Matrix Size Research Articles

Utility of under-sampled scans with iterative reconstruction and high-frequency preserving transform for high spatial resolution magnetic resonance cholangiopancreatography.

Under-sampled scans with iterative reconstruction and high-frequency preserving transform (Us-IRHF) can increase the acquisition speed without degrading the image quality by recovering image information from under-sampled data. We investigate the clinical applicability of high spatial resolution magnetic resonance cholangiopancreatography (MRCP) images without extending the scanning time using Us-IRHF. A slit phantom was scanned with conventional- (without Us-IRHF), Us-IR- (without HF), and Us-IRHF scanning. The matrix size was 320 × 320 for Us-IR- and Us-IRHF- and 288 × 208 for conventional scanning. Modulation transfer function (MTF) focused on the 1.0 lp/cm gauge for each scanning was calculated. For clinical study we acquired respiratory-triggered 3D MRCP scans with and without Us-IRHF (U+-, U-MRCP) in 41 patients. The matrix size was 320 × 320 for U+- and 288 × 208 for U-MRCP. The acquisition time and the relative duct-to-periductal contrast ratios (RCs) for the right- and left intrahepatic bile-, the common bile-, and the main pancreatic duct were recorded. Visualization of each duct and overall image quality was scored on 5-point confidence scales. For visualization of each duct the score ranged from 1 (not visible) to 5 (visible with excellent details), for the image quality, it ranged from 1 (undiagnostic) to 5 (excellent). Superiority for the qualitative visualization score and non-inferiority for the RC values with prespecified margins were assessed. Phantom study showed that compared to the conventional- and Us-IR (without HF) images, the MTF for the Us-IRHF image revealed the highest response. For clinical study, the mean acquisition time was 161s for U+- and 165s for U-MRCP. For all ducts, the RC value of U+MRCP was non-inferior to U-MRCP and the qualitative visualization score assigned to U+MRCP was superior to U-MRCP. Us-IRHF improved the image quality of high spatial resolution MRCP without extending the scanning time.

Influence of Solid Solution Time on Microstructure and Precipitation Strengthening of Novel Maraging Steels

Effective subsequent heat treatment is crucial for achieving the desired microstructure and excellent mechanical properties in laser-deposited high-performance maraging steel. In this paper, we systematically investigate the synergistic relationship and tuning mechanism of different solution treatment times on the microstructure-property synergy of new maraging steels fabricated using laser direct energy deposition (LDED). To determine the optimal heat treatment process, solution treatment was conducted at 840°C for varying durations, followed by aging at 530°C for 2 hours to induce precipitation strengthening. The results indicate that after 2 hours of solution treatment, the alloy exhibits optimal ductility with an elongation of 7.90% ± 0.15%, attributed to the refinement of the martensitic matrix and precipitated phases, along with the formation of a small amount of residual austenite. When the solution treatment time is extended to 4 hours, the alloy achieves its highest tensile strength, reaching 1958 ± 24 MPa. However, the elongation decreases to 7.31% ± 0.12% due to the coarsening of the martensite and secondary phase particles. After 6 hours of solution treatment, significant coarsening and aggregation of the martensite and Fe2Mo intermetallic compounds markedly reduce the hardness, strength, and toughness of the alloy. By adjusting the solution treatment time, the size, morphology, and distribution of the martensitic matrix, Fe2Mo, and nanoscale precipitated phases play a critical role in the strengthening and fracture processes. Therefore, optimizing the precipitation behavior of the martensitic matrix and Fe2Mo intermetallic compounds through rational solution heat treatment is key to enhancing the mechanical properties of laser-deposited new maraging steels.

