Matrix Operations Research Articles

CNUCTRAN: A program for computing final nuclide concentrations using a direct simulation approach

It is essential to precisely determine the evolving concentrations of radioactive nuclides within transmutation problems. It is also a crucial aspect of nuclear physics with widespread applications in nuclear waste management and energy production. This paper introduces CNUCTRAN, a novel computer program that employs a probabilistic approach to estimate nuclide concentrations in transmutation problems. CNUCTRAN directly simulates nuclei transformations arising from various nuclear reactions, diverging from the traditional deterministic methods that solve the Bateman equation using matrix exponential approximation. This approach effectively addresses numerical challenges associated with solving the Bateman equations, therefore, circumventing the need for matrix exponential approximations that risk producing nonphysical concentrations. Our sample calculations using CNUCTRAN shows that the concentration predictions of CNUCTRAN have a relative error of less than 0.001% compared to the state-of-the-art method, CRAM, in different test cases. This makes CNUCTRAN a valuable alternative tool for transmutation analysis. Program summaryProgram Title:CNUCTRANCPC Library link to program files:https://doi.org/10.17632/b484w2vx52.1Developer's repository link:https://github.com/rabieomar92/cnuctran/releasesLicensing provisions: MITProgramming language: C++Nature of problem:CNUCTRAN simulates the transmutation of various nuclides such as decays, fissions, and neutron induced reactions using a direct simulation approach. It has the capability of predicting the final concentration of a large system of nuclides altogether after a specified time step, tf.Solution method:CNUCTRAN works based on the novel probabilistic method such that it does not compute the final nuclide concentrations by solving Bateman equations. Instead, it statistically tracks nuclide transformations into one another in a transmutation problem. The technique encapsulates various possible nuclide transformations into a sparse transfer matrix, T, whose elements are made up of various nuclear reaction probabilities. Next, T serves as a matrix operator acting on the initial nuclide concentrations, y(0), producing the final nuclide concentrations, y.

Time-Varying Function Matrix Projection Synchronization of Caputo Fractional-Order Uncertain Memristive Neural Networks with Multiple Delays via Mixed Open Loop Feedback Control and Impulsive Control

This paper shows solicitude for the generalized projective synchronization of Caputo fractional-order uncertain memristive neural networks (FOUMNNs) with multiple delays. By extending the constant scale factor to the time-varying function matrix, we establish an extraordinary synchronization mode called time-varying function matrix projection synchronization (TFMPS), which is a generalized version of traditional matrix projection synchronization, modified projection synchronization, complete synchronization, and anti-synchronization. To achieve the goal of TFMPS, we design a novel mixed controller including the open loop feedback control and impulsive control, which employs the state information in the time-delayed interval and the sampling information at the impulse instants. It has a prominent advantage that impulse intervals are not restricted by time delays. To establish the connection between the error system and the auxiliary system, a generalized fractional-order comparison theorem with time-varying coefficients and impulses is established. Applying the stability theory, the comparison theorem, and the Laplace transform, new synchronization criteria of FOUMNNs are acquired under the mixed impulsive control schemes, and the derived synchronization theorem and corollary can effectively expand the correlative synchronization achievements of fractional-order systems.

Numerical computation of fractional Bloch equation by using Jacobi operational matrix

In this work, we present a numerical scheme based on the operational matrix of fractional Caputo-Fabrizio (CF) integration for handling fractional Bloch equation (FBE) in nuclear magnetic resonance (NMR). The understanding of Bloch equation provides us a fundamental framework for describing magnetic resonance phenomena, facilitating breakthrough in diverse fields such as medical diagnostics, quantum computing and materials characterization. The non-integer order derivative and integration are presented in the Caputo-Fabrizio sense. To construct the operational matrix, Jacobi polynomial is used as a basis. The fractional Bloch equation is transformed into a set of algebraic equations by using the operational matrix. In order to examine the fractional order problem, we obtain an approximate solution for FBE and present the numerical results in graphical and tabular forms.

Improving Measurement Accuracy of Deep Hole Measurement Instruments through Perspective Transformation.

