Coefficient Matrix Research Articles

An efficient high-order weak Galerkin finite element approach for Sobolev equation with variable matrix coefficients

An efficient high-order weak Galerkin finite element approach for Sobolev equation with variable matrix coefficients

Quantification of albumin and γ-globulin concentrations by multivariate regression based on admittance relaxation time distribution (mrARTD)

Albumin andγ-globulin concentrations in subcutaneous adipose tissues (SAT) have been quantified by multivariate regression based on admittance relaxation time distribution (mrARTD) under the fluctuated background of sodium electrolyte concentration. ThemrARTD formulatesP=Ac+Ξ(P: peak matrix of distribution function magnitudeγˆand relaxation timesτˆ,c: concentration matrix of albumincAlb,γ-globulinGloc, and sodium electrolyteNac,A: coefficient matrix of a multivariate regression model, andΞ: error matrix). ThemrARTD is implemented by two processes which are: (1) the training process ofAthrough the maximum likelihood estimation ofPand (2) the quantification process ofcAlb,Gloc, andNacthrough the model prediction. In the training process, a positive correlation is present betweencAlb,Gloc, andNactoγˆ1atτˆ1= 0.1 as well asγˆ2atτˆ2= 1.40 μs as under a fixed concentration of proteins solution into a porcine SAT (cAlb= 0.800-2.400 g/dL,Gloc= 0.400-1.200 g dl-1andNac= 0.700-0.750 g dl-1). ThemrARTD method quantifiescAlb,Gloc, andNacin SAT with an absolute error of 33.79%, 44.60%, and 2.18%, respectively.

Can charm fluctuation be a better probe to study the QCD critical point?

We study the diffusion properties of an interacting hadron gas and evaluate the diffusion coefficient matrix for the baryon, strange, electric, and charm quantum numbers. For the first time, this study sheds light on the charm current and estimates the diffusion matrix coefficient for the charmed states by treating them as a part of the quasithermalized medium. We explore the diffusion matrix coefficient as a function of temperature and center-of-mass energy. A van der Waals–like interaction is assumed between the hadrons, including attractive and repulsive interactions. The calculation of diffusion coefficients is based on relaxation time approximation to the Boltzmann transport equation. A good agreement with available model calculations is observed in the hadronic limit. To conclude the study, we discuss, with a detailed explanation, that charm fluctuation is expected to be a better tool for probing the QCD critical point. Published by the American Physical Society 2025

A wavelet packet transform-based domain adaptation method for rolling bearings fault diagnosis with fusion of local and global time–frequency features

Abstract Fault diagnosis transfer learning models commonly employ deep neural networks (DNN) to analyze time-frequency features. However, excessively deep neural networks can result in diminished generalization capabilities, leading to subpar performance of the model across various working conditions. Furthermore, inappropriate domain adaptation strategies significantly constrain the accuracy of the model. To address this issue, a Robustly Optimized Residual-Network and Vision Transformer Domain Adaptation Model (RoReViTDAM) is proposed in this article, combining Wavelet Packet Transform (WPT), residual networks, and self-attention mechanisms. Firstly, the WPT is utilized to construct Multi-band Wavelet Coefficient Matrix (MWCM) and corresponding Multi-band Wavelet Coefficient Time-Frequency Feature Matrix (MWSM) with small size and feature aggregation. Subsequently, a shallow Robustly Optimized Residual Network (RoResNet) is designed to effectively extract features from MWCM, considering the spatial distance dependencies of features. Additionally, ViT (Vision Transformer) is employed for time-frequency global feature extraction from MWSM. Furthermore, Domain Adversarial Neural Network (DANN) and Multi-Kernel Maximum Mean Discrepancy (MK-MMD) are employed to extract domain-invariant features from signals of different operating conditions and fault types. At last, three fault diagnosis experiments are conducted in multi-condition scenarios of bearings. The experimental results illustrate the superiority and effectiveness of the proposed model.

