Augmented Matrix Research Articles

A Nyström-Based Low-Complexity Algorithm with Improved Effective Array Aperture for Coherent DOA Estimation in Monostatic MIMO Radar

In this paper, we propose a computationally efficient algorithm with improved effective aperture for coherent angle estimation in a monostatic multiple-input multiple-output (MIMO) radar. First, the direction matrix of MIMO radar is mapped into a low-dimensional matrix of virtual uniform linear array (ULA). Then, an augmented data expansion matrix with improved effective aperture is obtained by exploiting the Vandermonde-like structure of the low-dimensional direction matrix and radar cross section (RCS) matrix to enlarge the aperture of the array. Next, a unitary transformation is used to transform the augmented matrix into a real value and the approximate signal subspace of the augmented matrix is obtained by the Nyström method, which can reduce the computational complexity. The eigenvectors of the approximate signal subspace are used to reconstruct the matrix for direct decorrelation processing. Finally, direction of arrivals (DOAs) can be estimated faster by utilizing the unitary ESPRIT algorithm since the rotation invariance of the extended reconstruction matrix still exists. The proposed algorithm has a lower total computational complexity, and the estimation accuracy is improved by utilizing real values and enlarging the array aperture for estimation. Several theoretical analyses and simulation results confirm the effectiveness and advantages of the proposed method.

Microgrid state and frequency estimation using Kalman filter: an approach considering an augmented measurement Jacobian matrix

Microgrid state and frequency estimation using Kalman filter: an approach considering an augmented measurement Jacobian matrix

Robust widely linear beamforming method for non-circular signals

Widely linear beamforming is known to outperform the conventional adaptive beamforming by fully employing the non-circularity of non-circular signals. In this paper, a robust widely linear beamformer (WLB) is proposed to achieve satisfactory output and robustness in low computational complexity. The augmented signal-of-interest (SOI) covariance matrix is built by performing integration over SOI angular sector. The principal eigenvector of the augmented SOI covariance matrix is taken as the SOI extended steering vector. The received signal vector is projected into the interference-plus-noise subspace to remove the SOI component and derive the augmented interference covariance matrix. The augmented noise covariance matrix is added to the derived augmented interference covariance matrix so that the augmented interference-plus-noise covariance matrix can be reconstructed. The proposed WLB possesses lower computational complexity than the state-of-the-art WLBs due to the avoidance of convex optimization programming. Numerical simulations illustrate the effectiveness of the proposed WLB.

Clinical and histological evaluation of the use of acellular dermal matrix (ADM) membrane in peri-implant vertical soft tissue augmentation: A controlled clinical trial.

The aim of this study was to clinically and histologically evaluate the efficacy of using acellular dermal matrix (ADM) for peri-implant vertical soft tissue augmentation at implant placement. Twenty patients were enrolled in this study. According to the initial thickness of vertical soft tissue, patients were assigned into the ADM group (≤2mm) or the control group (>2mm) prior to implant surgery +ADM grafting or implant surgery alone. Second-stage surgery was carried out 3months later, and a small piece of ridge membrane was harvested for histological and immunohistochemical evaluation. Vascular endothelial growth factor (VEGF) and platelet-derived growth factor (PDGF)-BB in peri-implant crevicular fluid (PICF) were also assessed 1week, 1month, and 5months after second-stage surgery. Clinical parameters were recorded to evaluate peri-implant health at 1week and 3months after implant restoration. All 20 implants healed uneventfully and successfully. Soft tissue thicknesses were comparable in the two groups at second-stage surgery (3.20±0.42mm vs. 3.50±0.58mm). In the ADM group, the mean increase in soft tissue thickness was 1.85±0.34mm. Histological and immunohistochemical outcomes showed no differences between the two groups. VEGF and PDGF-BB levels in PICF were significantly lower in the ADM group 1week after second-stage surgery (p<.01), yet they decreased in both groups later. The difference between the groups had disappeared by 5months after second-stage surgery. The clinical peri-implant parameters were good and stable by the end of the study (3months after restoration). Our results suggested that using ADM at implant placement was effective in increasing the thickness of peri-implant vertical soft tissue and achieved comparable clinical and histological performance to the control group. However, the incremental soft tissue showed inferior angiogenic ability in the early stage of wound healing.

