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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, detectability analysis is studied and extended to guide selection of measurements for the dynamic state estimation (DSE) of a synchronous machine. To make sure that the DSE converges, past studies suggested that enough measurements must be available to make the system observable. In this paper, the convergence condition is relaxed via detectability analysis to reduce the number of required measurements. Because the objective of the DSE is to estimate the current states as time progresses, it is shown that a DSE observer can converge not only for an observable system but also for an unobservable system if the eigenvalues corresponding to the unobservable states are stable. Simulation results using the IEEE 10-machine, 39-bus system show that the unscented-Kalman-filter-based DSE can converge when measurements are chosen such that the unobservable states have stable eigenvalues. In comparison with observability analysis, the proposed application of detectability analysis can reduce the number of measurements required for the existence of a DSE observer. [ABSTRACT FROM AUTHOR]

Randomness extraction against side information is the art of distilling from a given source a key which is almost uniform conditioned on the side information. This paper provides randomness extraction against quantum side information whose extractable key length is given by a quantum generalization of the collision entropy, which is smoothed and conditioned differently from how this is done in existing schemes. Based on the fact that the collision entropy is not subadditive, its optimization with respect to additional side information is introduced, and is shown to be asymptotically optimal. The lower bound derived there for general states is expressed as the difference between two unconditional entropies and its evaluation reduces to an eigenvalue problem of two states, which are the entire state and the marginal state of side information. [ABSTRACT FROM AUTHOR]

We present an algorithm for passivity verification and enforcement of multivariate macromodels whose state-space matrices depend in closed form on a set of external or design parameters. Uniform passivity throughout the parameter space is a fundamental requirement of parameterized macromodels of physically passive structures, that must be guaranteed during model generation. Otherwise, numerical instabilities may occur, due to the ability of nonpassive models to generate energy. In this paper, we propose the first available algorithm that, starting from a generic parameter-dependent state-space model, identifies the regions in the frequency-parameter space where the model behaves locally as a nonpassive system. The approach we pursue is based on an adaptive sampling scheme in the parameter space, which iteratively constructs and perturbs the eigenvalue spectrum of suitable skew-Hamiltonian/Hamiltonian pencils, with the objective of identifying the regions where some of these eigenvalues become purely imaginary, thus pinpointing local passivity violations. The proposed scheme is able to detect all relevant violations. An outer iterative perturbation method is then applied to the model coefficients in order to remove such violations and achieve uniform passivity. Although a formal proof of global convergence is not available, the effectiveness of the proposed implementation of the passivity verification and enforcement schemes is demonstrated on several examples. [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]

The eigenvalue diagram at the Dicke planes of the E-plane tee junction is not unlike that of the H-plane geometry available in the literature. The purpose of this paper is to remedy the situation. It includes an investigation of such a junction loaded with both inductive and capacitive vanes at its symmetry plane. This paper also introduces an alternate definition of the Dicke planes in terms of the location of a piston in the main waveguide, which produces a bandstop response between the other two and that of a similar piston in the side waveguide, which establishes a bandpass between the other two. The electrical symmetrical cases at the Altman and Dicke ports for which the magnitudes of the scattering parameters are those of a symmetrical wye junction are separately realized. Each solution has a distinct eigenvalue diagram, which is symmetric about the real axis. This paper includes the realization and fabrication of one device and is in excellent agreement with the theory. The work is undertaken in WR75 waveguide at a frequency of 13.25 GHz. [ABSTRACT FROM PUBLISHER]

This paper examines evolutionary nonlinear projection (NLP), a form of multidimensional scaling (MDS) performed with an evolutionary algorithm. MDS is a family of techniques for producing a low dimensional data set whose points have a one-to-one correspondence with the points of a higher dimensional data set with the added property that distances or dissimilarities in the higher dimensional space are preserved as much as possible in the lower dimensional space. The goal is typically visualization but may also be clustering or other forms of analysis. In this paper, we review current methods of NLP and go on to characterize NLP as an evolutionary computation problem, gaining insight into MDS as an optimization problem. Two different mutation operators, one introduced in this paper, are compared and parameter studies are performed on mutation rate and population size. The new mutation operator is found to be superior. NLP is found to be a problem where small population sizes exhibit superior performance. It is demonstrated experimentally that NLP is a multimodal optimization problem. Two broad classes of projection problems are identified, one of which yields consistent high-quality results and the other of which has many optima, all of low quality. A number of applications of the technique are presented, including projections of feature vectors for polyominos, of vectors that are members of an error correcting code, of behavioral assessments of a collection of agents, and of features derived from DNA sequences. [ABSTRACT FROM AUTHOR]

