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In this paper, the minimum norm partial eigenstructure assignment problems (PESAPs) in vibration system with time delay is studied via acceleration‐velocity‐displacement active control. A new explicit solution is given for solving PESAPs using orthogonality relations of symmetric vibration system. A new constructive technique is presented to solve the PESAPs in vibration system with time delay by singular value decomposition method. An optimization algorithm is proposed to solve the minimum norm PESAPs by a quasi‐Newton optimization method. The proposed algorithm works without using the knowledge of receptance matrices and without solving the Sylvester equation. The effectiveness of the proposed algorithm is verified by the results of two numerical examples. [ABSTRACT FROM AUTHOR]

To calculate the harmonic impedance on the system side is crucial for the safe and stable operation of the new power system. Existing algorithms for harmonic impedance estimation usually assume that the harmonic impedance on the system side is constant during the measurement period. However, the voltage on the system side always changes according to the working mode of the power grid or access of large power load demand, resulting in fluctuations of the harmonic impedance on the system side. Luckly, the harmonic impedance on the system side does not change much in the adjacent sampling time interval. On this basis, the paper proposes a new non-intervention solution for the variable harmonic impedance on the system side. In this method, the second-order change of the harmonic impedance and the second-order change of voltage in the adjacent sampling time interval are taken as the objective function. The harmonic impedance on the system side is solved by minimizing the target function. The proposed method is proved to be accurate and reliable by simulation and practical analysis, especially in the condition that the strong background harmonic or user-side harmonic impedance is not much stronger than the harmonic impedance on the system side.

Copyright of Electric Power Engineering Technology is the property of Editorial Department of Electric Power Engineering Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract The design of optimal Magnetic Resonance Imaging (MRI) coils is modeled as a minimum-norm problem (MNP), that is, as an optimization problem of the form min x ∈ R ∥ x ∥ $\min_{x\in\mathcal{R}}\|x\|$ , where R $\mathcal{R}$ is a closed and convex subset of a normed space X. This manuscript is aimed at revisiting MNPs from the perspective of Functional Analysis, Operator Theory, and Banach Space Geometry in order to provide an analytic solution to the following MRI problem: min ψ ∈ R ∥ ψ ∥ 2 $\min_{\psi\in\mathcal{R}}\|\psi\|_{2}$ , where R : = { ψ ∈ R n : ∥ A ψ − b ∥ ∞ ∥ b ∥ ∞ ≤ D } $\mathcal{R}:=\{\psi\in \mathbb{R}^{n}:\frac{\|A\psi-b\|_{\infty}}{\|b\|_{\infty}} \leq D\}$ , with A ∈ M m × n ( R ) $A\in\mathcal{M}_{m\times n}(\mathbb{R})$ , D > 0 $D>0$ , and b ∈ R m ∖ { 0 } $b\in\mathbb{R}^{m}\setminus\{0\}$ .

In magnetoencephalography (MEG) research there are a variety of inversion methods to transform sensor data into estimates of brain activity. Each new inversion scheme is generally justified against a specific simulated or task scenario. The choice of this scenario will however have a large impact on how well the scheme performs. We describe a method with minimal selection bias to quantify algorithm performance using human resting state data. These recordings provide a generic, heterogeneous, and plentiful functional substrate against which to test different MEG recording and reconstruction approaches. We used a Hidden Markov model to spatio-temporally partition data into self-similar dynamic states. To test the anatomical precision that could be achieved, we then inverted these data onto libraries of systematically distorted subject-specific cortical meshes and compared the quality of the fit using cross validation and a Free energy metric. This revealed which inversion scheme was able to identify the least distorted (most accurate) anatomical models, and allowed us to quantify an upper bound on the mean anatomical distortion accordingly. We used two resting state datasets, one recorded with head-casts and one without. In the head-cast data, the Empirical Bayesian Beamformer (EBB) algorithm showed the best mean anatomical discrimination (3.7 mm) compared with Minimum Norm/LORETA (6.0 mm) and Multiple Sparse Priors (9.4 mm). This pattern was replicated in the second (conventional dataset) although with a marginally poorer (non-significant) prediction of the missing (cross-validated) data. Our findings suggest that the abundant resting state data now commonly available could be used to refine and validate MEG source reconstruction methods and/or recording paradigms.

