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This paper proposes a new algorithm, named Householder Dice (HD), for simulating dynamics on dense random matrix ensembles with rotational invariance. Examples include the Gaussian ensemble, the Haar-distributed random orthogonal ensemble, and their complex-valued counterparts. A “direct” approach to the simulation, where one first generates a dense $n \times n$ matrix from the ensemble, requires at least $\mathcal {O}(n^{2})$ resource in space and time. The HD algorithm overcomes this $\mathcal {O}(n^{2})$ bottleneck by using the principle of deferred decisions: rather than fixing the entire random matrix in advance, it lets the randomness unfold with the dynamics. At the heart of this matrix-free algorithm is an adaptive and recursive construction of (random) Householder reflectors. These orthogonal transformations exploit the group symmetry of the matrix ensembles, while simultaneously maintaining the statistical correlations induced by the dynamics. The memory and computation costs of the HD algorithm are $\mathcal {O}(nT)$ and $\mathcal {O}(nT^{2})$ , respectively, with $T$ being the number of iterations. When $T \ll n$ , which is nearly always the case in practice, the new algorithm leads to significant reductions in runtime and memory footprint. Numerical results demonstrate the promise of the HD algorithm as a new computational tool in the study of high-dimensional random systems.

This work provides an efficient sampling method for the covariance matrix adaptation evolution strategy (CMA-ES) in large-scale settings. In contract to the Gaussian sampling in CMA-ES, the proposed method generates mutation vectors from a mixture model, which facilitates exploiting the rich variable correlations of the problem landscape within a limited time budget. We analyze the probability distribution of this mixture model and show that it approximates the Gaussian distribution of CMA-ES with a controllable accuracy. We use this sampling method, coupled with a novel method for mutation strength adaptation, to formulate the mixture model based evolution strategy (MMES) -- a CMA-ES variant for large-scale optimization. The numerical simulations show that, while significantly reducing the time complexity of CMA-ES, MMES preserves the rotational invariance, is scalable to high dimensional problems, and is competitive against the state-of-the-arts in performing global optimization.

In the present paper, the first three modal frequencies obtained through recorded vibration signal of a steel truss bridge is investigated at three different vehicular speeds. The denoising and extraction of modal frequencies from vibration response signals of steel truss bridge is performed using Hilbert transform (HT) in combination with high-frequency resolution enhancing techniques. The modal frequency extracting techniques applied includes Fast Fourier transform (FFT), multiple signal classification (MUSIC), and estimation of signal parameters by rotational invariance technique (ESPRIT). The comparisons of the outcomes of HT-FFT, HT-root-MUSIC, and HT- ESPRIT are computed. It is observed that HT-FFT computed results with the low resolution which hindered in obtaining distinct modal frequencies while HT-MUSIC and HT-ESPRIT achieved the most denoised, robust and reliable outcomes. The HT-ESPRIT outperforms HT-MUSIC in the elimination of unwanted noise. Further, the application of the sliding window HT-ESPRIT method clearly shows the variation of modal frequencies with the change in vehicular speeds. The first three analytical modal frequencies of 4.56 Hz, 10.44 Hz and 16.66 Hz frequencies are compared with the experimental frequencies obtained through vibrations at 10 km/h, 20 km/h and 30 km/h vehicular speeds, respectively. The joints (also denoted as nodes) 6, 7, and 8 exhibited irregular behaviour with no or minimum frequency peaks due to increased flexibility of member at these locations.

The Zernike and pseudo-Zernike moments (ZMs/PZMs) have been found useful for a variety of applications requiring feature extraction due to their favorable properties, such as low information redundancy, rotational invariance, higher noise resilience and extendibility to the color space. In this paper, we propose an approach for color face recognition based on Zernike/pseudo-Zernike quaternion moment vector (QMV) features and a novel normalized-discriminant hybrid color space. The proposed XnSBr color space is composed by taking Xn from the normalized-XYZ, S from HSV and Br from the discriminant RGB-r color spaces to capture the features efficiently. In addition, we propose the use of quaternion vector distance (QVD) similarity measure for the QMV features in order to enhance the recognition accuracy. The exhaustive comparative performance analyses with the state-of-the-art approaches in the different color spaces demonstrate the superiority of the proposed approach in terms of accuracy and speed.

Due to their good rotational invariance and stability, image continuous orthogonal moments are intensively applied in rotationally invariant recognition and image processing. However, most moments produce numerical instability, which impacts the image reconstruction and recognition performance. In this paper, a new set of invariant continuous orthogonal moments, polar harmonic Fourier moments (PHFMs), free of numerical instability is designed. The radial basis functions (RBFs) of the PHFMs are much simpler than those of the Chebyshev-Fourier moments (CHFMs), orthogonal Fourier-Mellin moments (OFMMs), Zernike moments (ZMs), and pseudo-Zernike moments (PZMs). For the same degree, the RBFs of the PHFMs have more zeros and are more evenly distributed than those of the ZMs and PZMs. Therefore, PHFMs do not suffer from information suppression problem; hence, the image description ability of the PHFMs is superior to that of the ZMs and PZMs. Moreover, the RBFs of the PHFMs are always less than or equal to 1.0 near the unit disk center, whereas those of the OFMMs, PZMs, CHFMs, and radial harmonic Fourier moments (RHFMs) are infinite (implying numerical instability). This indicates that PHFMs can outperform these moments in image reconstruction tasks. We theoretically and experimentally demonstrate that PHFMs outperform the above moments in reconstructing images and recognizing rotationally invariant objects considering noise and various attacks. This paper also details the significance of the PHFM phase in image reconstruction, angle estimation using PHFMs, and the accurate moment selection of the PHFMs.

