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A Newton-type method for the eigenvalue problem of analytic matrix functions is described and analysed. The method finds the eigenvalue and eigenvector, respectively, as a point in the level set of the smallest singular value function and the corresponding right singular vector. The algorithmic aspects are discussed and illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we use block matrix technique to give further lower bounds for the smallest singular value of a general complex matrix. In addition, we prove that the smallest singular value of A is no less than that of the block comparison matrix of A under suitable conditions. Finally, some examples are given. [ABSTRACT FROM AUTHOR]

This paper presents the Load Increase Index, which is a new computationally efficient loadability limit index derived from the continuation power flow method. The continuation power flow is a well-known procedure for identifying the maximum loading point of a static power system network. The proposed index is a byproduct of the continuation power flow, and may be obtained with little extra computational effort while yielding considerable information about the distance to the critical loading point. This paper also presents the mathematical relationship of the proposed index to two other commonly used voltage stability indices: the smallest singular value of the loadflow Jacobian and the determinant of the loadflow Jacobian. The proposed index has been verified on numerous test systems of various sizes. [ABSTRACT FROM AUTHOR]

Nekrasov matrices play an important role in various scientific disciplines. The estimation of infinity norm bounds for the inverse of Nekrasov matrices brings a lot of convinces in many fields. In this paper, we introduce two new bounds for the inverse of Nekrasov matrices. The advantages of our bounds and numerical examples are also presented. [ABSTRACT FROM AUTHOR]

To address the security of cyber-physical systems, stealthy attacks, a class of false data injection attacks that can impact a system without being detected, have been studied in the recent decade. The existing discussions on stealthy attack design have rarely considered systems with switching structures, but recent literature shows the importance of this problem. Therefore, we are motivated to investigate a stealthy man-in-the-middle attack strategy that can be applied to switched systems. Specifically, we first investigate how to design a stealthy attack without using mode information. Then, we consider whether the attacker can infer the mode information that can be used to design a stealthy attack. By combining mode identification and stealthy attack design, a stealthy man-in-the-middle attack strategy for switched systems is proposed. In addition, the feasibility and effectiveness of the strategy are discussed, and an illustrative numerical example is given to demonstrate the proposed strategy. [ABSTRACT FROM AUTHOR]

Uncertainty quantification (UQ) of the neutron multiplication factor is important to investigate the appropriate safety margin for a target system. Although the random sampling method is a practical and useful UQ method, a large computational cost is required to reduce the statistical error of the estimated uncertainty. Furthermore, if an input variable follows a normal distribution with a large standard deviation, the perturbed input variable by the random sampling method may become a physically inappropriate or negative value. To address these issues for the efficient and robust UQ, a modified deterministic sampling method using the simplex ensemble and the scaling method is proposed. The features of the proposed method are summarized as follows: The sample size is $\left({r + 2} \right)$ r + 2 , where $r$ r corresponds to the effective rank of the covariance matrix between the input variables; depending on a situation of target UQ, the amounts of perturbations for the input parameters can be arbitrarily given by the scaling factor method; the scaling factor can be updated to avoid physically inappropriate in the perturbed input variables. The effectiveness of the proposed method is demonstrated through the UQ of the neutron multiplication factor due to fuel manufacturing uncertainties for a typical PWR pin-cell burnup calculation. [ABSTRACT FROM AUTHOR]

In this paper, we present a two-step Noda iteration for computing the Perron root and Perron vector of an irreducible nonnegative matrix by successively solving two linear systems with the same coefficient matrix. For every positive initial vector, the two-step Noda iteration always converges and has a cubic asymptotic convergence rate. As an application, the two-step Noda iteration is applied to compute the smallest eigenpair of irreducible nonsingular M-matrices. Numerical examples are provided for testing the proposed method. [ABSTRACT FROM AUTHOR]

The numerical evaluation of parameters having practical interest in electromagnetic applications is often related to the determination of the set of values, named nonlinear eigenvalues, for which the nonlinear eigenvalue problem L(γ)f = 0 admits a non trivial solution. These values are usually computed, after properly discretization of L(γ), by SVD. However this approach has a main drawback that is very time consuming. In this work we propose a method for quickly evaluating these parameters. An application of the developed technique to a well-known electromagnetic problem is then presented and discussed. [ABSTRACT FROM AUTHOR]

