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In this paper, we study a fast algorithm for finding stationary joint probability distributions of sparse Markov chains or multilinear PageRank vectors which arise from data mining applications. In these applications, the main computational problem is to calculate and store solutions of many unknowns in joint probability distributions of sparse Markov chains. Our idea is to approximate large-scale solutions of such sparse Markov chains by two components: the sparsity component and the rank-one component. Here the non-zero locations in the sparsity component refer to important associations in the joint probability distribution and the rank-one component refers to a background value of the solution. We propose to determine solutions by formulating and solving sparse and rank-one optimization problems via closed form solutions. The convergence of the truncated power method is established. Numerical examples of multilinear PageRank vector calculation and second-order web-linkage analysis are presented to show the efficiency of the proposed method. It is shown that both computation and storage are significantly reduced by comparing with the traditional power method. [ABSTRACT FROM AUTHOR]

In this paper, we study a deblurring algorithm for distorted images by random impulse response. We propose and develop a convex optimization model to recover the underlying image and the blurring function simultaneously. The objective function is composed of 3 terms: the data-fitting term between the observed image and the product of the estimated blurring function and the estimated image, the squared difference between the estimated blurring function and its mean, and the total variation regularization term for the estimated image. We theoretically show that under some mild conditions, the resulting objective function can be convex in which the global minimum value is unique. The numerical results confirm that the peak-to-signal-noise-ratio and structural similarity of the restored images by the proposed algorithm are the best when the proposed objective function is convex. We also present a proximal alternating minimization scheme to solve the resulting minimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme. [ABSTRACT FROM AUTHOR]

This article constitutes the first in-depth study of press censorship in British Hong Kong during the first century of colonial rule. By revealing how the press, the Chinese press in particular, was continuously and systematically monitored and pervasively censored through the collaborative efforts of executive actions, legislative provisions and judicial decisions, this article further posits that the common law system practiced in British Hong Kong during the period under study was complicit in the imposition of an authoritarian form of law and order, and was more interested in preserving the British Empire's overseas territorial and economic possessions and managing the power equation in the region than in safeguarding individual liberties in Hong Kong. Hong Kong is often praised for its rule-of-law colonial legacy, but this article argues that such narrative does not stand up to the scrutiny of archival study. The English law in Hong Kong history, rather than constituting a lens through which one can witness Hong Kong's quest for modernity, is more akin to a mirror reflecting an ongoing cycle of coercion and resistance through law. Drawing on unexplored archival sources, the article first discusses how the colonial government used libel lawsuits to punish the press for criticism of the government in the 19th century, before turning to describing in detail the daily mandatory vetting of Chinese newspapers by colonial censors under the office of the Secretary for Chinese Affairs and related prosecution cases in the early 20th century. The paper concludes with an exploration of the tension between the notion of a free press and the governance fears of the British Empire in the Far East revealed by this history of silencing the press in Hong Kong. [ABSTRACT FROM PUBLISHER]

Individuals with Dupuytren disease (DD) are commonly seen by physicians and surgeons across multiple specialties. It is an increasingly common and disabling fibroproliferative disorder of the palmar fascia, which leads to flexion contractures of the digits, and is associated with other tissue-specific fibroses. DD affects between 5% and 25% of people of European descent and is the most common inherited disease of connective tissue. We undertook the largest GWAS to date in individuals with a surgically validated diagnosis of DD from the UK, with replication in British, Dutch, and German individuals. We validated association at all nine previously described signals and discovered 17 additional variants with p ≤ 5 × 10 −8 . As a proof of principle, we demonstrated correlation of the high-risk genotype at the statistically most strongly associated variant with decreased secretion of the soluble WNT-antagonist SFRP4, in surgical specimen-derived DD myofibroblasts. These results highlight important pathways involved in the pathogenesis of fibrosis, including WNT signaling, extracellular matrix modulation, and inflammation. In addition, many associated loci contain genes that were hitherto unrecognized as playing a role in fibrosis, opening up new avenues of research that may lead to novel treatments for DD and fibrosis more generally. DD represents an ideal human model disease for fibrosis research. [ABSTRACT FROM AUTHOR]

The task of transfer learning using pretrained convolutional neural networks is considered. We propose a convolution-SVD layer to analyze the convolution operators with a singular value decomposition computed in the Fourier domain. Singular vectors extracted from the source domain are transferred to the target domain, whereas the singular values are fine-tuned with a target data set. In this way, dimension reduction is achieved to avoid overfitting, while some flexibility to fine-tune the convolution kernels is maintained. We extend an existing convolution kernel reconstruction algorithm to allow for a reconstruction from an arbitrary set of learned singular values. A generalization bound for a single convolution-SVD layer is devised to show the consistency between training and testing errors. We further introduce a notion of transfer learning gap. We prove that the testing error for a single convolution-SVD layer is bounded in terms of the gap, which motivates us to develop a regularization model with the gap as the regularizer. Numerical experiments are conducted to demonstrate the superiority of the proposed model in solving classification problems and the influence of various parameters. In particular, the regularization is shown to yield a significantly higher prediction accuracy. [ABSTRACT FROM AUTHOR]

