Gaussian Matrix Research Articles

Response reconstruction based on measurement matrix optimization in compressed sensing for structural health monitoring

Structural health monitoring (SHM) data have a large volume, increasing the cost of data storage and transmission and the difficulties of structural parameter identification. The compressed sensing (CS) theory provides a signal acquisition and analysis strategy. Signal reconstruction using limited measurements and CS has attracted significant interest. However, the dynamic responses obtained from civil engineering structures contain noise, resulting in sparse samples and reducing the signal reconstruction accuracy. Therefore, we propose an optimization algorithm for the measurement matrix integrating the Karhunen-Loeve transform (KLT) and approximate QR decomposition (KLT-QR) to improve the accuracy of dynamic response reconstruction of SHM data. The KLT reduces the correlation between the measurement matrix and the sparse basis. The approximate QR decomposition is used to improve the independence between the column vectors of the measurement matrix, optimizing the measurement matrix. The experimental results for a laboratory steel beam indicate that the proposed KLT-QR algorithm outperforms three other algorithms regarding the accuracy of dynamic response reconstruction (acceleration, displacement, and strain), especially at high compression ratios. The acceleration responses from the Ji’an Bridge are utilized to verify the advantages of the proposed algorithm. The results demonstrate that the KLT-QR algorithm has the highest accuracy of reconstructing the vibration signals and yields better Fourier spectra than the conventional Gaussian measurement matrix.

Temperature-dependent density effects on oscillatory mixed convective flow across a non-conducting horizontal circular cylinder embedded in a porous medium

Temperature-dependent density and aligned magnetic field influence on mixed thermal convection heat and current density aspects over a non-conducting porous circular horizontal cylinder is the novelty of this investigation. The magnetic effects over the surface are minimal but maximum away from the surface. The density of the fluid is assumed as an exponential variable of temperature to record the heat and current density rates. The pertinent form of partial differential equations is designed using suitable dimensionless quantities. The computational outputs of fluid velocity, magnetic fields and temperature variations are drafted using fluctuating-stokes quantities. The primitive quantities are utilised to make similar and asymptotic programs in FORTRAN for geometrical and numerical outcomes. The transient and oscillating behaviour of gradient values is sketched by using steady results in the oscillating formula. The finite difference methodology is applied to examine the physical properties with the Gaussian elimination matrix scheme. Effects of buoyant force ( λ ), Prandtl (Pr), magnetic force ( ξ ), density factor ( m ) and MHD Prandtl factor ( γ ) on the thermal behaviour of magneto-hydrodynamic analysis are applied. Results are explored around three angles π / 6 , π / 3 , π of the cylinder. Increasing magnitude in fluid velocity is deduced with high amplitude as porosity, buoyant and density parameters are enhanced.

Analyzing vehicle path optimization using an improved genetic algorithm in the presence of stochastic perturbation matter

By analyzing the influence of stochastic perturbation matters on vehicle path optimization, a perturbation scheduling model for logistics and distribution with a carbon tax mechanism is established under the premise of time window variation and load capacity constraints. Herein, we propose an enhanced Genetic Algorithm (GA) based on a Gaussian matrix mutation (GMM) operator, which maintains the diversity of the population while speeding up the algorithm’s convergence. The model builds a Gaussian probability matrix using the site positional order distribution characteristics implied in the original site data information, and applies the Gaussian probability matrix to individual gene mutations using a roulette-wheel-selection method; thus, the study guarantees the genetic diversity of the population while guiding it to evolve in the high-fitness direction. Finally, an experimental simulation is performed using data obtained from a commercial supermarket, thereby verifying the effectiveness of the proposed algorithm and comparing it with other algorithms. The results reveal that compared with the classical GA, the average convergence speed of the improved GA can be increased by 50–60% and the consumed algorithm time can be reduced by 48% while maintaining the difference in solution accuracy within 1%.

Bulk universality for complex non-Hermitian matrices with independent and identically distributed entries

AbstractWe consider $$N\times N$$ N × N matrices with complex entries that are perturbed by a complex Gaussian matrix with small variance. We prove that if the unperturbed matrix satisfies certain local laws then the bulk correlation functions are universal in the large N limit. Assuming the entries are independent and identically distributed (iid) with a common distribution that has finite moments, the Gaussian component is removed by the four moment theorem of Tao and Vu.