A block α-circulant based preconditioned MINRES method for wave equations

In this work, we propose an absolute value block α-circulant preconditioner for the minimal residual (MINRES) method to solve an all-at-once system arising from the discretization of wave equations. Motivated by the absolute value block circulant preconditioner proposed in [E. McDonald, J. Pestana, and A. Wathen. SIAM J. Sci. Comput., 40(2):A1012-A1033, 2018], we propose an absolute value version of the block α-circulant preconditioner. Since the original block α-circulant preconditioner is non-Hermitian in general, it cannot be directly used as a preconditioner for MINRES. Our proposed preconditioner is the first Hermitian positive definite variant of the block α-circulant preconditioner for the concerned wave equations, which fills the gap between block α-circulant preconditioning and the field of preconditioned MINRES solver. The matrix-vector multiplication of the preconditioner can be fast implemented via fast Fourier transforms. Theoretically, we show that for a properly chosen α the MINRES solver with the proposed preconditioner achieves a linear convergence rate independent of the matrix size. To the best of our knowledge, this is the first attempt to generalize the original absolute value block circulant preconditioner in the aspects of both theory and performance the concerned problem. Numerical experiments are given to support the effectiveness of our preconditioner, showing that the expected optimal convergence can be achieved.

A resource-aware workload scheduling method for unbalanced GEMMs on GPUs

Abstract GEMM (General Matrix Multiplication) serves as a fundamental operator for deep learning computations. Especially in attention-based deep learning models, such as Bert, GPT, and SAM, the sizes of matrices involved in GEMMs exhibit an unbalanced distribution due to the variable input, resulting in the low utilization of hardware resources. To address the issue, this paper proposes inserting a novel GEMM processing layer into the deep learning inference stack and using an adaptive load balancing method to partition and schedule GEMM computation tasks. The method is implemented with hardware runtime resource information, such as the occupancy of computing units, etc. Experiment results show the remarkable performance of our method in unbalanced input GEMM scenarios, achieving an average performance improvement of 2.3x. The method also performs well in attention-based models (GPT-2 and SAM), achieving an average inference speed improvement of 1.1x. These findings highlight the effectiveness of resource-aware algorithm optimization, especially for computation task scheduling.

An Improved Nonnegative Matrix Factorization Algorithm Combined with K-Means for Audio Noise Reduction

Clustering algorithms have the characteristics of being simple and efficient and can complete calculations without a large number of datasets, making them suitable for application in noise reduction processing for audio module mass production testing. In order to solve the problems of the NMF algorithm easily getting stuck in local optimal solutions and difficult feature signal extraction, an improved NMF audio denoising algorithm combined with K-means initialization was designed. Firstly, the Euclidean distance formula of K-means has been improved to extract audio signal features from multiple dimensions. Combined with the initialization strategy of K-means decomposition, the initialization dictionary matrix of the NMF algorithm has been optimized to avoid getting stuck in local optimal solutions and effectively improve the robustness of the algorithm. Secondly, in the sparse coding part of the NMF algorithm, feature extraction expressions are added to solve the problem of noise residue and partial spectral signal loss in audio signals during the operation process. At the same time, the size of the coefficient matrix is limited to reduce operation time and improve the accuracy of feature extraction in high-precision audio signals. Then, comparative experiments were conducted using the NOIZEUS and NOISEX-92 datasets, as well as random noise audio signals. This algorithm improved the signal-to-noise ratio by 10–20 dB and reduced harmonic distortion by approximately −10 dB. Finally, a high-precision audio acquisition unit based on FPGA was designed, and practical applications have shown that it can effectively improve the signal-to-noise ratio of audio signals and reduce harmonic distortion.

A reciprocity-aware, low-rank regularization for multidimensional deconvolution

A novel factorization-based, low-rank regularization method is introduced to solve multidimensional deconvolution (MDD) problems in the frequency domain. In this approach, each frequency component of the unknown wavefield is represented as a complex-valued square matrix and approximated as the product of a rectangular matrix and its transpose. The benefit of such a parameterization is twofold. First, each frequency matrix is guaranteed to be symmetric. From a physical standpoint, the recovered wavefield inherently adheres to the principle of reciprocity; in other words, the response to a receiver from a virtual source does not change when the two are swapped. Therefore, we refer to this low-rank parameterization as reciprocity-aware in that it respects the underlying physics of wave propagation associated with the MDD solution. Second, the size of the unknown matrix is greatly reduced compared with that of the original wavefield of interest (and halved compared with the existing factorization-based low-rank approximations). We further show that the associated objective function can be successfully optimized using the accelerated proximal gradient algorithm and present a robust strategy to define the initial guess of the solution. Numerical examples on synthetic and field data demonstrate the effectiveness of the proposed method in compressing the retrieved Green’s function while preserving its accuracy.

