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The increasing use of power electronics converters to integrate renewable energy sources has been a subject of concern due to the resonance oscillatory phenomena caused by their interaction with poorly damped AC networks. Early studies are focused on assessing the controller influence of a single converter connected to simple networks, and they are no longer representative for existing systems. Lately, studies of multi-infeed grid-connected converters are of particular interest, and their main aim is to apply traditional criteria and identify their difficulties in the stability assessment. An extension of traditional criteria is commonly proposed as a result of these analysis, but they can be burdensome for large and complex power systems. The present work addresses this issue by proposing a simple criterion to assess the stability of large power systems with high-penetration of power converters. The criterion has its origin in the mode analysis and positive-net damping stability criteria, and it addresses the stability in the frequency domain by studying the eigenvalues magnitude and real component of dynamic models in the admittance matrix form. Its effectiveness is tested in two case studies developed in Matlab/Simulink which compare it with traditional criteria, proving its simplicity. [ABSTRACT FROM AUTHOR]

The thermodynamics of a biochemical reaction system can be treated at three levels. At level 1 the fundamental equation for the Gibbs energy G is written in terms of species, at level 2 the equilibrium pH is specified and the fundamental equation for the transformed Gibbs energy G‘ is written in terms of reactants (sums of species), and at level 3 the equilibrium pH and equilibrium concentrations of one or more reactants are specified and the fundamental equation for the further transformed Gibbs energy G‘ ‘ is written in terms of pseudoisomer groups of reactants. At each level it is convenient to use matrix notation because the conservation matrixes A, A‘, and A‘ ‘ are useful for identifying components and choosing alternate sets of components. These conservation matrixes can also be used to calculate the corresponding stoichiometric number matrixes ν, ν‘, and ν‘ ‘, which are useful for grouping terms for an independent set of reactions in the fundamental equation. The treatments of reactions at the three levels are similar, and there are mathematical relations between the thermodynamic properties at the three levels. The matrix form of the fundamental equation at each level is useful for identifying the set of properties that have to be specified to describe the extensive state of the system at equilibrium. These variables are used to specify the criterion for spontaneous change and equilibrium. The matrix form of the Gibbs−Duhem equation at each level is useful for identifying the set of intensive properties required to describe the intensive state of the system at equilibrium. The total number of degrees of freedom F is the same at all three levels.

AbstractIn this paper, we establish an extension of the matrix form of the Brunn-Minkowski inequality. As applications, we give generalizations on the metric addition inequality of Alexander.2000 Mathematics subject classification: primary 52A40.

The instrument line shape (ILS) of a Fourier-transform spectrometer is expressed in a matrix form. For all line shape effects that scale with wavenumber, the ILS matrix is shown to be transposed in the spectral and interferogram domains. The novel representation of the ILS matrix in the interferogram domain yields an insightful physical interpretation of the underlying process producing self-apodization. Working in the interferogram domain circumvents the problem of taking into account the effects of finite optical path difference and permits a proper discretization of the equations. A fast algorithm in O(N log_2 N), based on the fractional Fourier transform, is introduced that permits the application of a constant resolving power line shape to theoretical spectra or forward models. The ILS integration formalism is validated with experimental data.

This work recommends methods of construction of equations of motion of mechanical systems in matrix form. The use of a matrix form allows one to write an equation of dynamics in compact form, convenient for the investigation of multidimensional mechanical systems with the help of computers. Use is made of different methods of constructing equations of motion, based on the basic laws of dynamics as well as on the principles of D'Alambert-Lagrange, Hamilton-Ostrogradski and Gauss.

The pathogenic Gram-positive bacterium Streptococcus pyogenes (group A streptococcus) binds to fibronectin via protein F. In this study, we have investigated the binding properties of protein F to various multimeric tissue forms of fibronectin that appear on cell surfaces and in the extracellular matrix. We show that binding of S. pyogenes through protein F is more efficient to an in vitro-derived polymerized form of fibronectin (superfibronectin) than to soluble fibronectin immobilized in a solid phase. In addition, Chinese hamster ovary cells overexpressing the alpha5beta1 integrin produced an increased amount of a fibronectin matrix and consequently bound a higher number of S. pyogenes cells. Inhibition and direct binding assays using purified proteins demonstrated that binding to a fibronectin matrix involved both domains of protein F (UR and RD2) that have previously been implicated in interactions with fibronectin. Using intact S. pyogenes bacteria in which various domains of protein F were expressed as hybrids with the surface-exposed region of an unrelated protein, we revealed that, in contrast to the predominantly UR-mediated binding to soluble fibronectin, the maximal binding to the fibronectin matrix required RD2 in addition to UR. Since in some infections S. pyogenes may initially encounter a matrix form of fibronectin, these results suggest that UR and RD2 may be important for the initiation of streptococcal infectious processes.

