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Heterogeneous information network (HIN) embedding aims at learning the low-dimensional representation of nodes while preserving structure and semantics in a HIN. Existing methods mainly focus on static networks, while a real HIN usually evolves over time with the addition (deletion) of multiple types of nodes and edges. Because even a tiny change can influence the whole structure and semantics, the conventional HIN embedding methods need to be retrained to get the updated embeddings, which is time-consuming and unrealistic. In this paper, we investigate the problem of dynamic HIN embedding and propose a novel Dynamic HIN Embedding model (DyHNE) with meta-path based proximity. Specifically, we introduce the meta-path based first- and second-order proximities to preserve structure and semantics in HINs. As the HIN evolves over time, we naturally capture changes with the perturbation of meta-path augmented adjacency matrices. Thereafter, we learn the node embeddings by solving generalized eigenvalue problem effectively and employ eigenvalue perturbation to derive the updated embeddings efficiently without retraining. Experiments show that DyHNE outperforms the state-of-the-arts in terms of effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

This paper presents a dynamic event data-based stability risk assessment method for power grids with high penetrations of inverter-based resources (IBRs). This method relies on obtaining the IBRs’ DQ admittance through dynamic event data and computing the system’s eigenvalues based on the admittance models. Two critical technologies are employed in this research, including time-domain and frequency-domain data fitting and $dq$ -frame voltage and current signal derivation. The first technology is key to obtaining the $s$ -domain expressions from the transient response data, and the $s$ -domain DQ admittance model from the frequency-domain measurements. The second technology is key to obtaining the $dq$ -frame voltage and current signals from either the three-phase instantaneous measurements or the phasor measurement unit (PMU) data. The method is illustrated using data generated from a Type-4 wind power plant modeled in PSCAD. This paper demonstrates the technical feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

In this article we present our results from the SC19 Student Cluster Competition Reproducibility Challenge. The challenge entails reproducing the article entitled “Computing Planetary Interior Normal Modes with A Highly Parallel Polynomial Filtering Eigensolver” presented at SC’18, which proposes a parallel polynomial filtered Lanczos algorithm to directly calculate the planetary normal modes of heterogeneous planets. The proposed algorithm showed excellent performance with relatively low memory consumption and high parallel efficiency. In this work, we reproduce the scaling tests in that article on a cluster using Intel Cascade Lake architecture and use the proposed algorithm to illustrate specific normal modes of Mars. We compare the results obtained on our cluster with those in the original article. We also design a new metric to better analyze the results. In addition, we use the profiling tool Intel VTune Amplifier to explain our discoveries. Our results demonstrate that the given models show great scalability, which is similar to the original article. The required normal modes of Mars are also successfully calculated and visualized. [ABSTRACT FROM AUTHOR]

In this paper, we propose the $K$ K -Shot Contrastive Learning (KSCL) of visual features by applying multiple augmentations to investigate the sample variations within individual instances. It aims to combine the advantages of inter-instance discrimination by learning discriminative features to distinguish between different instances, as well as intra-instance variations by matching queries against the variants of augmented samples over instances. Particularly, for each instance, it constructs an instance subspace to model the configuration of how the significant factors of variations in $K$ K -shot augmentations can be combined to form the variants of augmentations. Given a query, the most relevant variant of instances is then retrieved by projecting the query onto their subspaces to predict the positive instance class. This generalizes the existing contrastive learning that can be viewed as a special one-shot case. An eigenvalue decomposition is performed to configure instance subspaces, and the embedding network can be trained end-to-end through the differentiable subspace configuration. Experiment results demonstrate the proposed $K$ K -shot contrastive learning achieves superior performances to the state-of-the-art unsupervised methods. [ABSTRACT FROM AUTHOR]

Construction of the linearized state-space model is the key step of eigenvalue analysis for SSO study of power systems with large-scale renewable power generation (RPG) integrated. This paper proposes a novel method to construct the state matrix of the AC/DC hybrid power system with RPG within the discrete-time domain. The continuous-time state-space model of each AC/DC component as well as RPG units in the power system, is discretized together with their corresponding control. The discretized equation of each component is then represented by an equivalent circuit consisting of parallel historical current and conductance. According to the power system configuration, the discrete-time equivalent circuit of the whole AC/DC hybrid system is established, and the nodal analysis method is applied for the construction of the discrete-time state-space model of the power system. In this way, the state matrix can be acquired much more conveniently than that of continuous-time state-space method, which needs topology analysis to find independent state variables of the network from the proper tree. The proposed method has been applied in the eigenvalue analysis for the SSO study of a case system adapted from the AC/DC hybrid transmission system in northwest China. Eigenvalue results are in high accordance with time-domain simulation results in PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

This paper develops a grey-box approach to small-signal stability analysis of complex power systems that facilitates root-cause tracing without requiring disclosure of the full details of the internal control structure of apparatus connected to the system. The grey-box enables participation analysis in impedance models, which is popular in power electronics and increasingly accepted in power systems for stability analysis. The Impedance participation factor is proposed and defined in terms of the residue of the whole-system admittance matrix. It is proved that, the so defined impedance participation factor equals the sensitivity of the whole-system eigenvalue with respect to apparatus impedance. The classic state participation factor is related to the impedance participation factor via a chain-rule. Based on the chain-rule, a three-layer grey-box approach, with three degrees of transparency, is proposed for root-cause tracing to different depths, i.e. apparatus, states, and parameters, according to the available information. The association of impedance participation factor with eigenvalue sensitivity points to the re-tuning that would stabilize the system. The impedance participation factor can be measured in the field or calculated from the black-box impedance spectra with little prior knowledge required. [ABSTRACT FROM AUTHOR]

