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In this article, we investigate the performance of the newly designed 4 × 4 optical wireless multiple-input-multiple-output (MIMO-OWC) system based on a linearly-shaped arrangement of transmitters and receivers, to achieve long-distance and high data rate transmission. To highlight the importance of selecting an appropriate arrangement for the optical elements, we carried on a comparative study, considering both the conventional square and the proposed horizontal linear constellation of optical modems. The performance of the bit error rate (BER) is experimentally evaluated at distances up to 65 m, using two important metrics inherent to the MIMO transmission channel matrix, i.e., the Frobenius norm and the condition number. The results show that the channel matrix shape characterized by the condition number dominates the BER if the Frobenius norm is smaller than 1. Furthermore, the proposed MIMO-OWC system employing a linearly-shaped arrangement of transmitters and receivers, shows to be more immune to the calibration error rather than the conventional square constellation optical modems. Moreover, the transmission of 100 Mbps data-rate and a BER lower than 10-4 could be successfully achieved at a 65 m communication range.

Neural Architecture Search Without Training (NASWOT) has been proposed recently to replace the conventional Neural Architecture Search (NAS). Pioneer works only deploy one or two indicator(s) to search. Nevertheless, the quantitative assessment for indicators is not fully studied and evaluated. In this paper, we first review several indicators, which are used to evaluate the network in a training-free manner, including the correlation of Jacobian, the output sensitivity, the number of linear regions, and the condition number of the neural tangent kernel. Our observation is that each indicator is responsible for characterizing a network in a specific aspect and there is no single indicator that achieves good performance in all cases, e.g. highly correlated with the test accuracy. This motivated us to develop a novel indicator where all properties of a network are taken into account. To obtain better indicator that can consider various characteristics of networks in a harmonized form, we propose a Fusion Indicator (FI). Specifically, the proposed FI is formed by combining multiple indicators in a weighted sum manner. We minimize the mean squared error loss between the predicted and actual accuracy of networks to acquire the weights. Moreover, as the conventional training-free NAS researches used limited metrics to evaluate the quality of indicators, we introduce more desirable metrics that can evaluate the quality of training-free NAS indicator in terms of fidelity, correlation and rank-order similarity between the predicted quality value and actual accuracy of networks. That is, we introduce the Pearson Linear Coefficient Correlation (PLCC), the Root Mean Square Error (RMSE), the Spearman Rank-Order Correlation Coefficient (SROCC), and Kendall Rank-Order Correlation Coefficient (KROCC). Extensive experiments on NAS-Bench-101 and NAS-Bench-201 demonstrate the effectiveness of our FI, outperforming existing methods by a large margin.

The recently proposed self-holography method has the potential to reduce the computational resources needed for calibration of individual receive paths in large arrays like LOFAR and SKA significantly. The method relies on forming different beams from which the receive path gains can be reconstructed. Self-holography has been applied successfully with different beamforming schemes. In this contribution, I present a generalised formulation of self-holography capturing any beamforming scheme and use that to assess its robustness to interfering sources. This analysis indicates that the relative gain bias is inversely proportional to the signal-to-interference ratio (SIR) regardless of the beamforming scheme used. This result is corroborated in simulations. However, the chosen beamforming scheme has significant impact on the condition number of the measurement matrix and, hence, on the susceptibility to measurement noise. A beamforming scheme with (nearly) orthogonal beamformer weight vectors is thus to be preferred.

The previous research on the controllability of complex networks is qualitative issue which can only identify whether the network is controllable or not, and it is difficult to assess the controlled ability of network. In this paper, a quantitative measurement index of network controllability is introduced. And the index is used to study the controllability of the IEEE power network system. The relationship between controllability and network parameters (including the average degree, the clustering coefficient, the average path length) of power network is analyzed by comparing with the ER random network, WS small world network, BA scale-free network and CM network. The results show that the power networks have a small average path length and a higher clustering coefficient, which belong to the small world network. And, the controllability of power networks is larger than the corresponding model networks, indicating that power networks are relatively easier to be controlled.