Deformation of superintegrability in the Miwa-deformed Gaussian matrix model

We consider an arbitrary deformation of the Gaussian matrix model parametrized by Miwa variables za. One can look at it as a mixture of the Gaussian and logarithmic (Selberg) potentials, which are both superintegrable. The mixture is not, still one can find an explicit expression for an arbitrary Schur average as a linear transform of a polynomial made from the values of skew Schur functions at the Gaussian locus pk=δk,2. This linear operation includes multiplication with an exponential eza2/2 and a kind of Borel transform of the resulting product, which we call multiple and enhanced. The existence of such remarkable formulas appears intimately related to the theory of auxiliary K-polynomials, which appeared in superintegrable correlators at the Gaussian point (strict superintegrability). We also consider in great detail the generating function of correlators ⟨(TrX)k⟩ in this model, and discuss its integrable determinant representation. At last, we describe deformation of all results to the Gaussian β-ensemble. Published by the American Physical Society 2024

High-Linearity Ta2O5 Memristor and Its Application in Gaussian Convolution Image Denoising.

In the image Gaussian filtering process, convolving with a Gaussian matrix is essential due to the numerous arithmetic computations involved, predominantly multiplications and additions. This can heavily tax the system's memory, particularly with frequent use. To address this issue, a W/Ta2O5/Ag memristor was employed to substantially mitigate the computational overhead associated with convolution operations. Additionally, an interlayer of ZnO was subsequently introduced into the memristor. The resulting Ta2O5/ZnO heterostructure layer exhibited improved linearity in the pulse response, which enhanced linearity facilitates easy adjustment of the conductance magnitude through a linear mapping of the number of pulses and the conductance. Subsequently, the conductance of the W/Ta2O5/ZnO/Ag bilayer memristor was employed as the weights for the convolution kernel in convolution operations. Gaussian noise removal in image processing was achieved by assembling a 5 × 5 memristor array as the kernel. When denoising was performed using memristor arrays, compared to denoising achieved through Gaussian matrix convolution, an average loss of less than 5% was observed. The provided memristors demonstrate significant potential in convolutional computations, particularly for subsequent applications in convolutional neural networks (CNNs).

A visual security multi-key selection image encryption algorithm based on a new four-dimensional chaos and compressed sensing

In this article, a visual security image encryption algorithm based on compressed sensing is proposed. The algorithm consists of two stages: the compression and encryption stage and the embedding stage. The key streams in the compression and encryption stage are generated by a newly constructed four-dimensional discrete chaotic map, while the Gaussian measurement matrix is generated by a Chebyshev map, and both of their generations are related to the feature code of the carrier image, which enhances the security of the ciphertext. In the compression and encryption stage, a scrambling-cyclic shift-diffusion encryption structure is adopted for the compressed image in which the shift number in the cyclic shift stage and the diffusion key streams are dynamically changed according to each pixel value, so the algorithm can resist chosen plaintext attack. In the embedding stage, the carrier image is first subjected to integer wavelet transform to obtain the high-frequency and low-frequency components of the image, and then the intermediate ciphertext information is embedded into its high-frequency components. Finally, the carrier image is subjected to inverse integer wavelet transform to obtain a visually secure ciphertext image. The experimental results and security analysis indicate that the encryption scheme has a large key space, high decryption key sensitivity, similar histogram distribution between the carrier image and the visual security ciphertext image, and good robustness to noise attacks.

Multi-label feature selection via similarity constraints with non-negative matrix factorization

Feature selection plays a key role in preprocessing, effectively addressing the curse of dimensionality in multi-label learning. While current approaches commonly utilize feature or label similarity to construct the weight matrix, typically through manifold learning regularization, there has been a dearth of progress in developing similarity-constrained regularization terms for multi-label feature selection. To address this gap, this paper conducts a comprehensive investigation and proposes a novel similarity constraint leveraging non-negative matrix factorization techniques. Subsequently, a new algorithm is introduced termed Multi-label Feature Selection via Similarity Constraints with Non-negative Matrix Factorization (SCNMF). Initially, the Gaussian similarity matrix among features is computed and factorized into a weight matrix using non-negative matrix factorization. Subsequently, the Cosine distance matrix among labels is computed to constrain the weight matrix. Finally, an objective function is formulated based on the aforementioned constraint mechanisms and iteratively optimized. Extensive experiments conducted across more than 10 multi-label datasets demonstrate the superior performance of our proposed approach. The source code is accessible at the URL: https://github.com/BIGOatMNNU/SCNMF.