Let $\mathrm {W}\in \mathbb {C}^{n\times n}$ be a single-spiked Wishart matrix in the class $\mathrm {W}\sim \mathcal {CW}_{n}(m,\mathrm {I}_{n}+ \theta \mathrm {v}\mathrm {v}^{\dagger}) $ with $m\geq n$ , where ${\mathrm {I}}_{n}$ is the $n\times n$ identity matrix, $\mathrm {v}\in \mathbb {C}^{n\times 1}$ is an arbitrary vector with unit Euclidean norm, $\theta \geq 0$ is a non-random parameter, and $(\cdot)^{\dagger} $ represents the conjugate-transpose operator. Let u1 and ${\mathrm {u}}_{n}$ denote the eigenvectors corresponding to the smallest and the largest eigenvalues of W, respectively. This paper investigates the probability density function (p.d.f.) of the random quantity $Z_{\ell }^{(n)}=\left |{\mathrm {v}^{\dagger} \mathrm {u}_\ell }\right |^{2}\in (0,1)$ for $\ell =1,n$. In particular, we derive a finite dimensional closed-form p.d.f. for $Z_{1}^{(n)}$ which is amenable to asymptotic analysis as $m,n$ diverges with $m-n$ fixed. It turns out that, in this asymptotic regime, the scaled random variable $nZ_{1}^{(n)}$ converges in distribution to $\chi ^{2}_{2}/2(1+\theta)$ , where $\chi _{2}^{2}$ denotes a chi-squared random variable with two degrees of freedom. This reveals that u1 can be used to infer information about the spike. On the other hand, the finite dimensional p.d.f. of $Z_{n}^{(n)}$ is expressed as a double integral in which the integrand contains a determinant of a square matrix of dimension $(n-2)$. Although a simple solution to this double integral seems intractable, for special configurations of $n=2,3$ , and 4, we obtain closed-form expressions. [ABSTRACT FROM AUTHOR]

Deep learning based models have excelled in many computer vision tasks and appear to surpass humans’ performance. However, these models require an avalanche of expensive human labeled training data and many iterations to train their large number of parameters. This severely limits their scalability to the real-world long-tail distributed categories, some of which are with a large number of instances, but with only a few manually annotated. Learning from such extremely limited labeled examples is known as Few-Shot Learning (FSL). Different to prior arts that leverage meta-learning or data augmentation strategies to alleviate this extremely data-scarce problem, this paper presents a statistical approach, dubbed Instance Credibility Inference (ICI) to exploit the support of unlabeled instances for few-shot visual recognition. Typically, we repurpose the self-taught learning paradigm to predict pseudo-labels of unlabeled instances with an initial classifier trained from the few shot and then select the most confident ones to augment the training set to re-train the classifier. This is achieved by constructing a (Generalized) Linear Model (LM/GLM) with incidental parameters to model the mapping from (un-)labeled features to their (pseudo-)labels, in which the sparsity of the incidental parameters indicates the credibility of the corresponding pseudo-labeled instance. We rank the credibility of pseudo-labeled instances along the regularization path of their corresponding incidental parameters, and the most trustworthy pseudo-labeled examples are preserved as the augmented labeled instances. This process is repeated until all the unlabeled samples are included in the expanded training set. Theoretically, under the conditions of restricted eigenvalue, irrepresentability, and large error, our approach is guaranteed to collect all the correctly-predicted pseudo-labeled instances from the noisy pseudo-labeled set. Extensive experiments under two few-shot settings show the effectiveness of our approach on four widely used few-shot visual recognition benchmark datasets including miniImageNet, tieredImageNet, CIFAR-FS, and CUB. Code and models are released at https://github.com/Yikai-Wang/ICI-FSL. [ABSTRACT FROM AUTHOR]