The ratio of |$\ell _{1}$| and |$\ell _{2}$| norms, denoted as |$\ell _{1}/\ell _{2}$|⁠ , has presented prominent performance in promoting sparsity. By adding partial support information to the standard |$\ell _{1}/\ell _{2}$| minimization, in this paper, we introduce a novel model, i.e. the weighted |$\ell _{1}/\ell _{2}$| minimization, to recover sparse signals from the linear measurements. The restricted isometry property based conditions for sparse signal recovery in both noiseless and noisy cases through the weighted |$\ell _{1}/\ell _{2}$| minimization are established. And we show that the proposed conditions are weaker than the analogous conditions for standard |$\ell _{1}/\ell _{2}$| minimization when the accuracy of the partial support information is at least |$50\%$|⁠. Moreover, we develop effective algorithms and illustrate our results via extensive numerical experiments on synthetic data in both noiseless and noisy cases. [ABSTRACT FROM AUTHOR]

Missing information, such as dead pixel values and cloud effects, is very common image quality degradation problems in remote sensing. Missing information can reduce the accuracy of the subsequent image processing, in applications such as classification, unmixing, and target detection, and even the quantitative retrieval process. The main aim of this paper is to study an adaptive weighted tensor completion (AWTC) method for the recovery of remote sensing images with missing data. Our idea is to collectively make use of the spatial, spectral, and temporal information to build a new weighted tensor low-rank regularization model for recovering the missing data. In the model, the weights are determined adaptively by considering the contribution of the spatial, spectral, and temporal information in each dimension. Experimental results based on both simulated and real data sets are presented to verify that the proposed method can recover missing data, and its performance is found to be better than the other tested methods. In the simulated experiments, the peak signal-to-noise ratio is improved by more than 3 dB, compared with the original tensor completion model. In the real data experiments, the proposed AWTC model can better recover the dead line problem in Aqua Moderate Resolution Imaging Spectroradiometer band 6 and the scan-line corrector-off problem in enhanced thematic mapper plus images, with the smallest spectral distortion. [ABSTRACT FROM PUBLISHER]

In this paper, we study a V-cycle multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations. The coefficient matrices of the linear systems are structured such that their matrix-vector multiplications can be computed efficiently. The main advantage using the multigrid method is to handle the space-fractional diffusion equations on non-rectangular domains, and to solve the linear systems with non-constant coefficients more effectively. The main idea of the proposed multigrid method is to employ two banded splitting iteration schemes as pre-smoother and post-smoother. The pre-smoother and the post-smoother take banded splitting of the coefficient matrix under the x -dominant ordering and the y -dominant ordering, respectively. We prove the convergence of the proposed two banded splitting iteration schemes in the sense of infinity norm. Results of numerical experiments for time-dependent two-dimensional space-fractional diffusion equations on rectangular, L-shape and U-shape domains are reported to demonstrate that both computational time and iteration number required by the proposed method are significantly smaller than those of the other tested methods. [ABSTRACT FROM AUTHOR]

Outlier detection is an important data analysis task in its own right and removing the outliers from clusters can improve the clustering accuracy. In this paper, we extend the k -means algorithm to provide data clustering and outlier detection simultaneously by introducing an additional “cluster” to the k -means algorithm to hold all outliers. We design an iterative procedure to optimize the objective function of the proposed algorithm and establish the convergence of the iterative procedure. Numerical experiments on both synthetic data and real data are provided to demonstrate the effectiveness and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Fractional partial differential equations (FPDEs) provide better modeling capabilities for challenging phenomena with long-range time memory and spatial interaction than integer-order PDEs do. A conventional numerical discretization of space–time FPDEs requires O ( N 2 + M N ) memory and O ( M N 3 + M 2 N ) computational work, where N is the number of spatial freedoms per time step and M is the number of time steps. We develop a fast finite difference method (FDM) for space–time FPDE: (i) We utilize the Toeplitz-like structure of the coefficient matrix to develop a matrix-free preconditioned fast Krylov subspace iterative solver to invert the coefficient matrix at each time step. (ii) We utilize a divide-and-conquer strategy, a recursive direct solver, to handle the temporal coupling of the numerical scheme. The fast method has an optimal memory requirement of O ( M N ) and an approximately linear computational complexity of O ( N M ( log N + log 2 M ) ) , without resorting to any lossy compression. Numerical experiments show the utility of the method. [ABSTRACT FROM AUTHOR]

Introduction Peripheral artery disease can lead to severe disability and limb loss. Therapeutic strategies focussing on macrovascular repair have shown benefit but have not significantly reduced amputation rates in progressive PAD. Proangiogenic small molecule therapies may substantially improve vascularisation in limb ischemia. The purpose of the current study was to assess the proangiogenic effects of simvastatin in a murine model of hind limb ischemia using longitudinal multimodal imaging. Methods Mice underwent surgical intervention to induce hind limb ischemia, and were treated with simvastatin orally for 28 days. Neovascularisation was assessed using 99m Tc-RGD SPECT imaging, and macrovascular volume was assessed by quantitative time of flight MRI. At each imaging time point, VEGF expression and capillary vessel density were quantified using immunohistochemical analysis. Results Simvastatin significantly increased 99m Tc-RGD retention in the ischemic hind limb by day 3 post-surgery, with maximal retention at day 8. Vascular volume was significantly increased in the ischemic hind limb of simvastatin treated animals, but only by day 22. Immunohistochemical analysis shows that simvastatin significantly augmented tissue VEGF expression from day 8 with increase in capillary density (CD31 + ) from day 14. Conclusions Early assessment of proangiogenic therapy efficacy can be identified using 99m Tc-RGD SPECT, which displays significant increases in retention before macrovascular volume changes are measureable with MRI. Advances in knowledge and implications for patient care Simvastatin offers an effective proangiogenic therapy as an adjunct for management of limb ischemia. Simvastatin induces integrin expression and vascular remodeling leading to neovascularisation and improved perfusion. [ABSTRACT FROM AUTHOR]