Deep hole measurement is a crucial step in both deep hole machining and deep hole maintenance. Single-camera vision presents promising prospects in deep hole measurement due to its simple structure and low-cost advantages. However, the measurement error caused by the heating of the imaging sensor makes it difficult to achieve the ideal measurement accuracy. To compensate for measurement errors induced by imaging sensor heating, this study proposes an error compensation method for laser and vision-based deep hole measurement instruments. This method predicts the pixel displacement of the entire field of view using the pixel displacement of fixed targets within the camera's field of view and compensates for measurement errors through a perspective transformation. Theoretical analysis indicates that the perspective projection matrix changes due to the heating of the imaging sensor, which causes the thermally induced measurement error of the camera. By analyzing the displacement of the fixed target point, it is possible to monitor changes in the perspective projection matrix and thus compensate for camera measurement errors. In compensation experiments, using target displacement effectively predicts pixel drift in the pixel coordinate system. After compensation, the pixel error was suppressed from 1.99 pixels to 0.393 pixels. Repetitive measurement tests of the deep hole measurement instrument validate the practicality and reliability of compensating for thermal-induced errors using perspective transformation.

Correction: Solution of linear and nonlinear singular value problems using operational matrix of integration of Fibonacci wavelets

Correction: Solution of linear and nonlinear singular value problems using operational matrix of integration of Fibonacci wavelets

SLMFNet: Enhancing land cover classification of remote sensing images through selective attentions and multi-level feature fusion.

Land cover classification (LCC) is of paramount importance for assessing environmental changes in remote sensing images (RSIs) as it involves assigning categorical labels to ground objects. The growing availability of multi-source RSIs presents an opportunity for intelligent LCC through semantic segmentation, offering a comprehensive understanding of ground objects. Nonetheless, the heterogeneous appearances of terrains and objects contribute to significant intra-class variance and inter-class similarity at various scales, adding complexity to this task. In response, we introduce SLMFNet, an innovative encoder-decoder segmentation network that adeptly addresses this challenge. To mitigate the sparse and imbalanced distribution of RSIs, we incorporate selective attention modules (SAMs) aimed at enhancing the distinguishability of learned representations by integrating contextual affinities within spatial and channel domains through a compact number of matrix operations. Precisely, the selective position attention module (SPAM) employs spatial pyramid pooling (SPP) to resample feature anchors and compute contextual affinities. In tandem, the selective channel attention module (SCAM) concentrates on capturing channel-wise affinity. Initially, feature maps are aggregated into fewer channels, followed by the generation of pairwise channel attention maps between the aggregated channels and all channels. To harness fine-grained details across multiple scales, we introduce a multi-level feature fusion decoder with data-dependent upsampling (MLFD) to meticulously recover and merge feature maps at diverse scales using a trainable projection matrix. Empirical results on the ISPRS Potsdam and DeepGlobe datasets underscore the superior performance of SLMFNet compared to various state-of-the-art methods. Ablation studies affirm the efficacy and precision of SAMs in the proposed model.

Text and Image Encryption using ECC

This project combines Elliptic Curve Cryptography (ECC) with Random Matrix Cryptography (RMC) for image encryption and ECC with the Lorenz algorithm to provide a comprehensive solution to data security. Chaotic equation for text encryption. While ECC-Lorenz uses chaotic dynamics for text encryption, ECC-RMC uses matrix operations to strengthen image encryption. The efficacy of both strategies in safeguarding the confidentiality and integrity of transmitted data is demonstrated through experimental validation, which therefore improves network communication security. A multi-layered encryption architecture is established by the integration of ECC-RMC and ECC-Lorenz, providing a strong defense against cyber attacks and unlawful access. This new encryption paradigm promises improved resilience in digital information transfer, marking a significant leap in data security measures. The suggested method gives a flexible way to combine computational complexity and mathematical rigor

The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements [formula omitted] and [formula omitted]

The non-first-order-factorizable contributions1 to the unpolarized and polarized massive operator matrix elements to three-loop order, AQg(3) and ΔAQg(3), are calculated in the single-mass case. For the F12-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to O(ε5) in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable x∈]0,∞[ using highly precise series expansions to obtain the imaginary part of the physical amplitude for x∈]0,1] at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-x region. We also derive expansions in the region of small and large values of x. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.