Multiple-input multiple-output (MIMO) is a technical hotspot in physical layer with numerous applications in wireless communications, radars, sonars, and well beyond. In this paper, we focus on the multi-dimensional angle estimation problem in a bistatic electromagnetic vector sensors (EMVS) MIMO system. Namely, we need to simultaneously estimate two-dimensional (2D) direction-of-arrival (DOA), 2D direction-of-departure (DOD), 2D receive polarization angle (RPA) and 2D transmit polarization angle (TPA). To tackle this issue, a parallel factor (PARAFAC) analysis-based estimator is proposed. Firstly, a third-order PARAFAC analysis data model is established, which can efficiently exploit the tensor structure of the array measurement. After performing PARAFAC decomposition on the tensor measurement, the factor matrices are achieved. By combining the estimation method of signal parameters via rotational invariance technique (ESPRIT) with the vector cross-product method, joint estimates of 2D-DOD, 2D-DOA, 2D-TPA and 2D-RPA are obtained without further pairing calculation. Compared with the state-of-the-art ESPRIT-Like approach, the proposed method can achieve better performance by enforcing the third-order structure information, and it is suitable for arbitrary array manifolds. Theoretical analyses are given and numerical results corroborate our analysis.

This paper presents a cumulant-based algorithm for near-field noncircular sources localization with a symmetric uniform linear array. It first constructs three extended matrices. Then, based on the rotational invariance property in extended cumulant-domain signal subspace, coarse direction-of-arrival (DOA) estimates are obtained. With the course results used as reference, the algorithm is able to disambiguate the cyclic phase ambiguities when the equivalent sub-array spacing exceeds a half wavelength. Thus, higher precision DOA estimates can be obtained. Finally, with the estimated DOAs, only one-dimensional searching is needed to obtain the range estimates via rank-reduction algorithm. The proposed algorithm avoids two-dimensional searching and parameters pairing. In addition, compared with the existing near-field noncircular sources localization algorithm, the significant characteristic of the proposed algorithm is that it exploits cumulant and the noncircularity of signal to achieve extended steering vector. Cumulant is insensitive to Gaussian (white or color) noise. Consequently, the proposed one provides DOA estimates with improved precision especially at low signal-to-noise ratios. Furthermore, it doubles the number of detectable sources. Total least square ESPRIT algorithm is exploited to yield search free estimates of near-field bearing parameters. Computer simulations are carried out to demonstrate the superiority of the proposed algorithm.

Huygens metasurface, composed of electric and magnetic dipoles, can fully control the transmission and reflection coefficient in theory. In this paper, a multi-phase hologram utilizing Huygens metasurface is presented in microwave regime. Here, we focus on the achievement of holographic rotation around the origin of Cartesian coordinates and the center of images individually. The spatial rotation operations are realized with calculated phase distribution based on time-shifting operations and rotational invariance of Fourier transform. Our designs expand the route to realize more powerful manipulations of electromagnetic (EM) wave propagation for flexible and continuous control of holographic images.

Distributed sources can be regarded as an assembly of point sources within a spatial distribution. In this paper, we explore the estimation of the two-dimensional incoherently distributed sources using double L-shape arrays. The rotational invariance properties of the nominal elevation and nominal elevation are firstly obtained by taking first-order Taylor series expansions with regard to the generalized steering vectors of two pairs of parallel subarrays. The rotation operators can be solved based on signal subspace. Then the nominal elevation and nominal elevation can be obtained from parameters matching method. Estimation of direction of arrival can be used in multi-source scenario and needn't peak-finding search. Lastly the angular spreads can be solved through two-dimensional Capon search based on nominal angles. The simulation experiments show that the proposed method has good performance on the estimation of two-dimensional incoherently distributed sources. Investigating different experimental conditions, sources with different angular spreads, simulations are conducted to validate better estimation accuracy of the proposed method.

A microscopic model analysis of the magnetic dipole (M1) properties of Pu-239 nucleus, which is a fissile material not only used in nuclear weapons but also used in some nuclear reactors as a source of energy, has been performed. The microscopic formalism used in the study is based on the Quasiparticle Phonon Nuclear Model (QPNM) and includes an axially symmetric Woods-Saxon potential as a mean field, a spin-spin residual interaction as well as the symmetry-restoring forces for the rotational invariance of the Hamiltonian. The investigations have been carried out in two steps. Firstly, the theoretical value of the ground-state magnetic moment and quenching spin gyromagnetic factor have been determined and it has been found that the predicted magnetic moment show a good agreement with the experimental data. Secondly, the calculations of M1 transitions from ground- to excited-states have been carried out in the energy range 2-4 MeV. A satisfactorily good agreement is obtained from the comparison of the theoretical results with the experimental data for 2-2.5 MeV. (C) 2019 Elsevier B.V. All rights reserved.

We construct a set of special complex-valued integral images and an algorithm that allows to calculate Zernike moments fast, namely in constant time. The technique is suitable for dense detection procedures, where the image is scanned by a sliding window at multiple scales, and where rotational invariance is required at the level of each window. We assume no preliminary image segmentation. Owing to the proposed integral images and binomial expansions, the extraction of each feature does not depend on the number of pixels in the window and thereby is an $O(1)$ calculation. We analyze algorithmic properties of the proposition, such as: number of needed integral images, complex-conjugacy of integral images, number of operations involved in feature extraction, speed-up possibilities based on lookup tables. We also point out connections between Zernike and orthogonal Fourier–Mellin moments in the context of computations backed with integral images. Finally, we demonstrate three examples of detection tasks of varying difficulty. Detectors are trained on the proposed features by the RealBoost algorithm. When learning, the classifiers get acquainted only with examples of target objects in their upright position or rotated within a limited range. At the testing stage, generalization onto the full $360^\circ$ angle takes place automatically.

