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An approach is presented for simulating multipulse nuclear magnetic resonance (NMR) spectra of polycrystalline solids directly in the frequency domain. The approach integrates the symmetry pathway concept for multipulse NMR with efficient algorithms for calculating spinning sideband amplitudes and performing interpolated finite-element numerical integration over all crystallite orientations in a polycrystalline sample. The numerical efficiency is achieved through a set of assumptions used to approximate the evolution of a sparse density matrix through a pulse sequence as a set of individual transition pathway signals. The utility of this approach for simulating the spectra of complex materials, such as glasses and other structurally disordered materials, is demonstrated. [ABSTRACT FROM AUTHOR]

Efficient utilization of processors in heterogeneous CPU–GPU systems is crucial for improving overall application performance by reducing workload completion time. This article introduces a framework designed to achieve maximum performance in scheduling the processing of sparse matrix-based applications within a heterogeneous CPU–GPU system. The framework suggests splitting the matrix into chunks, employing machine learning to find the optimal chunk size for scheduling efficiency, with the number of GPU streams regarded as a critical factor. The scheduling algorithm introduced is inspired by the concept of quartiles in statistics and is designed to operate in real-time, thereby striving to impose minimal overhead on the system. The evaluation of the proposed framework focused on the SpMV (Sparse Matrix–Vector Multiplication) kernel, essential for various applications such as matrix-based graph processing. This evaluation was conducted using a system equipped with an NVIDIA GTX 1070 GPU. Testing on real-world sparse matrices showed that the proposed scheduling algorithm significantly outperforms scenarios with no offloading, full offloading, and the Alternate Assignment method. [ABSTRACT FROM AUTHOR]

High-dimensional sparse matrix data frequently arise in various applications. A notable example is the weighted word–word co-occurrence count data, which summarizes the weighted frequency of word pairs appearing within the same context window. This type of data typically contains highly skewed non-negative values with an abundance of zeros. Another example is the co-occurrence of item–item or user–item pairs in e-commerce, which also generates high-dimensional data. The objective is to utilize these data to predict the relevance between items or users. In this paper, we assume that items or users can be represented by unknown dense vectors. The model treats the co-occurrence counts as arising from zero-inflated Gamma random variables and employs cosine similarity between the unknown vectors to summarize item–item relevance. The unknown values are estimated using the shared parameter alternating zero-inflated Gamma regression models (SA-ZIG). Both canonical link and log link models are considered. Two parameter updating schemes are proposed, along with an algorithm to estimate the unknown parameters. Convergence analysis is presented analytically. Numerical studies demonstrate that the SA-ZIG using Fisher scoring without learning rate adjustment may fail to find the maximum likelihood estimate. However, the SA-ZIG with learning rate adjustment performs satisfactorily in our simulation studies. [ABSTRACT FROM AUTHOR]

An intensive line of research on fixed parameter tractability of integer programming is focused on exploiting the relation between the sparsity of a constraint matrix A and the norm of the elements of its Graver basis. In particular, integer programming is fixed parameter tractable when parameterized by the primal tree-depth and the entry complexity of A, and when parameterized by the dual tree-depth and the entry complexity of A; both these parameterization imply that A is sparse, in particular, the number of its non-zero entries is linear in the number of columns or rows, respectively. We study preconditioners transforming a given matrix to a row-equivalent sparse matrix if it exists and provide structural results characterizing the existence of a sparse row-equivalent matrix in terms of the structural properties of the associated column matroid. In particular, our results imply that the ℓ 1 -norm of the Graver basis is bounded by a function of the maximum ℓ 1 -norm of a circuit of A. We use our results to design a parameterized algorithm that constructs a matrix row-equivalent to an input matrix A that has small primal/dual tree-depth and entry complexity if such a row-equivalent matrix exists. Our results yield parameterized algorithms for integer programming when parameterized by the ℓ 1 -norm of the Graver basis of the constraint matrix, when parameterized by the ℓ 1 -norm of the circuits of the constraint matrix, when parameterized by the smallest primal tree-depth and entry complexity of a matrix row-equivalent to the constraint matrix, and when parameterized by the smallest dual tree-depth and entry complexity of a matrix row-equivalent to the constraint matrix. [ABSTRACT FROM AUTHOR]

A mass was removed surgically from the right orbit of a 1-d-old Holstein calf. Grossly, the mass filled the rostral part of an enlarged orbit and compressed the globe toward the caudal pole of the orbit. The brown, 6-cm tumor had central yellow and brown areas, and a smooth, glistening cut surface. Microscopically, the neoplasm was highly cellular and composed of spindle cells arranged in irregular, broad, interlacing streams and bundles, forming a herringbone pattern and supported by a sparse collagenous matrix. Neoplastic cells infiltrated surrounding soft tissues and compressed the globe. The neoplastic cells had positive immunolabeling for α–smooth muscle actin, desmin, and vimentin, and negative immunolabeling for factor VIII, myoglobin, cytokeratin, and skeletal muscle actin. Histopathology and immunohistochemistry results confirmed a diagnosis of leiomyosarcoma. To our knowledge, congenital periocular leiomyosarcoma has not been reported in cattle previously. This rare tumor could be included as a differential diagnosis in newborn calves with periocular masses. [ABSTRACT FROM AUTHOR]

In this article, we derive the minimax detection boundary for testing a sub-block of variables in a precision matrix under the Gaussian distribution. Compared to the results on the minimum rate of signals for testing precision matrices in literature, our result gives the exact minimum signal strength in a precision matrix that can be detected. We propose a thresholding test that is able to achieve the minimax detection boundary under certain cases by adaptively choosing the threshold level. The asymptotic distribution of the thresholding statistic for precision matrices is derived. Power analysis is conducted to show the proposed test is powerful against sparse and weak signals, which cannot be detected by the existing L m a x and L 2 tests. Simulation studies show the proposed test has an accurate size around the nominal level and is more powerful than the existing tests for detecting sparse and weak signals in precision matrices. Real data analysis on brain imaging data is carried out to illustrate the utility of the proposed test in practice, which reveals functional connectivity between brain regions for Alzheimer's disease patients and normal healthy people. [ABSTRACT FROM AUTHOR]