Protein features fusion using attributed network embedding for predicting protein-protein interaction

BackgroundProtein-protein interactions (PPIs) hold significant importance in biology, with precise PPI prediction as a pivotal factor in comprehending cellular processes and facilitating drug design. However, experimental determination of PPIs is laborious, time-consuming, and often constrained by technical limitations.MethodsWe introduce a new node representation method based on initial information fusion, called FFANE, which amalgamates PPI networks and protein sequence data to enhance the precision of PPIs’ prediction. A Gaussian kernel similarity matrix is initially established by leveraging protein structural resemblances. Concurrently, protein sequence similarities are gauged using the Levenshtein distance, enabling the capture of diverse protein attributes. Subsequently, to construct an initial information matrix, these two feature matrices are merged by employing weighted fusion to achieve an organic amalgamation of structural and sequence details. To gain a more profound understanding of the amalgamated features, a Stacked Autoencoder (SAE) is employed for encoding learning, thereby yielding more representative feature representations. Ultimately, classification models are trained to predict PPIs by using the well-learned fusion feature.ResultsWhen employing 5-fold cross-validation experiments on SVM, our proposed method achieved average accuracies of 94.28%, 97.69%, and 84.05% in terms of Saccharomyces cerevisiae, Homo sapiens, and Helicobacter pylori datasets, respectively.ConclusionExperimental findings across various authentic datasets validate the efficacy and superiority of this fusion feature representation approach, underscoring its potential value in bioinformatics.

Duality in non-Hermitian random matrix theory

We consider 9 Gaussian matrix ensembles characterized by single symmetry among the 38-fold symmetry classification classes of non-Hermitian random matrices, and establish exact duality formulae of certain observables between them. Particularly, averaged products of K characteristic polynomials in an N×N matrix ensemble can be expressed in terms of another K×K matrix ensemble. Our method is to combine matrix-valued heat equations and differential identities for determinants and Pfaffians and has more possible applications.

Papr reduction through Gaussian pre-coding in DCO-OFDM systems

Visible light communication (VLC) utilizes commercially available light-emitting diodes (LEDs) for short-distance wireless data transmission, aligning with lighting standards for indoor wireless access. The inherent challenge of achieving high data rates in VLC due to the limited spectral bandwidth of white LEDs has led to the adoption of orthogonal frequency division multiplexing (OFDM). However, conventional OFDM presents issues with peak-to-average power ratio (PAPR), pushing LEDs into a nonlinear zone, resulting in energy inefficiencies and signal distortion that degrades the bit error rate (BER). The study focuses on pre-coding within DC-biased optical OFDM (DCO-OFDM) using a Gaussian matrix (GM) for PAPR reduction. The proposed Gaussian pre-coding method demonstrates superior PAPR performance compared to conventional discrete cosine transform (DCT) pre-coding method, especially when integrated with μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu$$\\end{document}-Law companding. Simulation results indicate that increasing the number of candidate GMs enhances PAPR performance, albeit with increased system complexity. The combination of DCT and Gauss pre-coding with μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu$$\\end{document}-Law companding exhibits a 2 dB improvement in PAPR, though at the expense of BER performance.

Research on Intelligent Monitoring System of Intelligent Transmission Line Based on Computer Internet of Things Technology

The author proposes an intelligent early-warning system for preventing external damage of transmission lines. The system uses TI-TMS320DM6446 as the core, the peripheral circuit configuration and video monitoring; The moving objects captured by PTZ camera are detected and identified by using mixed Gaussian model, background difference and minimum tangent matrix, and alarm signals are provided. According to the particularity of the power supply of the equipment on the transmission line, the basic power management of the system is analyzed in detail. A reliable power management scheme is designed. The practical application proves that this method has good real-time performance and has obvious effect on preventing power cable damage by force.