Let $\mathbf {X}\in \mathbb {C}^{n\times m}$ ($m\geq n$) be a random matrix with independent columns each distributed as complex multivariate Gaussian with zero mean and single-spiked covariance matrix $\mathbf {I}_{n}+ \eta \mathbf {u}\mathbf {u}^{*}$ , where $\mathbf {I}_{n}$ is the $n\times n$ identity matrix, $\mathbf {u}\in \mathbb {C}^{n\times 1}$ is an arbitrary vector with unit Euclidean norm, $\eta \geq 0$ is a non-random parameter, and $(\cdot)^{*}$ represents the conjugate-transpose. This paper investigates the distribution of the random quantity $\kappa _{\text {SC}}^{2}(\mathbf {X})=\sum _{k=1}^{n} \lambda _{k}/\lambda _{1}$ , where $0\le \lambda _{1}\le \lambda _{2}\le \ldots \leq \lambda _{n} < \infty $ are the ordered eigenvalues of $\mathbf {X}\mathbf {X}^{*}$ (i.e., single-spiked Wishart matrix). This random quantity is intimately related to the so called scaled condition number or the Demmel condition number (i.e., $\kappa _{\text {SC}}(\mathbf {X})$) and the minimum eigenvalue of the fixed trace Wishart-Laguerre ensemble (i.e., $\kappa _{\text {SC}}^{-2}(\mathbf {X})$). In particular, we use an orthogonal polynomial approach to derive an exact expression for the probability density function of $\kappa _{\text {SC}}^{2}(\mathbf {X})$ which is amenable to asymptotic analysis as matrix dimensions grow large. Our asymptotic results reveal that, as $m,n\to \infty $ such that $m-n$ is fixed and when $\eta $ scales on the order of $1/n$ , $\kappa _{\text {SC}}^{2}(\mathbf {X})$ scales on the order of $n^{3}$. In this respect we establish simple closed-form expressions for the limiting distributions. It turns out that, as $m,n\to \infty $ such that $n/m\to c\in (0,1)$ , properly centered $\kappa _{\text {SC}}^{2}(\mathbf {X})$ fluctuates on the scale $m^{\frac {1}{3}}$. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the anti-jamming problem of a directional modulation (DM) system with the aid of intelligent reflecting surface (IRS). As an efficient tool to combat malicious jamming, receive beamforming (RBF) is usually designed by using the statistical properties of the jamming received by Bob. Thus, it is very necessary to estimate the receive jamming covariance matrix (JCM) at Bob. To achieve a precise JCM estimation, three JCM estimation methods, including eigenvalue decomposition (EVD), parametric estimation method by gradient descend (PEM-GD) and parametric estimation method by alternating optimization (PEM-AO), are proposed. Here, the proposed EVD is derived according to the rank-2 constraint of JCM. The PEM-GD method fully explores the structure features of JCM and the PEM-AO is proposed to decrease the computational complexity of the former via dimensionality reduction. The simulation results show that the proposed three methods perform better than directly using sample covariance matrix. Additionally, the proposed PEM-GD and PEM-AO outperform EVD method and the clutter and disturbance covariance estimator RCML. [ABSTRACT FROM AUTHOR]

In secure spatial modulation with a malicious full-duplex attacker, how to obtain the interference subspace or channel state information (CSI) is very important for Bob to reduce or even completely cancel the interference from Mallory. In this paper, different from existing work with perfect CSI, the covariance matrix of malicious interference (CMMI) from Mallory is estimated to construct the interference subspace. To improve the estimation accuracy, a CMMI rank detector relying on the Akaike information criterion (AIC) is derived first. To achieve a high-precision CMMI estimation, two methods, principal component analysis-eigenvalue decomposition (PCA-EVD) and joint diagonalization (JD) are proposed. The proposed PCA-EVD is a rank deduction method whereas the JD method is a joint optimization method with improved performance in the low jamming-to-noise ratio (JNR) region at the expense of increased complexity. Simulation results show that the proposed PCA-EVD performs much better than existing methods like sample estimated covariance matrix (SCM) and EVD in terms of normalized mean square error (NMSE) and secrecy rate (SR). Additionally, the proposed JD has achieved a better NMSE performance than PCA-EVD in the low JNR region (JNR $\leq$ 0 dB) while the proposed PCA-EVD performs better than JD in the high JNR region. [ABSTRACT FROM AUTHOR]

It is well-known that the multiple signal classification (MUSIC) algorithm is computationally time-consuming because it requires a complex-valued full-dimension eigenvalue decomposition (EVD) and a complex-valued spectral searching. In this paper, we exploit the virtual signal model of forward/backward average of array covariance matrix (FBACM) to show that its real part (R-FBACM) is a real symmetric matrix. Based on that, we prove that by evaluating two half-dimension EVD after an orthogonally similar transformation performed on the estimated R-FBACM, we are able to reconstruct the original eigenspace whereas the maximum number of estimated sources is reduced as compared to the upper limit $\mathit{M}-\text{1}$ for original MUSIC. Numerical results show that the proposed method provides satisfactory estimation accuracy and improved resolution with reduced complexity. [ABSTRACT FROM AUTHOR]

This paper proposes an impedance/admittance-based methodology for stability assessment of converter-based device connections to power systems. The proposed methodology is designed to model the dynamics of detailed black-box converter models, derived from impedance frequency response measurements. From the converter’s impedance frequency response measurements, a linear time-invariant (LTI) representation of its dynamics is obtained in the $dq$ domain using a vector fitting technique. This representation is incorporated in the state-space representation of the whole power system in the $dq$ domain, which is used to perform stability assessment considering traditional eigenvalue analysis and participation factors computation. The proposed methodology is tested in the 39 Bus New England system, including detailed models of a VSC windfarm and a modular multilevel converter (MMC) technology-based STATCOM. It has been found that the proposed impedance-based methodology is able to accurately predict the dynamic performance of black-box converter models, unstable operating conditions and converter control interactions between devices. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel transmission scheme, called sparse layered MIMO (SL-MIMO), that combines non-orthogonal transmission and singular value decomposition (SVD) precoding. Non-orthogonality in SL-MIMO allows re-using of the eigen-channels which improves the spectral efficiency and error rate performance of the system through enhancing the coding gain and diversity gain. We also present a low-complexity message-passing (MP) detector for the proposed SL-MIMO system which performs quite close to maximum likelihood (ML). The joint moment generating function (MGF) of the ordered eigenvalues is calculated and used to derive a closed-form upper bound on the average word error probability (AWEP) of the SL-MIMO system, and this derived expression is then used to analyze the diversity gain of the system. We use our analytical results to design sub-optimal codebooks to minimize the error rate of the SL-MIMO system. Simulation results in $4\times 4$ and $6\times 6$ multiple-input multiple-output (MIMO) systems with 4-ary, 16-ary, and 64-ary constellations show that our proposed SL-MIMO scheme outperforms competing approaches such as X- and Y-codes in terms of system error rate performance. SL-MIMO has 5.6 dB advantage compared to X-codes and 4.7 dB advantage compared to Y-codes in $6\times 6$ MIMO system with a 64-ary constellation. [ABSTRACT FROM AUTHOR]

