Summary: In this article, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by using other unitary transform matrices than that by using discrete Fourier transform matrix. This would be more effective for robust tensor completion. Experimental results for hyperspectral, video and face datasets have shown that the recovery performance for the robust tensor completion problem by using transformed tensor SVD is better in peak signal‐to‐noise ratio than that by using Fourier transform and other robust tensor completion methods. [ABSTRACT FROM AUTHOR]

Summary: The higher order singular value decomposition, which is regarded as a generalization of the matrix singular value decomposition (SVD), has a long history and is well established, while the T‐SVD is relatively new and lacks systematic analysis. Because of the unusual tensor‐tensor product that the T‐SVD is based on, the form of the T‐SVD may be difficult to comprehend. The main aim of this article is to establish a connection between these two decompositions. By converting the form of the T‐SVD into the sum of outer product terms, we compare the forms of the two decompositions. Moreover, from establishing the connection, a new decomposition which has a specific nonzero pattern, is proposed and developed. Numerical examples are given to demonstrate the useful ability of the new decomposition for approximation and data compression. [ABSTRACT FROM AUTHOR]

In this paper, circulant preconditioners are studied for discretized matrices arising from finite difference schemes for a kind of spatial fractional diffusion equations. The fractional differential operator is comprised of left-sided and right-sided derivatives with order in (1 2 , 1) . The resulting discretized matrices preserve Toeplitz-like structure and hence their matrix-vector multiplications can be computed efficiently by the fast Fourier transform. Theoretically, the spectra of the circulant preconditioned matrices are shown to be clustered around 1 under some conditions. Numerical experiments are presented to demonstrate that the preconditioning technique is very efficient. [ABSTRACT FROM AUTHOR]

In many color image processing and recognition applications, one of the most important targets is to compute the optimal low-rank approximations to color images, which can be reconstructed with a small number of dominant singular value decomposition (SVD) triplets of quaternion matrices. All existing methods are designed to compute all SVD triplets of quaternion matrices at first and then to select the necessary dominant ones for reconstruction. This way costs quite a lot of operational flops and CPU times to compute many superfluous SVD triplets. In this paper, we propose a Lanczos-based method of computing partial (several dominant) SVD triplets of the large-scale quaternion matrices. The partial bidiagonalization of large-scale quaternion matrices is derived by using the Lanczos iteration, and the reorthogonalization and thick-restart techniques are also utilized in the implementation. An algorithm is presented to compute the partial quaternion singular value decomposition. Numerical examples, including principal component analysis, color face recognition, video compression and color image completion, illustrate that the performance of the developed Lanczos-based method for low-rank quaternion approximation is better than that of the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Ninety per cent of the human population has been right-handed since the Paleolithic, yet the brain signature and genetic basis of handedness remain poorly characterized. Here, we correlated brain imaging phenotypes from ∼9000 UK Biobank participants with handedness, and with loci found significantly associated with handedness after we performed genome-wide association studies (GWAS) in ∼400 000 of these participants. Our imaging-handedness analysis revealed an increase in functional connectivity between left and right language networks in left-handers. GWAS of handedness uncovered four significant loci (rs199512, rs45608532, rs13017199, and rs3094128), three of which are in-or expression quantitative trait loci of-genes encoding proteins involved in brain development and patterning. These included microtubule-related MAP2 and MAPT, as well as WNT3 and MICB, all implicated in the pathogenesis of diseases such as Parkinson's, Alzheimer's and schizophrenia. In particular, with rs199512, we identified a common genetic influence on handedness, psychiatric phenotypes, Parkinson's disease, and the integrity of white matter tracts connecting the same language-related regions identified in the handedness-imaging analysis. This study has identified in the general population genome-wide significant loci for human handedness in, and expression quantitative trait loci of, genes associated with brain development, microtubules and patterning. We suggest that these genetic variants contribute to neurodevelopmental lateralization of brain organization, which in turn influences both the handedness phenotype and the predisposition to develop certain neurological and psychiatric diseases. [ABSTRACT FROM AUTHOR]