The pathogenic Gram-positive bacteriumStreptococcus pyogenes(group A streptococcus) binds to fibronectin via protein F. In this study, we have investigated the binding properties of protein F to various multimeric tissue forms of fibronectin that appear on cell surfaces and in the extracellular matrix. We show that binding of S. pyogenesthrough protein F is more efficient to an in vitro-derived polymerized form of fibronectin (superfibronectin) than to soluble fibronectin immobilized in a solid phase. In addition, Chinese hamster ovary cells overexpressing the α5ॆ1integrin produced an increased amount of a fibronectin matrix and consequently bound a higher number of S. pyogenescells. Inhibition and direct binding assays using purified proteins demonstrated that binding to a fibronectin matrix involved both domains of protein F (UR and RD2) that have previously been implicated in interactions with fibronectin. Using intact S. pyogenesbacteria in which various domains of protein F were expressed as hybrids with the surface-exposed region of an unrelated protein, we revealed that, in contrast to the predominantly UR-mediated binding to soluble fibronectin, the maximal binding to the fibronectin matrix required RD2 in addition to UR. Since in some infections S. pyogenesmay initially encounter a matrix form of fibronectin, these results suggest that UR and RD2 may be important for the initiation of streptococcal infectious processes.

ABSTRACTDuring infection and inflammation, bacterial and inflammatory proteases break down extracellular matrices into macromolecular fragments. Fibronectin fragments are associated with disease severity in arthritis and periodontitis. The mechanisms by which these fragments contribute to disease pathogenesis are unclear. One likely mechanism is that fibronectin fragments induce apoptosis of resident cells, which can be further modulated by nitric oxide. Nitric oxide levels are increased at inflammatory sites in periodontitis patients. The aim of this study was to examine whether a proapoptotic fibronectin matrix (AFn) exerts its action by inducing nitric oxide and whether priming by bacterial and inflammatory components exacerbates this mechanism. Our data demonstrate that AFn increased the levels of nitric oxide and inducible nitric oxide synthase (iNOS) dose and time dependently in periodontal ligament (PDL) cells. These effects and apoptosis were inhibited by iNOS suppression and enhanced by iNOS overexpression. Nitric oxide and iNOS induction were paralleled by increased c-Jun N-terminal kinase 1 (JNK-1) phosphorylation. JNK-1 overexpression enhanced the expression of nitric oxide and iNOS, whereas inhibiting JNK-1 by small interfering RNA or a kinase mutant reversed these findings. Priming PDL cells with Porphyromonas gingivalis, its lipopolysaccharide (LPS), or gamma interferon (IFN-γ) further increased nitric oxide levels and apoptosis. Escherichia coliand Streptococcus mutansinduced lesser effects. Gingival fibroblasts and neutrophils responded to a lesser degree to these stimuli, whereas keratinocytes were resistant to apoptosis. Thus, proapoptotic matrices trigger nitric oxide release via JNK-1, promoting further apoptosis in host cells. LPS and IFN-γ accentuate this mechanism, suggesting that during inflammation, the affected matrices and bacterial and inflammatory components combined exert a greater pathogenic effect on host cells.

In this paper, we develop a tensor-based joint symbol detection and user sensing scheme for the three-dimensional uplink terahertz system with dual-wideband effects. To leverage the low-rank decomposition of tensor, the received matrix-form pilot at the selected subcarrier is rearranged into a real-valued tensor-form one, and the corresponding algorithm is designed for angle of arrival and Doppler estimation. Subsequently, symbol detection and time delay estimation are conducted by utilizing the received signals at the remaining subcarriers. Finally, user localization and tracking are achieved by using the estimated sensing parameters along with the location variations between adjacent time instances. Simulation results show that the proposed scheme provides superior joint symbol detection and user sensing performance compared with the existing complex-valued matrix-based and tensor-based methods.

Robust PCA is a popular anomaly detection technique and has been widely used in many applications. Although Robust PCA is promising, it is usually designed in a two-order matrix form, which is inferior to the tensor that can capture multilinearity features of data. Moreover, the detection accuracy under Robust PCA further suffers due to its sensitivity to the rank parameter which is hard to set in practice and the limitation of PCA method in capturing the non-linear feature in the data. To address the issues, we propose a Robust Tensor Convolutional Autoencoder (RTCAE) where the autoencoder instead of SVD is exploited to recover the normal data from the corrupted measurement tensor data. However, directly exploiting deep autoencoder may suffer from the problem of high memory consumption and computation overhead due to the large number of parameters used in autoencoder. To make our anomaly detection lightweight, we further design a Light Convolutional Autoencoder (LightCAE) which contains a compressed autoencoder by exploiting tensor factorization to largely compress the parameters while significantly reducing the computation complexity. We conduct extensive experiments on three real data traces to compare the performance of our proposed schemes (RTCAE and lightCAE) with that of seven baseline algorithms. The experiment results demonstrate that our proposed RTCAE achieves the highest anomaly detection accuracy. Moreover, our LightCAE requires over 60 times smaller memory storage than that required in RTCAE while achieving the similar anomaly detection accuracy.