We consider the preconditioned Krylov subspace method for linear systems arising from the finite volume discretization method of steady-state variable-coefficient conservative space-fractional diffusion equations. We propose to use a scaled-circulant preconditioner to deal with such Toeplitz-like discretization matrices. We show that the difference between the scaled-circulant preconditioner and the coefficient matrix is equal to the sum of a small-norm matrix and a low-rank matrix. Numerical tests are conducted to show the effectiveness of the proposed method for one- and two-dimensional steady-state space-fractional diffusion equations and demonstrate that the preconditioned Krylov subspace method converges very quickly. [ABSTRACT FROM AUTHOR]

In data science, data are often represented by using an undirected graph where vertices represent objects and edges describe a relationship between two objects. In many applications, there can be many relations arising from different sources and/or different types of models. Clustering of multiple undirected graphs over the same set of vertices can be studied. Existing clustering methods of multiple graphs involve costly optimization and/or tensor computation. In this paper, we study block spectral clustering methods for these multiple graphs. The main contribution of this paper is to propose and construct block Laplacian matrices for clustering of multiple graphs. We present a novel variant of the Laplacian matrix called the block intra-normalized Laplacian and prove the conditions required for zero eigenvalues in this variant. We also show that eigenvectors of the constructed block Laplacian matrix can be shown to be solutions of the relaxation of multiple graphs cut problems, and the lower and upper bounds of the optimal solutions of multiple graphs cut problems can also be established. Experimental results are given to demonstrate that the clustering accuracy and the computational time of the proposed method are better than those of tested clustering methods for multiple graphs. [ABSTRACT FROM AUTHOR]

Background: MicroRNAs (miRNAs) are involved in many biological processes by regulating post-transcriptional gene expression. The alterations of the regulatory pathways can cause different diseases including cancer. Although many works have been done to study the gene-miRNA regulatory network, the intertwined relationship is far from being fully understood. The objective of this study is to integrate both gene expression data and miRNA data so as to explore the complex relationships among them. Methods: By integrating the networks consisting of gene coexpression, miRNA coexpression, gene-miRNA coexpression, and the known gene-miRNA interactions, we aim to find the most connected network modules so as to study their functions and properties. In this paper, we proposed an optimization model for identification of the modules in the integrated networks. This model tries to find both the modules in the gene-gene and miRNA-miRNA coexpression networks and the densely connected gene-miRNA subneworks. An approximation computational method was developed to solve the optimization problem. Results: We applied the method to 556 human ovarian cancer samples with both gene expression data and miRNA expression data. The identified modules are significantly enriched by miRNA clusters, GO-BPs, and KEGG pathways. We compared our method with some existing methods and showed the better performance of our method. We also showed that the miRNAs and genes in our identified modules are associated with cancers, especially ovarian cancer. Conclusions: This study provides strong support that the subnetworks consisting of genes and miRNAs with close interactions contribute the cancers. The proposed computational method can be applied to other studies that are related to different types of networks. [ABSTRACT FROM AUTHOR]

Multi-instance multi-label (MIML) learning is one of challenging research problems in machine learning. In the literature, there are several methods for solving MIML problems. However, they may take a long computational time and have a huge storage cost for large MIML data sets. The main aim of this paper is to propose and develop an efficient Markov Chain learning algorithm for MIML problems, especially for data represented by non-negative features. Our idea is to perform labels classification iteratively through two Markov chains constructed by using objects and features respectively. The classification of objects can be obtained by using labels propagation via training data in the iterative method. Moreover, we demonstrate that the proposed method can be formulated by considering normalized linear kernel. Because linear kernel function is explicit and separable, it is not necessary to compute and store a huge affinity matrix among objects/instances compared with the use of other kernel functions. Therefore, both the storage and computational time of the proposed algorithm are very efficient. Experimental results are presented to show that the classification performance of the proposed method using normalized linear kernel function is about the same as those using the other kernel functions, while the required computational time is much less, which together suggest that the linear kernel can be good enough for MIML problem. Also experimental results on some benchmark data sets are reported to illustrate the effectiveness of the proposed method in one-error, ranking loss, coverage and average precision, and show that it is competitive with the other MIML methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the linear systems arising from the discretization of timedependent space-fractional diffusion equations. By using a finite difference discretization scheme for the time derivative and a finite volume discretization scheme for the space-fractional derivative, Toeplitz-like linear systems are obtained. We propose using the approximate inverse-circulant preconditioner to deal with such Toeplitz-like matrices, and we show that the spectra of the corresponding preconditioned matrices are clustered around 1. Experimental results on time-dependent and space-fractional diffusion equations are presented to demonstrate that the preconditioned Krylov subspace methods converge very quickly. [ABSTRACT FROM AUTHOR]