Timely and accurate monitoring of typical coastal targets using remote sensing technology is crucial for maintainingmarine ecological stability. Hyperspectral target detection technology proves to be an effective tool in extracting various typical materials along the coastline. Traditional target detection methods using spectral domain information can effectively retain the intrinsic properties of the material. However, it is difficult to effectively recognize targets in homogeneous regions by using only spectral domain information, which may lead to insufficient utilization of spatial information. In this study, a detector based on signal-to-noise ratio fusion constrained energy minimization with low-rank sparse decomposition (SFLRSD) is proposed. This detector improves the separability of background and target by obtaining spatial domain information from hyperspectral images and fusing spectral domain information. First, total variation regularization and fractional Fourier transform are applied to process spatial and spectral domain information, respectively. The constrained energy minimization (CEM) detector is used to improve the separability between the target and background of the processed data. Then, the background and anomalies are represented as low-rank and sparse components, respectively, using low-rank sparse matrix factorization. This transforms the model solution into a covariance matrix problem, which is then solved using marginal distance difference (MDD) to isolate anomalous parts. Subsequently, the anomaly parts are fused with CEM detector results, weighted by their respective signal-to-noise ratios. This detection model leverages unified hyperspectral image features, enhancing spectral discreteness of anomalous targets and backgrounds. Finally, experiments on custom created hyperspectral dataset show that the proposed method outperforms other baseline methods in terms of visualization and quantitative performance. In this paper, we not only propose a new hyperspectral target detection method, but we also collect three typicalmarine litter of different materials bymeans of airborne hyperspectral remote sensing and construct four hyperspectral datasets in a real environment. All the simulation experiments in this paper are conducted in these four datasets. [ABSTRACT FROM AUTHOR]

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EEG signals are widely utilized in brain-computer interface (BCI) applications. However, the non-linear and non-stationary nature of EEG signals poses a challenge when dealing with variations across subjects and sessions, leading to the covariate shift problem in recognition tasks. Conventional approaches often extract vector-form features for classifying EEG signals on a per-subject and per-session basis, resulting in the loss of discriminative features and decreased recognition performance. To address this issue, this paper presents a novel cross-subject EEG feature matrix classification method that leverages the feature matrix encompassing all subjects to recognize EEG signals. The proposed method begins by aligning the EEG covariances of each subject to an identity distribution, followed by extracting a feature matrix from the aligned EEG signals. To recognize EEG signals associated with specific mental tasks, a sparse support matrix machine is employed to select discriminative features from the feature matrix and perform classification based on these selected features. To evaluate the proposed method, two publicly available benchmark datasets containing motor imagery and event-related potentials were used in experiments. Comparative analyses with state-of-the-art methods demonstrated improved recognition performance with the proposed method. Furthermore, additional ablation studies were conducted to explore the potential application prospects of the proposed method in BCI researches. [ABSTRACT FROM AUTHOR]

Sparse matrix–matrix multiplication (SpMM) is essential for deep learning models and scientific computing. Recently, Tensor Cores (TCs) on GPUs, originally designed for dense matrix multiplication with mixed precision, have gained prominence. However, utilizing TCs for SpMM is challenging due to irregular memory access patterns and a varying number of non-zero elements in a sparse matrix. To improve data locality, previous studies have proposed reordering sparse matrices before multiplication, but this adds computational overhead. In this paper, we propose Tensor Core-Adapted SpMM (TCA-SpMM), which leverages TCs without requiring matrix reordering and uses the compressed sparse row (CSR) format. To optimize TC usage, the SpMM algorithm's dot product operation is transformed into a blocked matrix–matrix multiplication. Addressing load imbalance and minimizing data movement are critical to optimizing the SpMM kernel. Our TCA-SpMM dynamically allocates thread blocks to process multiple rows simultaneously and efficiently uses shared memory to reduce data movement. Performance results on sparse matrices from the Deep Learning Matrix Collection public dataset demonstrate that TCA-SpMM achieves up to 29.58× speedup over state-of-the-art SpMM implementations optimized with TCs. [ABSTRACT FROM AUTHOR]

There are many problems in space debris monitoring with ground‐based telescopes, such as too many stars in the same field of view, uneven background and optical distortion in the optical system. We propose a two‐stage weak debris detection algorithm. In the first stage, wavelet transform is used to extract different components of three frames of images, and the median of corresponding components of the images is taken respectively to eliminate the influence of stars. In the second stage, an improved version of the faint space target extraction based on principal component analysis. The algorithm uses a smooth‐detection idea to extract target information. Based on a 150 mm aperture telescope, we improved the existing method of faint space debris extraction based on principal component analysis by introducing the smooth‐detection idea, and transformed the target detection problem into the separation problem of sparse matrix and low‐rank matrix. We applied a certain preprocessing consisting of wavelet‐based star removal and median pre‐filtering to keep as little noise and other contaminants as possible. After experimental measurements by observers, the algorithm demonstrated advanced detection capabilities on multiple indicators. Plain Language Summary: In recent years, space activities have gradually increased, followed by a massive increase in space debris. Due to the extremely high speeds at which space debris travels, it is difficult to control. If these high‐speed debris collide with operational satellites, they pose a significant destructive, potentially leading to the complete loss of satellite functionality. Therefore, space debris poses a major threat to satellites in orbit and other space assets. Accurately monitoring space target information and promptly executing aircraft avoidance maneuvers are effective measures to prevent collisions. In the actual observation system, the space target energy in the image is small and weak, especially in the middle and high orbit, it is difficult to extract the target information. We propose a two‐stage faint target detection algorithm. In the first stage, the influence of stars and partial noise on target detection is eliminated. In the second stage, the idea of principal component analysis is applied to extract spatial target information. It is worth noting that our aim is to build an automated space target information extraction system, so we do not apply any prior information about the space target in the algorithm. Key Points: We propose a space debris detection algorithm under complex background, which can improve the space surveillance capability of telescopesThe faint target detection technique in complex background is transformed into the separation problem of low rank matrix and sparse matrixWe use a large number of images captured by real telescopes for experiments, qualitative and quantitative analysis to reach conclusions [ABSTRACT FROM AUTHOR]

The Jacobian-free Newton-Krylov (JFNK) method is a widely used and flexible numerical method for solving the neutronic/thermal-hydraulic coupling system. The main property of JFNK is that the Jacobian-vector product is evaluated approximately by finite difference, avoiding the forming and storage of Jacobian explicitly. However, the lack of an efficient preconditioner is a major bottleneck for the JFNK method, leading to poor convergence. The finite difference Jacobian-based Newton-Krylov (DJNK) method is another advanced numerical method, in which the Jacobian matrix is formed and stored explicitly. The DJNK method can provide a better preconditioner for Krylov iteration than JFNK. However, how to compute the Jacobian matrix efficiently and automatically is a key issue for the DJNK method. By fully utilizing the sparsity of the Jacobian matrix and graph coloring algorithm, the Jacobian can be computed efficiently. Unfortunately, when there are dense rows/blocks, a huge computational burden will emerge due to the lack of sparsity, resulting in the extremely poor efficiency of Jacobian computation. In this work, a Jacobian-split Newton-Krylov (JSNK) method is proposed to resolve the dense row/block problem by combining the advantages of JFNK and DJNK. The main feature of the JSNK method is to split the Jacobian matrix into sparse and dense parts. The sparse part of the Jacobian matrix is explicitly constructed using the graph coloring algorithm while for the dense part, the Jacobian-vector product is approximated by finite difference. The computational complexity of the JSNK method is analyzed and compared to the JFNK method and the DJNK method from theoretical and experimental aspects and under different meshes. A simplified two-dimensional (2-D) high-temperature gas-cooled reactor (HTR) model and a simplified 2-D pressurized water reactor model are utilized to demonstrate the superiority of the JSNK method. The numerical results show that the JSNK method successfully resolved the dense rows/blocks. More importantly, its efficiency significantly outperforms the JFNK method and the DJNK method. [ABSTRACT FROM AUTHOR]

