Abstract: Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

Abstract: We present a new method for blind motion deblurring that uses a neural network trained to compute estimates of sharp image patches from observations that are blurred by an unknown motion kernel. Instead of regressing directly to patch intensities, this network learns to predict the complex Fourier coefficients of a deconvolution filter to be applied to the input patch for restoration. For inference, we apply the network independently to all overlapping patches in the observed image, and average its outputs to form an initial estimate of the sharp image. We then explicitly estimate a single global blur kernel by relating this estimate to the observed image, and finally perform non-blind deconvolution with this kernel. Our method exhibits accuracy and robustness close to state-of-the-art iterative methods, while being much faster when parallelized on GPU hardware.

Abstract: In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

Abstract: Cross-modal retrieval has recently drawn much attention due to the widespread existence of multimodal data. It takes one type of data as the query to retrieve relevant data objects of another type, and generally involves two basic problems: the measure of relevance and coupled feature selection. Most previous methods just focus on solving the first problem. In this paper, we aim to deal with both problems in a novel joint learning framework. To address the first problem, we learn projection matrices to map multimodal data into a common subspace, in which the similarity between different modalities of data can be measured. In the learning procedure, the $\ell _{21}$ -norm penalties are imposed on the projection matrices separately to solve the second problem, which selects relevant and discriminative features from different feature spaces simultaneously. A multimodal graph regularization term is further imposed on the projected data,which preserves the inter-modality and intra-modality similarity relationships.An iterative algorithm is presented to solve the proposed joint learning problem, along with its convergence analysis. Experimental results on cross-modal retrieval tasks demonstrate that the proposed method outperforms the state-of-the-art subspace approaches.

Abstract: In this paper, joint resource allocation and power control for energy-efficient device-to-device (D2D) communications underlaying cellular networks are investigated. The resource and power are optimized for maximization of the energy efficiency (EE) of D2D communications. Exploiting the properties of fractional programming, we transform the original nonconvex optimization problem in fractional form into an equivalent optimization problem in subtractive form. Then, an efficient iterative resource allocation and power control scheme is proposed. In each iteration, part of the constraints of the EE optimization problem are removed by exploiting the penalty function approach. We further propose a novel two-layer approach, which allows finding the optimum at each iteration by decoupling the EE optimization problem of joint resource allocation and power control into two separate steps. In the first layer, the optimal power values are obtained by solving a series of maximization problems through root finding, with or without considering the loss of cellular users' rates. In the second layer, the formulated optimization problem belongs to a classical resource-allocation problem with single allocation format, which admits a network flow formulation so that it can be solved to optimality. Simulation results demonstrate the remarkable improvements in terms of EE by using the proposed iterative resource allocation and power control scheme.

Abstract: This paper proposes a novel quaternion-based attitude estimator with magnetic, angular rate, and gravity (MARG) sensor arrays. A new structure of a fixed-gain complementary filter is designed fusing related sensors. To avoid using iterative algorithms, the accelerometer-based attitude determination is transformed into a linear system. Stable solution to this system is obtained via control theory. With only one matrix multiplication, the solution can be computed. Using the increment of the solution, we design a complementary filter that fuses gyroscope and accelerometer together. The proposed filter is fast, since it is free of iteration. We name the proposed filter the fast complementary filter (FCF). To decrease significant effects of unknown magnetic distortion imposing on the magnetometer, a stepwise filtering architecture is designed. The magnetic output is fused with the estimated gravity from gyroscope and accelerometer using a second complementary filter when there is no significant magnetic distortion. Several experiments are carried out on real hardware to show the performance and some comparisons. Results show that the proposed FCF can reach the accuracy of Kalman filter. It successfully finds a balance between estimation accuracy and time consumption. Compared with iterative methods, the proposed FCF has much less convergence speed. Besides, it is shown that the magnetic distortion would not affect the estimated Euler angles.

