Matrix Decomposition Research Articles

Crosstalk among proximal tubular cells, macrophages, and fibroblasts in acute kidney injury: single-cell profiling from the perspective of ferroptosis

The link between ferroptosis, a form of cell death mediated by iron and acute kidney injury (AKI) is recently gaining widespread attention. However, the mechanism of the crosstalk between cells in the pathogenesis and progression of acute kidney injury remains unexplored. In our research, we performed a non-negative matrix decomposition (NMF) algorithm on acute kidney injury single-cell RNA sequencing data based specifically focusing in ferroptosis-associated genes. Through a combination with pseudo-time analysis, cell–cell interaction analysis and SCENIC analysis, we discovered that proximal tubular cells, macrophages, and fibroblasts all showed associations with ferroptosis in different pathways and at various time. This involvement influenced cellular functions, enhancing cellular communication and activating multiple transcription factors. In addition, analyzing bulk expression profiles and marker genes of newly defined ferroptosis subtypes of cells, we have identified crucial cell subtypes, including Egr1 + PTC-C1, Jun + PTC-C3, Cxcl2 + Mac-C1 and Egr1 + Fib-C1. All these subtypes which were found in AKI mice kidneys and played significantly distinct roles from those of normal mice. Moreover, we verified the differential expression of Egr1, Jun, and Cxcl2 in the IRI mouse model and acute kidney injury human samples. Finally, our research presented a novel analysis of the crosstalk of proximal tubular cells, macrophages and fibroblasts in acute kidney injury targeting ferroptosis, therefore, contributing to better understanding the acute kidney injury pathogenesis, self-repairment and acute kidney injury-chronic kidney disease (AKI-CKD) progression.

An Optimized IWT–DCT Watermarking Scheme Based on Multiple Matrix Decomposition and MOWOA2

An Optimized IWT–DCT Watermarking Scheme Based on Multiple Matrix Decomposition and MOWOA2

Source identification and driving factor apportionment for soil potentially toxic elements via combining APCS-MLR, UNMIX, PMF and GDM

The contamination and quantification of soil potentially toxic elements (PTEs) contamination sources and the determination of driving factors are the premise of soil contamination control. In our study, 788 soil samples from the National Agricultural Park in Chengdu, Sichuan Province were used to evaluate the contamination degree of soil PTEs by pollution factors and pollution load index. The source identification of soil PTEs was performed using positive matrix decomposition (PMF), edge analysis (UNMIX) and absolute principal component score-multiple line regression (APCS-MLR). The geo-detector method (GDM) was used to analysis drivers of soil PTEs pollution sources to help interpret pollution sources derived from receptor models. Result shows that soil Cu, Pb, Zn, Cr, Ni, Cd, As and Hg average content were 35.2, 32.3, 108.9, 91.9, 37.1, 0.22, 9.76 and 0.15 mg/kg in this study area. Except for As, all are higher than the corresponding soil background values in Sichuan Province. The best performance of APCS-MLR was determined by comparison, and APCS-MLR was considered as the preferred receptor model for soil PTEs source distribution in the study area. ACPS-MLR results showed that 82.70% of Cu, 61.6% of Pb, 75.3% of Zn, 91.9% of Cr and 89.4% of Ni came from traffic-industrial emission sources, 60.9% of Hg came from domestic-transportation emission sources, 57.7% of Cd came from agricultural sources, and 89.5% of As came from natural sources. The GDM results showed that distance from first grade highway, population, land utilization and total potassium (TK) content were the main driving factors affecting these four sources, with q values of 0.064, 0.048, 0.069 and 0.058, respectively. The results can provide reference for reducing PTEs contamination in farmland soil.

QR decomposition of dual matrices and its application

Dual number matrix decompositions have played an important role in fields such as kinematics and computer graphics in recent years. In this paper, we present a QR decomposition algorithm for dual number matrices. When dealing with large-scale problems, we present the thin QR decomposition of dual number matrices, along with its algorithm with column pivoting. In numerical experiments, we discuss the suitability of different QR algorithms when confronted with various large-scale dual matrices, providing their respective domains of applicability. Finally, we employ the QR decomposition of dual matrices to compute the DMPGI, attaining results of higher precision.