As effective measures of energy savings and emission reduction, non-linear loads, such as variable-frequency drives, are widely used. However, the problem of harmonic pollution in power systems is becoming increasingly severe. A harmonic on-line monitoring system is required for statistically analyzing the harmonic distribution rule in a power network and for taking harmonic suppression measures. For solving the frequent topology adjustment issue in practical distribution networks, a new observability analysis method is proposed. The probability of a switch having a closed status is used to express the nodal observability degree in consideration of network topology changes. The condition number of the measurement matrix is used as the index for estimating the precision of the harmonic state. An optimal placement model of harmonic measuring devices is presented, which considers the system observability and the condition number of the measurement matrix. The genetic algorithm (GA) is improved to solve the optimal model. A simulation model is developed based on the improved IEEE33-node system. The simulation results demonstrate the validity of the optimal harmonic measuring device placement model in distribution networks.

In this study, the frequency and material independent reactions (FMIR) is combined with generalized single source tangential equivalence principle algorithm (GSST-EP A) to calculate the wideband RCS of finite period array structure. By Taylor series expansion of the exponent of Green function, a frequency independent matrix and a frequency dependent phase factor are generated. Therefore, the FMIR can accelerate the frequency sweep and improve the frequency sweep accuracy dynamically, while the memory requirement is large. To deal with this problem, the GSST-EPA can transfer the solution problem on the target to the equivalent surface, so it can improve the matrix condition number and decrease the number of unknowns. The characteristic basis function (CBF) is constructed on the equivalent surface to improve the efficiency of GSST-EPA. A numerical example is shown to prove the accuracy and efficiency of the method.

Manifold landmarking is the problem of selecting a subset of discrete locations on a continuous manifold for label assignment, in order to reduce interpolation error of subsequent semi-supervised learning. In this paper, we select landmarks to minimize the condition number (λ max /λ min ) of a submatrix of an alignment matrix Φ, which is equivalent to minimizing an interpolation error bound. Specifically, we design an efficient greedy scheme, where at each iteration t + 1 we choose one landmark i (thus deleting the corresponding row and column i of Φ t ) so that the resulting submatrix Φ t+1 has the smallest condition number. Towards fast landmark selection, at iteration t + 1, we first compute the two extreme eignevectors v 1 and v N corresponding to λ min and λ max of Φ t via known methods like LOBPCG. We show that λ min (λ max ) of submatrix Φ t+1 , from deleting the chosen row-column pair, can be approximated by an upper (lower) bound that is an easily computable function of eigen-pair {v 1 , λ min } ({v N , λ max }) of Φ t . The error bounds of the obtained approximations can be numerically computed during the greedy step. Leveraging these proofs, we minimize a bound of the condition number for submatrix Φ t+1 at each greedy step t + 1. Experiments on synthetic and real-world manifold data demonstrate the superiority of our proposed landmarking algorithm compared to several state-of-the-art schemes.

Within the context of recursive least squares (RLS) parameter estimation, the goal of the present paper is to study the effect of regularization-induced bias on the transient and asymptotic accuracy of the parameter estimates. We consider this question in three stages. First, we consider regression with random data, in which case persistency is guaranteed. Next, we apply RLS to finite-impulse-response (FIR) system identification and, finally, to infinite-impulse-response (IIR) system identification. For each case, we relate the condition number of the regressor matrix to the transient response and rate of convergence of the parameter estimates.

Often times in nonlinear systems, the control input can play a significant role in the system's observability. In this paper, we investigate the trade-off between observability and control performance for a mobile robot in target tracking, when only the distance to the target is measured. The problem is motivated by practical applications for autonomous robots when operating in GPS-denied environments. A nonlinear model predictive control (NMPC) framework is used to address the dilemma between localization and tracking, by jointly optimizing the tracking performance and an observability metric. Three measures of estimation performance are considered, including the determinant of the observability matrix, the inverse condition number of the observability matrix, and the trace of the covariance matrix in position estimation. By tuning the relative importance of the tracking objective and observation performance, we demonstrate the efficacy of the proposed NMPC approach. The trade-off is captured through two examples, one with unicycle dynamics on a plane, the other based on gliding robotic fish with complex 3D dynamics.

Digital Predistortion technique is the most economical and reliable technique among all the linearization techniques available. This paper adduces the idea of linearization based on piecewise polynomial or essential spline functions as an integral solution to the MIMO nonlinearity and compares with the Crossover Memory polynomial model. MIMO nonlinearity is strongly coupled together due to the combined effect of PA nonlinearity and crosstalk. For the proof of concept, the method is implemented over the air on 2X2 MIMO, and simulation is performed for 4X4, 8X8, 16X16 MIMO System. Numerical evaluation of the technique is exhibited in terms of NMSE, BER, and EVM., while numerical stability is presented in terms of Condition number and Dispersion coefficient.