We present a barycentric Lagrange interpolation collocation method (BLICM) and investigate its capability in avoiding volumetric locking in nearly incompressible and incompressible plane elasticity. Specifically, the governing equations of plane elasticity are expressed as mixed formulas combining displacement and pressure. The unknown functions of displacement and pressure are approximated using barycentric Lagrange interpolation. The governing equations and boundary conditions are discretized into algebraic equations in matrix form. The boundary conditions are imposed by additional method to form an over-constraint system of algebraic equations. A regular domain method is introduced to tackle irregularly shaped domains. Extensive numerical experiments were conducted to validate the proposed method and the results demonstrate its ability to avoid locking issues while achieving high precision in nearly incompressible and incompressible plane elasticity. [ABSTRACT FROM AUTHOR]

Twins play a crucial role in elucidating the structure and deformation characteristics of materials. However, in materials with low-symmetry crystal structures, solving the twin relationships remains a challenging task. In this study, we propose a general method for determining twin elements K1, η1, K2, and η2, which are essential for twin analysis. The proposed method involves three main steps: (1) representing misorientation data measured by electron back-scattered diffraction (EBSD) and transmission electron microscopy (TEM) in matrix form, (2) identifying additional 180° rotation elements related to twin elements K1or η1by traversing all symmetrically equivalent misorientations, and (3) using a minimum and crystal structure-dependent uniform shear as the constraint to determine the other twin elements (K2andη2). By combining the experimental data and the proposed method, we systematically analyze the complex twin relationships of Cu–Zn–Al shape memory alloys (SMAs) with monoclinic martensite (M18R). This methodology has been demonstrated to be effective and possesses broad applicability.

The paper develops the Green's function solution in matrix form for functionally graded and transversely isotropic material (FGTIM) due to the loading of a circular ring force vector. The force vector is concentrated along a horizontal circular ring and acts at any location in the interior of the FGTIM material occupying either a fullspace or a halfspace. Without loss of generality, the variations of the FGTIM's five elastic parameters are expressed as five arbitrary step functions with the depth as the independent variable. The two-dimensional Fourier integral transforms in the cylindrical coordinate system are used for the mathematical formulation and derivation in matrix form. The Green's function solution of the displacement and stress fields is explicitly expressed in the matrix form in terms of classical improper Hankel transform integrals of the orders of 0 to 3. The kernel functions of the Hankel transform integrals are explicitly expressed in the forms of backward transfer matrix. Their mathematical properties are analyzed analytically and numerically. The singular terms associated with the improper Hankel transform integrals are analytically isolated and expressed in the exact closed-form in terms of the complete elliptic integrals of the first, second and third kind. Such closed-form singular terms can be expressed as the matrix Green's function solution for the corresponding bi-material due to the same circular ring force vector. Numerical results show that the computation of the matrix Green's function solution can be achieved with high accuracy and efficiency and the heterogeneity and anisotropy can have significant effects on the elastic fields in the FGTIM induced by the circular ring force vector. [ABSTRACT FROM AUTHOR]

ABSTRACTAn analytical modelling approach is developed in this article to simulate the pull-out behaviour of a single straight/hooked end fibre that is embedded in concrete matrix. The partial-interaction model is used to simulate the interfacial bond between the fibre and matrix along the entire fibre length throughout all stages of loading where additional axial and frictional forces due to straightening a hook is incorporated by simulating it as plastic hinges at the apex of bends. The analytical model is presented in a concise matrix form that helps to minimise the number of solution steps for the involved individual cases and provides a monolithic simplified implementation. A significant advantage of the approach is that it does not require fitting of a smoothing polynomial to show the full-range of fibre load-slip behaviour as it simulates the forces for straightening the fibre as it pulls through a bend and directly couples this to the interfacial bond forces.

The binary polarization state analyzer (PSA) made of magnetooptic crystal (MO) rotators is a promising technology for achieving low-cost and high-efficiency state of polarization (SOP) analysis. To eliminate the influence of wavelength, temperature, and optical power noise on the internal optical components and data analysis of the PSA, a multivariable optimization method is proposed to solve the self-calibration problem and improve the SOP analysis accuracy. An overdetermined equation is constructed to describe the self-calibration problem of a 4-bit PSA, which consists of the rotation angle of the MO rotator, the retardation angle of the quarter-wave plate (QWP), and the relative orientation angle between the QWP and the polarizer (POL). Then, an optimization model is built using the least squares method in matrix form, and the optimization objective function is reasonably constructed by considering the optical power residual error and the degree of polarization (DOP). The trust region reflective algorithm is utilized to address the above model. Furthermore, the sensitivity of the proposed model is analyzed to choose the appropriate SOP for improving the self-calibration accuracy, and Monte Carlo analysis is executed to evaluate the accuracy of self-calibration and SOP analysis. Experimental results are consistent with simulation results. Compared with the method directly solving the linear equations of the 4-bit PSA, the presented method could achieve more accurate and self-calibrated measurements of the SOP.

Terahertz (THz) inverse synthetic aperture radar (ISAR) imaging of space targets has the advantage of high resolution and all-day capability for spatial situational awareness (SSA). However, compared with microwave ISAR imaging, microvibrations of the radar platform and target can cause image defocusing and quality degradation in the THz band. Commonly, the existing algorithms considered vibration as simple harmonic motion in a rigid body and estimated the vibration parameters for phase error compensation. Nevertheless, these methods are dependent on the prominent points and cannot focus on the complex nonrigid vibration of the space target. Aiming at these problems, an ISAR imaging framework that can be leveraged for complex nonrigid vibration compensation is proposed. First, a compressed sensing (CS) model is established to compensate for the vibration phase error in ISAR imaging. Then, the alternating direction method of multipliers (ADMMs) is employed to optimize the CS model. Subsequently, considering that strong scattering points of space targets will cover up the weak scattering information in ISAR images, a sidelobe suppression constraint is appended. Thus, the weak scattering information is retained while removing the sidelobe and noise. It is worth mentioning that the ISAR imaging algorithm is derived to a 2-D matrix form to reduce memory usage and improve computational efficiency. Finally, simulated and measured data are utilized to verify the superiority of the proposed algorithm and prove the potential of ISAR imaging for practical space targets.