Sequential inertial linear ADMM algorithm for nonconvex and nonsmooth multiblock problems with nonseparable structure

The alternating direction method of multipliers (ADMM) has been widely used to solve linear constrained problems in signal processing, matrix decomposition, machine learning, and many other fields. This paper introduces two linearized ADMM algorithms, namely sequential partial linear inertial ADMM (SPLI-ADMM) and sequential complete linear inertial ADMM (SCLI-ADMM), which integrate linearized ADMM approach with inertial technique in the full nonconvex framework with nonseparable structure. Iterative schemes are formulated using either partial or full linearization while also incorporating the sequential gradient of the composite term in each subproblem’s update. This adaptation ensures that each iteration utilizes the latest information to improve the efficiency of the algorithms. Under some mild conditions, we prove that the sequences generated by two proposed algorithms converge to the critical points of the problem with the help of KŁ property. Finally, some numerical results are reported to show the effectiveness of the proposed algorithms.

Secure Key Exchange in Tropical Cryptography: Leveraging Efficiency with Advanced Block Matrix Protocols

In the quest for robust and efficient digital communication, this paper introduces cutting-edge key exchange protocols leveraging the computational prowess of tropical semirings and the structural resilience of block matrices. Moving away from the conventional use of finite fields, these protocols deliver markedly faster processing speeds and heightened security. We present two implementations of our concept, each utilizing a different platform for the set of commuting matrices: one employing tropical polynomials of matrices and the other employing Linde–de la Puente matrices. The inherent simplicity of tropical semirings leads to a decrease in operational complexity, while using block matrices enhances our protocols’ security profile. The security of these protocols relies on the Matrix Decomposition Problem. In addition, we provide a comparative analysis of our protocols against existing matrix block-based protocols in finite fields. This research marks a significant shift in cryptographic protocol design, is specifically tailored for demanding engineering applications, and sets a new standard in secure and efficient digital communication.

Meta graph network recommendation based on multi-behavior encoding

As traditional recommendation systems ignore the hidden information among different user behaviors (such as clicks, add-to-favorites, add-to-cart, and purchases), this often leads to low accuracy in recommendation results. We propose a meta-graph network recommendation system via multi-behavior encoding (MBGR). Firstly, the graph convolutional neural network is used to extract features from various interactive behavior heterogeneous graphs of user-items for behavior heterogeneous modeling. Secondly, matrix decomposition algorithm and meta-knowledge learner are used respectively to process the semantic information of user behavior, and then attention mechanism is used to learn and distinguish the importance of different types of user item interaction behaviors. Finally, meta-knowledge transfer network is used to combine meta-learning paradigm and neural network framework to establish user target behavior recommendation. We conducted comparative experiments comparing MBGR with 7 different baseline models such as NCF and DMF. Extensive experiments on three real datasets (Tmall, Yelp, ML10M) demonstrate that the proposed MBGR method outperforms the baselines. The performance of MBGR is improved by 10.97 % on average with the metric of HR@10 and 10.96 % with the metric of NDCG@10. Under different top-N value evaluation conditions (HR@10, HR@7, NDCG@10, NDCG@7, etc.), the proposed model's performance can also be improved by more than 10 %, which proves the rationality and effectiveness of the proposed MBGR method.

An improved algorithm for Finite Particle Method considering Lagrange-type remainder

The Finite Particle Method (FPM) is a significant improvement to the traditional Smoothed Particle Hydrodynamics method (SPH), which can greatly improve the computational accuracy of the entire computational domain. However, unstable calculation results and long computational time are still major obstacles to the development of FPM. Based on matrix decomposition, the fundamental equations of the traditional Finite Particle Method are rewritten and a Generalized Finite Particle Method (GFPM) is derived by introducing Lagrange-type remainder. By deriving and rewriting the fundamental equations, the GFPM method can be theoretically proven to be always stable. Numerical examples show that the GFPM method can utilize a smaller computational scale to achieve the same computational accuracy as the FPM method, with a corresponding reduction in computational time. Finally, the GFPM method is applied to a one-dimensional stress wave propagation problem and a one-dimensional heat conduction problem, and the computational results are compared with those of the SPH method and the FPM method, which verify that the GFPM has higher computational accuracy and stability.

Generalizability of foot placement control strategies during unperturbed and perturbed gait.