As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) distance has shown the potential for matching problems of structured data like point clouds and graphs. However, its application in practice is limited due to the high computational complexity. To overcome this challenge, we propose a novel importance sparsification method, called Spar-GW, to approximate GW distance efficiently. In particular, instead of considering a dense coupling matrix, our method leverages a simple but effective sampling strategy to construct a sparse coupling matrix and update it with few computations. The proposed Spar-GW method is applicable to the GW distance with arbitrary ground cost, and it reduces the complexity from O (n 4) to O (n 2 + δ) for an arbitrary small δ > 0 . Theoretically, the convergence and consistency of the proposed estimation for GW distance are established under mild regularity conditions. In addition, this method can be extended to approximate the variants of GW distance, including the entropic GW distance, the fused GW distance, and the unbalanced GW distance. Experiments show the superiority of our Spar-GW to state-of-the-art methods in both synthetic and real-world tasks. for this article are available online. [ABSTRACT FROM AUTHOR]

A recent study on the condition numbers of the mixed least squares-total least squares (MTLS) problem is due to Zheng and Yang (Numer Linear Algebra Appl. 2019;26(4):e2239). However, the associated expressions are not compact and the Kronecker-product operations make the computation costly. In this paper, we first present new and alternative closed formula for the first order perturbation estimate and condition numbers of the MTLS solution. Then we reveal the relationship between the new formula and Zheng and Yang's result. Several new computable formulae and perturbation bounds for the normwise condition number of the MTLS solution are also provided. Finally, mixed and componentwise condition numbers, structured condition numbers are investigated. Through a number of tests, they are shown to be tighter than the normwise condition numbers for sparse and structured problems. [ABSTRACT FROM AUTHOR]

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The topological structure of distribution network system is complex, and the operation state changes frequently, so the obtained distribution network topological information has a high error. Therefore, this article proposes a clustering feature extraction method of load curve based on singular value decomposition. The load curve is given by the invariance of singular vectors to improve the generalization ability of feature processing. On the basis of considering the weight of load feature, the data integrity is ensured by singular value curve, and the clustering accuracy is high, which makes the load feature have practical physical significance. The experimental results show that this method can achieve good clustering effect, reduce the clustering time, improve the reliability of data transmission and communication coverage, and meet the communication access requirements of the power Internet of Things sensing layer. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical properties of a reaction-diffusion susceptible infected susceptible (SIS) epidemic model under a linear external source. A numerical scheme is constructed with a finite difference scheme for the space discretization and an Implicit-Explicit (IMEX) method in time integration. A threshold value, numerical basic reproduction number, is proposed in the long-time stability analysis of numerical solutions. Differently from previous works on the same model, the numerical basic reproduction number can preserve the behaviours of the basic reproduction number of the model, towards which it converges when the spatial stepsize vanishes. Moreover, it plays a role for the discrete dynamics similar to the one played by its continuous counterpart. Some numerical experiments are given in the end to confirm the conclusions and detect the conjecture on the stability of endemic equilibrium (EE) in general case. [ABSTRACT FROM AUTHOR]

The current paper develops and analyzes a numerical scheme for the space–time fractional stochastic nonlinear diffusion wave equations. The implicit scheme is based on the matrix transform technique for discretizing the Riesz-space fractional derivative, (3 − α) -order approximation to the Caputo-fractional derivative in time and Taylor's series method to linearize the nonlinear source term, and has been successfully applied to solve a class of nonlinear fractional diffusion wave equation. We prove that the implicit scheme is convergent with β-order in space and (3 − α) order in time, respectively. The optimum error estimates in the temporal-spatial direction and unconditional stability of the implicit scheme have been theoretically investigated. Moreover, several specific numerical experiments confirm the consistency and high efficacy of the provided algorithms, which minimizes the computational costs. [ABSTRACT FROM AUTHOR]

The boundary knot method (BKM) is a boundary meshless method for solving homogeneous boundary value problems. The fact that the BKM uses non-singular general solution without the need of source points outside the domain is at the expense of the accuracy when compared to the well-known method of fundamental solutions. In this paper, a new approach called the enhanced BKM (EBKM) is proposed to greatly improve the accuracy of the BKM by introducing fictitious sources which can be placed inside and/or outside the domain quite freely. We also adopt various techniques to place these fictitious sources in an optimal way. [ABSTRACT FROM AUTHOR]