The identification of generator coherency is crucial to design intentional controlled power system islanding. Due to high penetration of nonsynchronous generation, power system inertia changes both temporally and spatially. Thus, the dynamics in system oscillations and associated slow coherency of generators are directly affected by this. Therefore, their sensitivity deserves investigation. In this paper, the slow coherency with variable inertia is systematically discussed by incremental analysis. Specifically, the approach to study the impacts of variable inertia, based on the matrix perturbation theory, is deployed to provide the explicit eigen-solution sensitivity of slow coherency. To investigate the dependency of coherency grouping on inertia, the changing trends of eigenvector and possible alteration of coherency grouping are estimated. The unusual and abrupt alteration of slow coherency is observed in special scenarios near to modal resonance, i.e. close eigenvalue. The analysis in such scenarios was hardly found in the previous work of coherency sensitivity. Since close eigenvalue can make the traditional matrix perturbation inapplicable, the feasible perturbation in such special scenarios is proposed in this paper. The proposed approach has been thoroughly tested using the classic IEEE 118-bus system. The quantitative results are compared with those obtained analytically. [ABSTRACT FROM AUTHOR]

This paper introduces a node-asynchronous communication protocol in which an agent in a network wakes up randomly and independently, collects states of its neighbors, updates its own state, and then broadcasts back to its neighbors. This protocol differs from consensus algorithms and it allows distributed computation of an arbitrary eigenvector of the network, in which communication between agents is allowed to be directed. (The graph operator is still required to be a normal matrix). To analyze the scheme, this paper studies a random asynchronous variant of the power iteration. Under this random asynchronous model, an initial signal is proven to converge to an eigenvector of eigenvalue 1 (a fixed point) even in the case of operator having spectral radius larger than unity. The rate of convergence is shown to depend not only on the eigenvalue gap but also on the eigenspace geometry of the operator as well as the amount of asynchronicity of the updates. In particular, the convergence region for the eigenvalues gets larger as the updates get less synchronous. Random asynchronous updates are also interpreted from the graph signal perspective, and it is shown that a non-smooth signal converges to the smoothest signal under the random model. When the eigenvalues are real, second order polynomials are used to achieve convergence to an arbitrary eigenvector of the operator. Using second order polynomials the paper formalizes the node-asynchronous communication model. As an application, the protocol is used to compute the Fiedler vector of a network to achieve autonomous clustering. [ABSTRACT FROM AUTHOR]

This paper presents an efficient approach to enforce passivity of rational-based fitted systems. The origin of non-passivity is thoroughly reviewed and analyzed. The proposed approach identifies and modifies, from the original non-passive rational approximation, only the partial fractions that generate passivity violations. It is shown in this paper that these partial fractions generally correspond to out-of-band poles. As for proper-type rational approximations, a new method is proposed to force the constant matrix to be positive-definite. The proposed approach is verified via three case studies with highly non-passive conditions. [ABSTRACT FROM AUTHOR]

Noise power estimation is central to efficient radio resource allocation in modern wireless communication systems. In the literature, there exist many noise power estimation methods that can be classified based on underlying theoretical principle; the most common are spectral averaging, eigenvalues of sample covariance matrix, information theory, and statistical signal analysis. However, how these estimation methods compare against each other in terms of accuracy, stability, and complexity is not well studied, and the focus instead remains on the enhancement of individual methods. In this paper, we adopt a common simulation methodology to perform a detailed performance evaluation of the prominent estimation techniques. The basis of our comparison is the signal-to-noise ratio estimation in the simulated industrial, scientific and medical band transmission, while the reference noise signal is acquired from an industrial production plant using a software-defined radio platform, USRP-2932. In addition, we analyze the impact of different techniques for noise-samples’ separation on the estimation process. As a response to defects in the existing techniques, we propose a novel noise-samples’ separation algorithm based on the adaptation of rank-order filtering. Our analysis shows that the proposed solution, apart from its low complexity, has a very good root-mean-squared error of 0.5 dB and smaller than 0.1-dB resolution, thus achieving a performance comparable with the methods exploiting information theory concepts. [ABSTRACT FROM AUTHOR]

