Coefficient Matrix Research Articles

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.

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.

Quantification of Albumin and ɣ-Globulin Concentrations by Multivariate Regression Based on Admittance Relaxation Time Distribution (mrARTD).

Albumin and γ-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. The mraRTD formulates P = Ac + Ξ (P: peak matrix of distribution function magnitude ɣP and frequency τP, c: concentration matrix of albumin cAlb, γ-globulin Gloc, and sodium electrolyte Nac, A: coefficient matrix of a multivariate regression model, and Ξ: error matrix). The mraRTD is implemented by two processes which are: 1) the training process of A through the maximum likelihood estimation of P and 2) the quantification process of cAlb, Gloc, and Nac through the model prediction. In the training process, a positive correlation is present between cAlb, Gloc, and Nac to ɣP1 at τP1= 0.1 as well as ɣP2 at τP2= 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 and Nac = 0.700-0.750 g/dL). The mraRTD method quantifies cAlb, Gloc, and Nac in SAT with an absolute error of 33.79%, 44.60%, and 2.18%, respectively.

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

3D airborne electromagnetic forward modeling based on the multiscale hexahedral finite-element method

Slow forward modeling is the main factor that restricts the practical use of 3D inversion and interpretation of airborne electromagnetic (AEM) data. To improve modeling efficiency with 3D AEM data, we develop a new multiscale finite element (MsFE) method based on unstructured hexahedral meshes. Compared to traditional 3D AEM forward modeling, the main advantage of our newly developed method is that it can simulate complex underground structures in the earth quickly. Because we can fit the earth’s topography or the anomalous bodies underground using a small number of hexahedral grids, we can quickly model them using MsFE. The main idea of the MsFE forward-modeling method is to construct an interpolation operator between a coarse and a dense mesh and use the interpolation operator to map the conventional finite-element coefficient matrix to the MsFE coefficient matrix and thus reduce the number of unknowns in the modeling process. This will vastly reduce the scale of the linear equations system. We validate our method by simulating a typical mountain peak model and determine its effectiveness by simulating numerous synthetic models and a model from Voisey Bay’s Ovoid sulfide deposit, Canada.

OPTIMIZATION OF THE SCATTERING MATRIX OF FREQUENCY -DETUNED ADD/DROP FILTERS FOR MULTIPLEXERS BUILT ON SYSTEMS OF OPTICAL DIELECTRIC RESONATORS WITH WHISPERING GALLERY MODES