Two-dimensional phase unwrapping (2-D PU) is a crucial step in interferometric signal processing. The accuracy of phase unwrapping (PU) will significantly affect subsequent processing. Existing algorithms perform poorly in areas with rapid terrain changes or with low coherence. In order to solve the above problems, this letter proposes a method of using a neural network to predict residuals, followed by the minimum $L^{1}$ -norm algorithm for phase reconstruction. The network for predicting residuals is called residual prediction network (RPNet). To construct more complex loss terms, the continuous relaxation strategy is applied to its training. The proposed method overcomes the effects of noise and terrain changes due to the accurate prediction of residuals. The compensated phase gradients enable the minimum $L^{1}$ -norm algorithm to reconstruct phases more accurately. The experimental results performed on simulation and interferometric synthetic aperture radar (InSAR) data demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the minimum-norm least squares solution to a quaternion tensor system A 1 ∗ N X 1 = C 1 , A 1 ∗ N X 2 + A 2 ∗ N X 3 = C 2 , E 1 ∗ N X 1 ∗ M F 1 + E 1 ∗ N X 2 ∗ M F 2 + E 2 ∗ N X 3 ∗ M F 2 = D by using the Moore–Penrose inverses of block tensors. As an application, we discuss the quaternion tensor system A ∗ N X = C , E ∗ N X ∗ M F = D for minimum-norm least squares reducible solutions. To illustrate the results, we present an algorithm and a numerical example. [ABSTRACT FROM AUTHOR]

In the paper, the partial eigenstructure assignment problems are investigated using acceleration–velocity–displacement active control in a singular vibrating structure. The problems are transformed into solving matrix equations using the receptance matrix method. Iterative sequences are constructed, and the iterative feasibility is presented for solving the matrix equations. The partial eigenvectors of the closed-loop system are reassigned by imposing modal constraints. An algorithm is proposed to get numerical solutions of the derived matrix equations. The initial value condition is discussed to obtain the minimum norm solution of the partial eigenstructure assignment problems. The designed acceleration–velocity–displacement active control can solve the partial eigenstructure assignment problems depending only on original vibrating structure information. The proposed numerical algorithm can obtain the minimum norms of controller gain, which implies minimum energy consumption. Numerical examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The Hermite interpolation problem in the Euclidean space is considered, where the value of the function of several variables and its first-order and second-order Gateaux differentials at the interpolation nodes are given. The problem is shown to have a unique solution of minimum norm generated by a scalar product with Gaussian measure in the finite-dimensional Euclidean space. Conditions for invariant solvability and uniqueness of the problem solution are obtained. [ABSTRACT FROM AUTHOR]

Copyright of Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz is the property of V.M. Glushkov Institute of Cybernetics of NAS of Ukraine and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The Hermite problem in the Euclidean space is considered, where the value of a function of several variables and its first-order Gateaux differentials at the interpolation nodes are given. The problem is shown to have a unique minimum-norm solution in the case of underdefiniteness. Conditions for invariant solvability and uniqueness of the problem solution are obtained. [ABSTRACT FROM AUTHOR]

The design of optimal Magnetic Resonance Imaging (MRI) coils is modeled as a minimum-norm problem (MNP), that is, as an optimization problem of the form min x ∈ R ∥ x ∥ , where R is a closed and convex subset of a normed space X. This manuscript is aimed at revisiting MNPs from the perspective of Functional Analysis, Operator Theory, and Banach Space Geometry in order to provide an analytic solution to the following MRI problem: min ψ ∈ R ∥ ψ ∥ 2 , where R : = { ψ ∈ R n : ∥ A ψ − b ∥ ∞ ∥ b ∥ ∞ ≤ D } , with A ∈ M m × n (R) , D > 0 , and b ∈ R m ∖ { 0 } . [ABSTRACT FROM AUTHOR]

