Matrix Inversion Method Research Articles

Using independent cross-sectional survey data to predict post-migration health trajectories among refugees by estimating transition probabilities and their variances.

Health research is often concerned with the transition of health conditions and their relation with given exposures, therefore requiring longitudinal data. However, such data is not always available and resource-intensive to collect. Our aim is to use a pseudo-panel of independent cross-sectional data (e.g., data of and ) to extrapolate and approximate longitudinal health trajectories ( - ). Methods will be illustrated by examples of studying contextual effects on health among refugees by calculating transition probabilities with associated variances. The data consist of two cross-sectional health surveys among randomly selected refugee samples in reception ( ) and accommodation centers ( ) located in Germany's third-largest federal state. Self-reported measures of physical and mental health, health-related quality of life, health care access, and unmet medical needs of 560 refugees were collected. Missing data were imputed by multiple imputation. For each imputed data set, transition probabilities were calculated based on (i) probabilistic discrete event systems with Moore-Penrose generalized inverse matrix method (PDES-MP) and (ii) propensity score matching (PSM). By application of sampling approaches, exploiting the fact that status membership is multinomially distributed, results of both methods were pooled by Rubin's Rule, accounting for within and between-imputation variance. Most of the analyzed estimates of the transition probabilities and their variances are comparable between both methods. However, it seems that they handle sparse cells differently: either assigning an average value for the transition probability for all states with high certainty (i) or assigning a more extreme value for the transition probability with large variance estimate (ii).

Structure-borne sound power analysis for quantifying arbitrary structural modifications

A scalar quantity referred to as the Modification Power (MP) is presented as a means of characterizing a structure’s response to modifications. The structural modifications are modeled as a perturbation of arbitrary rank to the impedance matrix describing the unmodified structure’s dynamics. Perturbed matrix inversion methods are utilized to develop the MP. It is shown that this method of calculating the inverse of the modified impedance matrix is better numerically conditioned when compared to using a direct inversion method. The MP provides the analyst with information regarding not only the magnitude of the change in power flow, but the direction as well, indicating an increase or decrease in power flow into a structure. Additionally, expressions for the original and modified impedance matrices are derived in physical coordinates and reduced modal coordinates using primal assembly methods from the field of dynamic substructuring. Two case studies are presented, one using a pinned beam structure and the other a cantilevered plate structure, to demonstrate the properties of the MP, as well as to show the improved numerical conditioning of the modified impedance matrices.

An Inverse Solution Algorithm for Industrial Robot

The inverse solution process of industrial robot is complex. Because the traditional matrix algorithm involves a lot of matrix operation, its process is complex. Numerical algorithms usually do not yield all the solutions, generally, the selection of initial value and the search algorithm have great influence on the convergence and accuracy. The geometric algorithms is simple and intuitionistic with simple expression and small computation. In this paper, a hybrid algorithm combining the geometric method and the inverse transformation matrix method is proposed for puma 560 industrial robots. The geometric algorithms is used to solve the first three joints and the matrix algorithm is used to obtain the final three joint angles. This paper introduces the inverse solution algorithm for this kind of robot in detail, and verifies the effectiveness of the proposed algorithm through matlab simulation.

An Efficient Approach for Nodal Water Demand Estimation in Large-scale Water Distribution Systems

Real-time modeling of a water distribution system (WDS) is a critical step for the control and operation of such systems. The nodal water demand, as the most important time-varying parameter, must be estimated in real time. The computational burden of nodal water demand estimation is intensive, leading to inefficiency in the modeling of large-scale networks. The Jacobian matrix computation and Hessian matrix inversion are the main processes that dominate the computation time. To address this problem, an approach for shortening the computation time for real-time demand estimation in large-scale network is proposed. This approach allows the Jacobian matrix to be efficiently computed based on solving a system of linear equations, and a Hessian matrix inversion method based on matrix partitioning and the iterative Woodbury-Matrix-Identity Formula is proposed. The developed approach is applied to a large-scale network, in which the number of nodal water demands is 12523, and the number of measurements ranges from 10 to 2000. The results show that the time consumptions for the Jacobian computation and Hessian matrix inversion are within 465.3 ms and 1219.0 ms, respectively. The time consumption is significantly shortened compared with the existing approach, especially for nodal water demand estimation in large-scale WDSs.