Hyperspectral imagery typically exhibits high spectral resolution but low spatial resolution due to limitations in imaging sensors. This limitation results in a large quantity of mixed pixels especially in noisy environments. Hyperspectral image super-resolution aims to enhance spatial resolution and reduce redundant interference, but it is often an ill-posed inverse problem. So far, the classical NMF-based method needs to unfold the remotely sensed cubic data into matrix form, resulting in the loss of 3-D structure knowledge. Also, the deep-learning-based algorithms suffer from massive hyperparameter tuning and weak interpretability. Furthermore, the tensor-based models also poses a lot of challenges, such as the uncertainty of exact rank and high complexity. To address the aforementioned issues, this article reformulates a novel tensor-based super-resolution model that incorporates multimode low-rank and graph-based manifold regularization (M-LGMR) for performance enhancement of reconstruction images. First, the low-rank relaxation is redefined to eliminate the nonuniqueness of tensor rank and suppress minor components. Next, owing to local similarity in hyperspectral cubic data, Laplace embedding-based manifold regularization is imposed on both spatial and spectral components to denoise and preserve the spatial-spectral structure. In the end, using matrix-vector operators, we also develop a set of efficient solvers to reduce the computational load. The simulation and experimental results on several real datasets demonstrate that the proposed method enhances the spatial resolution of reconstruction images effectively and also greatly improves the classification accuracy in practical applications of hyperspectral images.

It has been long known that the Euler–Lagrange dynamical equations of fixed-base manipulators with single-degree-of-freedom joints can be formulated on Lie groups following exponential joint parameterizations. Whereas, dynamics of symmetric vehicles can be captured using the Euler–Poincaré equations on Lie groups, with no need to choose any local parameterization. We utilize a combined form of these two geometric approaches called the Lagrange–Poincaré Equations (LPE) to develop a singularity-free Lagrangian formalism for the dynamics of vehicle-manipulator systems. We consider vehicles whose configuration manifolds are Lie subgroups of the special Euclidean group, encompassing arbitrary base vehicle motions corresponding to, e.g., ball, planar, or free joints. We revisit the Lagrange-d'Alembert principle for systems on principal bundles to derive the LPE for vehicle-manipulators with possibly symmetry-breaking externally applied wrenches. These equations effectively separate the external (locked-arm system) and internal dynamics (arm's motion) by introducing a block-diagonalized inertia matrix. We then incorporate the exponential parameterization of manipulators to explicitly formulate the reduced dynamics on Lie groups. The resulting equations are in matrix form and can be immediately implemented in simulations and model-based control strategies. The geometrical significance of the proposed formalism is further demonstrated via the step-by-step presentation of a case study.

Online modeling of the magneto-thermal coupled field (MCF) in permanent-magnet eddy-current couplings (PMECCs) has long been challenging since it exists in the copper layer and cannot be directly measured. This article proposes an online magneto-thermal coupled model (OMCM) to reconstruct the MCF using measured boundaries. The magnetic field (MF), eddy-current field (ECF), and temperature field (TF) in the MCF are coupled in an identical space-time united discretization system. Virtual boundary nodes are added to the system, which can adapt to different boundary conditions in electromagnetic and thermal analysis. The measured data of single-point sensors are spanned to continuous boundary conditions. An approximate solution of the MCF is derived based on the measured boundaries and the general solutions of Laplace's equation and Poisson's equation in magneto-thermal analysis. The three-dimensional distribution of the MF, ECF, and TF at each spatial node and time segment can be simultaneously calculated in matrix form by the OMCM. Furthermore, the output torque is estimated and compared with the conventional methods. A verification process is carried out to assess the reconstructed results, showing that the OMCM can yield results close to the verification sensors for various slips and air gaps.

In this article, we develop an accurate and fast numerical method to analyze stochastics scattering from stratified media consisting of inhomogeneous layers with random constitutive parameters. The permittivity and/or permeability of each layer may vary continuously. Full-domain cubic B-spline basis functions are employed in the stochastic method of moment (SMoM), for calculating the scattered fields by converting the governing Helmholtz’s differential equation to a matrix form. It is shown that the complexity of the proposed full-wave approach is not affected significantly by the number of existing random parameters. The proposed method is vindicated by comparing its results with the Monte Carlo (MC) method.

This paper proposes an analytical design procedure for a class of 2D filters with a directional characteristic in the frequency plane. The method starts from two types of low-pass prototypes, namely a Gaussian filter and a wide-band filter. The two prototypes and the resulted 2D filters are zero-phase, a very useful property in image processing tasks. The prototypes are parametric and can be scaled along the frequency axis, thus resulting narrower or wider. A 1D to 2D frequency mapping, based on accurate approximations, is derived and applied to each prototype, obtaining the desired directional 2D frequency response with specified selectivity and orientation. The designed filters are adjustable, with a frequency response in factored matrix form depending on specifications. The Gaussian prototype yields very selective directional filters, used in detecting oriented straight lines in images, as show simulation results on several test images. Using oriented wide-band filters, other useful 2D filters result, namely square and parallelogram filters. The designed filters have accurate frequency responses, good directional selectivity and high linearity at relatively low order. An advantage of this analytical approach is that the filter transfer function results in parametric form and allows for easy tunability. [ABSTRACT FROM AUTHOR]