Analog least mean square (ALMS) loop is a promising method to cancel self-interference (SI) in in-band full-duplex (IBFD) systems. In this paper, the steady state analyses of the residual SI powers in both analog and digital domains are firstly derived. The eigenvalue decomposition is then utilized to investigate the frequency domain characteristics of the ALMS loop. Our frequency domain analyses prove that the ALMS loop has an effect of amplifying the frequency components of the residual SI at the edges of the signal spectrum in the analog domain. However, the matched filter in the receiver chain will reduce this effect, resulting in a significant improvement of the interference suppression ratio (ISR). It means that the SI will be significantly suppressed in the digital domain before information data detection. This paper also derives the lower bounds of ISRs given by the ALMS loop in both analog and digital domains. These lower bounds are joint effects of the loop gain, tap delay, number of taps, and transmitted signal properties. The discovered relationship among these parameters allows the flexibility in choosing appropriate parameters when designing the IBFD systems under given constraints. [ABSTRACT FROM AUTHOR]

In this paper, the conditions of the existence of backward-wave modes in closed, lossless waveguides filled with inhomogeneous and anisotropic medium that has coupling between transverse and longitudinal field components are presented. In these waveguides, Maxwell’s equations are transformed into an infinite linear algebraic equation system by application of the Galerkin version of moment method. Propagation constants of the problem are found as the eigenvalues of the coefficient matrix of this infinite linear algebraic equation system. In this paper, the derivative of the eigenvalue is obtained analytically using the result expressions of moment method and group velocity is determined. It is utilized to reveal necessary and sufficient conditions for the existence of backward-wave mode. These conditions are adequate to determine whether this waveguide supports the backward-wave mode in a frequency range of interest. [ABSTRACT FROM AUTHOR]

Several groups are currently working on integrated optical resonators. In this context, one of the most interesting implementations is based on high-contrast gratings, featuring high- $Q$ Fano resonances. Mastering these phenomena can potentially open up the possibility to exploit such devices for the implementation of vertical-coupled filters or compact monolithic lasers. To this aim, in this paper, the novel analytic framework introduced in Part I is applied to complement the design guidelines present in the literature. Through explicit expressions of the loop gain eigenvalues, it is possible to predict the positions and quality factors of resonances in crossing and anticrossing points. Moreover, a quantitative connection between these points and Fano resonances is established. The framework presented in this paper has been useful for identifying, in a low-contrast grating, resonance features similar to those well known in high-contrast structures. [ABSTRACT FROM PUBLISHER]

The problem of maximizing secrecy rate of multiple-input multiple-output multiple-eavesdropper (MIMOME) channels with arbitrary numbers of antennas at each node is studied in this paper. First, the optimization problem corresponding to the secrecy capacity of the MIMOME channel is converted to an equivalent optimization based on Givens rotations and eigenvalue decomposition of the covariance matrix. In this new formulation, precoder is a rotation matrix which results in a positive semi-definite (PSD) covariance matrix by construction. This removes the PSD matrix constraint and makes the problem easier to tackle. Next, a Broyden-Fletcher-Goldfarb-Shanno (BFGS)-based algorithm is developed to find the rotation and power allocation parameters. Further, the generalized singular value decomposition (GSVD)-based precoding is used to initialize this algorithm. The proposed rotation-BFGS method provides an efficient approach to find a near-optimal transmit strategy for the MIMOME channel and outperforms various state-of-the-art analytical and numerical methods. In particular, the rotation-BFGS precoding achieves higher secrecy rates than the celebrated GSVD precoding, with a reasonably higher computational complexity. Extensive numerical results elaborate on the effectiveness of the rotation-BFGS precoding. The new framework developed in this paper can be applied to a variety of similar problems in the context of multi-antenna channels with and without secrecy. [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]