Cyclic shift short-distance attention for defect detection of fine etching mesh

Abstract Based on the deficiency of the existing Swin Transformer in the detection of surface defects in metal etched grids, i.e. the isolation of information transmission between different windows, and the limitations of image matrix size and network structure,which make it not suitable for long sequence data processing and dense prediction scenarios, a defect detection method for metal etching nets based on Cyclic shift Long Short Distance Attention (C-LSDA) is proposed. In the proposed method, cross-scale features are used to capture long and short distance relationships,and enhance the feature transfer between windows. Tracking position bias (TPB) is also used to improve relative position bias (RPB), in order to help the model to better understand the spatial relationships in the input data. In addition, the image is downsampled at various scales, so that the proposed method can be suitable for long sequence data processing and dense prediction scenarios. In order to improve the detection accuracy of small targets. a multi-feature fusion pyramid network (MFFPN) for feature fusion is also proposed. The experimental results show that the proposed method is significantly superior to the traditional CNN recognition method and the transformer recognition method. The proposed methodhas good identification accuracy and low computational cost.

Spectral fluctuations of multiparametric complex matrix ensembles: evidence of a single parameter dependence

Abstract We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of effective sparsity among the matrix elements, such ensembles can serve as good models for a wide range of phase transitions e.g. localization to delocalization in non-Hermitian systems or Hermitian to non-Hermitian one. Our analysis reveals a rich behavior hidden beneath the spectral statistics e.g. a crossover of the spectral statistics from Poisson to Ginibre universality class with changing variances for finite matrix size, an abrupt transition for infinite matrix size and the role of complexity parameter, a single functional of all system parameters, as a criteria to determine critical point. We also confirm the theoretical predictions in \cite{psgs, psnh}, regarding the universality of the spectral statistics in non-equilibrium regime of non-Hermitian systems characterized by the complexity parameter.

Generalizing Random Butterfly Transforms to Arbitrary Matrix Sizes

Parker and Lê introduced random butterfly transforms (RBTs) as a preprocessing technique to replace pivoting in dense LU factorization. Unfortunately, their FFT-like recursive structure restricts the dimensions of the matrix. Furthermore, on multi-node systems, efficient management of the communication overheads restricts the matrix’s distribution even more. To remove these limitations, we have generalized the RBT to arbitrary matrix sizes by truncating the dimensions of each layer in the transform. We expanded Parker’s theoretical analysis to generalized RBT, specifically that in exact arithmetic, Gaussian elimination with no pivoting will succeed with probability 1 after transforming a matrix with full-depth RBTs. Furthermore, we experimentally show that these generalized transforms improve performance over Parker’s formulation by up to 62 % while retaining the ability to replace pivoting. This generalized RBT is available in the SLATE numerical software library.

Parallel cyclic reduction of padded bordered almost block diagonal matrices

The solution of linear systems is a crucial and indispensable technique in the field of numerical analysis. Among linear system solvers, the cyclic reduction algorithm stands out for its natural inclination to parallelization. So far, the cyclic reduction has been applied primarily to linear systems with almost block diagonal matrices. Some of its variants widen the usage to almost block diagonal matrices with a last block of rows introducing a set of non-zero elements in the first group of columns. In this work, we extend cyclic reduction to matrices with additional non-zero elements below and to the right without any limitations. These matrices, called padded bordered almost block diagonal, arise from the discretization of optimal control problems featuring arbitrary boundary conditions and free parameters. Nonetheless, they also appear in two-point boundary value problems with free parameters. The proposed algorithm is based on the LU factorizations, and it is designed to be executed in parallel on multi-thread architectures. The algorithm performance is assessed through numerical experiments with different matrix sizes and threads. The computation times and speedups obtained with the parallel implementation indicate that the suggested algorithm is a robust solution for solving padded bordered almost block diagonal linear systems. Furthermore, its structure makes it suitable for the use of different matrix factorization techniques, such as QR or SVD. This flexibility enables tailored customization of the algorithm on the basis of the specific application requirements.