Control of foot placement is an essential strategy for maintaining balance during walking. During unperturbed, steady-state walking, foot placement can be accurately described as a linear function of the body's centre of mass (CoM) state at midstance. However, it is uncertain if this mapping from CoM state to foot placement generalizes to larger perturbations that could potentially cause falls. Recovery from these perturbations may require reactive control strategies not observed during unperturbed walking. Here, we used unpredictable changes in treadmill belt speed to assess the generalizability of foot placement mappings identified during unperturbed walking. We found that foot placement mappings generalized poorly from unperturbed to perturbed walking and differed for forward perturbation versus backward perturbation. We also used the singular value decomposition of the mapping matrix to reveal that people were more sensitive to backward versus forward perturbations. Together, these results indicate that a single linear mapping cannot describe the foot placement control during both forward and backward losses of balance induced by treadmill belt speed perturbations. Better characterization of human balance control strategies could improve our understanding of why different neuromotor disorders result in heightened fall risk and inform the design of controllers for balance-assisting devices.

Influence of spatial variability of soil shear-wave velocity considering intralayer correlation on seismic response of engineering site

Shear-wave velocity uncertainty significantly impacts seismic response analysis at engineering sites. Previous studies focused on the correlations of shear-wave velocities within soil layers. However, the influence of the vertical spatial variability of shear-wave velocity within individual soil layers was not considered. This study selected a typical Site Class II engineering site to investigate this influence based on the equivalent linear seismic response analysis method of layered soil deposits. Existing field test data on shear-wave velocity were used to discretize the shear-wave velocity within soil layers into a one-dimensional (1D) random field through covariance matrix decomposition and local average process theory. Monte Carlo simulations generated random shear-wave velocity profiles with different vertical correlation distances. Three artificial records with different earthquake return periods were used as input motions at the engineering bedrock for the 1D free-field model. Considering soil shear-wave velocity uncertainty, the peak shear strain increased by 19–27% with the input ground motion amplitude. Moreover, the site peak shear strain variability increased by 25–34% with the vertical correlation distance. The proposed 1D random field model effectively simulated the interlayer correlation and spatial variability of shear-wave velocity within soil layers, demonstrating its significance in seismic response analysis.

A novel thermal turbulence reconstruction method using proper orthogonal decomposition and compressed sensing coupled based on improved particle swarm optimization for sensor arrangement

With the development of offshore wind turbine single power toward levels beyond 10 MW, the increase in heat loss of components in the nacelle leads to a high local temperature in the nacelle, which seriously affects the performance of the components. Accurate reconstruction and control of thermal turbulence in the nacelle can alleviate this problem. However, the physical environment of thermal turbulence in the nacelle is very complex. Due to the intermittent and fluctuating nature of turbulence, the turbulent thermal environment is highly nonlinear when coupled with the temperature field. This leads to large reconstruction errors in existing reconstruction methods. Therefore, we improve the sparse reconstruction method for compressed sensing (CS) based on the concept of virtual time using proper orthogonal decomposition (POD). The POD-CS method links the turbulent thermal environment reconstruction with matrix decomposition to ensure computational accuracy and computational efficiency. The improved particle swarm optimization (PSO) is used to optimize the sensor arrangement to ensure stability of the reconstruction and to save sensor resources. We apply this novel and improved PSO-POD-CS coupled reconstruction method to the thermal turbulence reconstruction in the nacelle. The effects of different basis vector dimensions and different sensor location arrangements (boundary and interior) on the reconstruction errors are also evaluated separately, and finally, the desired reconstruction accuracy is obtained. The method is of research value for the reconstruction of conjugate heat transfer problems with high turbulence intensity.

Personalised Outfit Recommendation System Using Deep Learning

Abstract: Fashion engineering presents a significant challenge in efficiently coordinating outfits to suit personal preferences. In this study, we introduce a Fashion Coordination Assistant featuring a hybrid recommendation system. Our approach combines content-based and collaborative filtering techniques, utilizing Singular Value Decomposition (SVD) and Non-negative Matrix Factorization (NMF) algorithms. By thoroughly analyzing clothing characteristics and user behavior, we address the technical complexities of fashion coordination. Leveraging the latent features identified by SVD and the non-linear relationships captured by NMF, our system generates tailored outfit suggestions based on individual preferences and style profiles. Extensive testing validates the system's ability to provide diverse and efficient recommendations. By integrating innovative recommendation methods, the Fashion Coordination Assistant adapts to evolving fashion trends and user preferences, enhancing its practical utility in real-world scenarios

Research on Covert Communication Technology Based on Matrix Decomposition of Digital Currency Transaction Amount