Upper Triangular Operator Matrices and Stability of Their Various Spectra

Upper Triangular Operator Matrices and Stability of Their Various Spectra

Alleviated Shifted Gegenbauer Spectral Method for Ordinary and Fractional Differential Equations

This article introduces two numerical methods to address boundary value problems associated with secondorder and fractional differential equations. These methods employ two parameters related to shifted Gegenbauer polynomials as their basis functions. The process involves establishing a differentiation operational matrix for the shifted Gegenbauer polynomials. Subsequently, the initial/boundary value problems for ordinary and fractional differential equations are transformed into a system of equations through the Galerkin, collocation, and tau methods. The convergence analysis is ensured by leveraging theorems pertaining to the shifted Gegenbauer polynomials. To validate the accuracy of the approach, numerous numerical examples are presented.

Precise feature selection via non-convex regularized graph embedding and self-representation for unsupervised learning

In graph embedding learning with unsupervised feature selection fields, similarity matrices are usually obtained only from the initial noise-laden samples, and the probable association between various features is often ignored. To tackle the issues described above, this article proposes an effective unsupervised group feature selection approach via non-convex regularized graph embedding and self-representation (NLGMS). NLGMS integrates the similarity matrix and feature selection as a joint system on the basis of graph. It combines self-representation learning into the system to preserve the global structure and learns the nonconvex projection matrix to direct the procedure of feature selection. Specifically, first, NLGMS presents a unified framework for global structure learning, local structure learning, and feature selection process so the data’s intrinsic structure is excellently captured and learned adaptively. Second, nonconvex ℓ2,0-norm is enforced upon the projection matrix to perform the process of feature selection, ensuring that the optimal feature subset can be picked precisely. Nonconvex ℓ2,0-norm constraint considers the probable association between various features so that it can deliver optimal performance by considering the feature subset as an integral whole, which other convex regularized constraints often fail to achieve. Finally, the introduction to self-representation learning can facilitate the reconstruction of samples in low-rank subspaces, strengthening the model’s robustness. To tackle this challenging nonconvex model, an innovative alternative optimization technique is exploited. In addition, to validate the superiority of NLGMS, exhaustive experiments are performed on one synthetic dataset, six benchmark datasets, and one fish image dataset. The source code is available at: https://github.com/hrbai/NLGMS.

TA-YOLO: a lightweight small object detection model based on multi-dimensional trans-attention module for remote sensing images

Object detection plays a vital role in remote sensing applications. Although object detection has achieved proud results in natural images, these methods are difficult to be directly applied to remote sensing images. Remote sensing images often have complex backgrounds and small objects, which results in a highly unbalanced distribution of foreground and complex background information. In order to solve the above problems, this paper proposes a multi-head channel and spatial trans-attention (MCSTA) module, which performs remote pixel interaction from the channel and spatial dimensions respectively to complete the attention feature capture function. It is a plug-and-play module that can be easily embedded in any other natural image object detection convolutional neural network, making it quickly applicable to remote sensing images. First, in order to reduce computational complexity and improve feature richness, we use a special linear convolution to obtain three projection features instead of the simple matrix multiplication transformation in Transformer. Second, we obtain trans-attention maps in different dimensions in a manner similar to the self-attention mechanism to capture the interrelationships of features in channels and spaces. In this process, we use a multi-head mechanism to perform parallel operations to improve speed. Furthermore, in order to avoid large-scale matrix operations, we specially designed an attention blocking mode to reduce computer memory usage and increase operation speed. Finally, we embedded the trans-attention module into YOLOv8, added a new detection head and optimized the feature fusion method, thus designing a lightweight small object detection model named TA-YOLO for remote sensing images. It has fewer parameters than the benchmark model YOLOv8, and its mAP on the PASCAL VOC and VisDrone data sets increased by 1.3% and 6.2% respectively. The experimental results prove the powerful function of the trans-attention module and the excellent performance of TA-YOLO.