The asymptotic synchronization of coupled reaction–diffusion neural networks with proportional delay and Markovian switching topologies is considered in this brief where the diffusion space does not need to contain the origin. The main objectives of this brief are to save communication resources and to reduce the conservativeness of the obtained synchronization criteria, which are carried out from the following two aspects: 1) mode-dependent quantized control technique is designed to reduce control cost and save communication channels and 2) Wirtinger inequality is utilized to deal with the reaction–diffusion terms in a matrix form and reciprocally convex technique combined with new Lyapunov–Krasovskii functional is used to derive delay-dependent synchronization criteria. The obtained results are general and formulated by linear matrix inequalities. Moreover, combined with an optimal algorithm, control gains with the least magnitude are designed. [ABSTRACT FROM AUTHOR]

We present a high-performance evaluation method for 4-center 2-particle integrals over Gaussian atomic orbitals with high angular momenta (l≥ 4) and arbitrary contraction degrees on graphical processing units (GPUs) and other accelerators. The implementation uses the matrix form of McMurchie–Davidson recurrences. Evaluation of the four-center integrals over four l= 6 (i) Gaussian AOs in double precision (FP64) on an NVIDIA V100 GPU outperforms the reference implementation of the Obara-Saika recurrences (Libint) running on a single Intel Xeon core by more than a factor of 1000, easily exceeding the 73:1 ratio of the respective hardware peak FLOP rates while reaching almost 50% of the V100 peak. The approach can be extended to support AOs with even higher angular momenta; for lower angular momenta (l≤ 3), additional improvements will be reported elsewhere. The implementation is part of an open-source LibintXlibrary freely available at github.com:ValeevGroup/LibintX.

This article studies the constrained switching (linear) system which is a discrete-time switched linear system whose switching sequences are constrained by a deterministic finite automaton. The stability of a constrained switching system is characterized by its constrained joint spectral radius that is known to be difficult to compute or approximate. Using the semitensor product of matrices, the matrix-form expression of a constrained switching system is shown to be equivalent to that of a lifted arbitrary switching system. Then, the constrained joint/generalized spectral radius of a constrained switching system is proven to be equal to the joint/generalized spectral radius of its lifted arbitrary switching system which can be approximated by off-the-shelf algorithms. [ABSTRACT FROM AUTHOR]

A patent application has been submitted for a display device and mobile electronic device that aim to improve the portability and convenience of display devices. The inventors have embedded a photosensor in the display panel to enhance sensing performance. The display panel consists of subpixels arranged in a matrix form, with a sensor pixel detecting biometric information using red, green, and blue light emitted from the subpixels. The patent application provides detailed descriptions and embodiments of the display device and mobile electronic device, and this technology has potential applications in healthcare and medical monitoring. [Extracted from the article]

Traffic prediction serves as a crucial role in intelligent transportation systems for applications including routing planning and traffic control. With the advances of sensor technologies and Internet of Things (IoTs), the exploitation of traffic data motivates us to reformulate the traffic-state prediction problem based on the big-data characteristics. In order to infer multifarious traffic information, the standard one/two-relational traffic data in the vector/matrix form needs to be expanded to multi-relational traffic data in an arbitrary tensor form. However, none of the existing approaches is capable of performing traffic prediction by characterizing and tracking the inherent multi-relational nonlinear dynamics which are often encountered in the realistic time-series analysis. Furthermore, there hardly exist convergence studies on convergence condition and convergence speed pertinent to the existing traffic-prediction methods. In order to combat the aforementioned challenges, we propose a new tensor Levenberg-Marquadt algorithm (TLMA) to conduct the multi-relational nonlinear regression for traffic prediction involving tensorized data. Meanwhile, we also derive the lower-bound of the number of iterations required to make the error-norm below a specified tolerance for global convergence. Besides, we derive the conditions for our proposed TLMA to converge to the optimal solution. The convergence rates with respect to different nonlinear cost functions have been derived theoretically. The computational- and memory-complexities of our proposed new TLMA are studied as well. Finally, numerical experiments are conducted to evaluate the traffic prediction performance of our proposed new TLMA over real traffic data in comparison with other existing multi-relational prediction methods.

• A novel non-parallel bounded support matrix machine (NPBSMM) is proposed. • A constraint norm group (CNG) is constructed, which can suppress negative influence of outliers and enhance robustness. • The dual problem of NPBSMM avoids the calculation of matrix inversion. • Multi-rank left and right projection matrices are employed to realize a better ability of data fitting. At present, the excellent performance of support vector machine (SVM) has made it successfully applied in many fields. However, when SVM is used for two-dimensional matrix data classification, vectorization of these data easily leads to dimension curse and the loss of structural information. Moreover, SVM is sensitive to outliers, which causes the hyperplane to move towards outliers. Therefore, this paper proposes a novel classification method for data in matrix-form, named non-parallel bounded support matrix machine (NPBSMM). In NPBSMM, a constraint norm group (CNG) is constructed and applied to objective function, which can not only suppress the negative impact of outliers on the model, but also make NPBSMM has better sparsity. By constructing CNG, the operation of matrix inversion in dual problem of traditional classification methods is avoided, so NPBSMM is more suitable for solving large-scale data problems. Further, to extract structure information of matrix for modeling, multi-rank left and right projection matrices are employed to establish objective function, which makes NPBSMM has a better ability of data fitting. Experiments performed on three roller bearing fault datasets show that the proposed NPBSMM method has powerful performance and robustness as compared with other typical classification methods. [ABSTRACT FROM AUTHOR]