Wave-packet continuum discretisation for nucleon–nucleon scattering predictions

In this paper we analyse the efficiency, precision, and accuracy of computing elastic nucleon–nucleon (NN) scattering amplitudes with the wave-packet continuum discretisation method (WPCD). This method provides approximate scattering solutions at multiple scattering energies simultaneously. We therefore utilise a graphics processing unit to explore the benefits of this inherent parallelism. From a theoretical perspective, the WPCD method promises a speedup compared to a standard matrix-inversion method. We use the chiral NNLOopt interaction to demonstrate that WPCD enables efficient computation of NN scattering amplitudes provided one can tolerate an averaged method error of 1–5 mb in the total cross section at scattering energies 0–350 MeV in the laboratory frame of reference. Considering only scattering energies ∼40–350 MeV, we find a smaller method error of ≲ 1–2 mb. By increasing the number of wave-packets we can further reduce the overall method error. However, the parallel leverage of the WPCD method will be offset by the increased size of the resulting discretisation mesh. In practice, a GPU-implementation is mainly advantageous for matrices that fit in the fast on-chip shared memory. We find that WPCD is a promising method for computationally efficient, statistical analyses of nuclear interactions from effective field theory, where we can utilise Bayesian inference methods to incorporate relevant uncertainties.

Dispersive analysis of glueball masses

We develop an inverse matrix method to solve for resonance masses from a dispersion relation obeyed by a correlation function. Given the operator product expansion (OPE) of a correlation function in the deep Euclidean region, we obtain the nonperturbative spectral density, which exhibits resonance structures naturally. The value of the gluon condensate in the OPE is fixed by producing the $\rho$ meson mass in the formalism, and then input into the dispersion relations for the scalar, pseudoscalar and tensor glueballs. It is shown that the low-energy limit of the correlation function for the scalar glueball, derived from the spectral density, discriminates the lattice estimate for the triple-gluon condensate from the single-instanton estimate. The spectral densities for the scalar and pseudoscalar glueballs reveal a double-peak structure: the peak located at lower mass implies that the $f_0(500)$ and $f_0(980)$ ($\eta$ ad $\eta'$) mesons contain small amount of gluonium components, and should be included into scalar (pseudoscalar) mixing frameworks. Another peak determines the scalar (pseudoscalar) glueball mass around 1.50 (1.75) GeV with a broad width about 200 MeV, suggesting that the $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$ ($\eta(1760)$) mesons are the glue-rich states. We also predict the topological susceptability $\chi_t^{1/4}=75$-78 MeV, deduced from the correlation function for the pseudoscalar glueball at zero momentum. Our analysis gives no resonance solution for the tensor glueball, which may be attributed to the insufficient nonperturbative condensate information in the currently available OPE.

A Non-Iterative Method Combined with Neural Network Embedded in Physical Model to Solve the Imaging of Electromagnetic Inverse Scattering Problem

The main purpose of this paper is to solve the electromagnetic inverse scattering problem (ISP). Compared with conventional tomography technology, it considers the interaction between the internal structure of the scene and the electromagnetic wave in a more realistic manner. However, due to the nonlinearity of ISP, the conventional calculation scheme usually has some problems, such as the unsatisfactory imaging effect and high computational cost. To solve these problems and improve the imaging quality, this paper presents a simple method named the diagonal matrix inversion method (DMI) to estimate the distribution of scatterer contrast (DSC) and a Generative Adversarial Network (GAN) which could optimize the DSC obtained by DMI and make it closer to the real distribution of scatterer contrast. In order to make the distribution of scatterer contrast generated by GAN more accurate, the forward model is embedded in the GAN. Moreover, because of the existence of the forward model, not only is the DSC generated by the generator similar to the original distribution of the scatterer contrast in the numerical distribution, but the numerical of each point is also approximate to the original.