Blind noise-level estimation (NLE) is a fundamental issue in digital image processing. This paper provides a noise-level estimator for additive white Gaussian noise and multiplicative Gaussian noise using principal texture patches (PTPs). The proposed algorithm first identifies the principal texture of the noisy image by using the principal component analysis, and then, it chooses PTPs to calculate the noise level. The major contributions of this paper toward addressing the challenges in the NLE literature include: 1) analyzing the nonlinear relationship between the smallest eigenvalue, true noise level, number of chosen patches, and block size; 2) extracting PTPs; and 3) computing noise level using PTPs. The abundant experimental results show that the proposed method works well for various natural images over a large range of noise levels and it performs well for multiplicative noise. Compared with some state-of-the-art approaches, our method has the best performance and a faster running speed. [ABSTRACT FROM AUTHOR]

This paper considers leader-following bipartite consensus of single-integrator multiagent systems in the presence of measurement noise. To attenuate the noise, a time-varying consensus gain ${q}$ (${t}$) is introduced into the stochastic approximation-type protocol. Necessary and sufficient conditions for ensuring a strong mean square leader-following bipartite consensus are given. In particular, in the absence of measurement noise, the convergence speed of error dynamics is dependent on the eigenvalues of Laplacian and the rate of ${\int ^{{t}}_{0}{q}({s})\text {d}{s}}$ approaching infinity. By appropriately choosing ${q}$ (${t}$), the speed of leader-following bipartite consensus convergence can be improved in a fixed communication topology. It is proven that conditions for the signed digraph to be structurally balanced and having a spanning tree are necessary and sufficient to ensure leader-following bipartite consensus, regardless of measurement noise. [ABSTRACT FROM AUTHOR]

This paper presents a design of a power system damping controller using partial right eigenstructure assignment. The eigenstructure assignment technique selects a set of closed-loop eigenvalues along with their right or left eigenvectors. The selection of eigenvectors offers extra flexibility which is exploited in this paper by designing a robust damping controller which provides the required damping under multiple operating conditions. A multi-input controller is used to increase the degrees of freedom available for the design. Remote measurements available from synchronised phasor measurements are also considered. The problem is formulated as a multi-objective nonlinear optimization problem and solved using the nonlinear simplex function in MATLAB. The proposed technique is used to design a robust power system stabilizer for the interconnected New England New York simplified power system model. Four contingencies are selected as additional operating conditions. The designed controller is validated using a nonlinear simulation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a frequency domain approach for eigenvalue-based detection of a primary user, based on equal gain combining (EGC) and spectrum estimation with Bartlett’s method. This paper considers two techniques for eigenvalue detection which are Maximum Eigenvalue Detection (MED) and the Maximum-Minimum Eigenvalue (MME) detector. We exploit the eigenvalues that are associated with the Hermitian form representation of Bartlett’s estimate to assess the performance of the aforementioned eigenvalue techniques in the frequency domain. For each case, we quantify the performance based on the probabilities of false alarm and missed detection over Rayleigh and Rician fading. A bivariate Mellin transform approach is employed to obtain the probability distribution function for the ratio of the extreme eigenvalues under each hypothesis. All obtained formulas are validated via Monte-Carlo simulations, and the results give a clear insight into the performance of the investigated methods. In frequency domain, MED outperforms both the MME detector and Periodogram-based energy detection even in a worst case scenario of noise uncertainty, while the MME detector exhibits heavy-tailed statistical characteristics and thus its receiver operating characteristics tend to stay on the line of no-discrimination. The performance of MED is further enhanced by careful choice of combinations of the total length of the sensing frame and number of sub-slots. [ABSTRACT FROM PUBLISHER]