An Alignment‐Agnostic Methodology for the Analysis of Designed Separations Data

ABSTRACTChemical separations data are typically analyzed in the time domain using methods that integrate the discrete elution bands. Integrating the same chemical components across several samples must account for retention time drift over the course of an entire experiment as the physical characteristics of the separation are altered through several cycles of use. Failure to consistently integrate the components within a matrix of samples and variables creates artifacts that have a profound effect on the analysis and interpretation of the data. This work presents an alternative where the raw separations data are analyzed in the frequency domain to account for the offset of the chromatographic peaks as a matrix of complex Fourier coefficients. We present a generalization of the factorization, permutation testing, and visualization steps in ANOVA‐simultaneous component analysis (ASCA) to handle complex matrices and use this method to analyze a synthetic dataset with known significant factors and compare the interpretation of a real dataset via its peak table and frequency domain representations.

Integer programs with bounded subdeterminants and two nonzeros per row

We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our approach is the first polynomial-time algorithm for the weighted stable set problem on graphs that do not contain more than k vertex-disjoint odd cycles, where k is any constant. Previously, polynomial-time algorithms were only known for k =0 (bipartite graphs) and for k =1. We observe that integer linear programs defined by coefficient matrices with bounded subdeterminants and two nonzeros per column can be also solved in strongly polynomial-time, using a reduction to b -matching.

Increasing the Accuracy of Solving Boundary Value Problems with Linear Ordinary Differential Equations Using the Bubnov-Galerkin Method

Introduction. This study investigates the possibility of increasing the accuracy of numerically solving boundary value problems using the modified Bubnov-Galerkin method with a linear ordinary differential equation, where the coefficients and the right-hand side are continuous functions. The order of the differential equation n must be less than the number of coordinate functions m.Materials and Methods. A modified Petrov-Galerkin method was used to numerically solve the boundary value problem. It employs a system of linearly independent power-type basis functions on the interval [−1,1], each normalized by the unit Chebyshev norm. The system of linear algebraic equations includes only the linearly independent boundary conditions of the original problem.Results. For the first time, an integral quadrature formula with a 22nd order error was developed for a uniform grid. This formula is used to calculate the matrix elements and coefficients in the right-hand side of the system of linear algebraic equations, taking into account the scalar product of two functions based on the new quadrature formula. The study proves a theorem on the existence and uniqueness of a solution for boundary value problems with general non-separated conditions, provided that n linearly independent particular solutions of a homogeneous differential equation of order n are known.Discussion and Conclusion. The hydrodynamic problem in a viscous strong boundary layer with a third-order equation was precisely solved. The analytical solution was compared with its numerical counterpart, and the uniform norm of their difference did not exceed 5·10‒15. The formulas derived using the generalized Bubnov-Galerkin method may be useful for solving boundary value problems with linear ordinary differential equations of the third and higher orders.

Low-rank decomposition on the antisymmetric product of geminals for strongly correlated electrons

We investigated some variational methods to compute a wavefunction based on antisymmetric product of geminals (APG). The Waring decomposition on the APG wavefunction leads a finite sum of antisymmetrized geminal power (AGP) wavefunctions, each for which the variational principle can be applied. We call this as AGP-CI method which provides a variational solution of the APG wavefunction efficiently. However, number of AGP wavefunctions in the exact AGP-CI formalism become exponentially large in case of many-electron systems. Therefore, we also investigate the low-rank APG wavefunction, in which the coefficient matrices of geminals are factorized by the Schur decomposition. Interestingly, only a few non-zero eigenvalues (up to half number of electrons) were found from the Schur decomposition on the APG wavefunction. We developed some methods to approximate the APG wavefunction by lowering the ranks of coefficient matrices of geminals, and demonstrate their performance. Our new geminal method based on the low-rank decomposition can drastically reduce the number of variational parameters, although no efficient formalism has been elaborated so far, due to the difficulty of optimization caused by the inability to compute analytical derivatives.