This paper proposes an inequality constraints based method to efficiently and quickly estimate stability regions of droop control slopes for modular multilevel converter (MMC)-based multi-terminal dc (MTDC) systems. At first, a general small-signal model of the MMC-MTDC system is developed, which consists of the dc network and the MMCs with $dq$ controllers and multiple droop controllers. When deriving corresponding nonlinear state-space models, the edge-node matrix is introduced for the dc network modeling with arbitrary grid topology and transmission line model. Then, based on the eigenvalues sensitivity and the Taylor Series of eigenvalues, a set of inequality constraints are proposed to expeditiously estimate the suprema of the droop slopes and identify the droop slope stability regions for the MMC-MTDC system. To verify the state-space model, a comparison of dynamic responses between the math model calculation in MATLAB and the EMT simulation in PSCAD/EMTDC is conducted, which demonstrates the accuracy and the correctness of the developed small-signal model. The effectiveness of the proposed parameter stability region estimation method is demonstrated by several examinations including the supremum tests of droop slopes, the stability region sketches on accuracy, and the predicted unstable operations in PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

Agnostic matrix phase retrieval (AMPR) is a general low-rank matrix recovery problem given a set of noisy high-dimensional data samples. To be specific, AMPR is targeting at recovering an $r$ -rank matrix $\mathbf {M}^*\in \mathbb {R}^{d_1\times d_2}$ as the parametric component from $n$ instantiations/samples of a semi-parametric model $y=f(\langle \mathbf {M}^*, \mathbf {X}\rangle, \epsilon)$ , where the predictor matrix is denoted as $\mathbf {X}\in \mathbb {R}^{d_1\times d_2}$ , link function $f(\cdot, \epsilon)$ is agnostic under some mild distribution assumptions on $\mathbf {X}$ , and $\epsilon$ represents the noise. In this paper, we formulate AMPR as a rank-restricted largest eigenvalue problem by applying the second-order Stein's identity and propose a new spectrum truncation power iteration (STPower) method to obtain the desired matrix efficiently. Also, we show a favorable rank recovery result by adopting the STPower method, i.e., a near-optimal statistical convergence rate under some relatively general model assumption from a wide range of applications. Extensive simulations verify our theoretical analysis and showcase the strength of STPower compared with the other existing counterparts. [ABSTRACT FROM AUTHOR]

This paper proposes an improved stochastic estimation method based on contour integral to estimate the number of critical eigenvalues. The stochastic estimation method transforms the eigenvalue numbers' calculation into summing the traces of a series of inverse matrices. And then, a stochastic strategy is used to estimate the trace of the inverse matrix. However, the method results in an unacceptable error when the state matrices of many practical power systems are ill-conditioned. To solve this problem, the improved algorithm is proposed by formulating a satisfactory matrix for trace calculation artificially instead of randomly with the help of the well-known greedy algorithm based on graph coloring. It is proved to be much more reliable when dealing with ill matrix. The proposed method based on contour integral is very suitable for large-scale power systems due to the element distribution of descriptor matrices makes it possible to construct only one fixed matrix at all integral points. Moreover, the calculation efficiency is further improved by calculating implicitly without destroying the sparsity of descriptor systems. Numerical experiments indicate that the proposed method can significantly improve accuracy without considerably increasing the calculation time. And the approximate eigenvalue number can fully meet the needs of subsequent algorithms based on contour integral to calculate the specific eigenvalues. [ABSTRACT FROM AUTHOR]

This paper develops an accurate small signal model for line commutated converter based HVDC (LCC-HVDC). The overall process of the model establishment is demonstrated from five parts: AC system, DC system, control system, phase-locked loop (PLL) and the converter. Considering the limitations of the traditional converter equations, the proposed small signal model takes the commutation process into account so that the overlap angle and AC current are calculated with the actual value rather than the estimated value. The accuracy of the proposed model is verified both in the time-domain simulation in PSCAD/EMTDC and by eigenvalue analysis. The results show better performance than the traditional modeling methods, which provides valuable guidance for future LCC-HVDC project design. [ABSTRACT FROM AUTHOR]