Recently, an opinion dynamics model has been proposed to describe a network of individuals discussing a set of logically interdependent topics. For each individual, the set of topics and the logical interdependencies between the topics (captured by a logic matrix) form a belief system. We investigate the role the logic matrix and its structure plays in determining the final opinions, including existence of the limiting opinions, of a strongly connected network of individuals. We provide a set of results that, given a set of individuals’ belief systems, allow a systematic determination of which topics will reach a consensus, and of which topics will disagreement arise. For irreducible logic matrices, each topic reaches a consensus. For reducible logic matrices, which indicates a cascade interdependence relationship, conditions are given on whether a topic will reach a consensus or not. It turns out that heterogeneity among the individuals’ logic matrices, and a cascade interdependence relationship, are necessary conditions for disagreement. Thus, this article attributes for the first time, a strong diversity of limiting opinions to heterogeneity of belief systems in influence networks, in addition to the more typical explanation that strong diversity arises from individual stubbornness. [ABSTRACT FROM AUTHOR]

In order to explore the Leonardo sequence, the process of complex-ification of this sequence is carried out in this work. With this, the Gaussian and octonion numbers of the Leonardo sequence are presented. Also, the recurrence, generating function, Binet’s formula, and matrix form of Leonardo’s Gaussian and octonion numbers are defined. The development of the Gaussian numbers is performed from the insertion of the imaginary component iin the one-dimensional recurrence of the sequence. Regarding the octonions, the terms of the Leonardo sequence are presented in eight dimensions. Furthermore, the generalizations and inherent properties of Leonardo’s Gaussians and octonions are presented.

This paper presents a general analytical fault model in a compact matrix form for surface-mounted permanent magnet (SPM) machines with parallel-connected coils, which is useful to study the machine performance under the inter-turn short circuit (ITSC) fault. To simplify the fault model, the multiphase Clarke transformation has been proposed. In the model, the branch currents rather than the phase currents are employed as state variables to describe machine behaviours under fault. Additionally, self- and mutual-inductances are obtained by winding function approach (WFA) plus slot permeance method. The proposed analytical fault model is applied to a 3 kW 96-slot 32-pole SPM machine and validated by time-stepping FE simulations. A small scale 12-slot 4-pole SPM machine prototype has also been built to further validate the accuracy of the proposed fault model.

The emerging research line of cross-modal learning focuses on the issue of transferring feature representation manner learned from limited multimodal data with labelings to the testing phase with partial modalities. This is essentially common and practical in the remote sensing (RS) community when only modal-incomplete data are in users’ hands due to inevitable imaging or access restrictions under large-scale observation scenarios. However, most of the existing cross-modal learning methods have been designed with exclusive reliance on labeling, which can be either limited or noisy due to their costly production. To address this issue, we explore, in this article, the possibility to learn cross-modal feature representation in an unsupervised fashion. By integrating the multimodal data into a fully recombined matrix form, we propose the following: 1) the use of common subspace representation as the regression target instead of conventionally adopted binary labels and 2) the orthogonality and manifold alignment regularization terms to shrink the solution space while preserving the pairwise manifold correlations. Through this manner, the modality-specific and mutual latent representations in this common subspace as well as their corresponding projections can be learned simultaneously, and their optimums can be efficiently reached through a nearly one-step computation with the help of eigendecomposition. Finally, we show the superiority of our method through extensive image classification experiments on three multimodal datasets with four remotely sensed modalities involved (i.e., hyperspectral (HS), multispectral, synthetic aperture radar, and light detection and ranging (LiDAR) data). The code and dataset will be made freely available at https://github.com/jingyao16/UCSL to encourage the reproduction of our method and further use.

The asymptotical synchronization in mean square of reaction–diffusion neural networks (RDNNs) with random delays is studied in this article. By sampling on both the time domain and spatial domain, a time–space sampled-data controller (TSSDC) is designed, which can efficiently save the network communication resources for RDNNs. A new processing method for the TSSDC is provided. Compared with the existing methods, the processing method here can capture more sampling information and is more concise. An extended Poincaré–Wirtinger inequality is proposed, which is in matrix form and less conservative. Then by constructing a sampling-dependent LKF, using the extended Poincaré–Wirtinger inequality and Hölder inequality, new mean square asymptotical synchronization criteria are set up for RDNNs with random delays, and the desired TSSDC gain is obtained. At length, a numerical example is given to verify the effectiveness and superiority of the obtained results.