On rotated CMV operators and orthogonal polynomials on the unit circle

Split-step quantum walk operators can be expressed as a generalized version of CMV operators with complex transmission coefficients, which we call rotated CMV operators. Following the idea of Cantero, Moral and Velazquez's original construction of the original CMV operators from the theory of orthogonal polynomials on the unit circle (OPUC), we show that rotated CMV operators can be constructed similarly via a rotated version of OPUCs with respect to the same measure, and admit an analogous LM -factorization as the original CMV operators. We also develop the rotated second kind polynomials corresponding to the rotated OPUCs. We then use the LM -factorization of rotated alternate CMV operators to compute the Gesztesy–Zinchenko transfer matrices for rotated CMV operators.

Numerical solution for stochastic Volterra-Fredholm integral equations with delay arguments

We present a method for computing the stochastic operational matrix of integration to advance the study of stochastic Volterra-Fredholm integral equations (SVFIEs) based on delay arguments. First, the method evaluates the combined effects of the delay and its parameters on the accuracy improvement of the convergence rate. Our results can be applied to SVFIEs, with the operational delay matrices of the block pulse function simplified to algebraic ones. Numerical calculations were performed on a PC using Python 3 programs. Results also demonstrate the accuracy of approximate solutions; arithmetic operations are carried out without the need for derivation or integration.

Youth Experiencing Parental Death Due to Drug Poisoning and Firearm Violence in the US, 1999-2020

Youth (those aged <18 years) parental death has been associated with negative health outcomes. Understanding the burden of parental death due to drug poisoning (herein, drugs) and firearms is essential for informing interventions. To estimate the incidence of youth parental death due to drugs, firearms, and all other causes. This cross-sectional observational study was conducted using vital registration, including all US decedents, and census data from January 1990 through December 2020. Data were analyzed from May 30, 2023, to March 28, 2024. Parental death due to drug poisoning or firearms. A demographic matrix projection model was used to estimate the number and incidence of youth experiencing parental death, defined as the death of 1 or more parents, per 1000 population aged less than 18 years. Analyses evaluated parental deaths by drugs, firearms, and all other causes from 1999 through 2020 by race and ethnicity. Between 1999 and 2020, there were 931 785 drug poisoning deaths and 736 779 firearm-related deaths with a mean (SD) age of 42.6 (16.3) years. Most deaths occurred among males (73.8%) and White decedents (70.8%) followed by Black (17.5%) and Hispanic (9.5%) decedents. An estimated 759 000 (95% CI, 722 000-800 000) youth experienced parental death due to drugs and an estimated 434 000 (95% CI, 409 000-460 000) youth experienced parental death due to firearms, accounting for 17% of all parental deaths. From 1999 to 2020, the estimated number of youth who experienced parental death increased 345% (95% CI, 334%-361%) due to drugs and 39% (95% CI, 37%-41%) due to firearms compared with 24% (95% CI, 23%-25%) due to all other causes. Black youth experienced a disproportionate burden of parental deaths, based primarily on firearm deaths among fathers. In 2020, drugs and firearms accounted for 23% of all parental deaths, double the proportion in 1999 (12%). Results of this modeling study suggest that US youth are at high and increasing risk of experiencing parental death by drugs or firearms. Efforts to stem this problem should prioritize averting drug overdoses and firearm violence, especially among structurally marginalized groups.

Numerical radius inequalities for certain operator matrices

Numerical radius inequalities for certain operator matrices

Semi-supervised bipartite graph construction with active EEG sample selection for emotion recognition.