Communities in multi-layer networks consist of nodes with similar connectivity patterns across all layers. This article proposes a tensor-based community detection method in multi-layer networks, which leverages available node-wise covariates to improve community detection accuracy. This is motivated by the network homophily principle, which suggests that nodes with similar covariates tend to reside in the same community. To take advantage of the node-wise covariates, the proposed method augments the multi-layer network with an additional layer constructed from the node similarity matrix with proper scaling, and conducts a Tucker decomposition of the augmented multi-layer network, yielding the spectral embedding vector of each node for community detection. Asymptotic consistencies of the proposed method in terms of community detection are established, which are also supported by numerical experiments on various synthetic networks and two real-life multi-layer networks. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified generalized SOR-like (MGSOR) method for solving an absolute value equation (AVE), which is obtained by reformulating equivalently AVE as a two-by-two block nonlinear equation and by introducing the transformation P y := | x | with a general nonsingular matrix P. The convergence results of the MGSOR method are obtained under certain assumptions imposed on the involved parameters. Furthermore, the optimal parameters minimizing the convergence rate of the MGSOR method for solving AVE are studied in detail. Numerical experiments further illustrate that the MGSOR method is efficient and has better performance than some existing iteration methods in aspects of the number of iteration steps and CPU time. [ABSTRACT FROM AUTHOR]

The technique of surrogate optimisation is to use a simpler function to approximate a complex function that is time-consuming to evaluate. We show that the maximum of a special type of surrogate function f (U) = Tr (A U) , U ∈ O (n) is at A T (A A T ) 1 / 2 , and that there is one and only one local maximum both in S O (n) and O (n) − S O (n). This function f (U) has been found to be useful in various aspects of electronic structure theory, including proving the Carlson-Keller theorem, and localising orbitals. As one other example, we apply it here to optimise the ground state of molecules using the Generalised Valence Bond wavefunction. [ABSTRACT FROM AUTHOR]

Cloud removal is an essential task in remote sensing data analysis. As the image sensors are distant from the earth ground, it is likely that part of the area of interests is covered by cloud. Moreover, the atmosphere in between creates a constant haze layer upon the acquired images. To recover the ground image, we propose to use scattering model for temporal sequence of images of any scene in the framework of low rank and sparse models. We further develop its variant, which is much faster and yet more accurate. To measure the performance of different methods objectively, we develop a semi-realistic simulation method to produce cloud cover so that various methods can be quantitatively analysed, which enables detailed study of many aspects of cloud removal algorithms, including verifying the effectiveness of proposed models in comparison with the state-of-the-arts, including deep learning models, and addressing the long standing problem of the determination of regularization parameters. Theoretic analysis on the range of the sparsity regularization parameter is provided and verified numerically. [ABSTRACT FROM AUTHOR]

Mobile laser scanning data can be used for effective extraction of road edge information, which is important in the domain of road maintenance and intelligent transportation. This paper proposes a road edge detection method that combines a deep learning and spatial statistics of point cloud data. Semantic segmentation using a deep neural network enables the effective extraction of point cloud fragments recognized as road. The process continues with the spatial statistical analysis of voxel features of data organized into a 3D voxel grid. Filtered voxels are clustered into spatially proximate clusters of similar shape, i.e. straight or curved edges. [ABSTRACT FROM AUTHOR]

This study presents a separable nonlinear least squares (SNLLS) implementation of the minimum distance (MD) estimator employing a fixed-weight matrix for estimating structural equation models (SEMs). In contrast to the standard implementation of the MD estimator, in which the complete set of parameters is estimated using nonlinear optimization, the SNLLS implementation allows a subset of parameters to be estimated using (linear) least squares (LS). The SNLLS implementation possesses a number of benefits, such as faster convergence, better performance in ill-conditioned estimation problems, and fewer required starting values. The present work demonstrates that SNLLS, when applied to SEM estimation problems, significantly reduces the estimation time. Reduced estimation time makes SNLLS particularly useful in applications involving some form of resampling, such as simulation and bootstrapping. [ABSTRACT FROM AUTHOR]

This paper presents the design of robust hierarchical control for homogeneous linear multi-agent systems (MAS) subject to parametric uncertainty and external disturbance. Specifically, the control design is based on a two-layer hierarchical structure consisting of an upper layer and a lower layer. In the lower layer, each agent is represented by a linear time-invariant system and executes a local action. Moreover, each agent exchanges information with neighbouring agents in the upper layer through an undirected graph to achieve the global goal of stabilisation and disturbance attenuation for the MAS. We propose two robust control designs, namely, robust H ∞ hierarchical control and robust H 2 hierarchical control. The design of local and global feedback control laws is formulated as a constrained optimisation over linear matrix inequalities (LMI). The LMI formulation can effectively incorporate the design objective to minimise disturbance attenuation. Numerical results show that the proposed robust controls ensure robust stability of MAS and outperform the existing nominal controls by improving the disturbance attenuation. [ABSTRACT FROM AUTHOR]