GraNDe: Efficient Near-Data Processing Architecture for Graph Neural Networks

Graph Neural Network (GNN) models have attracted attention, given their high accuracy in interpreting graph data. One of the primary building blocks of a GNN model is aggregation, which gathers and averages the feature vectors corresponding to the nodes adjacent to each node. Aggregation works by multiplying the adjacency and feature matrices. The size of both matrices exceeds the on-chip cache capacity for many realistic datasets, and the adjacency matrix is highly sparse. These characteristics lead to little data reuse, causing intensive main-memory accesses during the aggregation process. Thus, aggregation exhibits memory-intensive characteristics and dominates most of the total execution time. In this paper, we propose GraNDe, an NDP architecture that accelerates memory-intensive aggregation operations by locating NDP modules near DRAM datapath to exploit rank-level parallelism. GraNDe maximizes bandwidth utilization by separating the memory channel path with the buffer chip in between so that pre-/post-processing in the host processor and reduction in NDP modules operate simultaneously. By exploring the preferred data mappings of the operand matrices to DRAM ranks, we architect GraNDe to support adaptive matrix mapping that applies the optimal mapping for each layer depending on the dimension of the layer and the configuration of a memory system. We also propose adj-bundle broadcasting and re-tiling optimizations to reduce the transfer time for adjacency matrix data and to improve feature vector data reusability by exploiting tiling with consideration of adjacency between nodes. GraNDe achieves 3.01× and 1.69× on average, and up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4.00\times$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.98\times$</tex-math></inline-formula> speedups of GCN aggregation over the baseline system and the state-of-the-art NDP architecture for GCN, respectively.

Influence of TiC and Ni addition on densification and mechanical properties of microwave sintered ZrB2 based composites

The effects of TiC (10–30 vol%) and Ni (1–2 vol%) incorporation on densification, microstructural evolution and mechanical properties of microwave sintered ZrB2 matrix-based composites were investigated in the present study. The findings reveal that TiC addition significantly improves the densification of ZrB2 based composites, while the inclusion of Ni further improves densification of ZrB2–20 vol% TiC composite by reducing porosity and restricting the grain growth of both ZrB2 and TiC phases. Additionally, the highest Vickers hardness of 22.25 ± 1.33 GPa and compressive strength of 1556.2 ± 40.17 MPa were obtained for the ZrB2–20 vol% TiC composite due to lower porosity, lower grain size and higher TiC diffusion in the ZrB2 matrix. The fracture toughness enhanced with TiC and Ni addition and the maximum fracture toughness was observed as 6.66 ± 0.47 MPa.m0.5 along with the highest critical energy release rate of 95.16 ± 11.68 J/m2 for the ZrB2–20 vol% TiC-2 vol% Ni composite owing to the activation of toughening mechanisms like crack bridging, crack deflection and open pores as crack deflectors. Nanoindentation studies revealed significant improvements in elastic modulus and stiffness with the addition of TiC. The maximum elastic modulus and stiffness were observed as 482.91 ± 36.36 GPa and 237.24 ± 20.28 μN/nm for ZrB2–20 vol% TiC composite. The study highlights the potential of incorporating metallic additives with secondary reinforcements to enhance the mechanical properties and microstructures of ZrB2 matrix, making them potential materials for high-temperature applications such as control surfaces, nose caps and leading edges of supersonic aircrafts.