While the practical application of adaptive filters has indeed garnered substantial attention, two pressing issues persist that have a profound impact on their performance—system sparsity and the presence of contaminated Gaussian impulsive noise. In this research paper, we propose a novel approach to tackle both of these issues simultaneously by introducing the concept of a proportionate matrix. Specifically, we present a proportionate maximum total complex correntropy algorithm based on the errors-in-variables model. The paper presents a theoretical analysis of the steady-state weight error power under the influence of impulsive noise. Furthermore, it discusses the performance comparison in system identification and highlights the robustness of the proposed algorithm. To validate its effectiveness, a simulation involving stereophonic acoustic echo cancellation is conducted, and the results confirm the clear advantages of the proposed Proportionate Maximum Total Complex Correntropy algorithm. [ABSTRACT FROM AUTHOR]

Cognitive diagnostic assessment (CDA) is widely used because it can provide refined diagnostic information. The Q-matrix is the basis of CDA, and can be specified by domain experts or by data-driven estimation methods based on observed response data. The data-driven Q-matrix estimation methods have become a research hotspot because of their objectivity, accuracy, and low calibration cost. However, most of the existing data-driven methods require known prior knowledge, such as initial Q-matrix, partial q-vector, or the number of attributes. Under the G-DINA model, we propose to estimate the number of attributes and Q-matrix elements simultaneously without any prior knowledge by the sparse non-negative matrix factorization (SNMF) method, which has the advantage of high scalability and universality. Simulation studies are carried out to investigate the performance of the SNMF. The results under a wide variety of simulation conditions indicate that the SNMF has good performance in the accuracy of attribute number and Q-matrix elements estimation. In addition, a set of real data is taken as an example to illustrate its application. Finally, we discuss the limitations of the current study and directions for future research. [ABSTRACT FROM AUTHOR]

The unique non‐coding RNA molecule known as circular RNA (circRNA) is distinguished from conventional linear RNA by having a longer half‐life, greater degree of conservation and inherent solidity. Extensive research has demonstrated the profound impact of circRNA expression on cellular drug sensitivity and therapeutic efficacy. There is an immediate need for the creation of efficient computational techniques to anticipate the potential correlations between circRNA and drug sensitivity, as classical biological research approaches are time‐consuming and costly. In this work, we introduce a novel deep learning model called SNMGCDA, which aims to forecast the relationships between circRNA and drug sensitivity. SNMGCDA incorporates a diverse range of similarity networks, enabling the derivation of feature vectors for circRNAs and drugs using three distinct calculation methods. First, we utilize a sparse autoencoder for the extraction of drug characteristics. Subsequently, the application of non‐negative matrix factorization (NMF) enables the identification of relationships between circRNAs and drugs based on their shared features. Additionally, the multi‐head graph attention network is employed to capture the characteristics of circRNAs. After acquiring the characteristics from these three separate components, we combine them to form a unified and inclusive feature vector for each cluster of circRNA and drug. Finally, the relevant feature vectors and labels are inputted into a multilayer perceptron (MLP) to make predictions. The outcomes of the experiment, obtained through 5‐fold cross‐validation (5‐fold CV) and 10‐fold cross‐validation (10‐fold CV), demonstrate SNMGCDA outperforms five other state‐of‐art methods in terms of performance. Additionally, the majority of case studies have predominantly confirmed newly discovered correlations by SNMGCDA, thereby emphasizing its reliability in predicting potential relationships between circRNAs and drugs. [ABSTRACT FROM AUTHOR]

Mesh processing algorithms are often communicated via concise mathematical notation (e.g., summation over mesh neighborhoods). However, conversion of notation into working code remains a time-consuming and error-prone process, which requires arcane knowledge of low-level data structures and libraries—impeding rapid exploration of high-level algorithms. We address this problem by introducing a domain-specific language (DSL) for mesh processing called I MESH, which resembles notation commonly used in visual and geometric computing and automates the process of converting notation into code. The centerpiece of our language is a flexible notation for specifying and manipulating neighborhoods of a cell complex, internally represented via standard operations on sparse boundary matrices. This layered design enables natural expression of algorithms while minimizing demands on a code generation backend. In particular, by integrating I MESH with the linear algebra features of the I LA DSL and adding support for automatic differentiation, we can rapidly implement a rich variety of algorithms on point clouds, surface meshes, and volume meshes. [ABSTRACT FROM AUTHOR]

Sparse general matrix–matrix multiplication (SpGEMM) is a crucial and complex computational task in many practical applications. Improving the performance of SpGEMM on SIMT processors like modern GPUs is challenging due to the unpredictable sparsity of sparse matrices. Although existing GPU solutions have made progress in improving performance through advanced algorithm design, they ignore some optimizations related to specific processor architectures. This can result in a partially inefficient implementation of their algorithms. This paper focuses on optimizing four inefficient parts of the NSparse algorithm on DCU (a GPU-like accelerator). The optimizations include: 1) setting parameters to improve the load balance of the second matrix by extracting maximum row information at runtime; 2) reducing overhead of binning operations by making full use of registers and shared memory effectively; 3) improving numerical SpGEMM performance by adjusting its calculation mode; and 4) enhancing global load balance through finer-grained grouping and kernel configurations. Experiment results demonstrate that when compared to five state-of-the-art SpGEMM algorithms (bhSparse, KokkosKernels, NSparse, rocSparse, and spECK), our optimized method achieves an average of 7.99x (up to 18.2x), 8.01x (up to 20.83x), 2.37x (up to 6.16x), 1.82x (up to 4.20x), and 1.63x (up to 5.01x) speedups on 29 sparse matrices with different sparse structures, respectively. [ABSTRACT FROM AUTHOR]

The use of matrix completion methods to predict the association between microbes and diseases can effectively improve treatment efficiency. However, the similarity measures used in the existing methods are often influenced by various factors such as neighbourhood size, choice of similarity metric, or multiple parameters for similarity fusion, making it challenging. Additionally, matrix completion is currently limited by the sparsity of the initial association matrix, which restricts its predictive performance. To address these problems, we propose a matrix completion method based on adaptive neighbourhood similarity and sparse constraints (ANS‐SCMC) for predict microbe‐disease potential associations. Adaptive neighbourhood similarity learning dynamically uses the decomposition results as effective information for the next learning iteration by simultaneously performing local manifold structure learning and decomposition. This approach effectively preserves fine local structure information and avoids the influence of weight parameters directly involved in similarity measurement. Additionally, the sparse constraint‐based matrix completion approach can better handle the sparsity challenge in the association matrix. Finally, the algorithm we proposed has achieved significantly higher predictive performance in the validation compared to several commonly used prediction methods proposed to date. Furthermore, in the case study, the prediction algorithm achieved an accuracy of up to 80% for the top 10 microbes associated with type 1 diabetes and 100% for Crohn's disease respectively. [ABSTRACT FROM AUTHOR]