Temperature and refractive index sensing using a chirped tilted fiber Bragg grating (CTFBG) cascaded with a fiber Bragg grating (FBG)

This article introduces a dual-parameter sensing structure based on the combination of a chirped tilted fiber Bragg grating (CTFBG) and a fiber Bragg grating (FBG). The distinct modal responses of these gratings enable differentiated sensing of the surrounding refractive index (SRI) and temperature. The FBG was unaffected by the SRI. By analyzing the shift of the center wavelength in the spectrum, a sensitivity coefficient matrix is constructed to simultaneously measure both parameters while addressing their cross-sensitivity. The experimental results demonstrate that the proposed sensing structure exhibits low cross-sensitivity, stable sensitivity, and ease of fabrication when simultaneously measuring refractive index and temperature. It enables accurate synchronous measurements and offers significant advantages in practical applications of multi-parameter sensing. This design provides a balanced solution between performance and cost, making it suitable for diverse application scenarios.

Exploring Brain Imaging and Genetic Risk Factors in Different Progression States of Alzheimer's Disease Through OSnetNMF-Based Methods.

Alzheimer's disease (AD) is a neurodegenerative disease with no effective treatment, often preceded by mild cognitive impairment (MCI). Multimodal imaging genetics integrates imaging and genetic data to gain a deeper understanding of disease progression and individual variations. This study focuses on exploring the mechanisms that drive the transition from normal cognition to MCI and ultimately to AD. As an effective joint feature extraction and dimensionality reduction method, non-negative matrix factorization (NMF) and its improved variants, particularly the network-based non-negative matrix factorization (netNMF), have been widely used in multimodal analysis to mine brain imaging and genetic data by considering the interactions between different features. However, many of these methods overlook the importance of the coefficient matrix and do not address issues related to data accuracy and feature redundancy. To address these limitations, we propose an orthogonal sparse network non-negative matrix factorization (OSnetNMF) algorithm, which introduces orthogonal and sparse constraints based on netNMF. By establishing linear relationships between structural magnetic resonance imaging (sMRI) and corresponding gene expression data, OSnetNMF reduces feature redundancy and decreases correlation between data, resulting in more accurate and reliable biomarker extraction. Experiments demonstrate that the OSnetNMF algorithm can accurately identify risk regions of interest (ROIs) and key genes that characterize AD progression, revealing significant trends in ROI pairs such as l4thVen-HIF1A, rBst-MPO, and rBst-PTK2B. Comparative experiments show that the improved algorithm outperforms traditional methods, identifying more disease-related biomarkers and achieving better reconstruction performance.

Identifying Common Properties of Coefficient Matrices Appearing in Conventional or Invariant Scheme of Method of Fundamental Solutions

In previous studies on the method of fundamental solutions applied to Dirichlet problems, the only method for verifying the regularity of coefficient matrix has been by calculating the determinant and checking if it is non‐zero directly. These verifications were carried out in some specific cases. This paper presents an identification of common properties of coefficient matrices within the method of fundamental solutions related to regularity. It establishes sufficient conditions for coefficient matrices to be regular and diagonally dominant in the two‐dimensional plane or the three‐dimensional space. However, when dealing with both the conventional scheme and the invariant scheme, we encounter issues where achieving a good arrangement of charges while maintaining diagonal dominance is challenging. One advantage of the invariant scheme over the conventional scheme is found to be based on the solvability of the shift of the boundary data. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Quantifying Anisotropic Properties of Old–New Concrete Interfaces Using X-Ray Computed Tomography and Homogenization

The interface between old and new concrete is a critical component in many construction practices, including concrete pavements, bridge decks, hydraulic dams, and buildings undergoing rehabilitation. Despite various treatments to enhance bonding, this interface often remains a weak layer that compromises overall structural performance. Traditional design methods typically oversimplify the interface as a homogeneous or empirically adjusted factor, resulting in significant uncertainties. This paper introduces a novel framework for quantifying the anisotropic properties of old–new concrete interfaces using X-ray computed tomography (CT) and finite element-based numerical homogenization. The elastic coefficient matrix reveals that specimens away from the interface exhibit higher values in both normal and shear directions, with normal direction values averaging 33.15% higher and shear direction values 39.96% higher than those at the interface. A total of 10 sampling units along the interface were collected and analyzed to identify the “weakest vectors” in normal and shear directions. The “weakest vectors” at the interface show consistent orientations with an average cosine similarity of 0.62, compared with an average cosine similarity of 0.23 at the non-interface, which demonstrates directional features. Conversely, the result of average cosine similarity at the interface shows randomness that originates from the anisotropy of materials. The average angle between normal and shear stresses was found to be 88.64°, indicating a predominantly orthogonal relationship, though local stress distributions introduced slight deviations. These findings highlight the importance of understanding the anisotropic properties of old–new concrete interfaces to improve design and rehabilitation practices in concrete and structural engineering.