Accelerating DNA Sequence Alignment using Altera DE2-115

DNA sequence alignment is a technique for discovering information between two base sequences which the Smith-Waterman algorithm is the accurate method that provides a precise result for alignment compared to others. However, the performance was influence by size of dataset and a long DNA base sequence which resulted the time required for the alignment process is much longer in relation to the number of DNA sequence samples. There are many ways to accelerate DNA sequence alignment, and Field Programmable Gate Array (FPGA) is a good choice due to its parallel processing and cost efficiency. Although FPGA acceleration approaches are not new, this work investigates a purely software-based FPGA acceleration using the Altera Cyclone IV EP4CE115F29C7N FPGA as the target device. The SW algorithm was developed using the C language in Quartus II version 18.1 and the Nios II software build tools for Eclipse. The development starts with setting up the Qsys architecture before developing the code in Eclipse to determine the computational performance. The result shows the computational timing and speed of the implementation, with the highest speed achieved being 198.76 cells per millisecond. To summarise, the computational performance ultimately depends on the maximum matrix size of the FPGA, which is also influenced by the DNA-based pair length and able to complete using low-cost FPGA.

A Survey On Image Registration Techniques Using FFT

Image Registration is the process of straightening two or more images of the same scene with testimonial to a particular image. The images are captured from various sensors at different times and at multiple viewpoints. Thus, to get a better picture of any change of a scene/object over a considerable period of time image registration is important. Image registration finds application in medical sciences, remote sensing and in computer vision. This paper presents a detailed review of several approaches which are classified accordingly along with their contributions and drawbacks. The main steps of an image registration procedure are also discussed. Different performance measures are presented that determine the registration quality and accuracy. The scope for the future research are presented as well. Applications based on Fast Fourier Transform (FFT) such as signal and image processing require high computational power, plus the ability to experiment with algorithms. Reconfigurable hardware devices in the form of Field Programmable Gate Arrays (FPGAs) have been proposed as a way of obtaining high performance at an economical price. At present, however, users must program FPGAs at a very low level and have a detailed knowledge of the architecture of the device being used. To try to reconcile the dual requirements of high performance and ease of development, this paper reports on the design and realization of a High-Level framework for the implementation of 1-D and 2-D FFTs for real-time applications. Results show that the parallel implementation of 2-D FFT achieves virtually linear speed-up and real-time performance for large matrix sizes. Finally, an FPGA-based parametrizable environment based on the developed parallel 2-D FFT architecture is presented as a solution for frequency domain image filtering application

Numerical semigroups from rational matrices I: power-integral matrices and nilpotent representations

Our aim in this paper is to initiate the study of exponent semigroups for rational matrices. We prove that every numerical semigroup is the exponent semigroup of some rational matrix. We also obtain lower bounds on the size of such matrices and discuss the related class of power-integral matrices.

New constructions of MSRD codes

In this work, we provide four methods for constructing new maximum sum-rank distance (MSRD) codes. The first method, a variant of cartesian products, allows faster decoding than known MSRD codes of the same parameters. The other three methods allow us to extend or modify existing MSRD codes in order to obtain new explicit MSRD codes for sets of matrix sizes (numbers of rows and columns in different blocks) that were not attainable by previous constructions. In this way, we show that MSRD codes exist (by giving explicit constructions) for new ranges of parameters, in particular with different numbers of rows and columns at different positions.

Dispersion and Attenuation Estimation of Ultrasonic Guided Waves using Multi-Subarrays Matrix Pencil Method

Abstract Dispersion and attenuation estimation of ultrasonic guided waves is important for waveguide characterization. Matrix pencil (MP) method has been proposed for multimode complex wavenumber estimation, but its performance highly depends on the signal to noise ratio (SNR), which still brings challenges for high attenuation waveguide evaluation. In addition, the model order, i.e., matrix size in MP method, significantly impacts the dispersion curve extraction. In this study, to avoid the model order interference and compensate the SNR sensitivity of the classical MP algorithm, a multi-subarrays MP method is proposed for accurate dispersion and attenuation estimation. Considering with different Hankel matrix sizes, the multi-subarrays MP method estimates the complex wavenumbers from each pair of submatrices to filter uncertain results. A soft threshold strategy is applied to compensate the noise sensitivity of the estimation. Simulated results prove the proposed method can improve the dispersion and attenuation curve estimation.