In this paper, we study a discretization scheme and the corresponding fast solver for multi-dimensional time–space fractional diffusion equation with variable coefficients, in which L 1 formula and shifted Grünwald formula are employed to discretize the temporal and spatial derivatives, respectively. A divide-and-conquer strategy is applied to the large linear system assembling discrete equations of all time levels, which in turn requires to solve a series of multidimensional linear systems related to the spatial discretization. Preconditioned generalized minimal residual method is employed to solve the spatial linear systems resulting from the spatial discretization. The discretization is proven to be unconditionally stable and convergent in the sense of infinity norm for general nonnegative coefficients. Numerical results are reported to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The dominant recent legal discourse concerning Bitcoin and later virtual currencies has been focused on regulatory issues such as anti-money laundering and financial and securities regulation. By contrast, scant attention has been given to the intersection between the uses of Bitcoin and commercial law even as its popularity has grown as both an asset class and as a means of payment for goods and services. In determining the commercial law consequences of transactions involving Bitcoin, the likely cross-border nature of Bitcoin-related transactions will give rise to choice of law issues which may have a determinative effect on a given dispute. Commercial disputes involving virtual currencies have already made their way into common law courts. This paper examines one of the most significant choice of law problems that arises – the law applicable to determine disputes concerning property in Bitcoins (and determining the situs of Bitcoins) through the lens of English conflict of laws. [ABSTRACT FROM AUTHOR]

In this paper, we study the discovery of unknown dynamical systems with observed noisy data of the dynamics by neural networks. It is well-known that the performance of the neural network approach is degraded when observed data is noisy, even if the noise level is small. The main contribution of this paper is to propose a new network-based formulation for the dynamics discovery using numerical quadrature rules and to employ a self-supervision network to denoise observed data from the underlying dynamics. Our experimental results show that the performance of the proposed approach is better than that of existing dynamical discovery methods. • Design a neural network method for the discovery of unknown and noisy dynamical systems. • Propose a new quadrature rule. • Consider self-supervised denoising scheme in the network. [ABSTRACT FROM AUTHOR]

In this paper, we study the Crank-Nicolson alternative direction implicit (ADI) method for two-dimensional Riesz space-fractional diffusion equations with nonseparable coefficients. Existing ADI methods are only shown to be unconditional stable when coefficients are some special separable functions. The main contribution of this paper is to show under mild assumptions the unconditional stability of the proposed Crank-Nicolson ADI method in discrete l² norm and the consistency of cross perturbation terms arising from the Crank-Nicolson ADI method. Also, we demonstrate that several consistent spatial discretization schemes satisfy the required assumptions. Numerical results are presented to examine the accuracy and the efficiency of the proposed ADI methods. [ABSTRACT FROM AUTHOR]

Image colorization aims to recover the whole color image based on a known grayscale image (luminance or brightness) and some known color pixel values. In this paper, we generalize the graph Laplacian to its second-order variant called graph bi-Laplacian, and then propose an image colorization method by using graph bi-Laplacian. The eigenvalue analysis of graph bi-Laplacian matrix and its corresponding normalized bi-Laplacian matrix is given to show their properties. We apply graph bi-Laplacian approach to image colorization by formulating it as an optimization problem and solving the resulting linear system efficiently. Numerical results show that the proposed method can perform quite well for image colorization problem, and its performance in terms of efficiency and colorization quality for test images can be better than that by the state-of-the-art colorization methods when the randomly given color pixels ratio attains some level. [ABSTRACT FROM AUTHOR]

In this paper, we study the ensemble Kalman filter (EnKF) method for chemical species simulation in air quality forecast data assimilation. The main contribution of this paper is that we study the sparse observation data and make use of the matrix structure of the EnKF update equations to design an algorithm for the purpose of computing the analysis of chemical species in an air quality forecast system efficiently. The proposed method can also handle the combined observations from multiple chemical species together. We applied the proposed method and tested its performance in real air quality data assimilation. Numerical examples are presented to demonstrate the efficiency of the proposed computation method for EnKF updating and the effectiveness of the proposed method for NO2, NO, CO, SO2, O3, PM2.5, and PM10 prediction in air quality forecast data assimilation. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study and analyze the regularized least squares for functional linear regression model. The approach is to use the reproducing kernel Hilbert space framework and the integral operators. We show with a more general and realistic assumption on the reproducing kernel and input data statistics that the rate of excess prediction risk by the regularized least squares is minimax optimal. [ABSTRACT FROM AUTHOR]