Shear tests on rectangular plate sandstone containing two pre-existing holes were performed to analyze the shear mechanical responses and cracking evolution mechanisms. With generation of the penetrating fracture surfaces, both shear stress and normal displacement show a dramatic drop. Then, during the shear slipping process, the shear stress increases once again due to wear and shear off of the surface asperities, and three different variation trends of the normal deformation including shear dilation, fluctuation, and shear contraction are respectively identified. The role of ligament length and normal stress on several key indices such as peak shear stress, peak normal displacement and residual shear stress was investigated. Violent AE (acoustic emission) responses occur along with penetration of the fracture surfaces, and in the shear slipping process, AE events continue to occur due to wear of surface asperities, while the increase rate of accumulative AE events declines. Cracks coalesced at the rock bridge and running through the rock matrix form the main failure planes of the samples. From the PFC2Dsimulation results, the crack clusters first initiate from hole-walls and coalesce at the rock bridge for a small ligament length, while first produce the main failure planes at the right/left rock matrix for a large ligament length. The total number of micro cracks shows a “calm → rapid increase → decreasing growth amplitude” variation during shearing, and the induced cracks become more concentrated for a larger normal stress, implying a cumulative damage of the failure surfaces.

Incremental feature selection methods have gained increasing research attention as they improve the efficiency of feature selection for dynamic datasets. Multigranulation rough set, as an extension of rough set theory, allows for a comprehensive and rational analysis of problems from multiple hierarchical and granular perspectives. However, existing research on granularity partitioning relies on the decision maker's subjective experience, which lacks convincing power. In this paper, we propose a generalized multigranulation neighborhood rough set based on weight partition model, using a matrix form. We discuss several properties and define a new entropy measure to evaluate feature importance. A heuristic feature selection algorithm is developed based on this entropy to search for the optimal subset. Furthermore, we discuss dynamic updating mechanism and design two incremental feature selection algorithms. Finally, we conduct experiments on 12 public datasets to evaluate the performance of the proposed algorithms and validate their effectiveness and efficiency in feature selection for both static and dynamic datasets. [ABSTRACT FROM AUTHOR]

Two-dimensional biharmonic boundary-value problems are considered by the linear barycentric rational collocation method, and the unknown function is approximated by the barycentric rational polynomial. With the help of matrix form, the linear equations of the discrete biharmonic equation are changed into a matrix equation. From the convergence rate of barycentric rational polynomial, we present the convergence rate of linear barycentric rational collocation method for biharmonic equation. Finally, several numerical examples are provided to validate the theoretical analysis.

In this study, we have introduced a fractional series solution method to solve fractional pantograph differential equations numerically. The method is constructed by collocation approach and Bernstein polynomials. Each term of the equation is converted into a matrix form by the fractional Bernstein series. Then, the problems are reduced into a set of algebraic equations including unknown Bernstein coefficients by using the collocation nodes. Hence, by determining the coefficients, the approximate solution is obtained. For the error analysis of this method, we give two techniques which estimate or bound the absolute error. To demonstrate the efficiency and applicability of the method, some illustrative examples are given. We also compare the method with some known methods in the literature.

In this paper, a novel real-time obstacle avoidance method based on Dynamic System (DS), is proposed. The proposed method ensures the impenetrability of multiple convex obstacles by online modulating the original velocity field of the DS. It can be applied to perform obstacle avoidance in the state space of the DS with both autonomous and non-autonomous DS-based controllers. While realizing the obstacle avoidance, the equilibrium points of the original DS can be saved. The modulation matrix form is extended based on the earlier dynamic system modulation methods of the literature. The asymmetric modulation provided by this method allows the modulated DS to satisfy the dynamic constraints of a class of DSs. In addition, the proposed method has the inherent ability of multiple-obstacle avoidance and the direction selectivity of avoidance maneuver. Moreover, to solve the simultaneous guidance and obstacle avoidance problem, a guidance law for Unmanned Aerial Vehicles (UAVs) based on the proposed method, is designed. Finally, a numerical simulation is performed to analyze the performance of the proposed method and the obstacle avoidance guidance law.

No company is completely free of organization problems, and companies that use the matrix form are no exception. Some of the ailments matrix organizations suffer, such as power struggles and collapse during an economic crunch, other companies suffer as well. But many of the problems a matrix organization falls prey to occur because of the nature of the matrix design itself. For instance, it is not difficult to understand how managers in a matrix organization, where there are dual chains of command, might develop too little or too much control, thus succumbing to anarchy or decision strangulation. The authors of this article have studied a number of companies employing some form of the matrix and have observed nine different pathologies to which they are particularly vulnerable. Here, they present the pathologies, diagnose why and how they arise in matrix forms, and then prescribe prevention and treatment measures that matrix managers suffering these ills can take. [ABSTRACT FROM PUBLISHER]

In 1967 Dow Corning Corporation, which is jointly owned by the Dow Chemical Company and Corning Glass Works, reorganized from a conventional divisionalized type of organization into a matrix form of organization. As top management continued to experiment and innovate, the matrix form turned into what the company now calls a multidimensional organization. Judging from employees' reactions to the new pattern, as well as from impressive gains in sales, profits, productivity, and exports, the multidimensional organization is a striking success. This article examines the underlying philosophy of this organization pattern, its working parts, its use by management, and its advantages and disadvantages. [ABSTRACT FROM AUTHOR]

A new study from Malayer University explores the use of fractional calculus in modeling brain tumors. The researchers developed a numerical approach using orthonormal Bernoulli polynomials to estimate the solution of a two-dimensional brain tumor model. The proposed method simplifies calculations by obtaining the fractional derivative in matrix form and converts the problem into a system of nonlinear algebraic equations, which are solved using Newton's method. The study concludes by comparing the numerical results with other works to demonstrate the accuracy of the approach. [Extracted from the article]