• Spatial accuracy of 6 linear distributed inverse solutions for interictal high-density EEG source localisation was evaluated. • Low-Resolution Electromagnetic Tomography and Local Autoregressive Average best localised both patients' and simulated sources. • These two algorithms' superiority over newer inverse solutions was due to their relative robustness towards noise. To compare the spatial accuracy of 6 linear distributed inverse solutions for EEG source localisation of interictal epileptic discharges: Minimum Norm, Weighted Minimum Norm, Low-Resolution Electromagnetic Tomography (LORETA), Local Autoregressive Average (LAURA), Standardised LORETA, and Exact LORETA. Spatial accuracy was assessed clinically by retrospectively comparing the maximum source of averaged interictal discharges to the resected brain area in 30 patients with successful epilepsy surgery, based on 204-channel EEG. Additionally, localisation errors of the inverse solutions were assessed in computer simulations, with different levels of noise added to the signal in both sensor space and source space. In the clinical evaluations, the source maximum was located inside the resected brain area in 50–57% of patients when using LORETA or LAURA, while all other inverse solutions performed significantly worse (17–30%; corrected p < 0.01). In the simulation studies, when noise levels exceeded 10%, LORETA and LAURA had substantially smaller localisation errors than the other inverse solutions. LORETA and LAURA provided the highest spatial accuracy both in clinical and simulated data, alongside with a comparably high robustness towards noise. Among the different linear inverse solution algorithms tested, LORETA and LAURA might be preferred for interictal EEG source localisation. [ABSTRACT FROM AUTHOR]

In this article, the minimum norm partial eigenstructure assignment problem (MNPESAP) is considered in a symmetric high‐order system using feedback control law with the highest‐order derivative term. Two new orthogonality relations are constructed using the system matrices and undetermined feedback gains. The parametric expressions of the feedback controller and the necessary and sufficient condition for solving the partial eigenstructure assignment problem are derived. The Sylvester matrix equations and gradient formula are presented for solving MNPESAP. An algorithm is proposed to obtain the minimum norm solutions of feedback gains using gradient‐based optimization method. Numerical examples are provided to verify the effectiveness of given results. [ABSTRACT FROM AUTHOR]

The partial eigenstructure assignment problem is to replace a small number of eigenvalues and eigenvectors of system while the remaining eigenvalues and corresponding eigenvectors are kept unchanged. The paper studies partial eigenstructure assignment problem for vibration system via acceleration–velocity feedback control. Two new orthogonality relations are established to construct a feedback control law which can solve the proposed partial eigenstructure assignment problem. The solvability condition and parametric expressions of feedback gains are derived for solving this problem. The minimum norm partial eigenstructure assignment problem is further considered by using gradient‐based optimization method. An optimization algorithm is proposed for solving the minimum norm partial eigenstructure assignment problem. Numerical examples are provided to show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

The Hermite–Birkhoff interpolation problem for a nonlinear operator in the Hilbert space is considered. For this problem, the theorem on the interpolation polynomial of minimum norm generated by a scalar product with a Gaussian measure is proved. It is shown that such interpolant is unique. [ABSTRACT FROM AUTHOR]

The Hermite–Birkhoff interpolation problem for a nonlinear operator in the Hilbert space is considered. For this problem, the theorem on the interpolation polynomial of minimum norm generated by a scalar product with a Gaussian measure is proved. Such interpolant is shown to be unique. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we study a Bishop–Phelps–Bollobás type property called the property L o , o of a pair of Banach spaces. Getting motivated by this, we introduce the notion of Approximate minimizing property (AMp) of a pair of Banach spaces and characterize finite dimensionality of Banach spaces with respect to this property. We further introduce the notion of approximate minimum norm attainment set of a bounded linear operator and characterize the AMp with the help of Hausdorff convergence of the sequence of approximate minimum norm attainment sets of bounded linear operators. We also investigate sufficient conditions for the holding of some weaker forms of the AMp for a pair of Banach spaces. Finally, we define and study uniform ε -approximation of a bounded linear operator in terms of its minimum norm. [ABSTRACT FROM AUTHOR]

The present study developed a fast MEG source imaging technique based on Fast Vector-based Spatio-Temporal Analysis using a L1-minimum-norm (Fast-VESTAL) and then used the method to obtain the source amplitude images of resting-state magnetoencephalography (MEG) signals for different frequency bands. The Fast-VESTAL technique consists of two steps. First, L1-minimum-norm MEG source images were obtained for the dominant spatial modes of sensor-waveform covariance matrix. Next, accurate source time-courses with millisecond temporal resolution were obtained using an inverse operator constructed from the spatial source images of Step 1. Using simulations, Fast-VESTALs performance was assessed for its 1) ability to localize multiple correlated sources; 2) ability to faithfully recover source time-courses; 3) robustness to different SNR conditions including SNR with negative dB levels; 4) capability to handle correlated brain noise; and 5) statistical maps of MEG source images. An objective pre-whitening method was also developed and integrated with Fast-VESTAL to remove correlated brain noise. Fast-VESTALs performance was then examined in the analysis of human median-nerve MEG responses. The results demonstrated that this method easily distinguished sources in the entire somatosensory network. Next, Fast-VESTAL was applied to obtain the first whole-head MEG source-amplitude images from resting-state signals in 41 healthy control subjects, for all standard frequency bands. Comparisons between resting-state MEG sources images and known neurophysiology were provided. Additionally, in simulations and cases with MEG human responses, the results obtained from using conventional beamformer technique were compared with those from Fast-VESTAL, which highlighted the beamformers problems of signal leaking and distorted source time-courses.