Summary: The main objective of this paper is to study an approximation of symmetric tensors by symmetric orthogonal decomposition. We propose and study an iterative algorithm to determine a symmetric orthogonal approximation and analyze the convergence of the proposed algorithm. Numerical examples are reported to demonstrate the effectiveness of the proposed algorithm. We also apply the proposed algorithm to represent correlated face images. We demonstrate better face image reconstruction results by combining principal components and symmetric orthogonal approximation instead of combining principal components and higher‐order SVD results. [ABSTRACT FROM AUTHOR]

In this paper, we propose an efficient preconditioner for the linear systems arising from the one-sided space fractional diffusion equation with variable coefficients. The shifted Gru¨nwald formula is employed to discretize the one-sided Riemann-Liouville fractional derivative. The matrix structure of resulting linear systems is Toeplitz-like, which is a summation of an identity matrix and a diagonal-times-nonsymmetric-Toeplitz matrix. A diagonal-times-nonsymmetric-Toeplitz preconditioner is proposed to reduce the condition number of the Toeplitz-like matrix, where the diagonal part comes from the variable coefficients and the nonsymmetric Toeplitz part comes from the Riemann-Liouville derivative. Theoretically, we show that the condition number of the preconditioned matrix is uniformly bounded by a constant independent of discretization step-sizes under certain assumptions on the coefficient function. Due to the uniformly bounded condition number, the Krylov subspace method for the preconditioned linear systems converges linearly and independently on discretization step-sizes. Numerical results are reported to show the efficiency of the proposed preconditioner and to demonstrate its superiority over other tested preconditioners. [ABSTRACT FROM AUTHOR]

Feature extraction is a prerequisite in many machine learning and data mining applications. As the advancement of data acquisition techniques, nowadays tensor objects are accumulated with respect to frequency or time information in a great number of fields. For instance color or hyperspectral faces in multichannel information, and human gait motion in time information are obtained. In this paper, we propose and develop a block principal component analysis (BPCA) to extract features for this kind of tensor objects. Our idea is to unfold tensor objects according to their spatial information and frequency/time information, and represent them in block matrix form. The corresponding covariance matrix for frequency/time information can be captured and used. The block eigen-decomposition of such covariance matrix is employed to seek for projection solution as features. Both reconstruction and classification problems can be solved via these projected features. Extensive experiments have been conducted on various face or gait databases to demonstrate the superiority of BPCA compared with existing methods such as PCA, (2D) 2 PCA, MPCA, and UMPCA in terms of effectiveness. Moreover, the proposed BPCA is competitively efficient compared to these existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we study orthogonal nonnegative matrix factorization. We demonstrate the coefficient matrix can be sparse and low-rank in the orthogonal nonnegative matrix factorization. By using these properties, we propose to use a sparsity and nuclear norm minimization for the factorization and develop a convex optimization model for finding the coefficient matrix in the factorization. Numerical examples including synthetic and real-world data sets are presented to illustrate the effectiveness of the proposed algorithm and demonstrate that its performance is better than other testing methods. [ABSTRACT FROM AUTHOR]

Selective image segmentation is an important topic in medical imaging and real applications. In this paper, we propose a weighted variational selective image segmentation model which contains two steps. The first stage is to obtain a smooth approximation related to Mumford-Shah model to the target region in the input image. Using weighted function, the approximation provides a larger value for the target region and smaller values for other regions. In the second stage, we make use of this approximation and perform a thresholding procedure to obtain the object of interest. The approximation can be obtained by the alternating direction method of multipliers and the convergence analysis of the method can be established. Experimental results for medical image selective segmentation are given to demonstrate the usefulness of the proposed method. We also do some comparisons and show that the performance of the proposed method is more competitive than other testing methods. [ABSTRACT FROM AUTHOR]