Recently, subspace clustering (SC) has received an increasing amount of attention. Generally, SC methods are implemented on sample data in matrix form. Even for multiway or tensor data, which is prevalent in reality, traditional SC methods should convert each sample to a vector and then form a data matrix. However, the vectorization process will damage the underlying inherent spatial structure of the data. To address this problem, in this paper, we propose a novel consensus tensor low-rank representation (CTLRR) method, which is directly implemented on tensor data. First, the tensor nuclear norm (TNN) and t-product, which is defined as the multiplication of two tensors, are employed to model the data and obtain the low-rank representation tensor. Second, spectral clustering is unified into CTLRR to explore the consensus information among the low-rank representation tensor, which helps obtain the final fusion similarity matrix with the k connected components, where k is the number of clusters. Third, the cluster structure is characterized, and the clustering performance is substantially improved. Last, an optimization procedure for CTLRR is presented. Experimental results on certain challenging datasets show that the proposed CTLRR method outperforms the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Attitude estimation is a core problem in many mobile robotic systems, such as unmanned aerial and ground vehicles. The configuration space of these systems is properly modeled by exploiting the theory of Lie groups. In this article, we propose a second-order-optimal minimum-energy filter on the matrix Lie group TSE(2), the tangent bundle of the special Euclidean group SE(2), where the optimality is with respect to a cost function in the unknown input and output error measurements. In this article, the measurement equation consists of a global positioning system-like device with two antennas attached to the planar rigid body and an inertial measurement unit-like device. Even though the mathematics is quite complicated, the accuracy of the filter justifies this approach. Simulations show the effectiveness of the proposed filter. [ABSTRACT FROM AUTHOR]

The optimization of facility-based systems (FBSs) is considered. First, the congestion game is converted into a matrix form so that the matrix approach is applicable. Then, an FBS with a system performance criterion is considered. A necessary and sufficient condition is given to assure that the system is convertible into a congestion game with the given system performance criterion as its potential function by designing proper facility-cost functions. Using this technology, for a dynamic FBS, the global optimization may be reached when each agent optimizes its payoff functions. Finally, the approach is extended to those systems that are partly or nearly convertible. Note that the proposed methodology can only be applied to classical congestion games, where the user with multiple unit demands is not allowed. [ABSTRACT FROM AUTHOR]

Explainable clustering provides human-understandable reasons for decisions in black-box learning models. In a previous work, a decision tree built on the set of dimensions was used to define ranges of values for k -means clusters. For explainable graph clustering, we use expander graphs instead of dense subgraphs since powering an expander graph is guaranteed to result in a clique after at most a logarithmic number of steps. Consider a set of multi-dimensional points labeled with k labels. We introduce the heat map sorting problem as reordering the rows and columns of an input matrix (each point is a column and each row is a dimension) such that the labels of the entries of the matrix form connected components (clusters). A cluster is preserved if it remains connected, i.e., if it is not split into several clusters and no two clusters are merged. In the massively parallel computation model (MPC), each machine has a sublinear memory and the total memory of the machines is linear. We prove the problem is NP-hard. We give a fixed-parameter algorithm in MPC and an approximation algorithm based on expander decomposition. We empirically compare our algorithm with explainable k-means on several graphs of email and computer networks. • A general method for explainable clustering of high-dimensional data. • A fixed-parameter algorithms for explainable graph clustering. • A Massively Parallel Computation (MPC) algorithm for explainable clustering. • An approximation algorithm for graph clustering on expander graphs. [ABSTRACT FROM AUTHOR]

In general, the laminated composite plates and stiffeners may exhibit the bending-extension coupling effect with the transverse shear deformations significantly induced. In this paper, for the first time we develop the associated boundary element method (BEM) for bending-extension coupling shear deformable laminated composite plates with multiple beams attached as stiffeners. Based upon the first order shear deformation theory, the individual boundary integral equations (BIEs) for plates and stiffeners are obtained from their corresponding matrix-form basic equations. To account for perfect bonding conditions between plate and stiffeners, we establish displacement continuity and interaction load equilibrium relations at their interfaces. To calculate the domain integrals related to unknown interaction loads, we discretize each stiffener into a series of cells using quadratic interpolation. By collecting the individual BIEs for plates and stiffeners and employing the continuity and equilibrium relations at the interfaces, we construct the entire system of linear equations to solve for all the unknown nodal quantities. Additionally, the complete solutions at the plate boundary, at internal points or along a stiffener are provided. The correctness of our present BEM formulation is verified through two representative examples by comparison with the commercial finite element software ANSYS. The numerical results demonstrate that our BEM formulation surpasses the conventional finite element method and is highly desirable for general stiffened laminated plates with bending-extension coupling and transverse shear deformations. [ABSTRACT FROM AUTHOR]

A fast simulation method for time-derivative cellular neural networks (TDCNN) is proposed. Using forward Euler approximation (FEA) for the derivative of the cell state and the backward Euler approximation (BEA) for the derivatives of the neighboring cell states enables the recursive computation of the cell state and provides a speed advantage of orders of magnitude. The state equations are then packed into a vector-matrix form which enables the previously empirically given time constraint to be expressed as a matrix condition. It is shown that using both FEA and BEA leads to a second-order difference equation whose corresponding second-order differential equation is derived and shown to yield the same simulation results. [ABSTRACT FROM PUBLISHER]