The solution of large linear systems of equations with sparse matrices is a critical component of finite element analyses. Three linear solvers are investigated here: MUMPS, UMFPACK, and Intel DSS (PARDISO). Often, these solvers are employed as "black boxes." However, some caveats in their implementation must be observed. For instance, the solvers may yield incorrect results or perform extremely poorly in a multithread environment. These issues are demonstrated, and suggestions to fix them are provided. Some performance benchmarks are also presented with a focus on the multithreaded behavior. [ABSTRACT FROM AUTHOR]

We give an integer linear program formulation for the star bicolouring of bipartite graphs. We develop a column generation method to solve the linear programming relaxation to obtain a lower bound for the minimum number of colours needed. We determine the star bicolouring using the iterative rounding method. We give computational results on arrowhead matrices, sparse random matrices, complete bipartite graphs, and matrices from the Harwell–Boeing collection. The findings demonstrate that the proposed method effectively establishes lower and upper bounds for the minimum number of colours needed for a star bicolouring of bipartite graphs, particularly for sparse bipartite graphs. [ABSTRACT FROM AUTHOR]

Aircraft icing seriously threatens flight safety. This paper describes a modified shallow-water icing thermodynamic model that is applicable to unstructured grids and considers the effects of changes in water physical parameters and sublimation on icing. An icing calculation method enables the automatic determination of whether freezing occurs and the type of icing. An autonomous icing calculation program is developed to extract the geometric coordinates and mesh information of the icing surface and combine this information with the multiphase flow field of air-supercooled water droplets. The icing equations in the Godnov format are discretized to produce a large-scale sparse matrix that is solved iteratively using the biconjugate gradient stabilized method. The output includes parameter distributions for the ice thickness, water film thickness, and equilibrium temperature. Taking the National Advisory Committee for Aeronautic 0012 airfoil as the study object, the results of icing simulations are compared with experimental data from an ice wind tunnel and the ice shapes calculated by the FENSAP-ICE software. The results are found to be in good agreement with the experimental data, and the ice height errors at stagnation points are less than 15%. In the case of rime ice, single-horned ice shapes are simulated for both conventional and large supercooled droplets. For mixed ice and glaze ice, double-horned ice shapes are simulated for both droplet conditions. FENSAP-ICE fails to simulate the ice horns and produces large errors in ice thickness and ice range. [ABSTRACT FROM AUTHOR]

The complex nonlinear characteristics of atmospheric chemistry necessitate the development of new methods for calculating source–receptor (S–R) relationships for secondary air pollutants. In this study, the monthly characteristics and S–R relationships of anthropogenic total nitrate (i.e., the sum of N from nitric acid, inorganic nitrate, and peroxyacetyl nitrate) in Northeast Asia were simulated and analyzed. The Community Multiscale Air Quality (CMAQ), Fifth-Generation NCAR/Penn State Mesoscale (MM5), and Sparse Matrix Operator Kernel Emissions (SMOKE) models were employed for air quality modeling, meteorological fields, and emissions processing, respectively. The study area encompassed Republic of Korea, Japan, and most of China. Five source/receptor regions were defined to derive the S–R relationships: three in China, one in Republic of Korea, and one in Japan. To produce data for the calculation of the S–R relationship, several experiments were conducted with a 20% reduction in NOx emission sources. As a result of the S–R relationships, China was rarely impacted by the other two countries. The total depositions in other countries were significantly dominated by China (i.e., 43.5% and 40.7% in Republic of Korea and Japan, respectively, and up to 82.3% in December for Republic of Korea). [ABSTRACT FROM AUTHOR]

We present a new inversion scheme for 2D magnetotelluric data. In contrast to established approaches, it is based on a mesh‐free formulation of the Quasi‐Newton Broyden–Fletcher–Goldfarb–Shanno (BFGS) iteration which uses the cost function gradient to implicitly construct approximations of the Hessian inverse to update the unknown conductivity. We introduce conventional first–order regularization as well as second–order regularization where inversions based on the latter are more appropriate for sparse data and can be read as maximum likelihood estimation of the unknown conductivity. We apply first–order finite element method (FEM) discretizations of the inversion scheme, forward and adjoint problems, where the latter is required for the construction of the cost function gradients. We allow for unstructured first–order triangular meshes supporting an enhanced ground level resolution including topographical features and coarsening at the far field leading to significant reduction in computational costs from using structured mesh. Formulating the inversion iteration in continuous form prior to discretization eliminates bias due to local refinements in the mesh and gives way for computationally efficient sparse matrix techniques in the implementation. A keystone in the new scheme is the multi‐grid approximation of the Hessian of the regularizations to construct efficient preconditioning for the inversion iteration. The method is applied to the Commeni4 benchmark and two field data sets. Tests show that for both first and second–order regularization an anisotropic approach is important to address the vast differences in horizontal and vertical spatial scale which in conventional approaches is implicitly introduced through the elongated shape of grid cells. Plain Language Summary: We have developed a new inversion scheme for 2D MT data. Like most inversion methods, the cost function is composed of data misfit and a measure of the smoothness of the model (regularization). Inversion solutions are found by taking the derivative of the cost function and setting it to zero to minimize the function. The minimizing equation is solved iteratively using a quasi‐Newton method. Different to most other approaches, our method uses a discretize last strategy. Only once the quasi‐Newton iteration is derived, will discretization occur using an irregular triangular finite element mesh. The mesh is fine at ground level, very fine near measurement stations and extremely coarse at the edges of the model leading to significant reductions in computational costs compared to regular mesh. An additional feature of our method is two different types of regularization, conventional first‐order regularization and second‐order regularization, both with spatial anisotropy. This leads to multiple inversion solutions showing the variation of allowable solutions. Testing on benchmark and field data shows our method's robustness and its potential for real‐world applications. Key Points: New 2D MT inversion with both first and second–order anisotropic regularization for resolving different spacial characteristicsThe discretize‐last‐strategy implements a mesh‐free, gradient based inversion schemeMulti‐resolution preconditioning with efficient sparse matrix techniques accelerates computations [ABSTRACT FROM AUTHOR]