Willingness to Pay for Renewable Energy

Increasing renewable energy footprints now features prominently in the clean energy transition plan for many countries. Consumer’s Willingness To Pay (WTP) for renewable energy is an important variable in this plan. A concept-centric review of 70 research articles conducted in this study reveals that first and most commonly, consumer’s willingness to pay for renewable energy indicates the social acceptance of renewable energy, quantifying the extent of public financial support for meeting nationally set renewable energy targets. Second, it reflects the preferred attributes of renewable electricity supply in deregulated retail electricity markets. And third, it mirrors the non use values of renewable energy sources. A concept augmented matrix presented in the paper helps understand the most popular valuation techniques used to quantify WTP estimates in included studies. This paper concludes by presenting policy enablers to accelerate renewable energy transition in developing economies - where the transition is still in nascent stages.

Dynamic slow feature analysis and random forest for subway indoor air quality modeling

The indoor air quality of a metro station is closely related to the health of passengers. In order to monitor the concentration of particulate matter in the air more stably and reduce the monitoring cost, a soft sensing model based on dynamic slow feature analysis (DSFA) and random forest (RF) is proposed in this paper. First, the augmented matrix technique is embedded into the slow feature analysis model to create a DSFA model to cope with the time lag inherent in the actual measurement process. Then, the constructed DSFA model is used to extract slowly varying latent variables to capture the dynamic trend within the input data. Finally, taking the latent variables as the input and aiming at the nonlinearity in the data, RF is used to predict the particle concentration. The results show that the prediction performance of the DSFA-RF model is better than some traditional soft sensor models, including partial least squares, support vector regression, single RF, and a hybrid model. The root mean square error value of DSFA-RF is improved by 21.93% compared with the hybrid model based on principal component analysis and support vector regression. In addition, DSFA also outperforms in health risk assessment.

Observer‐Based Synchronization and Quasi‐Synchronization for Multiple Neural Networks with Time‐Varying Delays

In this paper, we study the synchronization of a class of multiple neural networks (MNNs) with delay and directed disconnected switching topology based on state observer via impulsive coupling control. The coupling topology is connected sequentially, and the controller adjusts the state value through event‐triggering strategies. Different from the related works on MNNs, its state in this paper is assumed to be unmeasurable, and the time delay is also unmeasurable. Therefore, the observer does not contain the time‐delay term. The impulsive switching controller and observer controller adjust the system through the observed value. By constructing the corresponding augmented matrix, the system can finally achieve quasi‐synchronization (synchronization). Through derivation, we give the sufficient conditions ensuring quasi‐synchronization (synchronization) via the event‐triggered impulse control mechanism. In addition, numerical simulation examples are given to test our results of the theorem.

Peri-implant soft-tissue esthetic outcome after immediate implant placement in conjunction with xenogeneic acellular dermal matrix or connective tissue graft: A randomized controlled clinical study.

This randomized comparative study evaluated the clinical esthetic outcome of the peri-implant mucosa following extraction and immediate implant placement in conjunction with anorganic bovine bone mineral (ABBM) and the use of a porcine acellular dermal matrix (pADM) versus an autogenous connective tissue graft (CTG) in the anterior maxilla. Twenty patients (11 men, 9 women) with a mean age of 48,9 years (range 21-72) were included in the study and randomly assigned to either the test (pADM) or control group (CTG). They underwent extraction and immediate implant placement together with ABBM for socket grafting and either pADM or CTG for soft tissue augmentation. Twelve months after implant placement color measurements of the peri-implant mucosa and a reference tooth were performed using a spectophotometer and the color difference (ΔE) was calculated. The overall esthetic appearance of the peri-implant soft tissue was evaluated using the Pink Esthetic Score (PES). Statistical analysis was performed using Student's T-Test, the alpha was set to 0.05. All implants received osseointegration and were restored. The mean color difference of the peri-implant mucosa 1year after surgery amounted ΔE 4.06 ± 1.6 for the test group (pADM) and ΔE 3.58 ± 1.36 mm for the control group (CTG), showing no statistically significant difference (p=0.47). The mean PES of the pADM group was 11.4 ± 1.4 and for the CTG group 10.7 ± 1.5, showing no statistically significant difference (p=0.29). Twelve months after surgery, a porcine acellular dermal matrix for soft tissue augmentation in conjunction with immediate implant placement showed no difference in the overall esthetic appearance regarding color match and Pink Esthetic Score in comparison to autogenous soft tissue graft. Connective tissue grafts have become a standard in order to enhance the soft tissue quality and esthetic appearance in immediate implant placement. The use of new biomaterials like porcine acellular dermal matrices may avoid the need to harvest autogenous grafts resulting in simplified treatment and less postoperative morbidity.