Lax-Wendroff Difference Scheme with Richardson Extrapolation Method for One Dimensional Wave Equation Subjected To Integral Condition

In this paper, the Lax-Wendroff difference scheme has been presented for solving the one-dimensional wave equation with integral boundary conditions. First, the given solution domain is discretized and the derivative involving the spatial variable is replaced by the central finite difference approximation of functional values at each grid point by using Taylor series expansion. Then, for solving the resulting second-order linear ordinary differential equation, the displacement function is discretized in the direction of a temporal variable by using Taylor series expansion and the Lax-Wendroff difference scheme is developed, then it gives a system of algebraic equations. The derivative of the initial condition is also discretized by using the central finite difference method. Then the obtained system of algebraic equations is solved by the matrix inverse method. The stability and convergent analysis of the scheme are investigated. The established convergence of the scheme is further accelerated by applying the Richardson extrapolation which yields fourth-order convergent in spatial variable and sixth-order convergent in a temporal variable. To validate the applicability of the proposed method, three model examples are considered and solved for different values of the mesh sizes in both directions. Numerical results are presented in tables in terms of maximum absolute error,    and    norm.  The numerical results presented in tables and

Efficient Implementations of Rainbow and UOV using AVX2

A signature scheme based on multivariate quadratic equations, Rainbow, was selected as one of digital signature finalists for NIST Post-Quantum Cryptography Standardization Round 3. In this paper, we provide efficient implementations of Rainbow and UOV using the AVX2 instruction set. These efficient implementations include several optimizations for signing to accelerate solving linear systems and the Vinegar value substitution. We propose a new block matrix inversion (BMI) method using the Lower-Diagonal-Upper decomposition of blocks matrices based on the Schur complement that accelerates solving linear systems. Compared to UOV implemented with Gaussian elimination, our implementations with the BMI result in speedups of 12.36%, 24.3%, and 34% for signing at security categories I, III, and V, respectively. Compared to Rainbow implemented with Gaussian elimination, our implementations with the BMI result in speedups of 16.13% and 20.73% at the security categories III and V, respectively. We show that precomputation for the Vinegar value substitution and solving linear systems dramatically improve their signing. UOV with precomputation is 16.9 times, 35.5 times, and 62.8 times faster than UOV without precomputation at the three security categories, respectively. Rainbow with precomputation is 2.1 times, 2.2 times, and 2.8 times faster than Rainbow without precomputation at the three security categories, respectively. We then investigate resilience against leakage or reuse of the precomputed values in UOV and Rainbow to use the precomputation securely: leakage or reuse of the precomputed values leads to their full secret key recoveries in polynomial-time.

State-Feedback Control in Descriptor Discrete-Time Fractional-Order Linear Systems: A Superstability-Based Approach

In this article, the superstabilizing state-feedback control problem in descriptor discrete-time fractional-order linear (DDFL) systems with a regular matrix pencil is studied. Methods for investigating the stability and superstability of the considered class of dynamical systems are presented. Procedures for the computation of the static state-feedback (SSF) and dynamic state-feedback (DSF) gain matrices such that the closed-loop DDFL (CL-DDFL) system is superstable are presented. A numerical example is used to show the efficacy of the presented approach. Our considerations were based on the Drazin inverse matrix method.

APPLICATION OF LINEAR ALGEBRA TO ECONOMIC QUESTIONS

In the analysis of intersectoral balancing model economic problems, Kramer's rule, Gaussian method, and matrix methods are commonly utilized. The inverse matrix method was used to tackle the three-sector economic system's balance problems in particular. The dynamic model of intersectoral balance deals with challenges that arise over a period of time, such as one year of manufacturing.

Finite Crack in a Thermoelastic Transversely Isotropic Medium Under Green-Naghdi Theory

In this paper, we have studied a model of finite linear Mode-I crack in a thermoelastic transversely isotropic medium under Green Naghdi theory. The crack is subjected to a prescribed temperature and a known tensile stress. The plane boundary surface is considered as isothermal and all the field variables are sufficiently smooth. The heat conduction equation is written under two temperature theory (2TT) for Green Naghdi model which contains absolute temperature as well as conductive temperature. The analytical expressions of displacement components, stress components and temperature variables are obtained by normal mode analysis and matrix inversion method. Comparisons have been made within Green Naghdi (G-N) theory of type I, type II and type III for displacement, stress and absolute temperature variables against the crack width for a transversely isotropic material (Cobalt) by virtues of graphs. Also, Comparison have been made among displacement, thermal stress and absolute temperature for different depths.