The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail., 21 pages, 1 figure

This work analyses the performance-complexity tradeoff for different direction of arrival (DoA) estimation techniques. Such tradeoff is investigated taking into account uniform linear array structures. Several DoA estimation techniques have been compared, namely the conventional Delay-and-Sum (DS), Minimum Variance Distortionless Response (MVDR), Multiple Signal Classifier (MUSIC) subspace, Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Unitary-ESPRIT and Fourier Transform method (FT-DoA). The analytical formulation of each estimation technique as well the comparative numerical results are discussed focused on the estimation accuracy versus complexity tradeoff. The present study reveals the behavior of seven techniques, demonstrating promising ones for current and future location applications involving DoA estimation, especially for 5G massive MIMO systems., 35 pages, 10 figures, 4 tables

Light-field cameras capture sub-views from multiple perspectives simultaneously, with possibly reflectance variations that can be used to augment material recognition in remote sensing, autonomous driving, etc. Existing approaches for light-field based material recognition suffer from the entanglement between angular and spatial domains, leading to inefficient training which in turn limits their performances. In this paper, we propose an approach that achieves decoupling of angular and spatial information by establishing correspondences in the angular domain, then employs regularization to enforce a rotational invariance. As opposed to relying on the Lambertian surface assumption, we align the angular domain by estimating sub-pixel displacements using the Fourier transform. The network takes sparse inputs, i.e. sub-views along particular directions, to gain structural information about the angular domain. A novel regularization technique further improves generalization by weight sharing and max-pooling among different directions. The proposed approach outperforms any previously reported method on multiple datasets. The accuracy gain over 2D images is improved by a factor of 1.5. Ablation studies are conducted to demonstrate the significance of each component.

The performance of direction-of-arrival (DOA) estimation for sparse arrays applied to the distributed source is worse than that applied to the point source model. In this paper, we introduce the coprime array with a large array aperture into the DOA estimation algorithm of the exponential-type coherent distributed source. In particular, we focus on the fourth-order cumulant (FOC) of the received signal which can provide more useful information when the signal is non-Gaussian than when it is Gaussian. The proposed algorithm extends the array aperture by combining the sparsity of array space domain with the fourth-order cumulant characteristics of signals, which improves the estimation accuracy and degree of freedom (DOF). Firstly, the signal-received model of the sparse array is established, and the fourth-order cumulant matrix of the received signal of the sparse array is calculated based on the characteristics of distributed sources, which extend the array aperture. Then, the virtual array is constructed by the sum aggregate of physical array elements, and the position set of its maximum continuous part array element is obtained. Finally, the center DOA estimation of the distributed source is realized by the subspace method. The accuracy and DOF of the proposed algorithm are higher than those of the distributed signal parameter estimator (DSPE) algorithm and least-squares estimation signal parameters via rotational invariance techniques (LS-ESPRIT) algorithm when the array elements are the same. Complexity analysis and numerical simulations are provided to demonstrate the superiority of the proposed method.

This paper proposes a novel algorithm for Two-Dimensional (2D) central Direction-of-Arrival (DOA) estimation of incoherently distributed sources. In particular, an orthogonal array structure consisting of two Non-uniform Linear Arrays (NLAs) is considered. Based on first-order Taylor series approximation, the Generalized Array Manifold (GAM) model can first be established to separate the central DOAs from the original array manifold. Then, the Hadamard rotational invariance relationships inside the GAMs of two NLAs are identified. With the aid of such relationships, the central elevation and azimuth DOAs can be estimated through a search-free polynomial rooting method. Additionally, a simple parameter pairing of the estimated 2D angular parameters is also accomplished via the Hadamard rotational invariance relationship inside the GAM of the whole array. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao lower bound. The simulation results show that the proposed algorithm can achieve a remarkably higher precision at less complexity increment compared with the existing low-complexity methods, which benefits from the larger array aperture of the NLAs. Moreover, it requires no priori information about the angular distributed function. Keywords: Array signal processing, Cramer-Rao lower bound, Direction-of-Arrival (DOA) estimation, Hadamard rotational invariance, Incoherently distributed sources, Non-uniform orthogonal array

In modern validity theory, a major concern is the construct validity of a test, which is commonly assessed through confirmatory or exploratory factor analysis. In the framework of Bayesian exploratory Multidimensional Item Response Theory (MIRT) models, we discuss two methods aimed at investigating the underlying structure of a test, in order to verify if the latent model adheres to a chosen simple factorial structure. This purpose is achieved without imposing hard constraints on the discrimination parameter matrix to address the rotational indeterminacy. The first approach prescribes a 2-step procedure. The parameter estimates are obtained through an unconstrained MCMC sampler. The simple structure is, then, inspected with a post-processing step based on the Consensus Simple Target Rotation technique. In the second approach, both rotational invariance and simple structure retrieval are addressed within the MCMC sampling scheme, by introducing a sparsity-inducing prior on the discrimination parameters. Through simulation as well as real-world studies, we demonstrate that the proposed methods are able to correctly infer the underlying sparse structure and to retrieve interpretable solutions.