Research on Covert Communication Technology Based on Matrix Decomposition of Digital Currency Transaction Amount

Event‐triggered secure control under denial‐of‐service attacks for cyber‐physical systems with positive constraint

AbstractThis paper investigates the stabilization problem for cyber‐physical systems subject to positive constraint and denial‐of‐service (DoS) attacks using the event‐triggered scheme. Unlike traditional modeling of cyber physical systems with DoS attack, this paper establishes a positive switched system model composed of two positive subsystems that according to the DoS attack is active or inactive. Considering the effect of positive constraint and DoS attack, a 1‐norm‐based event‐triggered mechanism is proposed in the sleep interval of DoS attacks. By incorporating switching theory with event‐triggered mechanism, the sufficient condition of positive property and exponential stabilization for the considered system is established. Thereafter, the gain matrix of the controller is calculated by matrix decomposition technique. Furthermore, the Zeno behavior is eliminated with a lower bound of the event‐triggered interval. Finally, an example is carried out to verify the validity of the theoretical results.

Multi-interest adaptive unscented Kalman filter based on improved matrix decomposition methods for lithium-ion battery state of charge estimation

Accurately predicting the state of charge (SOC) is crucial to improving Li-ion battery performance. However, available model-based estimation approaches still face challenges in handling model uncertainty and measurement noise effects on parameter identification. Besides, the widely used unscented Kalman filter (UKF) algorithm has limitations in electric vehicles as it requires the error covariance matrix to maintain positive definiteness, limiting its applicability under certain conditions. This study introduces the bias-compensated forgetting factor recursive least squares (BCFFRLS) method for parameter estimation within the second-order RC equivalent circuit model specific to the INR18650-20R battery. Furthermore, we propose a novel algorithm named the optimization multi-interest adaptive unscented Kalman filter (O-MIAUKF). This algorithm is designed to address stability and robustness issues with traditional UKF encounters in dynamic environments. Experimental validation demonstrates that the O-MIAUKF algorithm excels in maintaining strong stability and robustness in various working conditions, accurately estimating SOC even with a non-positive covariance matrix. The SOC estimation error remains stable at 0.8 %, which is lower than that of the current Extended Kalman Filter (EKF), UKF, and Dual Extended Kalman Filter (DEKF).

Almost sure and mean square convergence of iterative learning control system with state feedback under random packet dropouts

This paper investigates the almost sure and mean square convergence of a state feedback-based iterative learning control scheme for a class of discrete-time multi-input–multi-output linear systems with a direct feedback term in the presence of random data dropouts. Firstly, the realisability of the control system is considered. It is shown that the realisability of the control system is only determined by the direct feedback matrix, which has nothing to do with the input–output coupling matrix, and the direct feedback matrix to be full-row rank is enough to guarantee the system realisable. Secondly, the convergence of output tracking errors is analysed in both the almost sure and mean square senses, respectively. By the contraction mapping method combined with matrix decomposition and transformation techniques, it is strictly proved that the output sequence can converge to any given desired trajectory in the sense of almost sure and mean square, respectively, if and only if the general spectral radius condition is satisfied. Finally, an example is given to show the correctness of the theoretical analysis.

Tensile behavior of angle ply carbon reinforced PPS laminates under severe thermal aggressions: Homogeneous and heterogeneous temperature conditions

AbstractThis study explores the effects of critical temperature conditions on carbon fiber‐reinforced Poly Phenylene Sulfide (PPS) laminates, focusing on the coupling between thermal and mechanical behaviors. The thermo‐mechanical behavior of angle‐ply laminates is examined under both homogeneous (thermal decomposition and deformation/damage) and heterogeneous (fire) conditions following three primary objectives: (i) Investigate the impact of temperature distribution on the formation of porosities within the composite, considering their significance in thermal transfer and stress concentration—(ii) Evaluate the changes in residual mechanical behavior and properties under tension due to thermally‐induced damage—(iii) Improve the understanding of the interactions between severe thermal exposures and the mechanical behavior. X‐ray tomographic analyses and tensile tests were conducted to achieve these goals. Porosities resulting from thermal damage are identified as a key factor affecting the structural integrity of C/PPS laminates for high‐temperature applications. Mechanical testing reveals that the porosity content significantly reduces the tensile properties (axial stiffness and strength). Under homogeneous temperature conditions, the decrease in the tensile properties is significant up to Tonset (465°C) from which both the axial strength and stiffness dramatically decrease by −75 and −50%, respectively. As exposed to a kerosene flame during 60 s, corresponding to an aggression of 115 kW/m2 on one face of the laminates, the retention of the residual tensile properties remains good (−12% and −22% in stiffness and strength respectively), despite the dramatic decomposition of the polymer matrix. This can be explained from the stress redistribution from the exposed to the back face, and from the role of thermal insulator played by porosities.Highlights Carbon fibers/PPS laminates were subjected to severe thermal aggressions The formation of thermally‐induced porosities is studied A homogeneous aggression significantly decrease the tensile properties (−75%) Once the PPS matrix is severely decomposed, the load transfer is not possible After a 60 s flame exposure, the retention of tensile properties is good (−20%)