In this paper, we study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of partial differential equations. By using groupsort activation functions in adversarial network discriminators, network generators are utilized to learn the uncertainty in solutions of partial differential equations observed from the initial/boundary data. Under mild assumptions, we show that the generalization error of the computed generator converges to the approximation error of the network with high probability, when the number of samples are sufficiently taken. According to our established error bound, we also find that our physics-informed WGANs have higher requirement for the capacity of discriminators than that of generators. Numerical results on synthetic examples of partial differential equations are reported to validate our theoretical results and demonstrate how uncertainty quantification can be obtained for solutions of partial differential equations and the distributions of initial/boundary data. However, the quality or the accuracy of the uncertainty quantification theory in all the points in the interior is still the theoretical vacancy, and required for further research. • Wasserstein generative adversarial networks need little priors for uncertainty quantifications. • Physics-informed regularization term enforces the satisfaction of governing PDEs. • The proposed probabilistic model (WGAN-PINNs) is able to deal with non-Gaussian and spatially dependent noise. • WGAN-PINNs have good convergence and generalization properties. • Theoretically we have higher requirements on discriminators than generators. [ABSTRACT FROM AUTHOR]

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix–vector multiplication. The complexity needs O ( M N log 2 ⁡ M ) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a subspace clustering algorithm with automatic feature grouping for clustering high-dimensional data. In this algorithm, a new component is introduced into the objective function to capture the feature groups and a new iterative process is defined to optimize the objective function so that the features of high-dimensional data are grouped automatically. Experiments on both synthetic data and real data show that the new algorithm outperforms the FG- k -means algorithm in terms of accuracy and choice of parameters. [ABSTRACT FROM AUTHOR]

We propose some computational methods for extracting static backgrounds from surveillance videos corrupted by noise, blur, or both. The new methods are constructed based on the fact that the matrix representation of a static background consists of identical columns; hence the idea of median filtering is embedded in these methods. These new methods significantly differ from existing methods originating from the robust principal component analysis (RPCA) in that no nuclear-norm term is involved; thus the computation of singular value decomposition can be completely avoided when solving these new models iteratively. This is an important feature because usually the dimensionality of a surveillance video is large and so the involved singular value decomposition (which is inevitable for RPCA-based models) is very expensive computationally. We show that these methods can be easily solved by well-developed operator splitting methods in optimization literature such as the alternating direction method of multipliers. We compare the new methods with their RPCA-based counterparts via testing some synthetic and real videos. Our numerical results show that compared with RPCA-based models, these median filtering-based vaiational models can extract more accurate backgrounds when the background in a surveillance video is static, and numerically, they can be solved much more efficiently. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Deep neural networks have achieved great success in solving many machine learning and computer vision problems. In this paper, we propose a deep neural network called the Tucker network derived from the Tucker format and analyze its expressive power. The results demonstrate that the Tucker network has exponentially higher expressive power than the shallow network. In other words, a shallow network with an exponential width is required to realize the same score function as that computed by the Tucker network. Moreover, we discuss the expressive power between the hierarchical Tucker tensor network (HT network) and the proposed Tucker network. To generalize the Tucker network into a deep version, we combine the hierarchical Tucker format and Tucker format to propose a deep Tucker tensor decomposition. Its corresponding deep Tucker network is presented. Experiments are conducted on three datasets: MNIST, CIFAR-10 and CIFAR-100. The results experimentally validate the theoretical results and show that the Tucker network and deep Tucker network have better performance than the shallow network and HT network. [ABSTRACT FROM AUTHOR]

We study iterative methods for solving a set of sparse non-negative tensor equations (multivariate polynomial systems) arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper proposes a subspace clustering algorithm by introducing attribute weights in the affinity propagation algorithm. A new step is introduced to the affinity propagation process to iteratively update the attribute weights based on the current partition of the data. The relative magnitude of the attribute weights can be used to identify the subspaces in which clusters are embedded. Experiments on both synthetic data and real data show that the new algorithm outperforms the affinity propagation algorithm in recovering clusters from data. [ABSTRACT FROM AUTHOR]

This paper reports an empirical study of the use of simulated clients to assess (facilitate the learning of) interviewing skills and communicative competence of law students at the University of Hong Kong (HKU) from February 2013 to April 2014. In this period, about 400 HKU Postgraduate Certificate in Laws students participated in interviewing exercises with simulated clients, who are lay persons trained to portray clients in a realistic manner and to assess communicative competence by standardized rubrics designed in Scotland since 2006. HKU Faculty of Law is the first law school in Asia to adopt this standardized client program to assess law students’ interviewing skills. The paper will present the data analysis of assessment results of the students and their evaluation of this experiential learning program. Our analysis confirms the reliability and validity of using standardized clients as assessors of interviewing skills. It also reveals the necessity of modification of the original design of standardized client program, particularly in relation to the assessment aspect of it, according to specific cultural and commercial needs in an Asian business city like Hong Kong. [ABSTRACT FROM PUBLISHER]

Tone mapping methods aim to display a high-dynamic-range image on a common 8-bit liquid crystal display by compressing the dynamic range. We propose a simple but effective tone mapping operator (TMO) by using localized gamma correction. As the TMO involves the contrast and the color saturation components, our idea is to make use of gamma correction to adjust the values of these two components locally. The local weights can be determined according to the pixel values within local regions. Such an adaption can be handled more effectively for the contrast and color saturation in dark and bright regions of an image. Numerical examples are given to demonstrate the merit of the localized gamma correction scheme. The experiments reported in this paper illustrate that the proposed method can provide visually pleasing results, and it is also competitive with the other testing methods. [ABSTRACT FROM AUTHOR]