A computer aided detection scheme for the neural tube defect of spina bifida is proposed. Features from Zernike moments of fetal skull regions viewed by ultrasound are utilized in SVM classification. Rotational invariance of magnitudes of Zernike moments and their easy normalization with respect to translation and scale make them attractive for image and shape description. In particular, they are perfect candidates for classifying shapes of fetal skulls that possess markers of spina bifida. The automated detection system may act in decision support to help specialists avoid false negatives. Problems of rarity are handled with combinations of oversampling and undersampling. A variant of the synthetic minority oversampling technique (SMOTE) and random undersampling (RU) have been applied on training data. Experiments show the trade-off in various performance indicators depending on different sampling choices. The average values of 0.6276 F-measure and 0.6306 GMRP are achieved on non-sampled (original) test sets when training is performed using sampled data after 400% borderline-SMOTE followed by 50% RU with respective accuracy and specificity realizations of 94% and 98%. © 2018 Elsevier Ltd, 2007K120610 TÜTF-GOKAEK 2014/85, 09/07 Firat University Scientific Research Projects Management Unit: BAP 10A01D5, BAP 14A01P2, My thanks are for Füsun Varol from Trakya University and İbrahim Kalelioğlu from Istanbul University, especially for providing ultrasound data. Ethical approval was provided by the Scientific Research Ethical Committee of the Medical Faculty of Trakya University on 30/04/2014 with protocol code TÜTF-GOKAEK 2014/85 and decision reference 09/07. I also thank Fikret Gürgen and Lale Akarun from Boğaziçi University and the Computer Engineering Department of the Faculty of Engineering of Bülent Ecevit University. The funding resources are the Scientific Research Projects fund ( BAP 10A01D5 , BAP 14A01P2 ) of Boğaziçi University and the Turkish Ministry of Development under the TAM Project, number 2007K120610 .

High-resolution direction of arrival (DOA) estimation is a critical issue for mainbeam multitarget tracking in ground-based or airborne early warning radar system. A beam-Doppler unitary ESPRIT (BD-UESPRIT) algorithm is proposed to deal with this problem. Firstly, multiple snapshots without spatial aperture loss are obtained by using the technique of time-smoothing. Then the conjugate centrosymmetric discrete Fourier transform (DFT) matrix is used to transform the extracted data into beam-Doppler domain. Finally, the rotational invariance property of the space-time beam is exploited to estimate DOA of the target. The DOA estimation accuracy is improved greatly because the proposed algorithm takes full advantage of temporal information of the signal. Furthermore, the computational complexity of the presented algorithm is reduced dramatically, because the degree of freedom after beam transformation is very small and most of the operations are implemented in real-number domain. Numerical examples are given to verify the effectiveness of the proposed algorithm.

By applying the covariation statistics, this paper generalizes the non-circularity to the scenario of complex isotropic symmetric alpha-stable ( $$ S\alpha S $$ ) signals. The matrices based on fractional lower order moments for the extended sensor array outputs, which have been shown to have similar forms to the covariance matrix for the Gaussian distributed signals and noise, are formulated for the case of complex $$ S\alpha S $$ signals and noise. Therefore, the similarity transformation based estimating signal parameter via rotational invariance techniques can be applied to these matrices resulting to the improved direction of arrival estimates for noncircular signals in the presence of impulsive noise environments. The robustness of our proposed algorithm, especially for low generalized signal to noise ratio situations, and for quite highly impulsive noise environments is demonstrated by Monte-Carlo simulations.

In this paper, the problem of two-dimensional (2-D) direction-of-arrival (DOA) estimation for incoherently distributed (ID) noncircular sources is addressed. A low-complexity estimator with automatic pairing in the three-parallel uniform linear arrays (ULAs) is proposed. First, the signal non-circularity is applied to establish an extended generalized array manifold (GAM) model based on one-order Taylor series approximation. Resorting to such model, the generalized rotational invariance relationships are identified among the extended GAM matrices of the three ULAs. Thereafter, a modified propagator method is utilized to estimate the central elevation and azimuth DOAs. Without any spectrum searching, estimation or eigenvalue decomposition of the sample covariance matrix, the proposed approach is capable of considerably reducing the calculation cost in comparison with the existing methods. In addition, it can automatically pair the estimated central azimuth and central elevation DOAs. We also derive the Cramer-Rao lower bound regarding the 2-D DOA estimation of the ID noncircular source and conduct the computational complexity analysis. Numerical results demonstrate that the proposed method achieves better estimation performance than the existing methods. Furthermore, it can be applied in the multi-source scenario where different sources may have different angular distribution shapes.

A restoration method of a broken symmetry which allows self-consistent determination of the separable effective restoration forces is now adapted to odd-mass nuclei in order to restore violated rotational invariance (RI-) of the Quasiparticle Phonon Nuclear Model (QPNM) Hamiltonian. Because of the self consistency of the method, these effective forces contain no arbitrary parameters. Within RI-QPNM, the properties of the low-lying magnetic dipole excitations in odd-mass deformed Th229-233 and U233-239 nuclei have been investigated for the first time. It has been shown that computed fragmentation of the M1 strengths below 4 MeV in these nuclei is much stronger than that in neighboring doubly even Th228-232 and U232-238 nuclei. For U-235 the summed M1 strength in the energy range 1.5-2.8 MeV is in agreement with the relevant experimental data where the missing strength was extracted by means of a fluctuation analysis. (C) 2016 Elsevier B.V. All rights reserved.