In this paper, we consider massive multiple-input-multiple-output (MIMO) communication systems with a uniform planar array (UPA) at the base station (BS) and investigate the downlink precoder design with imperfect channel state information (CSI). By exploiting channel estimates and statistical parameters of channel estimation error, we aim to design precoding vectors to maximize the utility function on the ergodic rates of users subject to a total transmit power constraint. By employing an upper bound of the ergodic rate, we leverage the corresponding Lagrangian formulation and identify the structural characteristics of the optimal precoder as the solution to a generalized eigenvalue problem. The Lagrange multipliers play a crucial role in determining both precoding directions and power parameters, yet are challenging to be solved directly. To figure out the Lagrange multipliers, we develop a general framework underpinned by a properly designed neural network that learns directly from CSI. To further relieve the computational burden, we obtain a low-complexity framework by decomposing the original problem into computationally efficient subproblems with instantaneous and statistical CSI handled separately. With the offline pre-trained neural network, the online computational complexity of precoder is substantially reduced compared with the existing iterative algorithm while maintaining nearly the same performance. [ABSTRACT FROM AUTHOR]

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smallest, or zero, eigenvalue of a matrix representing a linear system. Incorporating this in deep learning frameworks would allow us to explicitly encode known notions of geometry, instead of having the network implicitly learn them from data. However, performing eigendecomposition within a network requires the ability to differentiate this operation. While theoretically doable, this introduces numerical instability in the optimization process in practice. In this paper, we introduce an eigendecomposition-free approach to training a deep network whose loss depends on the eigenvector corresponding to a zero eigenvalue of a matrix predicted by the network. We demonstrate that our approach is much more robust than explicit differentiation of the eigendecomposition using two general tasks, outlier rejection and denoising, with several practical examples including wide-baseline stereo, the perspective-n-point problem, and ellipse fitting. Empirically, our method has better convergence properties and yields state-of-the-art results. [ABSTRACT FROM AUTHOR]

Given a convex and differentiable objective $Q({\mathbf M})$ Q (M) for a real symmetric matrix ${\mathbf M}$ M in the positive definite (PD) cone—used to compute Mahalanobis distances—we propose a fast general metric learning framework that is entirely projection-free. We first assume that ${\mathbf M}$ M resides in a space ${\mathcal S}$ S of generalized graph Laplacian matrices corresponding to balanced signed graphs. ${\mathbf M}\in {\mathcal S}$ M ∈ S that is also PD is called a graph metric matrix. Unlike low-rank metric matrices common in the literature, ${\mathcal S}$ S includes the important diagonal-only matrices as a special case. The key theorem to circumvent full eigen-decomposition and enable fast metric matrix optimization is Gershgorin disc perfect alignment (GDPA): given ${\mathbf M}\in {\mathcal S}$ M ∈ S and diagonal matrix ${\mathbf S}$ S , where $S_{ii} = 1/v_i$ S i i = 1 / v i and ${\mathbf v}$ v is the first eigenvector of ${\mathbf M}$ M , we prove that Gershgorin disc left-ends of similarity transform ${\mathbf B}= {\mathbf S}{\mathbf M}{\mathbf S}^{-1}$ B = S M S - 1 are perfectly aligned at the smallest eigenvalue $\lambda _{\min }$ λ min . Using this theorem, we replace the PD cone constraint in the metric learning problem with tightest possible linear constraints per iteration, so that the alternating optimization of the diagonal / off-diagonal terms in ${\mathbf M}$ M can be solved efficiently as linear programs via the Frank-Wolfe method. We update ${\mathbf v}$ v using Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) with warm start as entries in ${\mathbf M}$ M are optimized successively. Experiments show that our graph metric optimization is significantly faster than cone-projection schemes, and produces competitive binary classification performance. [ABSTRACT FROM AUTHOR]

A new method of moments (MoM)-based approach is proposed to efficiently solve broadband radiation and scattering problems on triangulated, quadrilateral, and mixed mesh geometries. This approach is based on expanding the total current on a conducting body at any desired frequency in terms of entire-domain hyperbasis functions (HBFs), calculated at only one frequency. These HBFs must be found as eigenfunctions of the generalized eigenvalue equation (GEE), defined at that frequency. The developed approach is validated by comparing results with those obtained by direct MoM for different types of mesh. Finally, it is demonstrated for solving practical antenna problems. [ABSTRACT FROM AUTHOR]

Inspired by the mean calculation of RPCA_OM and inductiveness of IRPCA, we first propose an inductive robust principal component analysis method with removing the optimal mean automatically, which is shorted as IRPCA_OM. Furthermore, IRPCA_OM is extended to Schatten- $p$ p norm and a more general framework (i.e., EIRPCA_OM) is presented. The objective function of EIRPCA_OM includes two terms, the first term is a robust reconstruction error term constrained by an $\ell _{2,1}$ ℓ 2 , 1 -norm and the second term is a regularization term constrained by a Schatten- $p$ p norm. The proposed EIRPCA_OM method is robust, inductive and accurate. However, on the high-dimensional data, it would spend a large computation cost in training stage. To this end, a fast version of EIRPCA_OM called as FEIRPCA_OM is proposed, and its basic idea is to eliminate the zero eigenvalues of data matrix. More importantly, an effective theoretical proof is presented to ensure that FEIRPCA_OM has faster processing speed than EIRPCA_OM when processing high-dimensional data, but without any performance loss. Based on it, we also can exchange the less performance loss for the higher computation efficiency by removing the small eigenvalues of data matrix. Experimental results on the public datasets demonstrate that FEIRPCA_OM works efficiently on the high-dimensional data. [ABSTRACT FROM AUTHOR]