For solving a linear system with a large-scale coefficient matrix which is stored in a factorised form, we present a new interlaced randomised iterative method. The new method can take advantage of the factored form and avoid performing matrix multiplications. Furthermore, its convergence property is studied and theoretical analysis reveals that it is linearly convergent. Finally, some numerical results are given to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The QR-algorithm is one of the most important algorithms in linear algebra. Its several variants make feasible the computation of the eigenvalues and eigenvectors of a numerical real or complex matrix, even when the dimensions of the matrix are enormous. The first adaptation of the QR-algorithm to local fields was given by the first author in 2019. However, in this version the rate of convergence is only linear and in some cases the decomposition into invariant subspaces is incomplete. We present a refinement of this algorithm with a super-linear convergence rate in many cases. [ABSTRACT FROM AUTHOR]

This paper presents a detailed sensitivity analysis of the active manipulation scheme for electromagnetic (EM) fields in free space. The active EM fields control strategy is designed to construct surface current sources (electric and/or magnetic) that can manipulate the EM fields in prescribed exterior regions. The active EM field control is formulated as an inverse source problem. We follow the numerical strategies in our previous works, which employ the Debye potential representation and integral equation representation in the forward modelling. We consider two regularization approaches to the inverse problem to approximate a current source, namely the truncated singular value decomposition (TSVD) and the Tikhonov regularization with the Morozov discrepancy principle. Moreover, we discuss the sensitivity of the active scheme (concerning power budget, control accuracy, and quality factor) as a function of the frequency, the distance between the control region and the source, the mutual distance between the control regions, and the size of the control region. The numerical simulations demonstrate some challenges and limitations of the active EM field control scheme. [ABSTRACT FROM AUTHOR]

This paper presents a computationally efficient solution for constraint management of multi-input and multi-output (MIMO) systems. The solution, referred to as the Decoupled Reference Governor (DRG), maintains the highly-attractive computational features of Scalar Reference Governors (SRG) while having performance comparable to Vector Reference Governors (VRG). DRG is based on decoupling the input–output dynamics of the system, followed by the deployment of a bank of SRGs for each decoupled channel. We present two formulations of DRG: DRG-tf, which is based on system decoupling using transfer functions, and DRG-ss, which is built on state feedback decoupling. A detailed set-theoretic analysis of DRG, which highlights its main characteristics, is presented. We also show a quantitative comparison between DRG and the VRG to illustrate the computational advantages of DRG. The robustness of this approach to disturbances and uncertainties is also investigated. [ABSTRACT FROM AUTHOR]

In this article, a novel robust strategy is proposed for concurrent control of the synchronous generator's voltage and frequency in a single machine infinite bus plant. The methodology is based on infinity norm and Mu analysis and synthesis to prepare the robust function of the power system stabilizer, automatic voltage regulator, and load frequency control systems. Ten real structured uncertainties have been considered for the K1, K2 and K4to K6 coefficients of the Heffron–Phillips generator model, inertia constant, damping coefficient, the governor speed regulation coefficient, and the amplifier and exciter gains. Each uncertain parameter has a nominal value in the generator operating point with 25% tolerance excepts to amplifier and exciter gains where their tolerances are 12.5%. The proposed strategy efficiency lies in the strict converting of all ten real parametric uncertainties into the generalized structure of µ synthesis and the formation of efficient weighting functions. Based on the proposed strategy and H∞ norm optimization, µ-synthesis D-K iteration procedure and loop-shaping manner, three controllers have been obtained whose robust performances (RPs) are guaranteed. The supremacy of the offered controllers is shown by comparing their functions in four scenarios and three patterns. The simulation results reveal the good RP of the designed controllers. Also, for a benchmark problem as a single machine connected to a 230 kV network, the capabilities of the designed robust controllers have been shown. [ABSTRACT FROM AUTHOR]