Earlier work showed how a nucleon optical model wave function could be defined as a projection of a many-nucleon scattering state within a translationally invariant second quantized many-body theory. In this paper, an optical potential operator that generates this optical model wave function is defined through a particular off-shell extension of the elastic transition operator. The theory is expressed explicitly in terms of the many-nucleon Hamiltonian in a mixed representation in which localized target nucleus states feature. No reference to a mean-field concept is involved in the definition. It is shown that the resulting optical model operator satisfies the requirements of rotational invariance and translational invariance and has standard behavior under the time-reversal transformation. The contributions to the optical potential from two different exchange mechanisms are expressed in terms of an effective Hamiltonian involving a nucleon-number-conserving one-body interaction. In the weak-binding limit, the method reduces to a version of Feshbach's projection operator formulation of the optical potential with a truncated nucleon-nucleon potential including exchange terms and recoil corrections. Definitions of the nucleon single-particle Green's function and the corresponding Dyson self-energy modified by corrections for translational invariance are presented, and different definitions of the optical potential operator are compared.

We study the qualitative properties of ground states of the time-independent magnetic semilinear Schrödinger equation −(∇+iA) 2 u+u=, SCOPUS: ar.j, info:eu-repo/semantics/published

In this paper we analyze theoretical properties of bi-objective convex-quadratic problems. We give a complete description of their Pareto set and prove the convexity of their Pareto front. We show that the Pareto set is a line segment when both Hessian matrices are proportional. We then propose a novel set of convex-quadratic test problems, describe their theoretical properties and the algorithm abilities required by those test problems. This includes in particular testing the sensitivity with respect to separability, ill-conditioned problems, rotational invariance, and whether the Pareto set is aligned with the coordinate axis., 12 pages

Exact diagonalization and other numerical studies of quantum spin systems are notoriously limited by the exponential growth of the Hilbert space dimension with system size. A common and well-known practice to reduce this increasing computational effort is to take advantage of the translational symmetry $C_N$ in periodic systems. This represents a rather simple yet elegant application of the group theoretical symmetry projection operator technique. For isotropic exchange interactions, the spin-rotational symmetry SU(2) can be used, where the Hamiltonian matrix is block-structured according to the total spin- and magnetization quantum numbers. Rewriting the Heisenberg Hamiltonian in terms of irreducible tensor operators allows for an efficient and highly parallelizable implementation to calculate its matrix elements recursively in the spin-coupling basis. When combining both $C_N$ and SU(2), mathematically, the symmetry projection technique leads to ready-to-use formulas. However, the evaluation of these formulas is very demanding in both computation time and memory consumption, problems which are said to outweigh the benefits of the symmetry reduced matrix shape. We show a way to minimize the computational effort for selected systems and present the largest numerically accessible cases., 7 pages, 5 figures

In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this approach that embeds rotational invariance of the stress-stretch constitutive relation in the GPR representation. This approach requires fewer training examples and achieves higher accuracy while maintaining invariance to rotations exactly. Finally, we consider an approach that recovers the strain-energy density function and derives the stress tensor from this potential. Although the error of this model for predicting the stress tensor is higher, the strain-energy density is recovered with high accuracy from limited training data. The approaches presented here are examples of physics-informed machine learning. They go beyond purely data-driven approaches by embedding the physical system constraints directly into the Gaussian process representation of materials models.

We revise formal and numerical aspects of collinear and noncollinear density functional theory (DFT) in the context of a two-component self-consistent treatment of spin-orbit coupling (SOC). While the extension of the standard one-component theory to a noncollinear magnetization is formally well-defined within the local density approximation, and therefore results in a numerically stable theory, this is not the case within the generalized gradient approximation (GGA). Previously reported formulations of noncollinear DFT based on GGA exchange-correlation potentials have several limitations: (i) they fail at reducing (either formally or numerically) to the proper collinear limit (i.e., when the magnetization is parallel or antiparallel to the z axis everywhere in space); (ii) they fail at ensuring a quantitative rotational invariance of the total energy and even a qualitative rotational invariance of the spatial distribution of the magnetization when a SOC operator is included in the Hamiltonian; (iii) they are numerically very unstable in regions of small magnetization. All of the above-mentioned problems are here shown (both formally and through test examples) to be solved by using instead a new formulation of noncollinear DFT for GGA functionals, which we call the "signed canonical" theory, as combined with an effective screening algorithm for unstable terms of the exchange-correlation potential in regions of small magnetization. All methods are implemented in the CRYSTAL program and tests are performed on simple molecules to compare the different formulations of noncollinear DFT.

The self-similarity inspired local descriptor is proposed for non-rigid multi-modal registration.The Zernike moments is introduced into the proposed method to explore rotational self-similarity.The effective computation of self-similarity based both intensities and edge/texture features of the multi-modal images is utilized in the proposed method.The proposed method can achieve higher registration accuracy than the other state-of-the-art image representation based registration methods. Non-rigid multi-modal image registration plays an important role in medical image analysis. It remains a challenging problem due to the significant intensity distortion and the non-rigid transformation between images. Existing registration methods based on the information theoretic measures and image representations cannot address this problem effectively. In this paper, we have proposed a novel self-similarity inspired local descriptor to determine the similarity metrics, a key component in image registration. The self-similarity is determined based on the Zernike moments of image patches in a local neighborhood, and it is utilized to generate the local descriptor. The Euclidean distance between the local descriptors computed in the reference and moving images is used as the similarity metrics. Distinctively, the proposed local descriptor can provide an effective representation of complicated image features due to its robustness to noise and rotational invariance, which provides the proposed method with good registration performance. Extensive experiments on both simulated and real multi-modal image datasets demonstrate that the proposed method has higher registration accuracy appreciated by the target registration error (TRE) than the state-of-the-art registration methods based on the normalized mutual information (NMI), the sum of squared differences on entropy images (ESSD), the Weber local descriptor (WLD) and the modality independent neighborhood descriptor (MIND).