We present the R package galamm, whose goal is to provide common ground between structural equation modeling and mixed effect models. It supports estimation of models with an arbitrary number of crossed or nested random effects, smoothing splines, mixed response types, factor structures, heteroscedastic residuals, and data missing at random. Implementation using sparse matrix methods and automatic differentiation ensures computational efficiency. We here briefly present the implemented methodology, give an overview of the package and an example demonstrating its use. [ABSTRACT FROM AUTHOR]

Recent advances in spatial transcriptomics (ST) enable measurements of transcriptome within intact biological tissues by preserving spatial information, offering biologists unprecedented opportunities to comprehensively understand tissue micro-environment, where spatial domains are basic units of tissues. Although great efforts are devoted to this issue, they still have many shortcomings, such as ignoring local information and relations of spatial domains, requiring alternatives to solve these problems. Here, a novel algorithm for spatial domain identification in S patial T ranscriptomics data with S tructure C orrelation and S elf- R epresentation (ST-SCSR), which integrates local information, global information, and similarity of spatial domains. Specifically, ST-SCSR utilzes matrix tri-factorization to simultaneously decompose expression profiles and spatial network of spots, where expressional and spatial features of spots are fused via the shared factor matrix that interpreted as similarity of spatial domains. Furthermore, ST-SCSR learns affinity graph of spots by manipulating expressional and spatial features, where local preservation and sparse constraints are employed, thereby enhancing the quality of graph. The experimental results demonstrate that ST-SCSR not only outperforms state-of-the-art algorithms in terms of accuracy, but also identifies many potential interesting patterns. [ABSTRACT FROM AUTHOR]

In this paper, for solving a broad class of large-scale nonconvex and nonsmooth optimization problems, we propose a stochastic two-step inertial Bregman proximal alternating linearized minimization (STiBPALM) algorithm with variance-reduced stochastic gradient estimators. And we show that SAGA and SARAH are variance-reduced gradient estimators. Under expectation conditions with the Kurdyka–Łojasiewicz property and some suitable conditions on the parameters, we obtain that the sequence generated by the proposed algorithm converges to a critical point. And the general convergence rate is also provided. Numerical experiments on sparse nonnegative matrix factorization and blind image-deblurring are presented to demonstrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Summary: This paper targets to minimize the peak common mode voltage (CMV) in ultra sparse matrix converters (USMC) by applying new zero vectors for the space vector modulation technique (SVM). Conventional zero vectors in the SVM raise the peak CMV by 42.23%. An increased magnitude of CMV is associated with the occurrence of leakage current, hence resulting in insulation degradation. So, the reduction of peak CMV is necessary for USMC. The proposed method offers suitable switching arrangements using auxiliary shoot through (AST) switches to minimize the peak‐to‐peak CMV. This proposed method holds the advantages of the conventional method, like a wide range of modulation index and zero current switching at the rectifier side, and also reduces the CMV problem. This paper also provides a comparative analysis of the existing reported methods and the proposed method. The effectiveness of the proposed method is validated through both simulation and experimental results. [ABSTRACT FROM AUTHOR]

As data-driven deep learning (DL) has been applied in various scenarios, the privacy threats have become a widely recognized problem. To boost privacy protection in federated learning (FL), some methods adopt a one-shot differential privacy (DP) approach to obfuscate model updates, yet they do not take into account the dynamic balance between efficiency and privacy protection. To this end, we propose ASPFL—an efficient FL approach with adaptive sparsity-based pruning and differential privacy protection. We further propose the adaptive pruning mechanism by utilizing the Jensen-Shannon divergence as the metric to generate sparse matrices, which are then employed in the model updates. In addition, we introduce adaptive Gaussian noise by assessing the variation of sensitivity through post-pruning uploading. Extensive experiments validate that our proposed ASPFL boosts convergence speed by more than two times under non-IID data. Compared with existing DP-FL methods, ASPFL can maximally achieve over 82% accuracy on CIFAR-10, while the communication cost is greatly reduced by 40% under the same level of privacy protection. [ABSTRACT FROM AUTHOR]

The region in the complex plane containing the eigenvalues of all n × n stochastic matrices was described by Karpelevič in 1951, and it is since then known as the Karpelevič region. The boundary of the Karpelevič region is the union of arcs called the Karpelevič arcs. We provide a complete characterization of the Karpelevič arcs that are powers of some other Karpelevič arc. Furthermore, we find the necessary and sufficient conditions for a sparsest stochastic matrix associated with the Karpelevič arc of order n to be a power of another stochastic matrix. [ABSTRACT FROM AUTHOR]

A positive definite matrix is called logarithmically sparse if its matrix logarithm has many zero entries. Such matrices play a significant role in high-dimensional statistics and semidefinite optimization. In this paper, logarithmically sparse matrices are studied from the point of view of computational algebraic geometry: we present a formula for the dimension of the Zariski closure of a set of matrices with a given logarithmic sparsity pattern, give a degree bound for this variety and develop implicitization algorithms that allow to find its defining equations. We illustrate our approach with numerous examples. [ABSTRACT FROM AUTHOR]

With the continuous accumulation of massive amounts of mobile data, point-of-interest (POI) recommendation has become a vital task for location-based social networks. Deep neural networks or matrix factorization (MF) alone are challenging to effectively learn user–POI interaction functions. Moreover, the user–POI interaction matrix is sparse, and the heterogeneous characteristics of auxiliary information are underused. Therefore, we propose an innovative POI recommendation method that integrates attention-aware meta-paths based on deep neural matrix factorization (DNMF-AM). First, we develop a multi-relational heterogeneous information network of "user–POI–geographic region–POI category." Multiple-weighted isomorphic information networks based on meta-paths are employed to obtain node-embedding vectors across different relationships. Attention networks are employed to aggregate node vectors across various relationships and serve as auxiliary information to mitigate the challenges of data sparsity. Subsequently, the internal embedding vectors of the users and POIs are extracted using feature embedding based on the user–POI interaction matrix. Second, these vectors are integrated with the embedding vectors obtained by aggregating the attention networks. Third, deep neural matrix factorization is used to learn linear and nonlinear user–POI interactions to mitigate the implicit feedback problem. This outcome is achieved using generalized matrix factorization and convolution-constrained multi-head self-attention mechanism deep neural networks. Extensive experiments conducted on two real-world datasets demonstrate that the DNMF-AM outperforms the optimal baseline NeuMF-CAA by 4.24% and 5.04% in terms of HR@10 and NDCG@10, respectively. [ABSTRACT FROM AUTHOR]