Hide Digital Images in Encrypted Image Files After Two Stages

This paper introduces a novel encryption technique for concealing digital images within encrypted files through a two-stage process. The methodology incorporates sparse coding and compressive sensing, leveraging a learned dictionary to recover the sparse coding of plain images. Comprising compressive sampling and random projection with a Gaussian measurement matrix, the approach achieves joint compression and encryption. Pseudorandom encryption and chaos-based block scrambling are subsequently applied to produce the final encrypted image. Experimental results using 256 × 256 test photographs from the USC-SIPI dataset demonstrate the superiority of the proposed method in terms of both Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM). The study also conducts key sensitivity analysis, revealing the method's susceptibility to changes in the secret key, and statistical attack analysis, demonstrating its robustness against attacks exploiting statistical information. In conclusion, the proposed encryption technique not only ensures cryptographic strength but also excels in image reconstruction quality, making it a promising solution for secure image transmission and storage

Spatiotemporal modulation of a common set of muscle synergies during unpredictable and predictable gait perturbations in older adults.

Muscle synergies as functional low-dimensional building blocks of the neuromotor system regulate the activation patterns of muscle groups in a modular structure during locomotion. The purpose of the current study was to explore how older adults organize locomotor muscle synergies to counteract unpredictable and predictable gait perturbations during the perturbed steps and the recovery steps. Sixty-three healthy older adults (71.2±5.2 years) participated in the study. Mediolateral and anteroposterior unpredictable and predictable perturbations during walking were introduced using a treadmill. Muscle synergies were extracted from the electromyographic activity of 13 lower limb muscles using Gaussian non-negative matrix factorization. The four basic synergies responsible for unperturbed walking (weight acceptance, propulsion, early swing and late swing) were preserved in all applied gait perturbations, yet their temporal recruitment and muscle contribution in each synergy were modified (P<0.05). These modifications were observed for up to four recovery steps and were more pronounced (P<0.05) following unpredictable perturbations. The recruitment of the four basic walking synergies in the perturbed and recovery gait cycles indicates a robust neuromotor control of locomotion by using activation patterns of a few and well-known muscle synergies with specific adjustments within the synergies. The selection of pre-existing muscle synergies while adjusting the time of their recruitment during challenging locomotor conditions may improve the effectiveness to deal with perturbations and promote the transfer of adaptation between different kinds of perturbations.

Summing up perturbation series around superintegrable point

We work out explicit formulas for correlators in the Gaussian matrix model perturbed by a logarithmic potential, i.e. by inserting Miwa variables. In this paper, we concentrate on the example of a single Miwa variable. The ordinary Gaussian model is superintegrable, i.e. the average of the Schur functions SQ is an explicit function of the Young diagram Q. The question is what happens to this property after perturbation. We show that the entire perturbation series can be nicely summed up into a kind of Borel transform of a universal exponential function, while the dependence on R enters through a polynomial factor in front of this exponential. Moreover, these polynomials can be described explicitly through a single additional structure, which we call “truncation” of the Young diagram Q. It is unclear if one can call this an extended superintegrability, but at least it is a tremendously simple deformation of it. Moreover, the vanishing Gaussian correlators remain vanishing and, hence, are not deformed at all.

DOA Estimation of Broadband Sources Using Dimension-Reduced Matrix Filter with Deep Nulling in a Strong Interference Environment

To enhance the performance of the adaptive matrix filter with nulling, a dimension-reduced matrix filter with deep nulling (DR-MFDN) is proposed in this paper and used for direction of arrival (DOA) estimation of broadband sources in a strong interference environment. Consider the change of noise after filtering, the gaussian matrix is used for prewhitening to prevent the noise from converting into colored noise without affecting the response characteristics of the beam-space. Finally, the multiple measurement vector orthogonal matching pursuit (MOMP) algorithm is used for DOA estimation of weak targets after filtering, and the simulation results show a better DOA estimation performance compared to the OMP and MUSIC algorithms with short snapshots.