A novel kernel-based method is proposed for fast, highly accurate and numerically stable computations of polar harmonic transforms (PHT) in polar coordinates. Euler formula is used to derive a novel trigonometric formula where the later one is used in the kernel generation. The simplified radial and angular kernels are used in efficient computation PHTs. The proposed method removes the numerical approximation errors involved in conventional methods and provides highly accurate PHTs coefficients which results in highly improved image reconstruction capabilities. Numerical experiments are performed where the results are compared with those of the recent existing methods. In addition to the tremendous reduction in computational times, the obtained results of the proposed method clearly show a significant improvement in rotational invariance.

Optimized kernels for approximating first order spatial derivatives in the regularized Perona–Malik diffusion filter reveal an excellent degree of rotational invariance but produce small checkerboard artifacts in the processed image. In this work, our focus is to reduce these checkerboard artifacts, without a compromise in rotational invariance. To achieve the same, we propose a new 5 × 5 stencil scheme based on generalized finite difference idea. The free parameter in the proposed scheme can be set to recover various well-known schemes. Based on the numerical experiments, we suggest a value of the parameter to have less checkerboard artifacts. We also prove the consistency and the stability of the proposed scheme. A pre-smoothing with 3 × 3 Gaussian mask at every iteration step further improves the quality of the processed image. Simulation results show that the hybrid scheme obtained with such a pre-smoothing is more efficient in computational cost.

AMP and VAMP are two different algorithms that solve high-dimensional standard linear regression problems effectively and efficiently. In previous studies, they were long observed to have identical fixed points in their state evolutions (SEs), however, a formal justification is still missing. This issue is addressed in the paper. Instead of looking directly into the problem, we consider a scope more ambitious which puts aside all assumptions underlying the proven SEs. We then show that: 1) Having the spectrum of a Marchenko-Pastur law is a necessary and sufficient condition for the AMP-style and VAMP-style SEs to share an identical fixed point; 2) As the zero-mean i.i.d. Gaussian ensemble have a Marchenko-Pastur spectrum and satisfies all conditions required by the proven AMP SE and VAMP SE, this particular ensemble is the first example of having an identical fixed point. After that, we conjecture the proven VAMP SE might be extended to cover ensembles that break the right rotational invariance, among which the i.i.d. zero-mean sub-Gaussian ensemble could be a second example to yield identical fixed points. This conjecture is supported by experiments from wireless communications and compressive sampling.

In a model of physics taking place on a discrete set of points that approximates Minkowski space, one might perhaps expect there to be an empirically identifiable preferred frame. However, the work of Dowker, Bombelli, Henson, and Sorkin might be taken to suggest that random sprinklings of points in Minkowski space define a discrete model that is provably Poincar\'e invariant in a natural sense. We examine this possibility here. We argue that a genuinely Poincar\'e invariant model requires a probability distribution on sprinklable sets -- Poincar\'e orbits of sprinklings -- rather than individual sprinklings. The corresponding $\sigma$-algebra contains only sets of measure zero or one. This makes testing the hypothesis of discrete Poincar\'e invariance problematic, since any local violation of Poincar\'e invariance, however gross and large scale, is possible, and cannot be said to be improbable. We also note that the Bombelli-Henson-Sorkin argument, which rules out constructions of preferred timelike directions for typical sprinklings, is not sufficient to establish full Lorentz invariance. For example, once a pair of timelike separated points is fixed, a preferred spacelike direction {\it can} be defined for a typical sprinkling, breaking the remaining rotational invariance., Comment: Extended discussion in response to comments. Small number of further typos fixed. Accepted version

We develop a formalism for calculating the distribution of the axial quadrupole operator in the laboratory frame within the rotationally invariant framework of the configuration-interaction shell model. The calculation is carried out using a finite-temperature auxiliary-field quantum Monte Carlo method. We apply this formalism to isotope chains of even-mass samarium and neodymium nuclei, and show that the quadrupole distribution provides a model-independent signature of nuclear deformation. Two technical advances are described that greatly facilitate the calculations. The first is to exploit the rotational invariance of the underlying Hamiltonian to reduce the statistical fluctuations in the Monte Carlo calculations. The second is to determine quadruple invariants from the distribution of the axial quadrupole operator. This allows us to extract effective values of the intrinsic quadrupole shape parameters without invoking an intrinsic frame or a mean-field approximation., Comment: 12 pages, 8 figures, and 1 table. Added two references; minor changes in the text

We explore the estimation of a two-dimensional (2D) nonsymmetric coherently distributed (CD) source using L-shaped arrays. Compared with a symmetric source, the modeling and estimation of a nonsymmetric source are more practical. A nonsymmetric CD source is established through modeling the deterministic angular signal distribution function as a summation of Gaussian probability density functions. Parameter estimation of the nonsymmetric distributed source is proposed under an expectation maximization (EM) framework. The proposed EM iterative calculation contains three steps in each cycle. Firstly, the nominal azimuth angles and nominal elevation angles of Gaussian components in the nonsymmetric source are obtained from the relationship of rotational invariance matrices. Then, angular spreads can be solved through one-dimensional (1D) searching based on nominal angles. Finally, the powers of Gaussian components are obtained by solving least-squares estimators. Simulations are conducted to verify the effectiveness of the nonsymmetric CD model and estimation technique.