The method of determining optimal control of the thermoelastic state of piece-homogeneous body using a stationary temperature field

This paper proposes a new highly effective method for determining the optimal control of the stress-strain state of spatially multi-connected composite bodies using a stationary temperature field. The proposed method is considered based on the example of a stationary axisymmetric thermoelastic problem for a space with a spherical inclusion and cavity. The proposed method is based on the generalized Fourier method and reduces the original problem to an equivalent problem of optimal control, in which the state of the object is determined by an infinite system of linear algebraic equations, the right-hand side of which parametrically depends on the control. At the same time, the functional of the cost of the initial problem is transformed into a quadratic functional, which depends on the state of the equivalent system and parametrically on the control. The limitation on the temperature distribution is replaced by the value of the control norm in the space of square summable sequences. In fact, this paper considers for the first time the problem of optimal control of an infinite system of linear algebraic equations and develops a method for its solution. The proposed method is based on presenting the solutions of infinite systems in a parametric form, which makes it possible to reduce equivalent problem to the problem of conditional extremum of a quadratic functional, which explicitly depends on the control. A further solution to this problem A further solution to this problem is found by the Lagrange method using the spectral decomposition of the quadratic functional matrix. found by the Lagrange method using the spectral decomposition of the quadratic functional matrix. The method developed in this paper is strictly justified. For all infinite systems, the Fredholm property of their operators is proved. As an important result necessary for substantiation, for the first time, an estimate from below of the module of the multi-parameter determinant of the resolving system of the boundary value problem of conjugation – space with a spherical inclusion – was obtained when solving it using the Fourier method. The theorem that establishes the conditions for the existence and uniqueness of the solution of equivalent problem or optimal control problem without restrictions in the space of square summable sequences is proved. The numerical algorithm is based on a reduction method for infinite systems of linear algebraic equations. Estimates of the practical accuracy of the numerical algorithm demonstrated the stability of the method and sufficiently high accuracy even with close location of the boundary surfaces. Graphs showing the optimal temperature distribution for various geometric parameters of the problem and their analysis are provided. The proposed method extends to boundary value problems with different geometries.

A simple method to construct multivariate dual framelets with high-order vanishing moments

When constructing multivariate framelets, it is often unavoidable to work with matrices of multivariate trigonometric polynomials and complicated matrix decomposition problems. These problems become even harder when good properties such as high-order vanishing moments are required on the framelets. In this paper, we establish a new method for constructing multivariate dual framelets with high-order vanishing moments. The underlying scheme of our algorithm is the famous Mixed Extension Principle that allows us to derive the high-pass filters (or framelet generators) from a given pair of refinable filters with high-order linear-phase moments. Our method only involves two steps: (1) directly constructing the first few pairs of high-pass filters by using the linear-phase moment conditions of the refinement filters; (2) solving a system of linear equations to obtain the rest of the high-pass filters. Both are easy to implement for scientific computation, regardless of what dimension or dilation matrix we work with. Apart from high-order vanishing moments, we will see that if the refinement filters take coefficients from some subfield [Formula: see text] of [Formula: see text] that is closed under complex conjugation, so do the high-pass filters. Furthermore, our algorithm gives the upper bounds for the number of high-pass filters in arbitrary dimensions. At the end of the paper, we will give several illustrative examples, from which we can also see that the support sizes of the high-pass filters are comparable with those of the refinement filters.

Imbalanced instance selection based on Laplacian matrix decomposition with weighted k-nearest-neighbor graph

Imbalanced instance selection based on Laplacian matrix decomposition with weighted k-nearest-neighbor graph