Subspace clustering typically clusters data by performing spectral clustering to an affinity matrix constructed in some deterministic ways of self-representation coefficient matrix. Therefore, the quality of the affinity matrix is vital to their performance. However, traditional deterministic ways only provide a feasible affinity matrix but not the most suitable one for showing data structures. Besides, post-processing commonly on the coefficient matrix also affects the affinity matrix's quality. Furthermore, constructing the affinity matrix is separate from optimizing the coefficient matrix and performing spectral clustering, which can not guarantee the optimal overall result. To this end, we propose a new method, affinity adaptive sparse subspace clustering (AASSC), by adding Laplacian rank constraint into a subspace sparse-representation model to adaptively learn a high-quality affinity matrix having accurate p-connected components from a sparse coefficient matrix without post-processing, where p represents categories. In addition, by relaxing the Laplacian rank constraint into a trace minimization, AASSC naturally combines the operations of the coefficient matrix, affinity matrix, and spectral clustering into a unified optimization, guaranteeing the overall optimal result. Extensive experimental results verify the proposed method to be effective and superior. [ABSTRACT FROM AUTHOR]

In this article, a numerical scheme for solving two‐dimensional (2D) time‐dependent incompressible Navier–Stokes equations is presented. The artificial compressibility technique is used to incorporate a time derivative of pressure term to the continuity equation. It is employed for pressure–velocity coupling. The scheme consists of backward difference approximation for time derivatives and central difference approximation for spatial derivatives, implemented on a collocated grid. The discretization of the differential equations yields a system of algebraic equations with a block coefficient matrix. To solve this system efficiently, matrix inversion with sparse matrix computation is employed. The proposed numerical scheme is applied to solve three flow problems (lid‐driven cavity flow, rectangular channel flow, and Taylor–Green vortex problem) to validate the accuracy and applicability of the scheme. The results affirm the scheme's capability to provide precise approximations for solutions to the Navier–Stokes equations. With slight modifications, the scheme can be applied to solve various flow problems with high accuracy, less memory usage, and reduced computational time. [ABSTRACT FROM AUTHOR]

Target detection in infrared remote sensing images has important practical applications. Among the current high‐performance methods, the deep learning‐based methods require training samples, and their generalization ability is also limited by the training set. The separation of low‐rank and sparse matrix requires joint processing of multiple images with high computational complexity. The track‐before‐detect algorithms based on particle filtering also have high computational complexity. In this paper, the low‐rank and sparse matrix of a single image are proposed for target detection, and a differentiable objective function is used in the separation. At the same time, an extended multitarget tracking algorithm based on random sets is used for target filtering between frames, and the design of the filters adopts the conjugate distribution under the Bayesian framework. Finally, the practical infrared sequence images containing multiple targets and complex backgrounds were employed to verify the performance of the proposed algorithms by comparing them with state‐of‐the‐art algorithms. [ABSTRACT FROM AUTHOR]

Friction between the rake face of the tool and the chip is a primary contributor to tool rake face wear. Hence, reducing the friction coefficient between the tool's rake face and the chip proves to be an effective method for wear mitigation. To minimize the friction coefficient of cutting tools, distinctive microtextures were laser-engraved onto the rake face, employing hydrodynamic lubrication principles. To minimize the adverse impact of microtextures on the tool and simultaneously achieve hydrodynamic lubrication, a sparse matrix arrangement method was introduced for microtexture placement. For further enhancement of the hydrodynamic lubrication effect, finite element analysis was utilized to optimize both the depth and arrangement of microtextures. Friction and cutting experiments were performed to validate the lubrication efficiency of biomimetic microtextures, with an accompanying analysis of the lubrication mechanism. In summary, biomimetic microtextures successfully diminish friction between the tool's rake face and the chip, resulting in a significant reduction in three-dimensional cutting forces, notably decreasing the main cutting force and accomplishing the objective of reducing tool wear. [ABSTRACT FROM AUTHOR]

Using sparse matrix for total focusing method (TFM) imaging can improve computational efficiency in non-destructive testing (NDT). In sparse matrix design, binary particle swarm optimisation (BPSO) and genetic algorithm (GA) often fall into local optimal solution, and the computational efficiency decreases significantly with the expansion of array scale. In this paper, a discrete war strategy optimisation (DWSO) is proposed to realise sparse array ultrasonic imaging. This method uses equidistant scatter mapping to real-number encode the array position and limit the search range. Then, the fitness function is constructed with low side lobe peak and narrow main lobe width to obtain the optimal array element distribution. Experiments on standard test block demonstrate the DWSO algorithm has a narrower main lobe width and lower side lobe peaks than BPSO and GA. The imaging time of the sparse array constructed by this algorithm is reduced by more than 65% compared with the full array. As array scale grows, the running time variation of the proposed method is reduced by 73.2% and 77.3% compared with GA and BPSO, which has good adaptability and provides theoretical support for real-time defect detection. [ABSTRACT FROM AUTHOR]

Traditional near-field acoustic holography (NAH) based on the boundary element method (BEM) exhibits good performance for sound source identification. However, good reconstruction results can only be guaranteed if a sufficient number of sampling points are used. In this paper, the unitary matrix is used as the sparse basis matrix of source surface velocity and is obtained from the transfer matrix between the source surface sound pressure and vibration velocity by singular value decomposition (SVD). Based on this sparse basis, a sparse Bayesian learning (SBL) algorithm is introduced into BEM-based NAH to address the case of few sampling points. The use of a standard SBL algorithm in BEM-based NAH leads to hyperparameters that are overly sparse due to the large number of iterations, which results in large reconstruction errors. To solve this problem, a modified SBL algorithm is proposed. Good reconstruction results are maintained by selecting appropriate hyperparameters and revising the results using the steepest descent method. A simulated cuboid shell is used to explore the influence of the (i) number of sampling points and (ii) signal-to-noise ratio (SNR) on the reconstruction. Numerical results show that the proposed method can achieve effective reconstruction when the number of sampling points is approximately one-tenth of the number of discrete points on the source surface. The validity of the proposed method is verified by a comparison with experimental results. [ABSTRACT FROM AUTHOR]

Application of Godunov's method for constructing the spectral portrait of a matrix for estimating the rank of matrices of a special form that arise in a number of applications, such as analyzing the structures of nearest neighbor graphs, the theory of finite state machines, and estimating the spectrum of sparse matrices is studied. A computational algorithm for generating an ensemble of random distance matrices and associated nearest neighbor graphs is described. On the basis of a computational experiment, parameters of the distribution of degrees of vertices of random nearest neighbor graphs are estimated. Estimates can be obtained due to the fact that the specified distribution is independent of the distribution function of random distances and is a multidimensional normal distribution. It is proved that the rank of the incidence matrix of the nearest neighbor graph is equal to the total number of vertices with in-degrees zero and one, and the distribution of the rank of such a matrix is obtained. It is shown that in this problem of determining the rank of a matrix, a method based on the analysis of the distribution of vertex degrees is also very effective. [ABSTRACT FROM AUTHOR]

Large-scale optimization algorithms frequently require sparse Hessian matrices that are not readily available. Existing methods for approximating large sparse Hessian matrices have limitations. To try and overcome these, we propose a novel approach that reformulates the problem as the solution of a large linear least squares problem. The least squares problem is sparse but can include a number of rows that contain significantly more entries than other rows and are regarded as dense. We exploit recent work on solving such problems using either the normal equations or an augmented system to derive a robust approach for computing approximate sparse Hessian matrices. Example sparse Hessians from the CUTEst test problem collection for optimization illustrate the effectiveness and robustness of the new method. [ABSTRACT FROM AUTHOR]