Purpose Lipid signals measured by 1H MR spectroscopy cannot be adequately quantified by common fitting routines like VARPRO or AMARES, if lipid spectra are distorted by irregular spatial and temporal inhomogeneities of the static magnetic field during readout. A fully automatic reference deconvolution algorithm is presented that eliminates these distortions before application of fitting routines. Methods The measured signal of the dominant methyl resonance is isolated with aid of a spectral estimator (estimation of parameters via rotational invariance techniques) and used as reference signal for estimation of distortions. A Wiener filter is applied to deconvolve those distortions in the lipid spectrum. Performance of the algorithm is assessed for different bandwidths and shapes of distortions, using artificially distorted as well as measured data. Results Application of the fully automatic reference deconvolution algorithm on simulated spectra yields a distinct increase in quantification accuracy. Deconvolved in vivo spectra of subcutaneous fat indicate reduced spectral overlap after application of the proposed strategy. Conclusion The proposed method is helpful for in vivo magnetic resonance spectroscopy of adipose tissue to correct for effects of field inhomogeneities within the voxel and for inevitable eddy current effects. Quantification accuracy is improved by eliminating distortions before application of fitting routines. Magn Reson Med 75:1391–1401, 2016. © 2015 Wiley Periodicals, Inc.

This paper presents new methods based on fusion of Hilbert transform and high frequency resolution techniques (estimation of signal parameter by rotational invariance technique (ESPRIT), root multiple signal classification (root MUSIC)) to extract bearing defect frequencies of induction motor bearing faults using vibration signal. Further sliding window concept is introduced to tackle abnormal conditions like load variation and supply frequency variation. It also proposes a decision based approach to classify the severity of bearing fault. A series of results shows that both sliding window Hilbert-ESPRIT and sliding window Hilbert-root MUSIC are capable of extracting bearing defect frequencies accurately but, sliding window Hilbert-ESPRIT takes less computational time than the sliding window Hilbert-root MUSIC.

High-resolution remote-sensing images are widely used for object detection but are affected by various factors. During the detection process, the orientation sensitivity of the image features is crucial to the detection performance. This study presents a novel rotationally invariant object detection descriptor that can address the difficulties with object detection that are caused by different object orientations. We use orientation normalization, feature space mapping, and an elliptic Fourier transform to achieve rotational invariance of the histogram of oriented gradients. Validation experiments indicate that the proposed descriptor is robust to rotation, noise, and compression. We use this novel image descriptor to detect aircraft and cars in remote-sensing images. The results show that the proposed method offers robust rotational invariance in object detection.

In this paper a robust abnormal human activity recognition framework is proposed which goals to recognize any unusual activity to the elderly people and to strengthen the concept of independent and quality living. The framework is structured to construct a robust feature vector by computing integrated feature vector: Histogram of Oriented Gradients (HOG) and Zernike moments on Average Energy Images (AEI). Formation of AEI images provides a compact representation of the video sequences without any Spatio-temporal loss of information. Integration of HOG and Zernike moments augments inter-class separation and translational and rotational invariance. The depth silhouettes are acquired by Microsoft's Kinect sensor which are used to generate clean binary silhouettes by background subtraction making the pre-processing faster and simpler with accuracy. The combined feature vector dimensions are reduced by applying PCA and SVM is applied to classify the activities. The proposed work is validated on publically available UR fall detection and Kinect Activity Recognition Dataset (KARD) 3D dataset. The experiments exhibit impressive results with The average recognition accuracy achieved on these datasets are 94% and 95.22% ARA for UR fall dataset, and KARD dataset, respectively

In this paper, we propose a new approach to estimate the low-frequency oscillatory modes in power system by using Total Least Square-Estimation of Signal Parameters employing rotational invariance technique (TLS-ESPRIT) based on Least Mean Squares Sign-Data (LMSSD) Adaptive filtering. LMSSD adaptive filtering reduces the effect of Additive White Gaussian Noise (AWGN) from the signal. The proposed estimation scheme is compared with that of the ESPRIT, the LS-ESPRIT and the TLS-ESPRIT methods on a test signal at different Signal-to-Noise Ratio (SNRs). Robustness of the proposed method is demonstrated in the presence of AWGN through Monte-Carlo simulations of 50000 times. The proposed estimation scheme has been applied to Kundur's two-area power system. From the results obtained, it is observed that the proposed LMSSD scheme provides minimum mean and standard deviation in the low-frequency mode estimation as compared to the TLS-ESPRIT.

This paper proposes a multi-shell sampling scheme and corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The sampling scheme uses an optimal number of samples, equal to the degrees of freedom of the band-limited diffusion signal in the SPF domain, and allows for computationally efficient reconstruction. We use synthetic data sets to demonstrate that the proposed scheme allows for greater reconstruction accuracy of the diffusion signal than the multi-shell sampling schemes obtained using the generalised electrostatic energy minimisation (gEEM) method used in the Human Connectome Project. We also demonstrate that the proposed sampling scheme allows for increased angular discrimination and improved rotational invariance of reconstruction accuracy than the gEEM schemes., 4 pages, 4 figures presented at ISBI 2017

A novel scheme is proposed for direction finding with uniform rectangular planar array. First, the characteristics of noncircular signals and Euler’s formula are exploited to construct a new real-valued rectangular array data. Then, the rotational invariance relations for real-valued signal space are depicted in a new way. Finally the real-valued propagator method is utilized to estimate the pairing two-dimensional direction of arrival (2D-DOA). The proposed algorithm provides better angle estimation performance and can discern more sources than the 2D propagator method. At the same time, it has very close angle estimation performance to the noncircular propagator method (NC-PM) with reduced computational complexity.