We consider a distributed saddle point problem, in which a collection of nodes collaboratively optimize a sum of local component functions through local computations and information exchange with neighbouring nodes. To solve this problem, we propose a decentralized algorithm based on the Extragradient method, whose centralized implementation has been shown to achieve good performance on a wide range of min-max problems. We show that our proposed method achieves linear convergence under suitable assumptions and explicitly characterize how the convergence rate depends on the condition number and the spectral gap of the communication graph. We also present numerical simulations that corroborate our theoretical results.

In this paper, we study the influence of ill-conditioned regression matrix on two hyper-parameter estimation methods for the kernel-based regularization method: the empirical Bayes (EB) and the Stein’s unbiased risk estimator (SURE). First, we consider the convergence rate of the cost functions of EB and SURE, and we find that they have the same convergence rate but the influence of the ill-conditioned regression matrix on the scale factor are different: for upper bounds, the scale factor for SURE contains one more factor cond(ΦTΦ) than that of EB, where Φ is the regression matrix and cond(•) denotes the condition number of a matrix. This finding indicates that when Φ is ill-conditioned, i.e., cond(ΦTΦ) is large, the cost function of SURE converges slower than that of EB. Then we consider the convergence rate of the optimal hyper-parameters of EB and SURE, and we find that they are both asymptotically normally distributed and have the same convergence rate, but the influence of the ill-conditioned regression matrix on the scale factor are different. In particular, for the ridge regression case, we show that the optimal hyperparameter of SURE converges slower than that of EB with a factor of 1/n2, as cond(ΦTΦ) goes to ∞, where n is the FIR model order.

In this paper, we study the minimax optimization problem in the smooth and strongly convex-strongly concave setting when we have access to noisy estimates of gradients. In particular, we first analyze the stochastic Gradient Descent Ascent (GDA) method with constant stepsize, and show that it converges to a neighborhood of the solution of the minimax problem. We further provide tight bounds on the convergence rate and the size of this neighborhood. Next, we propose a multistage variant of stochastic GDA (M-GDA) that runs in multiple stages with a particular learning rate decay schedule and converges to the exact solution of the minimax problem. We show M-GDA achieves the lower bounds in terms of noise dependence without any assumptions on the knowledge of noise characteristics. We also show that M-GDA obtains a linear decay rate with respect to the error's dependence on the initial error, although the dependence on condition number is suboptimal. In order to improve this dependence, we apply the multistage machinery to the stochastic Optimistic Gradient Descent Ascent (OGDA) algorithm and propose the M-OGDA algorithm which also achieves the optimal linear decay rate with respect to the initial error. To the best of our knowledge, this method is the first to simultaneously achieve the best dependence on noise characteristic as well as the initial error and condition number.

Compared to standard descent-based algorithms, accelerated first-order methods for strongly convex smooth optimization problems may exhibit large transient responses. For quadratic problems, this phenomenon arises from the presence of non-normal dynamics and the modes that yield an algebraic growth in early iterations. In this paper, we employ the framework of integral quadratic constraints to examine the transient response of Nesterov’s accelerated method. We prove that a bound on the largest value of the Euclidean distance between the optimization variable and the global minimizer is proportional to the square root of the condition number. For problems with large condition numbers we demonstrate tightness of this bound up to constant factors, thereby establishing the merits of our approach.

The inverse solution of robot kinematics occupies a very important position in robotics, and it is directly related to robot design, analysis, calibration and control. Aiming at the Jacobian matrix singularity problem in the inverse kinematics of a six-degree-of-freedom series robot, based on the damped least squares method, combined with an inverted Gaussian distribution function, a new continuous damping coefficient adaptive adjustment method is proposed. And this method uses the condition number k as the singularity index. Simulation and experimental results verify the effectiveness of the algorithm, that is, the Jacobian matrix is inversely stable near the singular configuration, and the joints move smoothly.