In this paper, we address the total variation (TV)-based nonlinear image restoration problems. In nonlinear image restoration problems, an original image is corrupted by a spatiallyinvariant blur, the build-in nonlinearity in imaging system, and the additive Gaussian white noise. We study the objective function consisting of the nonlinear least squares data-fitting term and the TV regularization term of the restored image. By making use of the structure of the objective function, an efficient alternating direction method of multipliers can be developed for solving the proposed model. The convergence of the numerical scheme is also studied. Numerical examples, including nonlinear image restoration and high-dynamic range imaging are reported to demonstrate the effectiveness of the proposed model and the efficiency of the proposed numerical scheme. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study image enhancement by using sparse and redundant representations of the reflectance component in the Retinex model over a learned dictionary. This approach is different from existing variational methods, and the advantage of this approach is that the reflectance component in the Retinex model can be represented with more details by the dictionary. A variational method based on the dynamic dictionaries is adopted here, where it changes with respect to iterations of the enhancement algorithm. Numerical examples are also reported to demonstrate that the proposed methods can provide better visual quality of the enhanced high-contrast images than the other variational methods, i.e., revealing more details in the low-light part. [ABSTRACT FROM AUTHOR]

Deep neural networks have shown impressive performance in many areas, including computer vision and natural language processing. Millions of parameters in deep neural network limit its deployment in low-end devices due to intensive memory and expensive computational cost. In the literature, several network compression techniques based on tensor decompositions have been proposed to compress deep neural networks. Existing techniques are designed in each network unit by approximating linear response or kernel tensor using various tensor decomposition methods. What is more, research has shown that there exists significant redundancy between different filters and feature channels of kernel tensor in each convolution layer. In this paper, we propose a new algorithm to compress deep neural network by considering both nonlinear response and the multilinear low-rank constraint in the kernel tensor. To overcome the resulted difficulty of nonconvex optimization, we propose a convex relaxation scheme such that it can be solved by alternating direction method of multipliers (ADMM) directly. Thus, the Tucker-2 rank and the feature matrix of Tucker decomposition can be determined simultaneously. The effectiveness of the proposed method is evaluated on CIFAR-10 and large-scale ILSVRC12 datasets for CNNs including ResNet-18, AlexNet and GoogleNet. According to our numerical computation, the proposed method is able to obtain highly reduction in model size with a small loss in accuracy. The compression performance of the proposed method is better than existing methods. [ABSTRACT FROM AUTHOR]

This paper analyzes the cartoon and texture structures to inspect and visualize defective objects in a patterned fabric image. It presents a method of an image decomposition (ID) and solves it by a convex optimization algorithm. Our experimental results on benchmark fabric images are superior to those by other methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the problem of multi-label collective classification (MLCC) where instances are related and associated with multiple class labels. Such correlation of class labels among interrelated instances exists in a wide variety of data, e.g., a web page can belong to multiple categories since its semantics can be recognized in different ways, and the linked web pages are more likely to have the same classes than the unlinked pages. We propose an effective and novel Markov chain based learning method for MLCC problems. Our idea is to model the problem as a Markov chain with restart on transition probability graphs, and to propagate the ranking score of labeled instances to unlabeled instances based on the affinity among instances. The affinity among instances is set up by explicitly using the attribute features derived from the content of instances as well as the correlation features constructed from the links of instances. Intuitively, an instance which contains linked neighbors that are highly similar to the other instances with a high rank of a particular class label, has a high chance of this class label. Extensive experiments have been conducted on two DBLP datasets to demonstrate the effectiveness of the proposed algorithm. The performance of the proposed algorithm is shown to be better than those of the binary relevance multi-label algorithm, collective classification algorithms (wvRN, ICA and Gibbs), and the ICML algorithm for the tested MLCC problems. [Copyright &y& Elsevier]

The main aim of this paper is to develop a community discovery scheme in a multi-dimensional network for data mining applications. In online social media, networked data consists of multiple dimensions/entities such as users, tags, photos, comments, and stories. We are interested in finding a group of users who interact significantly on these media entities. In a co-citation network, we are interested in finding a group of authors who relate to other authors significantly on publication information in titles, abstracts, and keywords as multiple dimensions/entities in the network. The main contribution of this paper is to propose a framework (MultiComm)to identify a seed-based community in a multi-dimensional network by evaluating the affinity between two items in the same type of entity (same dimension)or different types of entities (different dimensions)from the network. Our idea is to calculate the probabilities of visiting each item in each dimension, and compare their values to generate communities from a set of seed items. In order to evaluate a high quality of generated communities by the proposed algorithm, we develop and study a local modularity measure of a community in a multi-dimensional network. Experiments based on synthetic and real-world data sets suggest that the proposed framework is able to find a community effectively. Experimental results have also shown that the performance of the proposed algorithm is better in accuracy than the other testing algorithms in finding communities in multi-dimensional networks. [ABSTRACT FROM AUTHOR]