For vision measurement in the center circle landmark location problem, an improved center of the ellipse based on Zernike moments sub-pixel positioning algorithm was proposed. First, using Sobel operator edge of the image pixel level positioning and then use the constructed Zernike moments to solve the model, combined with Zernike orthogonal polynomials and completeness and plural moment magnitude rotational invariance calculated edge sub-pixel position; followed by analysis of the principle deviation generated by the moments template and ideals model, a correction formula was proposed to compensate and improved edge criterion used to image sub-pixel edge positioning; finally, using the least-squares ellipse fitting algorithm fitting circle center, reverse edge point, filtered residuals larger point, and then precise positioning of the ellipse center. The experimental results show that this method has good stability and high positioning accuracy can be efficiently used in many applications.

Cosmological local observables are at best statistically determined by the fundamental theory describing inflation. When the scalar inflaton is coupled uniformly to a collection of subdominant massless gauge vectors, rotational invariance is obeyed locally. However, the statistical isotropy of fluctuations is spontaneously broken by gauge modes whose wavelength exceeds our causal horizon. This leads to a landscape picture where primordial correlators depend on the position of the observer. We compute the stochastic corrections to the curvature power spectrum, show the existence of a new local observable (the shape of the quadrupole), and constrain the theory using Planck limits. © 2014 The Authors., SCOPUS: ar.j, info:eu-repo/semantics/published

An improved method for joint angle and Doppler frequency estimation in bistatic multiple-input multiple-output (MIMO) radar is proposed. The characteristic of the Vandermonde matrix is employed to expand the virtual array in MIMO radar. Then the rotational invariance produced by the time delay sampling is extracted to estimate the angles and Doppler frequencies. The proposed algorithm is suitable for non-uniform linear arrays and the estimations of Doppler frequency, direction of departure (DOD) and direction of arrival (DOA) are automatically paired. The estimation performance of our approach is better than the estimation of signal parameters via rotational invariance techniques (ESPRIT)-based method due to the expansion of the virtual array, which also increase the maximum detection number of targets. Cramer–Rao bound of angle and Doppler frequency estimation in MIMO radar is derived. Simulation results verify the usefulness of our approach.

We present a new method to extract scale-invariant features from an image by using a Cosine Modulated Gaussian (CM-Gaussian) filter. Its balanced scale-space atom with minimal spread in scale and space leads to an outstanding scale-invariant feature detection quality, albeit at reduced planar rotational invariance. Both sharp and distributed features like corners and blobs are reliably detected, irrespective of various image artifacts and camera parameter variations, except for planar rotation. The CM-Gaussian filters are approximated with the sum of exponentials as a single, fixed-length filter and equal approximation error over all scales, providing constant-time, low-cost image filtering implementations. The approximation error of the corresponding digital signal processing is below the noise threshold. It is scalable with the filter order, providing many quality-complexity trade-off working points. We validate the efficiency of the proposed feature detection algorithm on image registration applications over a wide range of testbench conditions.

The traditional Hilbert method to detect broken rotor bar fault in induction motors is reviewed and its major drawbacks are clearly revealed, namely, deteriorating or even completely failing when a motor operating at low slip due to the fixed constraints of fast Fourier transform (FFT) is used in this method. To overcome this, the estimation of signal parameters via rotational invariance technique (ESPRIT) is then introduced to replace FFT, and an improved Hilbert method is thus presented by conjugating the Hilbert transform and ESPRIT together. Experimental results of a small motor in a laboratory and a large motor operating on an industrial site are reported to demonstrate the effectiveness of the improved Hilbert method.

For this final chapter, we move to the early Universe to ask what constraints we can put on the violation of Lorentz invariance during inflation. As discussed in Sect. 2.2, we can use Einstein-aether theory (ae-theory) Jacobson and Mattingly (Phys. Rev. D64, 024028, (2001), [1]), Jacobson (PoS, QG-PH, 020, (2007), [2]) to model Lorentz violation in the boost sector, i.e., while maintaining rotational invariance on spatial hypersurfaces, at low energies.

In this paper, we consider the generation of inverse synthetic aperture radar (ISAR) image of a target using polynomial phase signal (PPS) modeling of time histories. For a target under complex motion, the time histories in the backscatter signal with time-varying Doppler frequency shifts are modeled as multicomponent PPS. We propose the convolution of scaled high-order instantaneous moments to enable the use of high resolution spectral estimators, such as estimation of signal parameters via rotational invariance technique (ESPRIT), for estimation of the parameters of the multicomponent PPS. Using the proposed technique, the phase parameters are estimated with enhanced resolution and improved accuracy in terms of the MSE of the estimates, as compared to the conventionally used Fourier transform based method, for the considered multicomponent signal in medium to high signal-to-noise ratio. The proposed technique is utilized in ISAR imaging to achieve highly focused image of the target.

Doppler parameter estimation for Synthetic Aperture Radars (SAR) is considered in this work. These parameters include Doppler centroid and Doppler frequency rate. The proposed algorithm is based on Estimating Signal Parameters via Rotational Invariance Techniques (ESPRIT). The estimator can be used to both airborne and spaceborne SAR systems. Simulation and experiment results demonstrate that ESPRIT is providing highly improved accuracy.