It is well-known that an iterative time-reversal (TR) process, applied via a distributed sensing system, can be used to produce a space-time waveform that maximizes the energy scattered from a stationary target back to the sensors. The TR process accomplishes this by automatically focusing energy, both spatially and spectrally, on the stationary target. When scatterers are moving, however, the TR focusing can break down. This article shows how to modify the TR process so that it automatically focuses energy on a moving target. This new TR process automatically generates a distributed beam that: 1) follows the target as it moves and 2) enhances the target resonances by concentrating the energy spectrally. This focusing occurs without a priori knowledge of the target’s location or spectral response. The new TR algorithm is derived through a careful analysis of the idealized case of a single isotropic moving point scatterer. This article includes simulations that compare the TR focus both with and without the new modification. Although the simulations are carried out for the electromagnetic case, the theory applies equally well to the acoustic case when the target speed is significantly less than the ambient sound speed. Appendices are included with details of the calculations and with analysis of the range of relative velocities for which the modified TR process should be used. [ABSTRACT FROM AUTHOR]

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) method to approximate them. This instability arises in the presence of eigenvalues that are close to each other. This makes integrating eigendecomposition into deep networks difficult and often results in poor convergence, particularly when dealing with large matrices. While this can be mitigated by partitioning the data into small arbitrary groups, doing so has no theoretical basis and makes it impossible to exploit the full power of eigendecomposition. In previous work, we mitigated this using SVD during the forward pass and PI to compute the gradients during the backward pass. However, the iterative deflation procedure required to compute multiple eigenvectors using PI tends to accumulate errors and yield inaccurate gradients. Here, we show that the Taylor expansion of the SVD gradient is theoretically equivalent to the gradient obtained using PI without relying in practice on an iterative process and thus yields more accurate gradients. We demonstrate the benefits of this increased accuracy for image classification and style transfer. [ABSTRACT FROM AUTHOR]

Detecting and classifying the occurrence of multiple class events is important in enhancing the wide-area situational awareness ability of power distribution systems. Multiple class event classification based on voltage magnitude measurement has not been largely deployed due to the inadequate elucidation between the occurrence of events and the corresponding eigenvalue perturbations in the measurement data. Herein, a detection and classification method for multiple class events in power distribution systems is proposed based on an eigenvalue fluctuation model. We first elucidated the interrelation between event occurrence and the eigenvalue fluctuations in the system voltage magnitude measurement data. Based on the discovery that different classes of events lead to their respective data eigenvalue behavior, we proposed detection criteria CSRL, CMLP1, and CMLP2 to quantitatively assess these behaviors. Since the different value changes in CSRL, CMLP1 and CMLP2 can indicate the occurrence of different classes of events, we trained and utilized a supervised classifier to achieve multiple event detection and classification. Simulation tests are performed in 7 different test feeders. Eight classes of events can be accurately detected and classified with only voltage magnitude measurement data. An 80% correct detection rate can be obtained with only a 20% measurement device penetration rate. [ABSTRACT FROM AUTHOR]

In this article, the problems of inverse-optimal consensus control (IOCC) for single-integral dynamics in Caputo continuous-time and Grunwald–Letnikov (G-L) discrete-time fractional-order multiagent systems (FOMASs) are investigated. For continuous-time FOMASs, by virtue of the variational method, the optimal solution under the constraint of the global performance index function is presented, and then the optimal state-feedback gain matrix (OSFGM) is derived through the Laplace transform and the inverse transform of fractional order. For discrete-time FOMASs, the OSFGM based on the algebraic Riccati equation (ARE) is computed, then it is shown that the OSFGM is a (asymmetric) Laplace matrix which has a zero eigenvalue and the corresponding network structure is a complete graph. Moreover, we rigorously prove that consensus can be achieved under the optimal state-feedback gain matrices. Finally, two simulation examples are shown to check the validity of the proposed theorems. [ABSTRACT FROM AUTHOR]

A coupled-inductor-based fourth-order buck converter is introduced in this article. The salient features of this topology are lower source current ripples like in conventional buck converter with input filter, no need of connecting an additional damping network across the input filter capacitor, additional flexibility provided by the coupling in the performance tuning, and the existing input C1–L1m structure itself acts as a ripple steering network. The detailed steady-state analysis is evolved and conditions for source current ripple reductions are formulated. Subsequently, small-signal analysis is established and a proportional plus integral plus derivative type controller is designed to ensure load voltage regulation. To enhance the dynamic performance, a two-loop voltage-mode controller is designed. The stability analysis of the closed-loop coupled-inductor-based buck converter is carried out through the eigenvalue sensitivity and participation factors approach. The impact of converter parameters on the converter system stability is discussed. In comparison with the single-loop voltage-mode controller, the two-loop voltage-mode controller is able to ensure that the closed-loop poles stay away from the jω-axis and, thus, the two-loop voltage-mode controller exhibits better dynamic performance. Analytical findings are validated on a 75 W, 60 to 36 V prototype converter. Steady-state and dynamic performance characterizing measurement results are given for validation of the concept. [ABSTRACT FROM AUTHOR]