This paper proposes a new modal approach for evaluating $Q$ -factors of antennas based on newly introduced XeR/XmR modes rather than characteristic modes (CMs). In our new approach, $Q$ -factors could be represented as direct linear superpositions of eigenvalues of XeR and XmR modes. We validate the accuracy of the new formula for $Q$ -factors by studying two canonical wire antennas. Moreover, the relations between XeR/XmR, TE/TM, and Xe/Xm modes are presented, which show interesting properties. It is found that eigenvalues of XeR/XmR modes reveal useful information about minimum $Q$ -factors. Compared with the CMs, some disadvantages of the proposed modes are also discussed. [ABSTRACT FROM AUTHOR]

Subsynchronous control interaction (SSCI) is the interaction between the power-electronics control and the series-compensated transmission system that occurs at frequencies below the system nominal frequency. SSCI may occur between the doubly-fed induction generator (DFIG) control system and the series-compensated transmission line, to which the wind park (WP) is connected. Not only do the DFIG control system parameters, but also the WP operating conditions have a significant impact on SSCI. In this paper, the impact of WP operating conditions and DFIG control system parameters on SSCI is analyzed in detail. Guidelines are presented for modifying the DFIG control system parameters to ensure safe operation and acceptable transient responses due to faults. This paper also examines the accuracies of various analytical tools used for SSCI problem identification and proposes a new frequency scan analysis approach for accurate prediction of potential SSCI problems. [ABSTRACT FROM PUBLISHER]

The paper presents a comprehensive study of small-signal stability analysis of power systems based on matrix pencils and the generalized eigenvalue problem. Both primal and dual formulations of the generalized eigenvalue problem are considered and solved through a variety of state-of-the-art solvers. The paper also discusses the impact on the performance of the solvers of two formulations of the equations modelling the power systems, namely, the explicit and semi-implicit form of differential-algebraic equations. The case study illustrates the theoretical aspects and numerical features of these formulations and solvers through two real-world systems, namely, a 1,479-bus model of the all-island Irish system, and a 21,177-bus model of the ENTSO-E network. [ABSTRACT FROM PUBLISHER]

In this paper, the physical meanings and various computing methods of characteristic modes (CMs) of dielectric and magnetic bodies are investigated. Two types of surface integral equation (SIE) formulations based on the dependent relationships between the equivalent surface electric and magnetic currents are proposed. Following the two types of SIE formulations, two generalized eigenvalue equations are established to determine the CMs of dielectric or magnetic bodies. This is in contrast to the approach using induced volume currents. It is found that the eigenvalues possess clear physical meanings similar to those of perfectly electric conducting bodies. The CMs can be used to describe the resonant features, including resonant frequencies and resonant field distributions. Numerical results are presented to validate the proposed formulations. [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]

In this paper, we consider flocking of multiple inertial agents with second-order dynamics. For a single agent, its state is therefore velocity and position. There exists both velocity coupling and position coupling between agents that are not necessarily equal. The nonequal couplings are distinguished here, instead of the common assumption of the equal velocity coupling and position coupling in most literature, since they play different roles in the system dynamics. The main contributions are in two aspects: first, we provide a general geometric decomposition approach for analyzing such systems of the agents. Then, we provide some stability results via Lyapunov analysis as a function of couplings and gains that generalize existing results in this area, which are especially useful when the couplings are partially known. Although the stability results are only sufficient, they serve as important complements of the eigenvalue analysis, which generally requires complete knowledge of the couplings in the eigenvalue analysis. [ABSTRACT FROM AUTHOR]

This paper first introduces a simplified construction of the constitutive matrices for general polyhedral meshes. These constitutive matrices are geometrically defined by means of simple closed-form expressions involving the geometric elements of the primal and dual meshes. Then, we solve for the first time the Maxwell’s eigenvalue problem on general polyhedral meshes. In particular, we analyze the convergence of the eigenvalues when the mesh is adaptively refined by using the subgridding technique together with the constitutive inconsistency as error indicator. [ABSTRACT FROM AUTHOR]