Based on Gauss's variational equations (GVEs), the impulsive orbital-element corrections are investigated in orbit transfer problems. Both single impulse and multiple impulses are considered for the first-order and second-order GVEs. For the single impulse, a nonlinear least-squares iteration method for the minimum orbit error is provided to simultaneously solve for the impulse vector and the impulse position. For multiple impulses, a minimum-norm method for the energy cost is proposed to solve the three-impulse and two-impulse corrections for the in-plane and out-of-plane orbital elements, respectively. The impulse positions are analytically derived, and the impulse vectors are obtained by the minimum-norm method. Numerical examples are provided to verify the proposed single-impulse least-squares and multiple-impulse minimum-norm methods. The results show that the nonlinear solutions using the second-order GVEs are more accurate than those using the first-order GVEs. [ABSTRACT FROM AUTHOR]

Signal processing via subspace-based methods require subspace estimates taken from either the eigenvectors of the sample covariance matrix or the principal singular vectors of the received data matrix. The subspaces spanned by the singular vectors or eigenvectors are perturbed away from ground truth due to the additive noise in the received data. The perturbation reduces the accuracy of algorithms that make use of these estimates. A statistically optimal estimate of the unperturbed subspace in terms of the perturbed signal and orthogonal subspaces has been derived and is accurate up to the first-order terms in the additive noise matrix (Vaccaro, 2019). Here, the second-order optimal approximation for the unperturbed subspace is derived and applied to a uniform linear array (ULA) processing model for both full and sparse geometries. The approximation provides little improvement for a full ULA highlighting the importance of first-order terms for a fully sampled geometry. However, for a sparse array, the source estimation performance is much more clearly improved for a low signal-to-noise ratio (SNR) environment with few temporal samples. • Decomposition of received array data matrix provides zeroth-order perturbed subspace basis. • Second-order perturbation analysis increases optimality of noise-free subspace estimation. • Second-order subspace optimality depends on performance of numerical method used. • Estimation error halved employing second-order over first-order statistics for some shift-invariant arrays. [ABSTRACT FROM AUTHOR]

Minimum L1-norm solutions have been used by many investigators to analyze MEG responses because they provide high spatial resolution images. However, conventional minimum L1-norm approaches suffer from instability in spatial construction, and poor smoothness of the reconstructed source time-courses. Activity commonly "jumps" from one grid point to (usually) the neighboring grid points. Equivalently, the time-course of one specific grid point can show substantial "spiky-looking" discontinuity. In the present study, we present a new vector-based spatial-temporal analysis using a L1-minimum-norm (VESTAL). This approach is based on a principle of MEG physics: the magnetic waveforms in sensor-space are linear functions of the source time-courses in the imaging-space. Our computer simulations showed that VESTAL provides good reconstruction of the source amplitude and orientation, with high stability and resolution in both the spatial and temporal domains. "Spiky-looking" discontinuity was not observed in the source time-courses. Importantly, the simulations also showed that VESTAL can resolve sources that are 100% correlated. We then examined the performance of VESTAL in the analysis of human median-nerve MEG responses. The results demonstrated that this method easily distinguishes sources very spatially close to each other, including individual primary somatosensory areas (BA 1, 2, 3b), primary motor area (BA 4), and other regions in the somatosensory system (e.g., BA 5, 7, SII, SMA, and temporal-parietal junction) with high temporal stability and resolution. VESTAL's potential for obtaining information on source extent was also examined.