Objectives To review the use of fiducial markers and spacers in prostate radiotherapy ( RT). Materials and Methods We reviewed the literature on the use of fiducial markers to improve accuracy in delivery of RT for prostate cancer. We discuss the rationale for fiducials, the types available, the procedures and complications. We also reviewed the current literature on the novel use of spacers to reduce rectal toxicity during prostate irradiation. Results Prostate motion is a significant problem both during and between RT treatments. Intraprostatic fiducials allow accurate prostate localisation ensuring RT treatment accuracy. Insertion of gold fiducials are a cost-effective marker that can be easily and quickly implanted and at least three fiducials are recommended. Severe complications from fiducial implantation are uncommon and marker migration is very rarely clinically significant. Spacers are a novel method to distance the rectum from the prostate during RT, reducing acute rectal toxicity, and have no detrimental impact on health-related quality of life. Conclusions Intraprostatic fiducials are now standard of care when delivering prostate RT and early data shows benefit of spacers in reducing RT rectal toxicity. [ABSTRACT FROM AUTHOR]

In this paper, we propose and develop an iterative method to calculate a limiting probability distribution vector of a transition probability tensorarising from a higher order Markov chain. In the model, the computation of such limiting probability distribution vectorcan be formulated as a-eigenvalue problemassociated with the eigenvalue 1 ofwhere all the entries ofare required to be non-negative and its summation must be equal to one. This is an analog of the matrix case for a limiting probability vector of a transition probability matrix arising from the first-order Markov chain. We show that ifis a transition probability tensor, then solutions of this-eigenvalue problem exist. Whenis irreducible, all the entries of solutions are positie. With some suitable conditions of, the limiting probability distribution vector is even unique. Under the same uniqueness assumption, the linear convergence of the iterative method can be established. Numerical examples are presented to illustrate the theoretical results of the proposed model and the iterative method. [ABSTRACT FROM AUTHOR]

The JPEG compression method is among the most successful compression schemes since it readily provides good compressed results at a rather high compression ratio. However, the decompressed result of the standard JPEG decompression scheme usually contains some visible artifacts, such as blocking artifacts and Gibbs artifacts (ringing), especially when the compression ratio is rather high. In this paper, a novel artifact reducing approach for the JPEG decompression is proposed via sparse and redundant representations over a learned dictionary. Indeed, an effective two-step algorithm is developed. The first step involves dictionary learning and the second step involves the total variation regularization for decompressed images. Numerical experiments are performed to demonstrate that the proposed method outperforms the total variation and weighted total variation decompression methods in the measure of peak of signal to noise ratio, and structural similarity. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to develop a fast algorithm for solving weighted Toeplitz regularized least squares problems arising from image restoration. Based on augmented system formulation, we develop new Hermitian and skew-Hermitian splitting (HSS) preconditioners for solving such linear systems. The advantage of the proposed preconditioner is that the blurring matrix, weighting matrix, and regularization matrix can be decoupled such that the resulting preconditioner is not expensive to use. We show that for a preconditioned system that is derived from a saddle point structure of size (m+n) x (m+n), the preconditioned matrix has an eigenvalue at 1 with multiplicity n and the other m eigenvalues of the form 1 -- λ with |λ| < 1. We also study how to choose the HSS parameter to minimize the magnitude of λ, and therefore the Krylov subspace method applied to solving the preconditioned system converges very quickly. Experimental results for image restoration problems are reported to demonstrate that the performance of the proposed preconditioner is better than the other testing preconditioners. [ABSTRACT FROM AUTHOR]

We study the perturbation bound for the spectral radius of an mth-order n-dimensional nonnegative tensor A. The main contribution of this paper is to show that whenAis perturbed to a nonnegative tensor à by ΔA, the absolute difference between the spectral radii of A and à is bounded by the largest magnitude of the ratio of the ith component of ΔAxm-1 and the ith component xm-1, where x is an eigenvector associated with the largest eigenvalue of A in magnitude and its entries are positive. We further derive the bound in terms of the entries of Aonly when x is not known in advance. Based on the perturbation analysis, wemake use of the NQZ algorithmto estimate the spectral radius of a nonnegative tensor in general. On the other hand, we study the backward errormatrix ΔA and obtain its smallest error bound for its perturbed largest eigenvalue and associated eigenvector of an irreducible nonnegative tensor. Based on the backward error analysis, we can estimate the stability of computation of the largest eigenvalue of an irreducible nonnegative tensor by the NQZ algorithm. Numerical examples are presented to illustrate the theoretical results of our perturbation analysis. [ABSTRACT FROM AUTHOR]

Introduction The purpose of this study is to assess the efficacy and toxicity using once-daily reirradiation for patients with rectal cancer having received previous pelvic radiotherapy. Method Between June 1997 and June 2008, 56 patients were identified having received previous pelvic radiotherapy and received reirradiation for rectal cancer. Reirradiation intent was palliative in 43 patients, and preoperative/postoperative in 13 patients. Eighty per cent of patients received concurrent chemotherapy ( n = 45). Results The median dose-fractionation reirradiation schedule was 39.6 Gy in 22 fractions once daily (range 20-39.6 Gy), and the median cumulative radiation dose was 87.3 Gy. Seven patients experienced a grade 3 acute toxicity, with no grade 4 event. Fifty-one patients (91%) completed the treatment and five patients required a treatment break. The overall symptomatic response rate was 88% at three months post-reirradiation. There was one late effect of skin ulceration among patients reirradiated palliatively. Median overall survival was 39 months in patients undergoing radical surgery versus 15 months in patients reirradiated palliatively ( P < 0.001). Conclusion Once-daily reirradiation to a total dose of ≤39.6 Gy is relatively safe in the treatment of patients with rectal cancer after previous pelvic radiotherapy. It is effective in symptom control and provides an additional option in management of local recurrence. [ABSTRACT FROM AUTHOR]