This article proposes sparse and easy-to-interpret proximate factors to approximate statistical latent factors. Latent factors in a large-dimensional factor model can be estimated by principal component analysis (PCA), but are usually hard to interpret. We obtain proximate factors that are easier to interpret by shrinking the PCA factor weights and setting them to zero except for the largest absolute ones. We show that proximate factors constructed with only 5%–10% of the data are usually sufficient to almost perfectly replicate the population and PCA factors without actually assuming a sparse structure in the weights or loadings. Using extreme value theory we explain why sparse proximate factors can be substitutes for non-sparse PCA factors. We derive analytical asymptotic bounds for the correlation of appropriately rotated proximate factors with the population factors. These bounds provide guidance on how to construct the proximate factors. In simulations and empirical analyses of financial portfolio and macroeconomic data, we illustrate that sparse proximate factors are close substitutes for PCA factors with average correlations of around 97.5%, while being interpretable. [ABSTRACT FROM AUTHOR]

This study presents a visualization system in a third-person view for the teleoperation of a snake-like robot. The proposed system visualizes the robot, its surroundings, past path, and predicted path. The visualization is achieved by drawing a robot at self-position and the sensor information, such as a point cloud around the robot, in a virtual 3D space. Therefore, localization plays a key role in visualization. We propose a new localization method that relies only on the information from joint angles and an IMU. We evaluated the proposed method by comparing it with other methods on a flat ground and on a combination of a plane and a slope with a rough surface. The results demonstrated the effectiveness of the proposed method in both cases. Then, we examined the visualization system in room environments. The results showed that the proposed system successfully visualized the robot and its surroundings. We also confirmed the effectiveness of the visual aid by the predicted path. [ABSTRACT FROM AUTHOR]

In this paper, the assignability of linear time-invariant (LTI) systems with respect to arbitrary control structures is addressed. It is well established that the closed-loop spectrum of an LTI system with an arbitrary control structure is confined to the set containing the fixed-modes of the system with respect to that control structure. However, the assignment of the closed-loop spectrum is not merely limited by the existence of fixed-modes in practical scenarios. The pole assignment may require excessive control effort or even become infeasible due to the presence of small perturbations in the system dynamics. To offer more insights in such more realistic scenarios, a continuous measure known as fixed-mode radius is developed. However, its evaluation is confronted with a highly non-convex optimization problem combined with the need for a combinatorial search. This study utilises properties of positive-definite cones and duality theory to formulate the assignability assessment as an optimization problem with linear matrix inequality (LMI) constraints. Based on the suggested formulation, three alternative methods are proposed to evaluate the distance to unassignability. The first two methods offer alternative non-iterative and convex programs. The third method proposes an iterative convex optimization while updating the binary variables based on the dual variables. All the proposed methods rely on convex optimization, do not involve gridding over the complex plane and circumvent the combinatorial nature of the problem by using properties of positive definite cones. Simulation results confirm the effectiveness of the proposed methods in the assessment of fixed-mode radius with respect to arbitrary control structures. [ABSTRACT FROM AUTHOR]

Updating the augmented Lagrangian multiplier by closed-form expression yields efficient first-order infeasible approach for optimization problems with orthogonality constraints. Hence, parallelization becomes tractable in solving this type of problems. Inspired by this closed-form updating scheme, we propose a novel penalty function with compact convex constraints (PenC). We show that PenC can act as an exact penalty model which shares the same global minimizers as the original problem with orthogonality constraints. Based on PenC, we first propose a first-order algorithm called PenCF and establish its global convergence and local linear convergence rate under some mild assumptions. For the case that the computation and storage of Hessian is achievable, and we pursue high precision solution and fast local convergence rate, a second-order approach called PenCS is proposed for solving PenC. To avoid expensive calculation or solving a hard subproblem in computing the Newton step, we propose a new strategy to do it approximately which still leads to quadratic convergence locally. Moreover, the main iterations of both PenCF and PenCS are orthonormalization-free and hence parallelizable. Numerical experiments illustrate that PenCF is comparable with the existing first-order methods. Furthermore, PenCS shows its stability and high efficiency in obtaining high precision solution comparing with the existing second-order methods. [ABSTRACT FROM AUTHOR]