RFI Localization via Reweighted Nuclear Norm Minimization in Microwave Interferometric Radiometry

Radio frequency interference (RFI) has become an increasing and challenging problem in microwave interferometric radiometry (MIR). Accurate localization of RFI sources is helpful to provide location information for switching off unauthorized transmitters causing RFI and mitigating the impact of these RFI sources. In this article, we propose a new RFI localization method based on reweighted nuclear norm minimization (RNNM). This method exploits the low-rank property of augmented covariance matrix (ACM) collecting visibility samples in MIR and introduces a singular value weighting strategy to consider different contributions of ACM components. First, ACM is constructed from the original covariance matrix of sparse array, which increases the degree of freedom (DOF) for array processing and hence improves the angular resolution performance. Second, we present a fixed point iteration (FPI)-based RNNM Algorithm, named FRA, to achieve low-rank approximation of ACM involving contribution degrees of ACM components. In this way, the ACM components corresponding to RFI signals are retained well and ones corresponding to background noises are suppressed. Third, we use a subspace-based direction-of-arrival (DOA) estimation approach, i.e., MUSIC algorithm, on the weighted completed ACM (WCACM) (obtained by FRA in the second stage) to locate the potential RFI sources. Retrieved results using synthetic data and real soil moisture and ocean salinity (SMOS) satellite data demonstrate that the proposed RNNM-based method not only has the superiority on improved detection performance, especially for identifying weak sources, but also shows better or competitive localization accuracy and angular resolution, compared with the existing commonly used RFI localization methods in MIR.

DOA Estimation of Coherent Sources Using Coprime Array via Atomic Norm Minimization

In this letter, we develop an effective algorithm for direction-of-arrival (DOA) estimation of coherent sources with coprime arrays. Firstly, we generate a virtual uniform linear array (ULA) through coprime array interpolation. Subsequently, we derive an augmented noise-free covariance matrix that is constructed using the entries of the covariance matrix of the virtual ULA outputs, and recover the Hermitian Toeplitz matrix by solving an atomic norm minimization problem with multiple measurement vectors. Finally, the DOAs of coherent sources are estimated via MUSIC spectral search. Unlike the state-of-the-art approach, our algorithm is insensitive to the phase differences among sources. Numerical results demonstrate the superiority of the proposed algorithm over several existing techniques.

A distributed Gauss–Newton method for distribution system state estimation

State estimation techniques are expected to play a significant role in the management of future distribution systems. This paper proposes an efficient distributed algorithm for state estimation of distribution networks. The algorithm is designed to solve the sparse linear system of equations at each Gauss–Newton iteration with a multi-area architecture. According to this algorithm, the augmented matrix of the linear system is fully decomposed. Each area calculates and stores a part of the augmented matrix using only interior and border measurements. A distributed Gaussian elimination procedure is then performed, which relies solely on simple local calculation and limited data exchange between neighboring areas. The proposed scheme enables the distributed computation of the overall weighted least square estimation problem. Parallel processing abilities of area processors are fully utilized which makes the algorithm computationally efficient. Case studies performed on the unbalanced IEEE 33 and 123-bus systems demonstrate the good performance of the algorithm in terms of accuracy and efficiency.

Augmented saddle-point formulation of the steady-state Stefan–Maxwell diffusion problem

Abstract We investigate structure-preserving finite element discretizations of the steady-state Stefan–Maxwell diffusion problem, which governs mass transport within a phase consisting of multiple species. An approach inspired by augmented Lagrangian methods allows us to construct a symmetric positive definite augmented Onsager transport matrix, which in turn leads to an effective numerical algorithm. We prove inf-sup conditions for the continuous and discrete linearized systems and obtain error estimates for a phase consisting of an arbitrary number of species. The discretization preserves the thermodynamically fundamental Gibbs–Duhem equation to machine precision independent of mesh size. The results are illustrated with numerical examples, including an application to modelling the diffusion of oxygen, carbon dioxide, water vapour and nitrogen in the lungs.