Genetic polymorphism of promising raspberry varieties determined by SSR genotyping

In this research, we investigate the genetic polymorphism of raspberry varieties and a promising raspberry hybrid bred at the Federal Horticultural Center for Breeding, Agrotechnology, and Nursery. The research objects were the following varieties: Penguin, Skromnitsa, Arisha, Komsomolskaya Pravda, Ivan Kupala, Salut, Lavina, Yubileynaya Kulikova, and No. 10-165-11. To differentiate the studied genotypes by the degree of genetic similarity, an SSR marker analysis was performed using the following 15 loci: RhM011, RiM019, RhM003, RiG001, Rubus123a, Rubus285a, Rubus270a, Rubus275a, RhM043, RhM021, RiM017, RiM015, RcFH01, RiAS01, and RiMY01. Across all 15 loci, unique sets of polymorphic alleles were identifi ed, and genetic profi les for each specimen were compiled. The average number of polymorphic DNA fragments per locus was equal to 3.6. The highest number of polymorphic amplicons per locus reached 6. The results of genotyping were used to calculate the coeffi cients of genetic similarity of the studied varieties. The complied coeffi cient matrix was subsequently used for cluster analysis. As a result of clustering, groups of genetically similar varieties were identifi ed. The largest group included Arisha, Komsomolskaya Pravda, Salut, Yubileynaya Kulikova, Penguin, and No. 10-165-11. Lavina, Skromnitsa, and Ivan Kupala specimens showed the largest genetic variations. The data obtained elucidates the current understanding of the phenotypic features of raspberry varieties and can be used when developing eff ective crossing schemes in raspberry breeding.

GRESS: Grouping Belief-Based Deep Contrastive Subspace Clustering.

The self-expressive coefficient plays a crucial role in the self-expressiveness-based subspace clustering method. To enhance the precision of the self-expressive coefficient, we propose a novel deep subspace clustering method, named grouping belief-based deep contrastive subspace clustering (GRESS), which integrates the clustering information and higher-order relationship into the coefficient matrix. Specifically, we develop a deep contrastive subspace clustering module to enhance the learning of both self-expressive coefficients and cluster representations simultaneously. This approach enables the derivation of relatively noiseless self-expressive similarities and cluster-based similarities. To enable interaction between these two types of similarities, we propose a unique grouping belief-based affinity refinement module. This module leverages grouping belief to uncover the higher-order relationships within the similarity matrix, and integrates the well-designed noisy similarity suppression and similarity increment regularization to eliminate redundant connections while complete absent information. Extensive experimental results on four benchmark datasets validate the superiority of our proposed method GRESS over several state-of-the-art methods.

New order-dependent conditions to control a class of nonlinear real-order systems

In many application points of interest, controlling the responses of real-world applications that vary with time seems quite challenging and puzzling. A linear time-varying state feedback controller is widely known and can be useful to estimate bounds to the state control matrix in the design of many control systems. The issue of initialization of real-order control system enhancement remains a challenging issue in the systems analysis subject to random initial-time placed on a real number line. We address a new design of a class of real-order control systems that consists of separated linear and nonlinear terms affected by input functions to be controlled with an implemented time-varying linear state feedback controller. We utilize the fractional comparison method and under Lipschitz nonlinearity with a constant bounding matrix of time-varying coefficients of control systems to address new order-dependent conditions that provide local and global stabilization to controlled systems. Applications of results that include practical real-order single-machine-infinite-bus power systems have been illustrated to control the responses by the utility of theoretical conditions examined along with validation of numerical simulations. It is shown that the proposed controller is practically convenient and demonstrates the efficiency of measuring the performances of control systems.