We study an algorithm to compute minimum norm solution of ill-posed problems in Hilbert spaces and investigate its regularizing properties with discrepancy principle stopping rule. This algorithm results from straightly applying the LSQR method to the main problem before discretizing. In fact, the proposed algorithm obtains a sequence of approximate solutions of the original problem. In order to test the new algorithm, it is implemented to solve system of linear integral equations of the first kind and some examples are given. Moreover, we compare the presented algorithm with the Tikhonov regularization method to compute the least norm solution when there are more than one solution. [ABSTRACT FROM AUTHOR]

Pitch is a perceptual rather than physical phenomenon, important for spoken language use, musical communication, and other aspects of everyday life. Auditory stimuli can be designed to probe the relationship between perception and physiological responses to pitch-evoking stimuli. One technique for measuring physiological responses to pitch-evoking stimuli is the frequency following response (FFR). The FFR is an electroencephalographic (EEG) response to periodic auditory stimuli. The FFR contains nonlinearities not present in the stimuli, including correlates of the amplitude envelope of the stimulus; however, these nonlinearities remain undercharacterized. The FFR is a composite response reflecting multiple neural and peripheral generators, and their contributions to the scalp-recorded FFR vary in ill-understood ways depending on the electrode montage, stimulus, and imaging technique. The FFR is typically assumed to be generated in the auditory brainstem; there is also evidence both for and against a cortical contribution to the FFR. Here a methodology is used to examine the FFR correlates of pitch and the generators of the FFR to stimuli with different pitches. Stimuli were designed to tease apart biological correlates of pitch and amplitude envelope. FFRs were recorded with 256-electrode EEG nets, in contrast to a typical FFR setup which only contains a single active electrode. Structural MRI scans were obtained for each participant to co-register with the electrode locations and constrain a source localization algorithm. The results of this localization shed light on the generating mechanisms of the FFR, including providing evidence for both cortical and subcortical auditory sources. • MRI-constrained EEG analysis confirms cortical and subcortical generators of the FFR. • Low frequencies dominate cortical contribution but higher frequencies emerge also. • Source analysis reveals greater contribution to FFR from auditory relative to control regions. • A novel 10/5 EEG scalp labeling system for ∼ 256 sensors is devised and utilized. [ABSTRACT FROM AUTHOR]

When the number of assets (N) exceeds the number of time periods (T), the sample covariance matrix is singular, and the portfolio optimization problem cannot be solved via traditional mean-variance algebra. In such a case, the Moore–Penrose (MP) generalized inverse becomes handy: In this paper, we critically examine the MP solution of the portfolio optimization problem. Our findings include: i) the MP solution leads to a portfolio of “pseudo-riskfree composite assets”; ii) it is orthogonal to principal components, iii) most importantly, it is poorly diversified. We illustrate our findings using equity market data. [ABSTRACT FROM AUTHOR]

Aiming to accelerate convergence speed and reduce steady-state misalignment of adaptive filter, a new data-reusing algorithm is proposed. Different from conventional affine projection algorithm (APA) based on minimum disturbance principle (MDP), the proposed algorithm obtains its cost function based on a convex combination of the minimum norm principle (MNP) and the MDP. Weight factor (named as mixing parameter) used in the combination determines the approach for updating. The proposed algorithm has a performance similar to the APA when the mixing parameter closes to 0 and yields results to the data-reusing algorithm based on the MNP if the mixing parameter closes to 1. By minimizing mean-square deviation, the variable mixing parameter has a large value at initial stage and gradually decreases as iteration number increases. At the initial stage, the proposed algorithm achieves fast convergence since the MNP plays a leading role. At the steady-state, the proposed algorithm obtains a low misalignment since the MDP gives a major impact and the updated results have minimum disturbance from the previous ones. At the transition stage, the proposed algorithm is a combination of the APA and the MNP-based data-reusing algorithm. Simulation results show that the proposed algorithm exhibits faster convergence rate and lower steady-state misalignment than some other derivatives of the APA without significantly increasing computational complexity. [ABSTRACT FROM AUTHOR]

Objective: This paper presents the development of a fast and robust method which can be applied to multichannel physiologic signals for the purpose of either removing a selected interfering signal or separating signals that arise from temporally correlated and spatially distributed signals such as maternal or fetal cardiac waveform recordings. Methods: Projection operators based upon both the weighted and un-weighted minimum norm equations are presented. The weighted formulation uses models based on signal covariance and the un-weighted formulation requires that a statistical model be built using time-locked averaging. Results: We present examples that demonstrate the utility of our projection operators when applied to maternal and fetal magneto-cardiograms. In addition, we demonstrate the ability to separate fetal breathing signals from both maternal and fetal cardiac signals. Conclusion: The method is effective, robust, fast, and does not require significant input from a user. Significance: Although we demonstrate the utility of our projection operators applied to biomagnetic signals, the method can easily be adapted to other applications were the goal is to either separate or suppress selected signal components. [ABSTRACT FROM PUBLISHER]