Any sequence of uniformly bounded N\times N Hermitian Toeplitz matrices \{H_{N}\} is asymptotically equivalent to a certain sequence of N\times N circulant matrices \CN\ derived from the Toeplitz matrices in the sense that \left \|{HN- CN }\right \|F = o(\sqrt {N}) as $N\rightarrow \infty $ . This implies that certain collective behaviors of the eigenvalues of each Toeplitz matrix are reflected in those of the corresponding circulant matrix and supports the utilization of the computationally efficient fast Fourier transform (instead of the Karhunen-Loève transform) in applications like coding and filtering. In this paper, we study the asymptotic performance of the individual eigenvalue estimates. We show that the asymptotic equivalence of the circulant and Toeplitz matrices implies the individual asymptotic convergence of the eigenvalues for certain types of Toeplitz matrices. We also show that these estimates asymptotically approximate the largest and smallest eigenvalues for more general classes of Toeplitz matrices. [ABSTRACT FROM AUTHOR]

In this paper, we extract the fundamental resonant mode of a graphene patch using a variational method. We use 2-D eigenvalue problem obtained from the integral equation governing the surface current on graphene patterns under quasistatic approximation. To compute the eigenvalues, we propose three trial eigenfunctions, which meet the boundary conditions. We investigate the accuracy of these eigenfunctions with comparing to the results obtained by full wave simulations. Finally, we analyze square-lattice arrangements of graphene patches using the most accurate proposed eigenfunction and derive a very accurate surface impedance for it. The proposed surface impedance is much more precise than the surface impedance already reported by Padooru et al. for this structure. [ABSTRACT FROM AUTHOR]

This paper considers a distributed wave-based sensing system that probes a scene consisting of multiple interacting idealized targets. Each sensor is a collocated transmit–receive pair that is capable of transmitting arbitrary wideband waveforms. We address the problem of finding the space-time transmit waveform that provides the best target detection performance in the sense of maximizing the energy scattered back into the receivers. Our approach is based on earlier theoretical work that showed, for an idealized infinite half-space geometry, that the solution could be constructed by an iterative time-reversal (TR) process. In this paper, we give a more realistic example involving a two-sensor time-domain system. We show that for this system, the iterative TR process can be used to tune automatically to all the target resonances that are within the bandwidth of the interrogating radar system. We show that although obtaining eigenvalues (and hence resonances) of the scattering operator is in general unstable, using the iterative TR process to obtain the resonances is a stable process. Moreover, we show that these resonance frequencies are connected to the poles of the singularity expansion method. [ABSTRACT FROM PUBLISHER]

This paper develops a fully distributed self-triggered framework for achieving the second-order consensus in multiagent systems. In this framework, a fully distributed self-triggered scheme is proposed to schedule information transmission for each communication channel. Thus, the communication frequency of each channel is significantly reduced. Here, communication over different channels is independent with each other and, thus, a channel-based control protocol is further proposed. The update times of control protocol could be also lowered in this framework. Here, an iterative evaluation method is constructed to design a fully distributed self-triggered scheme without involving any global information, especially the eigenvalue information of the Laplacian matrix. In addition, by introducing several variables, some sufficient conditions for achieving the second-order consensus and average consensus are obtained, respectively, in a distributed fashion, and the Zeno behavior is successfully eliminated. Finally, a simulation example is provided to verify the theoretical analysis. [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]

This paper introduces a dynamic phasor model of a half-bridge modular multilevel converter based on variables in the stationary ABC frame. The application of the dynamic phasor theory makes it possible to use converter eigenvalues to study the effect of steady-state harmonics present in the modular multilevel converter (MMC) on its small-signal stability, since the model is inherently time invariant. Relying on a linear transformation, this paper uses a new set of variables with a modified frequency content, which results in lower order dynamic phasor models. A nonlinear dynamic phasor model is developed and linearized. The linear model is compared with a nonlinear averaged MMC model in time domain. Stability analysis by means of eigenvalues and participation factors is carried out for dynamic phasor models that include different frequency content, and the effect of the circulating current suppression controller is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, the upper bound and asymptotical approximation for the bit error rate (BER) as well as for the frame error rate of linear block codes under maximum-likelihood decoding operating over exponentially correlated (EC) generalized-fading channels are proposed. Particularly, our analysis takes the convolutional codes as an example and three different fading scenarios are considered, namely Rice, Nakagami- $m$ , and Weibull fading. Such scenarios have a common property that is spherically invariant random process (SIRP). Our analysis relies on the derivation of new lower bounds per each eigenvalue since the BER as well as the FER expressions are written in terms of the pairwise error probability, which by its turn depends on the eigenvalues of the channel covariance matrix. Based on that, the upper bounds and asymptotic expressions of the considered metrics subject to the three above fading models are derived, which show to be tighter than the previous results published elsewhere in the literature, especially for the high signal-to-noise ratio regions. [ABSTRACT FROM AUTHOR]