This paper presents a fast phased array calibration method which significantly reduces the number of antenna under test (AUT) amplitude and phase setting states. Multiple measuring probes are introduced to record transmission coefficients as AUT works at different states. A coefficient matrix with a small condition number is constructed to calculate the initial excitation coefficients of each antenna element. Simulation results show that the coefficient matrix condition number can be reduced to 1 by optimizing the geometry of the measurement system. When the signal-to-noise ratio is higher than 18dB, the amplitude error of the calibration result is less than 0.5dB and the phase error is less than 20 degrees in the optimal conditional number configuration. This method effectively reduces the measurement time for the phased array calibration and improves the stability of the calibration system.

In this paper, the application of minimum mean square error (MMSE) pre-cancellation prior to belief propagation (BP) is proposed as a detection scheme for overloaded multiple-input multiple-output (MIMO). In overloaded MIMO, the loops in a factor graph deteriorate the demodulation performance with BP. Therefore, the proposed scheme applies the MMSE pre-cancellation prior to BP and reduces the number of the loops. Furthermore, it is applied to the selected transmit and receive nodes so that the condition number of an inverse matrix in the MMSE weight matrix is minimized in order to suppress the residual interference and the noise after the MMSE precancellation. It is shown by numerical results obtained through computer simulation that the proposed scheme achieves better bit error rate (BER) performance than BP without the MMSE pre-cancellation. The proposed scheme improves the BER performance by 4.6-5.0 dB at a BER of 5.0 × 10−3 as compared with conventional BP. Numerical results also shows that the MMSE pre-cancellation reduces the complexity in BP by a factor of 1/896 in terms of the number of multiplication operations.

The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is one of the most popular algorithms for solving unconstrained problems. Recently, it has been widely adopted in large-scale optimization problems. However, its use of the Hessian approximation $B_{k}$ is very likely to become ill-conditioned, resulting in an inaccurate search direction. The contracting BFGS algorithm not only retains the positive definiteness of the Hessian approximation $B_{k}$ and the quadratic termination property but also contracts the distribution of the eigenvalues of $B_{k}$ in some sense. However, the argument is not sufficient concerning the improvement of the search direction's accuracy when $B_{k}$ is ill-conditioned. In this paper, we present a modification of the contracting BFGS algorithm for unconstrained optimization. In our algorithm, instead of using a constant contracting factor $c$ , we select a different $c_{k}$ in each step. Our algorithm preserves the positive definiteness of $B_{k}$ and the quadratic termination property. Moreover, by choosing a different contracting factor in each iteration, we prove the existence of the ‘best’ $c_{k}$ that minimizes the spectral condition number of $B_{k+1}$ . We present a method to find such $c_{k}$ based on the matrix rank-1 perturbation theory and the eigenvalue optimization. Finally, numerical experiments are presented to verify both the convergence property and the improvement of the sensitiveness of the linear systems used to solve for search directions.

This paper presents a method of estimating the dynamic parameters of robotic manipulators.The benefits of using the method called the modified Newton-Euler formula to determine the dynamic model of robotic arms are explained. It is shown, that the nonlinear model can be transformed into a linear-in-parameters model and the determination of the independently identifiable variables is explained.The differences between the applicability and efficiency of three estimators are presented, namely between the least-squares, weighted least-squares, and the maximum likelihood estimators. Several criteria are introduced to optimize the excitation trajectories. In a deterministic framework, the Frobenius norm as the condition number of the regression matrix can be used as the cost function to be minimized with a conditional nonlinear optimization algorithm, taken into account the limited joint angles, velocities, and accelerations.If the noises of the joint angles are not negligible, then the maximum likelihood estimator can be used in a stochastic framework and an iterative optimization can be applied to minimize the Cramer-Rao lower bound of the estimation.

For the same type of the parallel mechanism, the structure parameters affect the performance of the movement of kinematics and the static stiffness, so the design of the reasonable structure parameters becomes a key problem in the structural design of parallel mechanism. Taking the 3-UPU parallel mechanism as the research object, an optimum design method of parallel mechanism structure parameters based on the spectral norm is proposed. Firstly, the structure of the parallel mechanism deduces the mathematical model of the end executor and establishes Jacobi matrix, and then the mathematical model of Jacobi matrix condition number is established in the form of spectral norm according to the parallel mechanism dexterity evaluation system in the condition number of the evaluation index. Through the first-order influence coefficient and the eigenvalue of matrix, the analysis of the optimization and simulation is made on the structure parameters of the parallel mechanism whose workspace is known by using the Matlab software. The results show that: in the known workspace and considering the requirements of the design of mechanical structure, when the condition number is 1. $58\leq E\leq 1.72$, the optimized parameters meet the initial design requirements and the data lays a theoretical foundation for the follow-up analysis of the error of parallel mechanism.