Mitigating baryonic effects with a theoretical error covariance

ABSTRACTOne of the primary sources of uncertainties in modelling the cosmic-shear power spectrum on small scales is the effect of baryonic physics. Accurate cosmology for stage-IV surveys requires knowledge of the matter power spectrum deep in the non-linear regime at the per cent level. Therefore, it is important to develop reliable mitigation techniques to take into account baryonic uncertainties if information from small scales is to be considered in the cosmological analysis. In this work, we develop a new mitigation method for dealing with baryonic physics for the case of the shear angular power spectrum. The method is based on an augmented covariance matrix that incorporates baryonic uncertainties informed by hydrodynamical simulations. We use the results from 13 hydrodynamical simulations and the residual errors arising from a fit to a ΛCDM model using the extended halo model code HMCode to account for baryonic physics. These residual errors are used to model a so-called theoretical error covariance matrix that is added to the original covariance matrix. In order to assess the performance of the method, we use the 2D tomographic shear from four hydrodynamical simulations that have different extremes of baryonic parameters as mock data and run a likelihood analysis comparing the residual bias on Ωm and σ8 of our method and the HMCode for an LSST-like survey. We use different modelling of the theoretical error covariance matrix to test the robustness of the method. We show that it is possible to reduce the bias in the determination of the tested cosmological parameters at the price of a modest decrease in the precision.

SVM based on principal component augmented matrix for fault detection

To effectively improve the fault detection rate of the support vector machine (SVM) based method, we propose a fault detection method with SVM based on principal component augmented matrix (PCAM-SVM). Firstly, the principal component analysis (PCA) algorithm is used to obtain the scores of training data in principal component space. Secondly, the input characteristics of time delay and time difference for the scores are added to construct the augmented matrix. Then, the combined augmented matrix on normal data and fault data is used to obtain the discriminant function of SVM model for classification. Finally, the SVM model is used to perform the classification operation on test data. The proposed method increases the complexity of input characteristics of model, reduces data autocorrelation, and enhances the fault detection performance of SVM by constructing principal component augmented matrix. The method has been applied to a multivariate dynamic simulation case and the Tennessee-Eastman process. The simulation results validate the feasibility and effectiveness of PCAM-SVM by comparison with PCA, independent component analysis (ICA), kernel principal component analysis (KPCA), SVM and PCA-SVM.

Three methods for solving systems of linear equations: Comparing the advantages and disadvantages

This paper aims to introduce some prevalent techniques which have been used to solve linear systems. Firstly, we introduce the simplest method: how to eliminate variables in which the original systems would not be changed. We then introduce Gaussian eliminations, which work on the augmented matrix derived from a linear system. To the end, we present Cramer’s rule, which computes the solution to a linear system based on matrix determinants. These methods have their application scenarios. For instance, eliminating variables has no limited condition for its operations. However, Cramer’s rule needs to be under the condition of square matrices. At the same time, Gaussian elimination requires three elementary row operations, and Gaussian elimination paves the way for computing the rank of matrices. The choice between these methods depends on coefficient matrices in terms of dimensions and matrix properties such as singularity.

The Generalized Complex Kernel Affine Projection Algorithms

The complex kernel adaptive filter (CKAF) has been widely applied to the complex-valued nonlinear problem in signal processing and machine learning. However, most of the CKAF applications involve the complex kernel least mean square (CKLMS) algorithms, which work in a pure complex or complexified reproducing kernel Hilbert space (RKHS). In this paper, we propose the generalized complex kernel affine projection (GCKAP) algorithms in the widely linear complex-valued RKHS (WL-RKHS). The proposed algorithms have two main notable features. One is that they provide a complete solution for both circular and non-circular complex nonlinear problems and show many performance improvements over the CKAP algorithms. The other is that the GCKAP algorithms inherit the simplicity of the CKLMS algorithm while reducing its gradient noise and boosting its convergence. The second-order statistical characteristics of WL-RKHS have also been developed. An augmented Gram matrix consists of a standard Gram matrix and a pseudo-Gram matrix. This decomposition provides more underlying information when the real and imaginary parts of the signal are correlated and learning is independent. In addition, some online sparsification criteria are compared comprehensively in the GCKAP algorithms, including the novelty criterion, the coherence criterion, and the angle criterion. Finally, two nonlinear channel equalization experiments with non-circular complex inputs are presented to illustrate the performance improvements of the proposed algorithms.