On heavy-tailed risks under Gaussian copula: The effects of marginal transformation

In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a few interesting consequences. First, as the threshold increases, we note that the rate of decay of probabilities of tail sets varies depending on the type of tail sets considered and the Gaussian correlation matrix. Second, we discover that although any multivariate model with a Gaussian copula admits the so-called asymptotic tail independence property, the joint tail behavior under heavier tailed marginal variables is structurally distinct from that under Gaussian marginal variables. The results obtained are illustrated using examples and simulations.

Moving Object Detection Method Based on the Fusion of Online Moving Window Robust Principal Component Analysis and Frame Difference Method

The accuracy of moving object detection has a great impact on the accuracy of extracting the shape center coordinates of moving workpieces. The classic inter-frame difference method has "cavity" and "double shadow" issues for workpieces with comparable internal colors. In order to solve this problem, a moving object detection algorithm combining the three-frame difference method and Online Moving Window Robust Principal Component Analysis (OMWRPCA) is proposed. By using the OMWRPCA to extract the background image in the current frame and comparing it to the previous and current frames, the "cavity" and "double shadow" problems are avoided as well as the effects of background pixels. This paper presents a case study of a visual sorting experiment bench in an "intelligent manufacturing production demonstration line". The experiments show that the workpiece shape center coordinates obtained by the improved moving object detection algorithm are closer to the actual value than those obtained by the traditional algorithm, and the F-measure scores are above 0.8, which are more accurate than the other two algorithms. It is compared with the traditional algorithm of the frame difference method and the Online Mixture of Gaussian Matrix Factorization (OMoGMF).

Large deviations and phase transitions in spectral linear statistics of Gaussian random matrices

We evaluate, in the large-N limit, the complete probability distribution P(A,m) of the values A of the sum ∑i=1N|λi|m , where λ i ( i=1,2,…,N ) are the eigenvalues of a Gaussian random matrix, and m is a positive real number. Combining the Coulomb gas method with numerical simulations using a matrix variant of the Wang–Landau algorithm, we found that, in the limit of N→∞ , the rate function of P(A,m) exhibits phase transitions of different characters. The phase diagram of the system on the (A, m) plane is surprisingly rich, as it includes three regions: (i) a region with a single-interval support of the optimal spectrum of eigenvalues, (ii) a region emerging for m < 2 where the optimal spectrum splits into two separate intervals, and (iii) a region emerging for m > 2 where the maximum or minimum eigenvalue ‘evaporates’ from the rest of eigenvalues and dominates the statistics of A. The phase transition between regions (i) and (iii) is of second order. Analytical arguments and numerical simulations strongly suggest that the phase transition between regions (i) and (ii) is of (in general) fractional order p=1+1/|m−1| , where 0<m<2 . The transition becomes of infinite order in the special case of m = 1, where we provide a more complete analytical and numerical description. Remarkably, the transition between regions (i) and (ii) for m⩽1 and the transition between regions (i) and (iii) for m > 2 occur at the ground state of the Coulomb gas which corresponds to the Wigner’s semicircular distribution.

Audio source recording device recognition based on representation learning of sequential Gaussian mean matrix

Audio source recording device recognition is a critical digital forensic task that involves identifying the source device based on intrinsic audio characteristics. This technology finds widespread application in various digital audio forensic scenarios, including audio source forensics, tamper detection forensics, and copyright protection forensics. However, existing methods often suffer from low accuracy due to limited information utilization. In this study, we propose a novel method for source recording device recognition, grounded in feature representation learning. Our approach aims to overcome the limitations of current methods. We introduce a temporal audio feature called the “Sequential Gaussian Mean Matrix (SGMM),” which is derived from temporal segmented acoustic features. We then design a structured representation learning model that combines Convolutional Neural Networks (CNN) and Bidirectional Long Short-Term Memory Networks (BiLSTM). This model leverages temporal Gaussian representation and convolutional bottleneck representation to effectively condense spatial information and achieve accurate recognition through temporal modeling. Our experimental results demonstrate an impressive recognition accuracy of 98.78%, showcasing the effectiveness of our method in identifying multiple classes of recording devices. Importantly, our approach outperforms state-of-the-art methods in terms of recognition performance. Our implementing code is publicly available at https://github.com/CCNUZFW/SGMM.