We propose modeling signed networks by considering two layers in a social network for generation of positive and negative links where both the layers comprise of identical set of nodes. The growth process is modeled based on preferential attachment, formation of links probabilistically asserting structural balance of local groups, and internal growth which happens without addition of new nodes. We prove that the degree distribution of a generated network follows a power-law whose exponent depends on the largest eigenvalue of a matrix which governs the dynamics of growth of degrees of nodes with respect to positive and negative links. A computable formula for average degree and lower-bounds for the number of balanced and unbalanced triads of modelled networks are also obtained. A method for structural reconstruction of real signed networks is formulated through estimation the values of the model parameters to generate the network that can inherit different structural properties of the corresponding real network. Experimental results show that our model which we term as 2L-SNM can replicate properties of several real world signed networks much more robustly than competitive state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

The problem of passive localization of mixed near-field (NF) and far-field (FF) source signals in the presence of array gain-phase uncertainties is addressed. A new algorithm is aimed to use partly calibrated nonuniform linear arrays (NLAs), in which only three sensors have been fully-calibrated. Most of the existing algorithms deal with this problem by exploiting uniform linear arrays (ULAs). Moreover, they assume a simplified source-array model, in which the propagation magnitude scaling is completely neglected and the spatial phase difference is approximated by Taylor’s polynomial. As an opposite, the proposed algorithm is employed to accommodate a more general situation: the exact spatial geometries and nonuniform linear arrays. In the proposed algorithm, three cumulant matrices are firstly defined to construct two matrix pencils. Unambiguous range and angle parameter estimates of the NF sources are then obtained from the generalized eigenvalues of the two defined matrix pencils. After that, these estimates are utilized to calibrate array gain-phase errors. Finally, a spectrum-MUSIC like approach is applied to accomplish the angle estimation for the FF sources. The new algorithm is shown to be readily simple and effective and will be verified both mathematically and numerically. [ABSTRACT FROM AUTHOR]

The numerical mode matching (NMM) method is widely employed in the simulation of electromagnetic (EM) problems with cylindrical geometries. Its significant reduction of the computational cost is achieved by transforming the original 2.5-D problem to a 1-D eigenvalue problem in the radial direction, which is usually treated with the finite element method (FEM), and a semianalytical problem in the $z$ -direction, which can be easily tackled with the mode-matching strategy. However, when an extremely thin vertical layer is encountered, such as the steel casing in well logging, the conventional NMM method will be challenged. The extremely thin layer will cause the mesh for the FEM to be tremendously dense, thus greatly lowering its efficiency. Moreover, if the thin layer is extremely conductive, the matrices for the eigenvalue problem are highly ill-conditioned, making the solution of the eigenvalue/eigenvector inaccurate. To overcome these problems, we propose to apply the surface current boundary condition (SCBC) to substitute the extremely thin vertical layer in the NMM method. To employ the NMM-SCBC method, the mixed-order FEM is first implemented to treat the 1-D eigenvalue problem, and the capability of the corresponding mixed-order NMM method is shown in this article. Furthermore, the expression of the SCBC is derived and applied to the mixed-order NMM method. Several numerical examples show the accuracy and efficiency of the mixed-order NMM-SCBC method. [ABSTRACT FROM AUTHOR]

The performance of most clustering methods hinges on the used pairwise affinity, which is usually denoted by a similarity matrix. However, the pairwise similarity is notoriously known for its vulnerability of noise contamination or the imbalance in samples or features, and thus hinders accurate clustering. To tackle this issue, we propose to use information among samples to boost the clustering performance. We proved that a simplified similarity for pairs, denoted by a fourth order tensor, equals to the Kronecker product of pairwise similarity matrices under decomposable assumption, or provide complementary information for which the pairwise similarity missed under indecomposable assumption. Then a high order similarity matrix is obtained from the tensor similarity via eigenvalue decomposition. The high order similarity capturing spatial information serves as a robust complement for the pairwise similarity. It is further integrated with the popular pairwise similarity, named by IPS2, to boost the clustering performance. Extensive experiments demonstrated that the proposed IPS2 significantly outperformed previous similarity-based methods on real-world datasets and it was capable of handling the clustering task over under-sampled and noisy datasets. [ABSTRACT FROM AUTHOR]

For radiation and scattering problems, characteristic mode analysis (CMA) can provide intuitively physical insight. Generally, eigenpairs (eigenvalue/eigenvectors) for CMA are computed discretely at each frequency and then assigned to corresponding modes within the investigated frequency range using tracking algorithms. These two-stage mode processing methods have low efficiency and can run into problems, including mode discontinuity and inappropriate crossing avoidance handling. Intrinsically, the Rayleigh quotient iteration (RQI)-based algorithm proposed in this article can simultaneously achieve CMA’s mode tracking and eigenpair calculation. Compared to traditional techniques, the tracking efficiency is enhanced with third-order convergence since the number of examined modes calculated by RQI is far fewer than the number of eigenpairs solved by the impedance matrix. In addition, together with the von Neumann–Wigner theorem, the enhanced RQI can detect mode overlap and undesired switching caused by crossing avoidance and correct them on the spot without increasing the computational cost. [ABSTRACT FROM AUTHOR]