Convolutional neural network is an important model in deep learning, where a convolution operation can be represented by a tensor. To avoid exploding/vanishing gradient problems and to improve the generalizability of a neural network, it is desirable to have a convolution operation that nearly preserves the norm, or to have the singular values of the transformation matrix corresponding to the tensor bounded around 1. We propose a penalty function that can constrain the singular values of the transformation matrix to be around 1. We derive an algorithm to carry out the gradient descent minimization of this penalty function in terms of convolution kernel tensors. Numerical examples are presented to demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, a non-polynomial-based trigonometric cubic B-spline collocation method is developed to solve the reaction-diffusion singularly perturbed problems with Robin boundary conditions. These problems are more tedious to solve than those with Dirichlet and Neumann boundary conditions. The parameter ε in the differential equation results in a rapid change in the solution over a small region. A piecewise uniform mesh is constructed to handle this difficulty. Also, a modification of the proposed mesh is suggested to improve the accuracy of the numerical results by introducing a change in the transition parameter. Through rigorous analysis, it has been shown that the method is almost second-order uniformly convergent. The performance and theoretical findings of the proposed scheme are validated through numerical experiments presented for two test problems. The accuracy of the method is measured in the discrete maximum norm. The tabular results demonstrate that the newly added mesh produces better results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to develop a theory for designing the keyboard area of smartphones, and endowing the users with comfortable texting ability via one thumb. In light of the fact that most users tend to hold the smartphone in one hand and manipulate with one thumb in daily life, this paper extracts the thumb kinematic chain from the thumb anatomy of the human hand, and defines the manipulation comfort ellipsoid of the thumb. Then some indexes such as the morphology and volume of the comfort ellipsoid, and the condition number of the thumb Jacobian are presented to evaluate the manipulation comfort of the thumb. Finally, the design problem of the smartphone's keyboard area is transformed into an optimization problem that determines the most comfortable manipulation space for the human thumb. The proposed quantitative study method of the thumb manipulation comfort is verified by 12 subjects who hold a smartphone with one hand and manipulate the screen with one thumb, and the most comfortable keyboard layout of smartphone is determined for the 12 subjects. The proposed method for the manipulation comfort of the human thumb bridges the gap between the layout planning of soft keyboard of smartphones and the comfort of single thumb manipulation. [ABSTRACT FROM AUTHOR]

The theory of Pólya ensembles of positive definite random matrices provides structural formulas for the corresponding biorthogonal pair, and correlation kernel, which are well suited to computing the hard edge large N asymptotics. Such an analysis is carried out for products of Laguerre ensembles, the Laguerre Muttalib–Borodin ensemble, and products of Laguerre ensembles and their inverses. The latter includes, as a special case, the Jacobi unitary ensemble. In each case, the hard edge scaled kernel permits an expansion in powers of 1/N, with the leading term given in a structured form involving the hard-edge scaling of the biorthogonal pair. The Laguerre and Jacobi ensembles have the special feature that their hard edge scaled kernel – the Bessel kernel – is symmetric and this leads to there being a choice of hard edge scaling variables for which the rate of convergence of the correlation functions is O (1 / N 2). [ABSTRACT FROM AUTHOR]

Estimations and applications of factor models often rely on the crucial condition that the number of latent factors is consistently estimated, which in turn also requires that factors be relatively strong, data are stationary and weakly serially dependent, and the sample size be fairly large, although in practical applications, one or several of these conditions may fail. In these cases, it is difficult to analyze the eigenvectors of the data matrix. To address this issue, we propose simple estimators of the latent factors using cross-sectional projections of the panel data, by weighted averages with predetermined weights. These weights are chosen to diversify away the idiosyncratic components, resulting in "diversified factors." Because the projections are conducted cross-sectionally, they are robust to serial conditions, easy to analyze and work even for finite length of time series. We formally prove that this procedure is robust to over-estimating the number of factors, and illustrate it in several applications, including post-selection inference, big data forecasts, large covariance estimation, and factor specification tests. We also recommend several choices for the diversified weights. for this article are available online. [ABSTRACT FROM AUTHOR]

Prior distributions for high-dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients, which is inherently difficult. We instead propose a new class of shrinkage priors for linear regression via specifying a prior first on the model fit, in particular, the coefficient of determination, and then distributing through to the coefficients in a novel way. The proposed method compares favorably to previous approaches in terms of both concentration around the origin and tail behavior, which leads to improved performance both in posterior contraction and in empirical performance. The limiting behavior of the proposed prior is 1 / x , both around the origin and in the tails. This behavior is optimal in the sense that it simultaneously lies on the boundary of being an improper prior both in the tails and around the origin. None of the existing shrinkage priors obtain this behavior in both regions simultaneously. We also demonstrate that our proposed prior leads to the same near-minimax posterior contraction rate as the spike-and-slab prior. for this article are available online. [ABSTRACT FROM AUTHOR]