Energetic and exergetic analysis of a new double pass solar air collector with fins and phase change material

Advanced solar air collectors are widely implemented in research for drying purposes. This research study presents a new steady state energy balance and exergy equations for a novel double pass solar air collector with fins and phase change material (PCM) according to first and second law of thermodynamics. The mathematical equations of energy balance were solved using the matrix inversion method. The predictions were observed at mass flow rates ranging from 0.01 kg/sec to 0.15 kg/sec, and solar radiation ranging between 425 W/m2 and 1000 W/m2. The impacts of solar radiation levels and mass air rates on energy efficiency, exergy efficiency and the improvement potential have been estimated and evaluated. The optimum energy efficiency of proposed collector is 73% at mass air rate of 0.15 kg/sec. The exergy efficiency is nearly 2.5–4.2% at maximum solar radiation level of 1000 W/m2 as well as the lowest and highest improvement potential are 980–2287 W for a solar radiation of 425–1000 W/m2.

Experimental and model validation of photovoltaic-thermal (PVT) air collector: exergy analysis

Solar energy is a renewable energy that can produce heat via a thermal system and generate electricity via a photovoltaic (PV) module. A photovoltaic-thermal (PVT) collector is a system that has a PV module combined with a thermal collector system. The PVT collector is a popular technology for harvesting solar energy. A PVT collector can generate both electrical and thermal energies simultaneously. The study aims to validate the PV and outlet temperature for various mass flow rates and solar radiation. To develop a predictive model, a steady-state energy analysis of a PVT air collector was performed. An energy balance equation was solved using the matrix inversion method. The theoretical model was developed and validated against the experimental results, which have a similar trend and are consistent with the experimental results. On the other hand, the validated model was used to study the performances of PVT air collectors using exergy analysis for the mass flow rate ranging from 0.007 kg/s to 0.07 kg/s and solar radiation ranging from 385 W/m2 to 820 W/m2. The result from the mathematical model was found to be consistent with the experimental data with an accuracy of about 95 %. The average PVT exergy efficiency was found to be 12.7 % and 12.0 % for the theoretical and experimental studies, respectively.

Lax-Wend off Difference Scheme with Richardson Extrapolation Method for One Dimensional Wave Equation Subjected to Integral Condition

In this paper, the Lax-Wend off difference scheme has been presented for solving the one-dimensional wave equation with integral boundary conditions. First, the given solution domain is discretized and the derivative involving the spatial variable is replaced by the central finite difference approximation of functional values at each grid point by using Taylor series expansion. Then, for solving the resulting second-order linear ordinary differential equation, the displacement function is discretized in the direction of a temporal variable by using Taylor series expansion, and the Lax-Wend off difference scheme is developed, then it gives a system of algebraic equations. The derivative of the initial condition is also discretized by using the central finite difference method. Then the obtained system of algebraic equations is solved by the matrix inverse method. The stability and convergent analysis of the scheme are investigated. The established convergence of the scheme is further accelerated by applying the Richardson extrapolation which yields fourth-order convergent in spatial variable and sixth-order convergent in a temporal variable. To validate the applicability of the proposed method, three model examples are considered and solved for different values of the mesh sizes in both directions. Numerical results are presented in tables in terms of maximum absolute error, L2 and L∞ norm. The numerical results presented in tables and graphs confirm that the approximate solution is in good agreement with the exact solution.

A material decomposition method for dual-energy CT via dual interactive Wasserstein generative adversarial networks.