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the context of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Mnltiortd (CMG-)preeconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.11The research in this document was performed in connection with con-tract/instrument DARPA HR0011-12-C-0123 with the U.S. Air Force Research Laboratory and DARPA. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. Distribution Statement “A” (Approved for Public Release, Distribution Unlimited). The information in this report is proprietary information of Reservoir Labs, Inc.22Further support from the Department of Energy under DOE STTR Phase I/II Projects DE-FOA-00000760/DE-FOA-000101.

The problem of low-frequency breakdown in the Method of Moments is widely known and has been extensively studied. The loop-tree algorithm is a better solution for the basis function reorganization, but the impedance matrix condition number obtained by the loop-tree algorithm is bad. It is difficult to converge or even diverge using iterative algorithms to solve it. Preconditioning techniques and regularization methods solve this problem well.

Spectral Regression (SR) is a novel dimensionality reduction framework for efficient regularized subspace learning, which is fundamentally based on regression and spectral graph analysis. In this paper, we present a quantum algorithm for SR, where quantum Gram-Schmidt process are proposed and quantum singular value estimation (SVE) technique is applied for regression problem. The quantum algorithm involves two core phases: (1) With labels of the data set, we present a quantum Gram-Schmidt process subroutine based on the quantum block-encoding technique for generalized eigenvectors. (2) A quantum method for ridge regression is presented based on SVE, where the extended Hermitian form of the data matrix is not required. It is shown that our quantum algorithm can achieve an exponential speedup over the classical counterpart for the data matrix with well condition number and small sample size.

The article deals with robustness estimation of large deviations in free motion of continuous-time systems due to parameter variations in the state matrix. It is assumed that parameters of the system are linearly dependent on the uncertainties. The problem is solved with the state space approach and the sensitivity theory methods. An upper bound estimation of trajectory deviations for continuous-time systems is obtained. The estimation contains the condition number of the eigenvectors matrix of the system state matrix. Therefore, sensitivity functions of singular values of the eigenvectors matrix are used to calculate the robustness estimation of the deviations. Based on the obtained equations, an algorithm for the robustness estimation of large deviations in linear continuous-time systems with parametric uncertainties is proposed. The results are supported with an example.

A novel target detection algorithm for large array multi-input multi-output (MIMO) radar in spatially correlated noise is proposed in this paper using canonical correlation technique (CCT). In the signal model, two separate sub-arrays are employed as the receive array of a transmit diversity MIMO radar system. Assume that the elementary noise in each sub-array has spatial correlation, and the number of receive elements is large and grows as the same rate with the snapshots. The detection statistics is constructed based on the generalized likelihood ratio test (GLRT) criterion and the sample canonical correlation coefficient between the two subarrays. The expression of decision threshold is derived via the Tracy-Widom distribution of order 2 in random matrix theory. The simulation results show that the detection performance of the proposed algorithm is better than that of the conventional condition number (CN)-based algorithm in the presence of spatially correlated noise and large array.

The sensitivity distribution of the electromagnetic tomography (EMT) system based on tunneling magnetoresistance (TMR) is quite different from the traditional coil measurement EMT system due to the change of detection sensor. The sensitivity of the TMRs-EMT system is higher only near the TMR sensors but lower at other locations in the region of interest, which results in a more serious ill-conditioned problem of image reconstruction. Focusing on the ill-conditioned problem, the Landweber algorithm is optimized by using an appropriate weight and an appropriate relaxation strategy in this article. By verifying the consistency of variation of the spectral radius of the iterative matrix and variation of condition number for the Landweber method, a new weight matrix is introduced for the general Landweber method to reduce the condition number. On this basis, an optimal relaxation factor is determined based on the principle of minimizing the spectral radius of the newly derived iterative matrix. By comparing the imaging results of the new method with the Landweber with a relaxation factor of 1, it can be seen that the average correlation coefficient with the new approach for the five models used in this article is 0.8466, which is much higher than 0.7633 of the Landweber with a relaxation factor of 1. Meanwhile, the proposed method has a faster imaging speed. The convergence analysis of the two methods shows that the new relaxation factor determination strategy can overcome the semiconvergence problem of Landweber.