Assessment of interstitial lung disease in a systemic sclerosis patient cohort using photon-counting detector CT with ultra-high resolution and a 1024-pixel image matrix.

This study assessed the potential of ultra-high-resolution (UHR) and a 1024-matrix in photon-counting-detector CT (PCD-CT) for evaluating interstitial lung disease (ILD) in systemic sclerosis (SSc) patients. Sixty-six SSc patients who underwent ILD-CT screening on a first-generation PCD-CT were retrospectively included. Scans were performed in UHR mode at 100 kVp with two different matrix sizes (512x512 and 1024x1024) and reconstructed at slice thicknesses of 1.5 mm and 0.2 mm. Image noise, subjective image quality, and ILD changes (1) were evaluated on a 5-point Likert-scale by two independent readers. Interreader agreement for subjective image quality ranged from fair to almost perfect (Krippendorff-Alpha: 0.258-0.862). Overall image quality was highest for 1.5 mm/1024matrix images ((reader 1: 4 (4.4), reader 2: 5 (4.5)). Image sharpness was rated significantly better in 0.2 mm images (p < 0.001). Regarding ILD changes, 0.2 mm slice thickness outperformed 1.5 mm slice thickness significantly (p < 0.001), while there was no significant difference between the two matrix sizes. 1024 matrix size demonstrated superiority in evaluating coarse reticulations compared to 512matrix size. UHR mode with a 0.2 mm slice thickness showed enhanced image sharpness and improved visibility of ILD changes compared to standard reconstructions. This has the potential to enable the early detection of subtle disease manifestations. With the invention of PCD-CT different reconstruction algorithms need to be evaluated for specific pathologies. In our study ILD UHR mode with 0.2 mm slice thickness showed to be beneficial in the detection of parenchymal changes in patients with scleroderma.

Local limits in p$p$‐adic random matrix theory

AbstractWe study the distribution of singular numbers of products of certain classes of ‐adic random matrices, as both the matrix size and number of products go to simultaneously. In this limit, we prove convergence of the local statistics to a new random point configuration on , defined explicitly in terms of certain intricate mixed ‐series/exponential sums. This object may be viewed as a nontrivial ‐adic analogue of the interpolating distributions of Akemann–Burda–Kieburg, which generalize the sine and Airy kernels and govern limits of complex matrix products. Our proof uses new Macdonald process computations and holds for matrices with iid additive Haar entries, corners of Haar matrices from , and the ‐adic analogue of Dyson Brownian motion studied by the author (https://arxiv.org/pdf/2309.02865).

Three-dimensional radial echo-planar spectroscopic imaging for hyperpolarized 13C MRSI in vivo.

To demonstrate the feasibility of 3D echo-planar spectroscopic imaging (EPSI) technique with rapid volumetric radial k-space sampling for hyperpolarized (HP) 13C magnetic resonance spectroscopic imaging (MRSI) in vivo. A radial EPSI (rEPSI) was implemented on a 3 T clinical PET/MR system. To enable volumetric coverage, the sinusoidal shaped readout gradients per k-t-spoke were rotated along the three spatial dimensions in a golden-angle like manner. A distance-weighted, density-compensated gridding reconstruction was used, also in cases with undersampling of spokes in k-space. Measurements without and with HP 13C-labeled substances were performed in phantoms and rats using a double-resonant 13C/1H volume resonator with 72 mm inner diameter. Phantom measurements demonstrated the feasibility of the implemented rEPSI sequence, as well as the robustness to undersampling in k-space up to a factor of 5 without advanced reconstruction techniques. Applied to measurements with HP [1-13C]pyruvate in a tumor-bearing rat, we obtained well-resolved MRSI datasets with a large matrix size of 123 voxels covering the whole imaging FOV of (180 mm)3 within 6.3 s, enabling to observe metabolism in dynamic acquisitions. After further optimization, the proposed rEPSI method may be useful in applications of HP 13C-tracers where unknown or varying metabolite resonances are expected, and the acquisition of dynamic, volumetric MRSI datasets with an adequate temporal resolution is a challenge.