The stabilization problem for a class of discrete-time semi-Markov jump singular systems

This paper studies the stabilization problem for a class of discrete-time semi-Markov jump singular systems with mode-dependent singular matrix. Since our model is mode-dependent singular matrix, the previous methods are unable to achieve the stability. To overcome this difficulty, the novel and less conservative stability conditions with the original system coefficient matrices are constructed by developing new theories and methods. Based on the above conditions, the linear matrix inequality (LMI) based stabilizing controller design method is proposed.

A modified method for measuring geometric errors of rotary axes based on sensitivity analysis and error simulation

Complicated measurement for machine tools geometric errors limits the high-accuracy machining processes. This research is aimed at measuring and identifying geometric errors of rotary axes efficiently by designing and optimizing measurement method using double ballbar. First, the conical and tangential measurement patterns are designed to reduce the installation times of the double ballbar. Secondly, the effect of installation errors is reduced by analyzing the coefficient matrix to avoid error accumulation. Thirdly, measurement trajectories affected by position-independent geometric errors are simulated and eliminated. Finally, the error measurement and validation experiments were performed on a dual-turntable five-axis machine tool, and the machining precision was improved by 34.09%-48.89%. The results indicated that the scheme can effectively identify the geometric errors of rotary axes and has the advantages of high efficiency and accuracy.

Analytical Porothermoelastodynamic Modeling of Stress Wave Through a Fluid‐Saturated Porous Cylinder

ABSTRACTAnalytical porothermoelastodynamic (PTED) solutions are rare in the literature. The responses of fluid‐saturated porous materials subject to coupled mechanisms of loading frequency, fluid flow, stress, and temperature are unclear. In this paper, we use the PTED theory and derive the analytical solutions of pore pressure, temperature, stress, force, and displacement for an isotropic fluid‐saturated porous cylinder subject to a harmonic vibration. The coupled partial differential equations among pore pressure, displacement, and temperature are decoupled by matrix diagonalization and solved by further introducing a potential function and separation of variables. The PTED solution reproduces the poroelastodynamic (PED) one by easing the thermal effect. A demonstration example shows that the coupled mechanisms among pore pressure, stress, and displacement are highly frequency dependent. The thermal effect is more pronounced at low frequencies than at high frequencies when the inertial impact is more significant. Pore pressure is almost uniform in the ‐direction at low frequencies and becomes nonuniform at high frequencies for both PTED and PED cases. Displacements exhibit linear behavior at low frequencies and become nonlinear at high frequencies. Thermal stress and expansion significantly impact the pore pressure and displacement. A brief sensitivity analysis shows that pore pressure responds linearly and monotonically with the increase of the volumetric thermal expansion coefficient of the solid matrix at low frequencies and becomes nonlinear and nonmonotonic at high frequencies. The volumetric thermal expansion coefficient of the solid matrix has a minor effect on the vertical displacement and significantly influences the radial displacement.

A Structured L-BFGS Method with Diagonal Scaling and Its Application to Image Registration

We devise an L-BFGS method for optimization problems in which the objective is the sum of two functions, where the Hessian of the first function is computationally unavailable while the Hessian of the second function has a computationally available approximation that allows for cheap matrix–vector products. This is a prototypical setting for many inverse problems. The proposed L-BFGS method exploits the structure of the objective to construct a more accurate Hessian approximation than in standard L-BFGS. In contrast with existing works on structured L-BFGS, we choose the first part of the seed matrix, which approximates the Hessian of the first function, as a diagonal matrix rather than a multiple of the identity. We derive two suitable formulas for the coefficients of the diagonal matrix and show that this boosts performance on real-life image registration problems, which are highly non-convex inverse problems. The new method converges globally and linearly on non-convex problems under mild assumptions in a general Hilbert space setting, making it applicable to a broad class of inverse problems. An implementation of the method is freely available.

Unified Multi-view Data Clustering: Simultaneous Learning of Consensus Coefficient Matrix and Similarity Graph

Unified Multi-view Data Clustering: Simultaneous Learning of Consensus Coefficient Matrix and Similarity Graph