This paper focuses on the design, analysis and implementation of a new preconditioning concept for linear second order partial differential equations, including the convection‐diffusion‐reaction problems discretized by Galerkin or discontinuous Galerkin methods. We expand on the approach introduced by Gergelits et al. and adapt it to the more general settings, assuming that both the original and preconditioning matrices are composed of sparse matrices of very low ranks, representing local contributions to the global matrices. When applied to a symmetric problem, the method provides bounds to all individual eigenvalues of the preconditioned matrix. We show that this preconditioning strategy works not only for Galerkin discretization, but also for the discontinuous Galerkin discretization, where local contributions are associated with individual edges of the triangulation. In the case of nonsymmetric problems, the method yields guaranteed bounds to real and imaginary parts of the resulting eigenvalues. We include some numerical experiments illustrating the method and its implementation, showcasing its effectiveness for the two variants of discretized (convection‐)diffusion‐reaction problems. [ABSTRACT FROM AUTHOR]

Over the past two decades, a major advance that enabled airborne bathymetric lidar to benefit a much wider range of marine science applications was the development of procedures for creating seafloor reflectance mosaics from recorded intensity data. It was recognized that intensity data, derived from the amplitudes of laser returns from the seafloor, contained information related to seafloor albedo and composition. However, the raw intensity data were also found to be related to a number of nuisance parameters, such that, when grided, they exhibited discontinuities, seamlines and other artifacts, hindering their use in benthic habitat mapping. These realizations led to the development of tools and workflows for correcting lidar intensity data to produce seamless seafloor reflectance mosaics. At present, an opportunity exists for another major advance in airborne bathymetric lidar by utilizing not only intensity data, but a large suite of waveform features that describe the shape of the return signal from the seafloor, to characterize benthic habitats and perform ecological assessments. However, similar to raw intensity data, other waveform features exhibit salient discontinuities, seamlines, and other artifacts, if uncorrected. Furthermore, in contrast to the case of intensity data, little work has been done on correction of an entire suite of waveform features to create a set of seamless seafloor mosaics. This study aims to address this need through a novel normalization method that integrates two image blending techniques: Gaussian weighted color matching and Laplacian pyramid blending. The proposed approach, Simultaneous Invariant Normalization of Waveform Features (SINWav), is designed to be invariant to the type of input waveform features, such that feature-specific tuning is unnecessary. To handle vast amounts of data efficiently, we developed a memory-efficient sparse matrix representation. The methods were applied to bathymetric lidar data from Saipan containing 16 different waveform features. Both visual assessments and quantitative analyses using quality metrics indicated that the proposed approach outperforms results derived from raw data and conventional linear transform. [ABSTRACT FROM AUTHOR]

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In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in P ∩ Z n , assuming that P is a polyhedron, defined by systems A x ≤ b or A x = b , x ≥ 0 with a sparse matrix A. We develop algorithms for these problems that outperform state-of-the-art ILP and counting algorithms on sparse instances with bounded elements in terms of the computational complexity. Assuming that the matrix A has bounded elements, our complexity bounds have the form s O (n) , where s is the minimum between numbers of non-zeroes in columns and rows of A, respectively. For s = o (log n) , this bound outperforms the state-of-the-art ILP feasibility complexity bound (log n) O (n) , due to Reis & Rothvoss (in: 2023 IEEE 64th Annual symposium on foundations of computer science (FOCS), IEEE, pp. 974–988). For s = ϕ o (log n) , where ϕ denotes the input bit-encoding length, it outperforms the state-of-the-art ILP counting complexity bound ϕ O (n log n) , due to Barvinok et al. (in: Proceedings of 1993 IEEE 34th annual foundations of computer science, pp. 566–572, https://doi.org/10.1109/SFCS.1993.366830, 1993), Dyer, Kannan (Math Oper Res 22(3):545–549, https://doi.org/10.1287/moor.22.3.545, 1997), Barvinok, Pommersheim (Algebr Combin 38:91–147, 1999), Barvinok (in: European Mathematical Society, ETH-Zentrum, Zurich, 2008). We use known and new methods to develop new exponential algorithms for Edge/Vertex Multi-Packing/Multi-Cover Problems on graphs and hypergraphs. This framework consists of many different problems, such as the Stable Multi-set, Vertex Multi-cover, Dominating Multi-set, Set Multi-cover, Multi-set Multi-cover, and Hypergraph Multi-matching problems, which are natural generalizations of the standard Stable Set, Vertex Cover, Dominating Set, Set Cover, and Maximum Matching problems. [ABSTRACT FROM AUTHOR]

The irregular distribution of non-zero elements of large-scale sparse matrix leads to low data access efficiency caused by the unique architecture of the Sunway many-core processor, which brings great challenges to the efficient implementation of sparse matrix–vector multiplication (SpMV) computing by SW26010P many-core processor. To address this problem, a study of SpMV optimization strategies is carried out based on the SW26010P many-core processor. Firstly, we design a memorized data storage transformation strategy to transform the matrix in CSR storage format into BCSR (Block Compressed Sparse Row) storage. Secondly, the dynamic task scheduling method is introduced to the algorithm to realize the load balance between slave cores. Thirdly, the LDM memory is refined and designed, and the slave core dual cache strategy is optimized to further improve the performance. Finally, we selected a large number of representative sparse matrices from the Matrix Market for testing. The results show that the scheme has obviously speedup the processing procedure of sparse matrices with various sizes and sizes, and the master–slave speedup ratio can reach up to 38 times. The optimization method used in this paper has implications for other complex applications of the SW26010P many-core processor. [ABSTRACT FROM AUTHOR]