Background. A significant increase in the speed of information transmission in fiber-optic communication networks is determined by the strict requirements imposed on the elemental base of receiving and transmitting devices. One of the important components of such devices is diplexers built on different notch and bandpass filters, which are often performed on dielectric resonators (DR) with whispering gallery mode (WGM) oscillations. Calculation and optimization of the parameters of multilink filters and diplexers built on DR is impossible without further development of the theory of their design. The development of the theory of diplexers today is often based on electrodynamic modelling, which is built on preliminary calculations of filter scattering parameters in various transmission lines with a complex topology of connections. Objective. The aim of this study is to construct electrodynamics' models of wave scattering on complex multi-connected DR structures with degenerate types of WGM natural oscillations, which contain several frequency-detuned bandpass or notch filters located in one or several transmission lines. To solve the scattering problem, we proposed a system of equations derived from perturbation theory for Maxwell's equations [24], modified to describe the DR fields with whispering gallery oscillations in transmission lines. The construction of such solutions is complicated by the fact that each of the partial optical resonators of the filters, in the case of excitation of azimuthally inhomogeneous WGM in it, has, as a rule, two degenerate types of natural oscillations. Moreover, each such type of oscillation is characterized by different complex values of the coupling coefficients with the line, open space, and also with other resonators. The latter circumstance leads to the fact that the systems of equations for the amplitudes of natural and forced oscillations of resonators are doubled. The signs of the coefficients of mutual coupling are usually different, this leads to the fact that the behaviour of DRs in the system becomes more difficult to predict, therefore the second objective of this work is to study the patterns of the scattering characteristics of line waves on systems of frequency-detuned DRs with degenerate types of oscillations with the possibility of constructing multiplexers for modern optical communication systems. Methods. The methods of technical electrodynamics are used for calculating and analysing scattering matrices. The end result is obtaining new analytical equations and formulas for new complex structures of coupled dielectric resonators with whispering gallery oscillations in the different transmission lines. Results. Frequency dependences of scattering matrices on complex structures of frequency-detuned filters built on coupled optical DR with whispering gallery oscillations located in one or more transmission lines are considered. Electromagnetic models of bandstop and add/drop filters are built, consisting of various optical resonators with degenerate types of natural oscillations. General analytical expressions of vector coefficients and matrices for building systems of equations describing coupled oscillations, as well as forced oscillations of resonators in cases of their use in optical filters with serial and parallel arrangement, are given. General solutions for the scattering field on frequency-detuned resonators located in different optical transmission lines have been found. Examples of calculating frequency dependences of the scattering matrix for the most interesting structures consisting of two different frequency-detuned filters are given. The frequency scattering characteristics of several types of devices are calculated, which consist of two notch filters with different blocking bands, made on detuned DRs in one transmission line. The possibilities of the earlier proposed method are demonstrated in the example of calculating the scattering characteristics of known types of diplexers built on the basis of the use of two add/drop filters with different frequency bandwidths. The frequency dependences of the scattering matrices of the two most common types of devices, located in parallel between two or four regular transmission lines of add/drop filters with different numbers of resonators; laterally coupled add/drop filters; parallel-coupled add/drop filters; twisted double-channel side-coupled integrated space sequence of resonators (SCISSORs), were studied. New scattering models of diplexers consisting of optical resonators of different connection topologies were built: serial, parallel with the use of laterally coupled add/drop filters; parallel-coupled add/drop filters; twisted double-channel SCISSORs. The frequency dependences scattering matrix of the diplexers were also calculated. The characteristics of the designed diplexers obtained from the examined filters of different types were compared. Conclusions. The theory of diplexer construction, which takes place on the simultaneous optimization of the scattering matrix of several filters built on complex systems of dielectric resonators with degenerate types of whispering gallery oscillations is expanded. A calculation method was developed and new analytical relations were found for the scattering matrix coefficients of optical diplexers of various types.

Artisanal and small-scale limestone mining affects soil parameters in Sohra (Meghalaya), India.

In this study, we assessed the changes in the physical and chemical characteristics of the soil samples collected from the artisanal and small-scale limestone mining site in Sohra (Cherrapunjee), Meghalaya, by comparing them with the non-mining site. Eleven distinct soil parameters, namely pH, electrical conductivity (EC), texture (ST), moisture content (MC), bulk density (BD), total porosity (TP), water holding capacity (WHC), organic carbon (OC), total nitrogen (TN), available phosphorus (AP), and exchangeable potassium (EK), were evaluated seasonally (winter, pre-monsoon, and post-monsoon) for 2years. The results showed that limestone mining has significantly affected the soil quality. The effect is evident by the substantial increases in EC values, sand content, and alkaline soils coupled with noticeably low concentrations of OC and TN. In addition, prominent changes were perceived in the soil MC and EK content, as well as in WHC, BD, and TP percent. Results from ANOVA revealed significant differences (p < 0.05) in mean values at different sampling seasons and sites. The multivariate statistical analysis results showed that the computed correlation coefficient (r) matrix data ranged from - 1.00 to 0.974. A strong positive correlation was highest between OC and TN (0.974), followed by OC with EK (0.828). Principal component (PC) analysis revealed two major components, PC 1 and PC 2, having eigenvalues of 6.276 and 1.747, respectively. Cumulatively, these two components explained 80.23% of the total variance. The loading factor in PC 1 is high and is attributed to OC (.974), TN (.970), and EK (.903). However, in PC 2, the loading factor is positively pooled by MC (0.894) and TP (0.765). The present study concludes that artisanal and small-scale limestone mining altered the soil's physical and chemical properties, and these changes are likely to have a subsequent deteriorating impact on the area's biodiversity, landscape, and natural ecosystem. Therefore, to minimize the impact and ensure sustainable soil management in the area, approaches for effective mitigation and remediation measures, including formulating steps for the conservation and enhancement of the soil's environmental quality, are recommended.