In this paper, we study a τ-preconditioner for non-symmetric linear system arising from a steady-state multi-dimensional Riemann-Liouville (RL) fractional diffusion equation. The generalized minimal residual (GMRES) method is applied to solve the preconditioned linear system. Theoretically, we show that the GMRES solver for the preconditioned linear system has a convergence rate independent of discretization stepsizes. To the best of our knowledge, this is the first iterative solver with stepsize-independent convergence rate for the non-symmetric linear system. The proposed τ-preconditioner is diagonalizable by the sine transform matrix, thanks to which the matrix-vector multiplication in each iteration step can be fast implemented by the fast sine transform (FST). Hence, the total operation cost of the proposed solver for the non-symmetric problem is linearithmic. Numerical results are reported to show the efficiency of the proposed preconditioner. [ABSTRACT FROM AUTHOR]

Abdominal hernias are common and characterised by the abnormal protrusion of a viscus through the wall of the abdominal cavity. The global incidence is 18.5 million annually and there are limited non-surgical treatments. To improve understanding of common hernia aetiopathology, we performed a six-stage genome-wide association study (GWAS) of 62,637 UK Biobank participants with either single or multiple hernia phenotypes including inguinal, femoral, umbilical and hiatus hernia. Additionally, we performed multivariable meta-analysis with metaUSAT, to allow integration of summary data across traits to generate combined effect estimates. On individual hernia analysis, we identified 3404 variants across 38 genome-wide significant (p < 5×10−8) loci of which 11 are previously unreported. Robust evidence for five shared susceptibility loci was discovered: ZC3H11B, EFEMP1, MHC region, WT1 and CALD1. Combined hernia phenotype analyses with additional multivariable meta-analysis of summary statistics in metaUSAT revealed 28 independent (seven previously unreported) shared susceptibility loci. These clustered in functional categories related to connective tissue and elastic fibre homeostasis. Weighted genetic risk scores also correlated with disease severity suggesting a phenotypic-genotypic severity correlation, an important finding to inform future personalised therapeutic approaches to hernia. [ABSTRACT FROM AUTHOR]

Windshear is a kind of microscale meteorological phenomenon which can cause danger to the landing and takeoff of aircrafts. Accurate windshear detection plays a crucial role in aviation safety. With the development of machine learning, several learning-based methods are proposed for windshear detection, i.e., windshear and non-windshear classification. To obtain accurate detection results, it is significant to extract features that can distinguish windshear and non-windshear properly from the obtained wind velocity data. In this paper, we mainly introduce two statistical indicators derived from the Doppler Light Detection and Ranging (LiDAR) observational wind velocity data by plan position illustrate (PPI) scans for windshear features construction. Besides the indicators directly derived from the wind velocity data, we also study the visual information from the corresponding conical images of wind velocity. Based on the proposed indicators, we construct three feature vectors for windshear and non-windshear classification. Inspired by the idea of multiple instance learning, the wind velocity data collected in the 4 minutes within the reported time spot are considered in the procedure of feature vector construction, which can reduce the possibility of windshear features missing. Both statistical methods and clustering methods are applied to evaluate the effectiveness of the proposed feature vectors. Numerical results show that the proposed feature vectors have good effect on windshear and non-windshear classification and can be used to provide more accurate windshear alerting to pilots in practice. [ABSTRACT FROM AUTHOR]

In many sparsity-based image processing problems, compared with the convex ℓ 1 norm approximation of the nonconvex ℓ 0 quasi-norm, one can often preserve the structures better by taking full advantage of the nonconvex ℓ p quasi-norm (0 ≤ p < 1). In this paper, we propose a nonconvex ℓ p quasi-norm approximation in the total generalized variation (TGV)-shearlet regularization for image reconstruction. By introducing some auxiliary variables, the nonconvex nonsmooth objective function can be solved by an efficient alternating direction method of multipliers with convergence analysis. Especially, we use a generalized iterated shrinkage operator to deal with the ℓ p quasi-norm subproblem, which is easy to implement. Extensive experimental results show clearly that the proposed nonconvex sparsity approximation outperforms some state-of-the-art algorithms in both the visual and quantitative measures for different sampling ratios and noise levels. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to develop a new algorithm for computing a nonnegative low multi‐rank tensor approximation for a nonnegative tensor. In the literature, there are several nonnegative tensor factorizations or decompositions, and their approaches are to enforce the nonnegativity constraints in the factors of tensor factorizations or decompositions. In this paper, we study nonnegativity constraints in tensor entries directly, and a low rank approximation for the transformed tensor by using discrete Fourier transformation matrix, discrete cosine transformation matrix, or unitary transformation matrix. This strategy is particularly useful in imaging science as nonnegative pixels appear in tensor entries and a low rank structure can be obtained in the transformation domain. We propose an alternating projections algorithm for computing such a nonnegative low multi‐rank tensor approximation. The convergence of the proposed projection method is established. Numerical examples for multidimensional images are presented to demonstrate that the performance of the proposed method is better than that of nonnegative low Tucker rank tensor approximation and the other nonnegative tensor factorizations and decompositions. [ABSTRACT FROM AUTHOR]