Motivation World Health Organization estimates that there were over 10 million cases of tuberculosis (TB) worldwide in 2019, resulting in over 1.4 million deaths, with a worrisome increasing trend yearly. The disease is caused by Mycobacterium tuberculosis (MTB) through airborne transmission. Treatment of TB is estimated to be 85% successful, however, this drops to 57% if MTB exhibits multiple antimicrobial resistance (AMR), for which fewer treatment options are available. Results We develop a robust machine-learning classifier using both linear and nonlinear models (i.e. LASSO logistic regression (LR) and random forests (RF)) to predict the phenotypic resistance of Mycobacterium tuberculosis (MTB) for a broad range of antibiotic drugs. We use data from the CRyPTIC consortium to train our classifier, which consists of whole genome sequencing and antibiotic susceptibility testing (AST) phenotypic data for 13 different antibiotics. To train our model, we assemble the sequence data into genomic contigs, identify all unique 31-mers in the set of contigs, and build a feature matrix M , where M [ i , j ] is equal to the number of times the i th 31-mer occurs in the j th genome. Due to the size of this feature matrix (over 350 million unique 31-mers), we build and use a sparse matrix representation. Our method, which we refer to as MTB++, leverages compact data structures and iterative methods to allow for the screening of all the 31-mers in the development of both LASSO LR and RF. MTB++ is able to achieve high discrimination (F -1 >80%) for the first-line antibiotics. Moreover, MTB++ had the highest F -1 score in all but three classes and was the most comprehensive since it had an F -1 score >75% in all but four (rare) antibiotic drugs. We use our feature selection to contextualize the 31-mers that are used for the prediction of phenotypic resistance, leading to some insights about sequence similarity to genes in MEGARes. Lastly, we give an estimate of the amount of data that is needed in order to provide accurate predictions. Availability The models and source code are publicly available on Github at https://github.com/M-Serajian/MTB-Pipeline. [ABSTRACT FROM AUTHOR]

Motivation High-resolution Hi-C contact matrices reveal the detailed three-dimensional architecture of the genome, but high-coverage experimental Hi-C data are expensive to generate. Simultaneously, chromatin structure analyses struggle with extremely sparse contact matrices. To address this problem, computational methods to enhance low-coverage contact matrices have been developed, but existing methods are largely based on resolution enhancement methods for natural images and hence often employ models that do not distinguish between biologically meaningful contacts, such as loops and other stochastic contacts. Results We present Capricorn, a machine learning model for Hi-C resolution enhancement that incorporates small-scale chromatin features as additional views of the input Hi-C contact matrix and leverages a diffusion probability model backbone to generate a high-coverage matrix. We show that Capricorn outperforms the state of the art in a cross-cell-line setting, improving on existing methods by 17% in mean squared error and 26% in F 1 score for chromatin loop identification from the generated high-coverage data. We also demonstrate that Capricorn performs well in the cross-chromosome setting and cross-chromosome, cross-cell-line setting, improving the downstream loop F 1 score by 14% relative to existing methods. We further show that our multiview idea can also be used to improve several existing methods, HiCARN and HiCNN, indicating the wide applicability of this approach. Finally, we use DNA sequence to validate discovered loops and find that the fraction of CTCF-supported loops from Capricorn is similar to those identified from the high-coverage data. Capricorn is a powerful Hi-C resolution enhancement method that enables scientists to find chromatin features that cannot be identified in the low-coverage contact matrix. Availability and implementation Implementation of Capricorn and source code for reproducing all figures in this paper are available at https://github.com/CHNFTQ/Capricorn. [ABSTRACT FROM AUTHOR]

The spectrum of a kernel matrix significantly depends on the parameter values of the kernel function used to define the kernel matrix. This makes it challenging to design a preconditioner for a regularized kernel matrix that is robust across different parameter values. This paper proposes the adaptive factorized Nyström (AFN) preconditioner. The preconditioner is designed for the case where the rank k of the Nyström approximation is large, i.e., for kernel function parameters that lead to kernel matrices with eigenvalues that decay slowly. AFN deliberately chooses a well-conditioned submatrix to solve with and corrects a Nyström approximation with a factorized sparse approximate matrix inverse. This makes AFN efficient for kernel matrices with large numerical ranks. AFN also adaptively chooses the size of this submatrix to balance accuracy and cost. [ABSTRACT FROM AUTHOR]

Sparse matrix-vector multiplication (SpMV) plays a critical role in a wide range of linear algebra computations, particularly in scientific and engineering disciplines. However, the irregular memory access patterns, extensive memory usage, high bandwidth requirements, and underutilization of parallelism hinder the computational efficiency of SpMV on GPUs. In this paper, we propose a novel approach called block-wise dynamic mixed-precision (BDMP) to address these challenges. Our methodology involves partitioning the original matrix into uniformly sized blocks, with each block's size determined by considering architectural characteristics and accuracy requirements. Additionally, we dynamically assign precision to each block using a precision selection method that takes into account the value distribution of the original sparse matrix. We develop two distinct SpMV computation algorithms for BDMP: BDMP-PBP (Precision-based partitioning) and BDMP-TCKI (Tailored compression and kernel implementation). BDMP-PBP partitions the matrix into two independent matrices for separate computations based on block precision, offering flexibility for integration with other optimization techniques. Meanwhile, BDMP-TCKI focuses on achieving significant thread-level parallelism and memory utilization by tailoring an appropriate compressed storage format and kernel implementation for each block. We compare BDMP with NVIDIA's cuSPARSE library and three state-of-the-art SpMV methods, including SELLP, MergeBase, and BalanceCSR, using matrices from the University of Florida's SuiteSparse dataset collection. BDMP-PBP and BDMP-TCKI show average speedups up to 2.64 × and 2.91 × on Turing RTX 2080Ti, and up to 2.99 × and 3.22 × on Ampere A100. The results demonstrate that BDMP enables the optimization of computation speed without compromising the precision necessary for reliable results. [ABSTRACT FROM AUTHOR]

Existing methods in article recommendation fail to fully use the article information, or pay less attention to the correlations among articles and "User-Article"s, resulting in inaccurate recommendation performance and weak personalized recommendation ability. Therefore, we design an article recommendation model based on Dual-AutoEncoder & Bipartite Graph (DAEBG): we build a Dual-AutoEncoder, consisting of an Attention-based AutoEncoder and a Graph AutoEncoder, for article basic features of "Title and Abstract" and the correlation features among articles by the "Tag and Citation" information, which are the input of DAEBG. Second, we design a correlation extraction network with Resource Allocation-based Bipartite Graph to extract the correlation feature embeddings of "User-Article"s. Finally, we employ the Probabilistic Matrix Factorization to fuse and update these feature embeddings, consider all kinds of features comprehensively, and avoid the sparse matrix and cold start problems. The output of DAEBG is a rating matrix, which is used for article recommendation. Experimental results show that DAEBG outperforms the other recommended methods in all experiments with different data characteristics (sparse or dense), which could help people choose the targets that better match their interests from a huge amount of articles. [ABSTRACT FROM AUTHOR]

Aiming at solving the problem that the capability of direction of arrival method for estimation of nested arrays decreases sharply under unknown mutual coupling, an iterative weighted low‐rank matrix reconstruction algorithm is proposed here. First, the received data covariance matrix is extended, and a weighted low‐rank matrix recovery problem is formulated for joint estimations of the Toeplitz matrix and mutual coupling coefficients. Next, the direction of arrival from recovered Toeplitz matrix is retrieved by using the root multiple signal classification algorithm. Simulation results show that iterative weighted low‐rank matrix reconstruction algorithm can effectively avoid the influence of mutual coupling while solving the grid‐mismatch problem so that the accuracy and the resolution of estimation are improved. [ABSTRACT FROM AUTHOR]