We derive closed form bit error rate (BER) expression for orthogonal time frequency space (OTFS) zero-forcing (ZF) receiver with perfect and imperfect receive channel information. Depending on the delay-Doppler locations of the propagation paths of the OTFS channel H, the expression $\mathrm {H}^{H}\mathrm {H}$ is shown to have either distinct or repetitive eigenvalues. When $\mathrm {H}^{H}\mathrm {H}$ has two or less distinct eigenvalues and the remaining ones are repetitive, we derive the probability distribution function (pdf) of the signal-to-noise-plus-interference-ratio (SINR) of the ZF receiver. A closed form BER expression is then derived by averaging the conditional BER over the SINR pdf. When $\mathrm {H}^{H}\mathrm {H}$ has $n$ distinct eigenvalues, we use numerical integration to derive a generalized expression for the SINR pdf. We show that this pdf can be tightly approximated by the Gamma pdf, and then use it to derive the BER expression. The derived OTFS ZF BER expression therefore, unlike the existing ones in the literature, does not require averaging over multiple channel realizations. We show, for different modulation schemes and OTFS system parameters, that the BER calculated using the derived expressions closely matches the one calculated numerically. [ABSTRACT FROM AUTHOR]

This article presents the analysis and implementation of a predictive control method for dc-link regulation and voltage balance in a cascaded modular reduced dc-link solid-state transformer (SST). Passive components like bulky dc links limit the power density of power converters, especially medium-voltage (MV) SST. Reduced dc-link or low-inertia converters can dramatically reduce the size, cost, and weight by tolerating larger dc-link ripples and improve the reliability with electrolytic capacitor-less dc link. However, a small dc link leads to tight coupling between the input and the output stages, which is a challenge for control design. In stacked low-inertia converters (SLIC), the low-inertia converter modules are stacked for MV applications, resulting in coupling between the modules and making the control more challenging. A new model predictive control method that can achieve deadbeat regulation on the dc link without weighting factors has been proposed to address this novel problem. This article focuses on analyzing the condition of the low-inertia dc link up to 80% ripple, the robustness of the control under parameter mismatches, high-order terms, and important implementation issues, such as model-based sampling and computation delay compensation. Significantly, the high-order terms are introduced because of the large dc-link ripple. These high-order terms are unique to the SLIC and negligible in conventional high-inertia converters. A discrete-time large-signal model is built to capture the dc-link's nonlinear dynamics, and the eigenvalues of a small-signal Jacobian matrix are analyzed with Floquet theory to evaluate stability, using the modular soft-switching SST (M-S4T) as an example of the SLIC. Simulation and experimental results of an MVDC M-S4T verify the analysis and the predictive control method. Finally, the general application of the predictive control to low-inertia converters is compared against a conventional PI controller using a reduced dc-link active-front-end rectifier as an example. [ABSTRACT FROM AUTHOR]

In recent years, a new approach has been proposed in the study of the inverse scattering problem for electromagnetic waves. In particular, a study is made of the analytic properties of the scattering operator, and the results of this study are used to design target signatures that respond to changes in the electromagnetic parameters of the scattering medium. These target signatures are characterized by novel eigenvalue problems such that the eigenvalues can be determined from measured scattering data. Changes in the structural properties of the material or the presence of flaws cause changes in the measured eigenvalues. In this article, we provide a general framework for developing target signatures and numerical evidence of the efficacy of new target signatures based on recently introduced eigenvalue problems arising in electromagnetic scattering theory for anisotropic media. [ABSTRACT FROM AUTHOR]

This letter addresses eigenvalue calculation of linear time-periodic models for small-signal stability analysis of converter dominated power systems. An adaptive truncation order selection method is proposed to achieve a balance between computational accuracy and efficiency. Rigorous theoretical analysis and case studies on a grid-following voltage source converter and a modified IEEE 13-bus system validate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

This article studies the consensus of hybrid second-order multiagent systems (MASs), where the hybrid MAS is constituted by the continuous-time second-order (CTSO) and discrete-time second-order (DTSO) dynamic agents. First, a hybrid consensus algorithm is proposed, where a sample-data control is considered in the CTSO subsystems. Under the proposed hybrid consensus algorithm, the convergence of the hybrid second-order MAS matrix is analyzed. Second, a sufficient and necessary condition is proposed, which indicates that the controller parameters, such as coupling gains and the sampling interval, and eigenvalues of network topology have a significant impact on the system consensus. Finally, several simulation examples are presented to prove the validity of the results. [ABSTRACT FROM AUTHOR]

Spectral bounds on the minimum distance of quasi-twisted codes over finite fields are proposed, based on eigenvalues of polynomial matrices and the corresponding eigenspaces. They generalize the Semenov-Trifonov and Zeh-Ling bounds in a way similar to how the Roos and shift bounds extend the BCH and HT bounds for cyclic codes. The eigencodes of a quasi-twisted code in the spectral theory and the outer codes in its concatenated structure are related. A comparison based on this relation verifies that the Jensen bound always outperforms the spectral bound under special conditions, which yields a similar relation between the Lally and the spectral bounds. The performances of the Lally, Jensen and spectral bounds are presented in comparison with each other. [ABSTRACT FROM AUTHOR]