Electroencephalogram (EEG) signals are derived from the central nervous system and inherently difficult to camouflage, leading to the recent popularity of EEG-based emotion recognition. However, due to the non-stationary nature of EEG, inter-subject variabilities become obstacles for recognition models to well adapt to different subjects. In this paper, we propose a novel approach called semi-supervised bipartite graph construction with active EEG sample selection (SBGASS) for cross-subject emotion recognition, which offers two significant advantages. Firstly, SBGASS adaptively learns a bipartite graph to characterize the underlying relationships between labeled and unlabeled EEG samples, effectively implementing the semantic connection for samples from different subjects. Secondly, we employ active sample selection technique in this paper to reduce the impact of negative samples (outliers or noise in the data) on bipartite graph construction. Drawing from the experimental results with the SEED-IV data set, we have gained the following three insights. (1) SBGASS actively rejects negative labeled samples, which helps mitigate the impact of negative samples when constructing the optimal bipartite graph and improves the model performance. (2) Through the learned optimal bipartite graph in SBGASS, the transferability of labeled EEG samples is quantitatively analyzed, which exhibits a decreasing tendency as the distance between each labeled sample and the corresponding class centroid increases. (3) Besides the improved recognition accuracy, the spatial-frequency patterns in emotion recognition are investigated by the acquired projection matrix.

Application of the Fibonacci wavelet approach to the MHD boundary layer analysis of a Casson fluid past a stretching sheet

The current work investigates the MHD boundary layer flow of Casson fluid over a stretching sheet with the help of Fibonacci wavelet approach. The stable laminar MHD flow, mass and heat transport properties of a nanofluid over a stretching sheet in the presence of a fluctuating magnetic field has been under scrutiny. By choosing relevant non-dimensional parameters, the governing boundary layer equation undergoes transformation into a dimensionless Falkner-Skan equation. The Fibonacci integral operational matrix is used to solve the achieved nonlinear equation and it has been used for the first time to solve stretching sheet problem in fluid dynamics. The nature of the boundary layer flow are analyzed graphically for a range of distinct values of physical parameters. Impact of parameters on axial and transverse velocity has been investigated. It can be observed that local skinfriction coefficient grows for larger values of Casson parameter for ϵ = 0.3 and decreases for higher values of Casson parameter and decreases for higher values of magnetic parameter, angle of inclination and pressure gradient parameter. To ensure the accuracy of the findings, local skin friction is recorded and contrasted with various approaches that are already documented in research.

High-efficiency scattering field modeling in metallic components: a machine-learning-inspired approach

We present a highly efficient method for characterizing the scattering field distribution of surface plasmon polaritons in metallic components by combining the eXtended Pseudospectral Frequency-Domain (X-PSFD) method with an iterative, machine-learning-inspired procedure. Shifting away from traditional matrix operations, we utilize the “Adam” optimizer—an effective and swift machine learning algorithm—to solve the scattering field distribution. Our method encompasses the derivation of the associated cost function and gradient differentiation of the field, leveraging spectral accuracy at Legendre collocation points in the Helmholtz equation. We refine the total-field/scattered-field (TF/SF) formulation within the X-PSFD framework for optimized incident field management and employ Chebyshev–Lagrange interpolation polynomials for rapid, accurate computation of broad-band results. To ensure global accuracy, we introduce unique physical boundary conditions at subdomain interfaces. Demonstrating our method’s robustness and computational efficiency, we model perfect electric conductors (PECs) and silver nanocylinders, and we apply our approach to analyze the excited electric field on subtly distorted metallic surfaces, particularly plasmonic structures, thereby validating its wide-ranging effectiveness.

Legendre wavelet integration operational matrix method for the numerical solution of unsteady MHD nanofluid flow between moving parallel plates

This study proposes a novel method based on Legendre wavelet integration operational matrix for solving a system of nonlinear ODE’s to model the two-phase, unsteady nanofluid flow and heat transfer between parallel plates in presence of magnetic field. To validate the applicability of proposed method, system of nonlinear BVP with exact solutions is employed as a test problem. Test problem results are compared with exact solution, and other numerical methods. The governing equations were then changed using similarity transformation into a set of nonlinear ODE’s. . Following this, the LWOMM is applied for the proposed problem. Findings demonstrated that, for a constant Reynolds number, skin friction coefficient value increases with rising Hartmann and squeezing numbers. Furthermore, it is demonstrated that Eckert number is a reducing function of the squeeze number and Nusselt number is an increasing function of Hartmann number.