Dual-energy computed tomography (DECT) is highly promising for material characterization and identification, whereas reconstructed material-specific images are affected by magnified noise and beam-hardening artifacts. Although various DECT material decomposition methods have been proposed to solve this problem, the quality of the decomposed images is still unsatisfactory, particularly in the image edges. In this study, a data-driven approach using dual interactive Wasserstein generative adversarial networks (DIWGAN) is developed to improve DECT decomposition accuracy and perform edge-preserving images. In proposed DIWGAN, two interactive generators are used to synthesize decomposed images of two basis materials by modeling the spatial and spectral correlations from input DECT reconstructed images, and the corresponding discriminators are employed to distinguish the difference between the generated images and labels. The DECT images reconstructed from high- and low-energy bins are sent to two generators separately, and each generator synthesizes one material-specific image, thereby ensuring the specificity of the network modeling. In addition, the information from different energy bins is exploited through the feature sharing of two generators. During decomposition model training, a hybrid loss function including L1 loss, edge loss, and adversarial loss is incorporated to preserve the texture and edges in the generated images. Additionally, a selector is employed to define the generator that should be trained in each iteration, which can ensure the modeling ability of two different generators and improve the material decomposition accuracy. The performance of the proposed method is evaluated using digital phantom, XCAT phantom, and real data from a mouse. On the digital phantom, the regions of bone and soft tissue are strictly and accurately separated using the trained decomposition model. The material densities in different bone and soft-tissue regions are near the ground truth, and the error of material densities is lower than 3mg/ml. The results from XCAT phantom show that the material-specific images generated by directed matrix inversion and iterative decomposition methods have severe noise and artifacts. Regarding to the learning-based methods, the decomposed images of fully convolutional network (FCN) and butterfly network (Butterfly-Net) still contain varying degrees of artifacts, while proposed DIWGAN can yield high quality images. Compared to Butterfly-Net, the root-mean-square error (RMSE) of soft-tissue images generated by the DIWGAN decreased by 0.01g/ml, whereas the peak-signal-to-noise ratio (PSNR) and structural similarity (SSIM) of the soft-tissue images reached 31.43dB and 0.9987, respectively. The mass densities of the decomposed materials are nearest to the ground truth when using the DIWGAN method. The noise standard deviation of the decomposition images reduced by 69%, 60%, 33%, and 21% compared with direct matrix inversion, iterative decomposition, FCN, and Butterfly-Net, respectively. Furthermore, the performance of the mouse data indicates the potential of the proposed material decomposition method in real scanned data. A DECT material decomposition method based on deep learning is proposed, and the relationship between reconstructed and material-specific images is mapped by training the DIWGAN model. Results from both the simulation phantoms and real data demonstrate the advantages of this method in suppressing noise and beam-hardening artifacts.

The Design of a Virtual Reality Image Distortion Method for mobile devices

How to predict a more accurate next frame according to the current frame is still a problem. In this study, a method of generating intermediate frames in VR is proposed, which can effectively reduce the image jitter in VR games and increase the user experience; on the other hand, the inverse matrix method proposed in this study has a small amount of calculation and a fast calculation speed, and can complete the calculation in a short time. Therefore, this method can help us to complete the insertion of frames in the specified time. In this paper, firstly, the algorithm is constructed based on the principle of inverse matrix, and then the simulation experiment is carried out. The experimental results show that the scheme is a viable and effective solution.

Lotka-Volterra distributed power control model for OCDMA systems

Dynamic continuous Lotka-Volterra model is used to build two new distributed power control algorithms (DPCA) for optical code division multiple access systems (OCDMA) communication systems, namely DPCA-LV and DPCA-LV* algorithms. The DPCAs features are described, while comparative performance analyses are carried out involving both proposed LV-based DPCAs, the classical Sigmoid DPCA (by Uykan and Uykan), and the Matrix inversion method (MIM) by Tarhuni, including the convergence speed, the normalized mean square error (NMSE), the average consumption of energy per user and complexity measured by the floating-point operations (flops). Under conditions of estimated errors, the proposed DPCA-LV* exhibits minor discrepancy regarding the ideal power vector solution and better convergence, considering both fixed and adaptive factor convergence regarding the DPCA-LV, the conventional Sigmoid DPCA, and MIM approach. The superiority of the DPCA-LV* in terms of performance-complexity tradeoff is more remarkable under high dimension optical networks.

Transmission and reflection of SV waves at micropolar solid–liquid interface with dual-phase lag theory

The target of this study is to see the influence of the magnetic field, angular velocity, initial stress, and rotation on the incident SV wave. The SV waves are reflected as well transmitted at the interface of micropolar solid and liquid half-space. The dual-phase lag theory is used for energy equation; the basic equations have been discussed to drive results for transmitted thermal and P waves and reflected thermal, micro-rotation, SV and P waves. The transmission and reflection of SV waves are examined after applying the boundary conditions, and amplitude ratios are figured by the matrix inversion method. Graphs are sketched and discussed for various values pertinent parameters on amplitude ratios. We perceived that the amplitude ratio of the P wave is dominant.

Incremental holistic controller

The trace of inverse coefficient matrix method in state space is used to implement and simplify an iterative design of a control system with main interest in increasing dynamical performance quality or to check if stability danger exists. The tau -locus is a helpful design element. Various applications and examples are presented for illustration.