Mineralized Plasmatic Matrix for Horizontal Ridge Augmentation in Anterior Maxilla with and without a Covering Collagen Membrane

Mineralized Plasmatic Matrix for Horizontal Ridge Augmentation in Anterior Maxilla with and without a Covering Collagen Membrane

Characterization of bifurcations in the Zeeman catastrophe machine using singular value decomposition

Stable limit cycles of the dynamic Zeeman Catastrophe Machine are calculated and classified. As the geometry of the device is changed, they evolve into different types at discrete bifurcation points. The process is normally presented as a bifurcation diagram using a stroboscopic map, but this does not provide enough information to uniquely identify the bifurcation event. Three types of bifurcation are common: period-doubling, symmetry-breaking, and turning points. A method is developed to distinguish between these types by calculating the response to a change in device geometry. Assuming that the limit cycle has already been calculated, the response to a change in geometry is defined as the solution of a linear second-order differential equation. The equation is solved in finite-difference form by defining a matrix which contains the second-order response to a change in the limit cycle, as well as an augmented matrix which contains the response to a change in device geometry. At a bifurcation, the solution can be analyzed using singular value decomposition of these two matrices. The resulting singular values contain enough information to uniquely identify, and characterize, each type of event. The corresponding singular vectors can also be used to uniquely characterize the symmetry changes that occur in the response to change at each event.

Fault Detection and Health Assessment of Equipment Based on Fuzzy DPCA Spatial Eigenvalue Similarity

To improve the fault recognition rate of the dynamic principal component spatial data drive method, a fault diagnosis and equipment health status assessment method based on similarity fuzzy dynamics principal component analysis was proposed. First, the data are fuzzified according to the error function, and an augmented matrix is constructed. The eigenvalues are decomposed to obtain a score matrix and residual matrix of the fuzzy principal component. Further, the similarity between fault data and normal data is calculated. Meanwhile, a health assessment of the equipment is realized. The contribution rate of the observed variables is calculated. Finally, general Tennessee Eastman data and health assessment of a hydraulic press are used to validate the algorithm. The results show that the SFDPCA has a 100 % fault recognition rate for some faults, and the recognition rate for other faults is also higher than that of DPCA-Diss, DPCA-SPE, and PCA-SPE. The SDDPCA accurately identifies abnormal phenomena. It can determine the health level of prefilling and effectively make up for the shortcomings of PCA − T 2 , PCA-SPE, DPCA-Diss, and other methods and also can be applied to data-driven fault diagnosis to improve the fault recognition rate.

Collagen Matrix vs. Autogenous Connective Tissue Graft for Soft Tissue Augmentation: A Systematic Review and Meta-Analysis.

Soft tissues have been shown to be critical for the maintenance of both teeth and implants. Currently, regenerative soft tissue techniques propose the use of collagen matrices, which can avoid the drawbacks derived from the obtainment of autogenous tissue graft. A systematic review and meta-analysis were conducted to ascertain the efficacy of collagen matrices (CM) compared to autogenous connective tissue graft (CTG) to improve soft tissue dimensions. An electronic and manual literature searches were performed to identify randomized clinical trials (RCT) or controlled clinical trials (CCT) that compared CTG and CM. Pooled data of width of keratinized tissue (KT) and mucosal thickness (MT) were collected and weighted means were calculated. Heterogeneity was determined using Higgins (I2). If I2 > 50% a random-effects model was applied. Nineteen studies were included based on the eligibility criteria. When using CTG a higher MT gain (0.32 mm, ranging from 0.49 to 0.16 mm) was obtained than when employing CM. Similar result was obtained for the width of KT gain, that was 0.46 mm higher (ranging from 0.89 to 0.02 mm) when employing CTG. However, it can be stated that, although autogenous CTG achieves higher values, CM are an effective alternative in terms of total width of KT and MT gain.