The selection of systems of inputs and outputs forms part of the early system design that is important since it preconditions the potential for control design. Existing methodologies for input, output structure selection rely on criteria expressing distance to uncontrollability, unobservability. Although controllability is invariant under state feedback, its corresponding degrees expressing distance to uncontrollability is not. The paper introduces new criteria for distance to uncontrollability (dually for unobservability) which is invariant under feedback transformations. The approach uses the restricted matrix pencils developed for the characterisation of invariant spaces of the geometric theory and then deploys exterior algebra to define the invariant input and output decoupling polynomials. This reduces the overall problem of distance to uncontrollability (unobservability) to two optimisation problems: the distance from the Grassmann variety and distance of a set of polynomials from non-coprimeness. Results on the distance of Sylvester Resultants from singularity provide the new measures. [ABSTRACT FROM AUTHOR]

Parallel robots are preferred over serial robots owing to their enhanced accuracy and rigidity which comes from their higher stiffness. However, there are applications both in industry and in healthcare where higher accuracy is required alongside high compliance (reduced stiffness). Accuracy and compliance being conflicting to each other are difficult to achieve simultaneously. To address this issue, an intrinsically compliant 6-dof parallel robot is proposed in this work. Kinematic and analytical modeling is performed for its conceptual design to obtain the Jacobian matrix and thereby map the joint and Cartesian spaces. Robot's structure design is analyzed, and the wrench analysis is also carried out to estimate the link forces and stiffness. It is shown that by small changes in the proposed robot design; its compliance can be altered making it suitable for a range of applications. It is also shown mathematically that the robot design can be optimized to maintain higher accuracy together with higher compliance. To carry out design optimization, three important performance criteria, namely; global condition number (for higher accuracies), norm of link forces (to reduce actuator power requirement) and robot compliance (for response to an external wrench) are mathematically formulated. Later, a multi-criteria optimization is performed using an evolutionary algorithm to simultaneously optimize these performance criteria. From the final robot design selected, it is evident that a higher robot compliance with optimal condition number and link forces can be achieved. [ABSTRACT FROM AUTHOR]

For a family of real matrices with entries polynomially depending on parameters, symbolic algorithms are proposed for verification of the Routh – Hurwitz stability under parameter variations in a given box, and for the distance to instability computation in the case of perturbations over C . Both problems are reduced to the analysis of real zeros of a pair of univariate polynomials; one of these reductions is based on the discriminant computation in the Hankel determinant form. We also discuss a potential application of the suggested approach for finding an estimation for the accuracy of the distance to instability computations via numerical procedures. [ABSTRACT FROM AUTHOR]

The Optimal Reactive Power Dispatch (ORPD) is a very important study in planning the power system operation. The conventional ORPD formulations focus only on driving the objective functions toward optima and ignore the benefits to retain adequate Reactive Power Reserve (RPR) in the system. Studies show that inadequate RPR can jeopardize the power system voltage security under stressed conditions. In view of this, a Reserve Constrained ORPD (RC-ORPD) is proposed in this paper and solved using the recently developed, Coronavirus Herd Immunity Optimizer (CHIO). For this purpose, the minimum required Effective Reactive Reserve (ERR) is devised and introduced as a constraint in the ORPD problems. Here, the minimization of power loss and L-index are taken as objective functions, and the problem is formulated as a non-linear constrained optimization problem. The proposed problem is tested on standard IEEE 30 bus and IEEE 57 bus systems. To assess the impact of the proposed strategy, the same problems are also solved by relaxing the ERR constraint. Comparisons reveal that the added constraint improves voltage stability linked parameters and offers more RPR in the system without sacrificing much on the optimum solution. Further, the proficiency of CHIO is verified through various case studies and comparisons. [ABSTRACT FROM AUTHOR]

The random sampling and reconstruction algorithm of sparse time- and band-limited signals, which stem from bandlimited functions, is studied in this paper. For time- and band-limited signals, considering the projection on a finite-dimensional solution space, the reconstruction algorithm can therefore be described by a matrix. Especially, we study the case of the finite-dimensional spaces with regard to time- and band-limited signals. First, as the cardinality of the sample value { f (x j) : j ∈ J } is not less than the dimension of solution space, we prove that the coefficient matrix has full rank. Second, as sample value { f (x j) : j ∈ J } is insufficient, especially spare time- and band-limited signals, based on the Restricted Isometry Property (RIP) condition and the concentration inequality of a probability distribution for random sampling, we present a ℓ 1 − minimization reconstruction from few randomly chosen samples on [ − T , T ]. Finally, numerical experiments show that with high probability the time- and band-limited signals can be approximately recovered provided τ-sparsity of non-vanishing coefficients ak. [ABSTRACT FROM AUTHOR]