The estimation of a covariance matrix from an insufficient amount of data is one of the most common problems in fields as diverse as multivariate statistics, wireless communications, signal processing, biology, learning theory, and finance. In a joint work of Marzetta, Tucci, and Simon, a new approach to handle singular covariance matrices was suggested. The main idea was to use dimensionality reduction in conjunction with an average over the Stiefel manifold. In this paper, we continue with this research and we consider some new approaches to handle this problem. One of the methods is called the mean conjugate estimator under Ewens measure and uses a randomization of the sample covariance matrix over all the permutation matrices with respect to the Ewens measure. The techniques used to attack this problem are broad and run from random matrix theory to combinatorics. [ABSTRACT FROM AUTHOR]

This paper studies the event-triggered containment control (CC) problem of multiagent systems with a directed graph, where the followers’ communication graph is an undirected graph. A novel event-triggered CC protocol is presented to schedule communications between agents, which depends on both local states and control inputs. Different from traditional approaches using broadcasts, a unique property of the proposed protocol is that it enables agent-to-agent data transmission. To do so, each communication link is associated with a specific local event. The estimated relative interagent states are transmitted over a specific link only when the related input-based event is detected. We develop sufficient conditions to solve CC problem under this protocol and extend it to the adaptive event-triggered protocol that does not require the global knowledge on the smallest positive eigenvalue of the Laplacian. For both protocols, we derive positive low bounds on the interevent time intervals generated by individual events, which eliminate the “Zeno phenomenon.” Feasibility of the proposed algorithm is verified by an example. [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 this paper, a technique for designing fixed parameter decentralized power system stabilizers (PSSs) for interconnected power systems is proposed. In the proposed method, local information available at each machine in the multimachine environment, is used to tune parameters of PSS. Conventional design techniques such as P-Vr frequency response approaches, and the method of residues are based on complete system information, wherein phase angles of residues are consistent with the P-Vr phase response and can be used with confidence for design purposes. It is shown that magnitude and phase information of the proposed GEP TF agrees closely with that of P-Vr TF and yields a robust stabilizer. Nonlinear simulation and eigenvalue analysis show the efficacy of the proposed stabilizer to damp out the interarea and local modes of oscillations effectively over a wide range of operating conditions. Superiority of the proposed approach over the conventional approaches is demonstrated with simulation studies on two widely used multimachine systems. [ABSTRACT FROM AUTHOR]

This paper reports on the first use of strongly coupled microresonators to improve the sensitivity of resonant sensing systems. To date, the research on coupled resonant sensors has concentrated on weakly coupled systems, which rely on the measurement of signal amplitudes. Strongly coupled resonant sensor systems, on the other hand, provide a frequency-shift output that results in improved accuracy, precision, and dynamic range. A system model is developed to investigate the effect of perturbations on the eigenvalues of resonator arrays. The model is used to study the system sensitivity to perturbations as the coupling strength between the resonators is increased and demonstrates a multi-fold increase in sensitivity for strong coupling. The developed theory is employed to design strongly coupled resonant sensor systems. Proof-of-concept devices were fabricated in a custom microfabrication process that allowed for inclusion of piezoresistors on structural layers. Experimental results were used to validate the theoretical model and demonstrated an improvement of more than 20% in sensitivity with moderate coupling ratios. This paper lays the foundation for the design of strongly coupled resonant sensor systems for single or multiple measurands. [2015-0186] [ABSTRACT FROM PUBLISHER]