Marginal zone lymphomas (MZLs) are a rare, indolent group of non‐Hodgkin lymphomas with different diagnostic, genetic and clinical features and therapeutic implications. The most common is extranodal MZL of mucosa‐associated lymphoid tissue, followed by splenic MZL and nodal MZL. Patients with MZL generally have good outcomes with long survival rates but frequently have a relapsing/remitting course requiring several lines of therapy. The heterogeneous presentation and relapsing course present the clinician with several diagnostic and therapeutic challenges. This position statement presents evidence‐based recommendations in the setting of Australia and New Zealand. [ABSTRACT FROM AUTHOR]

Introduction: ABP 938 is being developed as a biosimilar candidate to aflibercept reference product (RP), a biologic used for certain angiogenic eye disorders. This study was designed to provide a comparative analytical assessment of the structural and functional attributes of ABP 938 and aflibercept RP sourced from the United States (US) and the European Union (EU). Methods: Structural and functional characterization studies were performed using state-of-the-art analytical techniques that were appropriate to assess relevant quality attributes and capable of detecting qualitative and quantitative differences in primary structure, higher-order structure and biophysical properties, product-related substances and impurities, general properties, and biological activities. Results: ABP 938 had the same amino acid sequence and exhibited similar secondary and tertiary structures, and biological activity as aflibercept RP. There were minor differences in a small number of biochemical attributes which are not expected to impact clinical performance. In addition, aflibercept RP sourced from the US and EU were analytically similar. Conclusions: ABP 938 was structurally and functionally similar to aflibercept RP. Since aflibercept RP sourced from the US and EU were analytically similar, this allows for the development of a scientific bridge such that a single-source RP can be used in nonclinical and clinical studies. Plain Language Summary: Eylea® (aflibercept) is a biologic medication approved for the treatment of patients with certain eye diseases that can result in low vision or blindness. Biosimilars are biologic medications that are highly similar to an existing approved biologic medication, often called a reference product. Biosimilars have the potential to reduce medication costs despite having no clinically significant differences in quality, efficacy, and safety from their reference products. ABP 938 is currently being developed as a biosimilar to aflibercept reference product. We have conducted similarity studies to compare multiple batches of ABP 938 and aflibercept reference product sourced from both the United States and the European Union, using state-of-the-art analytical methods. The results demonstrated that ABP 938 had the same amino acid sequence and similar structural and biological activities as aflibercept reference product. Before biosimilars can be used as medicines, studies such as this one are required by the Food and Drug Administration and other regulatory authorities to ensure that biosimilars are as safe and effective as their reference products. [ABSTRACT FROM AUTHOR]

In this paper, we develop a decomposition model to restore blurred images with missing pixels. Our assumption is that the underlying image is the superposition of cartoon and texture components. We use the total variation norm and its dual norm to regularize the cartoon and texture, respectively. We recommend an efficient numerical algorithm based on the splitting versions of augmented Lagrangian method to solve the problem. Theoretically, the existence of a minimizer to the energy function and the convergence of the algorithm are guaranteed. In contrast to recently developed methods for deblurring images, the proposed algorithm not only gives the restored image, but also gives a decomposition of cartoon and texture parts. These two parts can be further used in segmentation and inpainting problems. Numerical comparisons between this algorithm and some state-of-the-art methods are also reported. [ABSTRACT FROM AUTHOR]

The problem of multilabel classification has attracted great interest in the last decade, where each instance can be assigned with a set of multiple class labels simultaneously. It has a wide variety of real-world applications, e.g., automatic image annotations and gene function analysis. Current research on multilabel classification focuses on supervised settings which assume existence of large amounts of labeled training data. However, in many applications, the labeling of multilabeled data is extremely expensive and time consuming, while there are often abundant unlabeled data available. In this paper, we study the problem of transductive multilabel learning and propose a novel solution, called Trasductive Multilabel Classification (TraM), to effectively assign a set of multiple labels to each instance. Different from supervised multilabel learning methods, we estimate the label sets of the unlabeled instances effectively by utilizing the information from both labeled and unlabeled data. We first formulate the transductive multilabel learning as an optimization problem of estimating label concept compositions. Then, we derive a closed-form solution to this optimization problem and propose an effective algorithm to assign label sets to the unlabeled instances. Empirical studies on several real-world multilabel learning tasks demonstrate that our TraM method can effectively boost the performance of multilabel classification by using both labeled and unlabeled data. [ABSTRACT FROM AUTHOR]

We propose a new family of cost functions for signal and image recovery: they are composed of l1 data fitting terms combined with concave regularization. We exhibit when and how to employ such cost functions. Our theoretical results show that the minimizers of these cost functions are such that each one of their entries is involved either in an exact data fitting component or in a null component of the regularization part. This is a strong and particular property that can be useful for various image recovery problems. The minimization of such cost functions presents a computational challenge. We propose a fast minimization algorithm to solve this numerical problem. The experimental results show the effectiveness of the proposed algorithm. All illustrations and numerical experiments give a flavor of the possibilities offered by the minimizers of this new family of cost functions in solving specialized image processing tasks. [ABSTRACT FROM AUTHOR]

Nonsmooth nonconvex regularization has remarkable advantages for the restoration of piecewise constant images. Constrained optimization can improve the image restoration using a priori information. In this paper, we study regularized nonsmooth nonconvex minimization with box constraints for image restoration. We present a computable positive constant \theta for using nonconvex nonsmooth regularization, and show that the difference between each pixel and its four adjacent neighbors is either 0 or larger than \theta in the recovered image. Moreover, we give an explicit form of \theta for the box-constrained image restoration model with the non-Lipschitz nonconvex \ellp-norm (0