We present a numerical scheme for the solution of two-parameter singularly perturbed problems whose solution has multi-scale behaviour in the sense that there are small regions where the solution changes very rapidly (known as layer regions) otherwise the solution is smooth (known as a regular region) throughout the domain of consideration. In particular, to solve the problems whose solution exhibits twin boundary layers at both endpoints of the domain of consideration, we propose a collocation method based on the quintic B -spline basis functions. A piecewise-uniform mesh that increases the density within the layer region compared to the outer region is used. An (N + 1) × (N + 1) penta-diagonal system of algebraic equations is obtained after the discretization. A well-known fast penta-diagonal system solver algorithm is used to solve the system. We have shown that the method is almost fourth-order parameters uniformly convergent. The theoretical estimates are verified through numerical simulations for two test problems. [ABSTRACT FROM AUTHOR]

This paper presents a non-codebook based Multiple User Multiple Input Multiple Output (MU-MIMO) test-bed system for Time Division Duplex (TDD) Long Term Evolution-Advanced (LTE-A). The system was implemented for verifying the performance of a dynamic precoding procedure that selects the most appropriate precoder among a given set of precoding techniques. Using two parameters, the propagation path gain and the condition number of the channel matrix, the proposed MU-MIMO system can adaptively switch the precoding software to guarantee that the upper bound Bit Error Rate (BER) is maintained with a minimum computational burden. This paper also presents a novel procedure for accurately and simply calibrating the multiple Radio Frequency (RF) paths of the multiple antennas and RF transceivers of the MU-MIMO system. From various experimental measurements obtained from the implemented test-bed system, the upper bound BER, which was arbitrarily set to 10−3 in this paper, can be maintained with the simplest precoder, Zero Forcing (ZF), unless the propagation path gain becomes less than 0.25. It was also found in the experimental tests that, as the distance between 2 handsets becomes shorter than 1 meter, which causes the condition number of the channel matrix to be larger than 17, the precoder should be switched from Lattice Reduction (LR) to Tomlinson-Harashima Precoding (THP) when the minimum distance between base-station and each handset maintained is set to at least 6 meters. [ABSTRACT FROM AUTHOR]

This article presents an URV-based matrix decomposition, the truncated URV decomposition, and an updating algorithm for it. The complexity of the updating is [image omitted] for an m-by- n matrix of rank r. The theoretical and numerical results presented shows that the decomposition can be a good alternative to the singular value decomposition. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of determining and efficiently computing an approximation to the eigenvalues of the negative Laplacian - ▵ on a general domain Ω ⊂ 2 subject to homogeneous Dirichlet or Neumann boundary conditions. The basic idea is to look for eigenfunctions as the superposition of generalized eigenfunctions of the corresponding free space operator, in the spirit of the classical method of particular solutions (MPS). The main novelties of the proposed approach are the possibility of targeting each eigenvalue independently without the need for extensive scanning of the positive real axis and the use of small matrices. This is made possible by iterative inclusion of more basis functions in the expansions and a projection idea that transforms the minimization problem associated with MPS and its variants into a relatively simple zero-finding problem, even for expansions with very few basis functions. [ABSTRACT FROM AUTHOR]

Extremum seeking control (ESC) is a model-free control solution for real-time optimization of system operation where model acquisition is difficult and/or cost prohibitive. For many HVAC and refrigeration systems, there can be a large number of candidate inputs for ESC design; however, some inputs affect the performance measure to a greater degree than others. This article presents an online input selection method for multivariable ESC, which uses a singular value decomposition (SVD) analysis coupled with a dither-demodulation-based online Hessian estimate for the underlying static map. A subset of physical inputs or a new set of inputs via linear combination of the physical inputs can be determined using the proposed approach. We present an analysis for quantifying the loss bound of achievable optimum output with the underlying input selection. Further, the Hessian estimation error bound is quantified with perturbation analysis. The proposed method is evaluated with Modelica simulation models of chilled-water plants, one with a single chiller and the other with two parallel chillers. The simulation results validate the effectiveness of the proposed method of input selection. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) is an approach to improve the performance of a system that repeats the same operation. In this paper, we apply the theory of pseudospectra to transient analysis of ILC. The focus of this paper is on frequency-domain analysis of filter-based ILC. Moreover, the effect of finite trial length on the transient growth is discussed. [ABSTRACT FROM AUTHOR]