Abstract: Conventional compressed sensing theory assumes signals have sparse representations in a known dictionary. Nevertheless, in many practical applications such as line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional compressed sensing technique to such applications, the continuous parameter space has to be discretized to a finite set of grid points, based on which a “nominal dictionary” is constructed for sparse signal recovery. Discretization, however, inevitably incurs errors since the true parameters do not necessarily lie on the discretized grid. This error, also referred to as grid mismatch, leads to deteriorated recovery performance. In this paper, we consider the line spectral estimation problem and propose an iterative reweighted method which jointly estimates the sparse signals and the unknown parameters associated with the true dictionary. The proposed algorithm is developed by iteratively decreasing a surrogate function majorizing a given log-sum objective function, leading to a gradual and interweaved iterative process to refine the unknown parameters and the sparse signal. A simple yet effective scheme is developed for adaptively updating the regularization parameter that controls the tradeoff between the sparsity of the solution and the data fitting error. Theoretical analysis is conducted to justify the proposed method. Simulation results show that the proposed algorithm achieves super resolution and outperforms other state-of-the-art methods in many cases of practical interest.

Abstract: Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using the distributed nature of the electron cloud and atomic multipoles. In this work, an electrostatic force field is defined through a concise approximation of the electron density, for which the Coulomb interaction is trivially evaluated. This approximate “pro-density” is expanded in a minimal basis of atom-centered s-type Slater density functions, whose parameters are optimized by minimizing the Kullback–Leibler divergence of the pro-density from a reference electron density, e.g., obtained from an electronic structure calculation. The proposed method, Minimal Basis Iterative Stockholder (MBIS), is a variant of the Hirshfeld AIM method, but it can also be used as a density-fitting technique. An iterative algorithm to refine the pro-density is easily implemented with a line...

Abstract: This paper proposes a new technique to identify the parameters of a digital predistorter based on iterative learning control (ILC). ILC is a well-established control theory technique that can obtain the inverse of a system. Instead of focusing on identifying the predistorter parameters, the technique proposed here first uses an iterative learning algorithm to identify the optimal power amplifier (PA) input signal that drives the PA to the desired linear output response. Once the optimal PA input signal is identified, the parameters of the predistorter are estimated using standard modeling approaches, e.g., least squares. To this end, in this paper, we present a complete derivation of an ILC scheme suitable for the linearization of PAs, which includes convergence conditions and the derivation of two learning algorithms. The proposed ILC scheme and parameter identification technique were demonstrated experimentally and compared with the indirect learning architecture (ILA) and direct learning architecture (DLA). The experimental results show that, even for the most difficult cases, the proposed ILC scheme can successfully linearize the PA. The experimental results also indicate that the proposed parameter identification technique is more robust to measurement noise than ILA and can provide better linearity performance when the PA nonlinearities are strong. In addition, the proposed parameter identification technique can achieve similar or better linearity performance than DLA but with a simpler identification process.

Abstract: This paper addresses the problem of distributed multi-agent optimization in which each agent i has a local cost function hi(x), and the goal is to optimize a global cost function that aggregates the local cost functions. Such optimization problems are of interest in many contexts, including distributed machine learning, distributed resource allocation, and distributed robotics.We consider the distributed optimization problem in the presence of faulty agents. We focus primarily on Byzantine failures, but also briey discuss some results for crash failures. For the Byzantine fault-tolerant optimization problem, the ideal goal is to optimize the average of local cost functions of the non-faulty agents. However, this goal also cannot be achieved. Therefore, we consider a relaxed version of the fault-tolerant optimization problem.The goal for the relaxed problem is to generate an output that is an optimum of a global cost function formed as a convex combination of local cost functions of the non-faulty agents. More precisely, there must exist weights αi for i∈N such that αi ≥ 0 and ∑i≥ Nαi=1, and the output is an optimum of the cost function ∑i≥ N αihi(x). Ideally, we would like αi=1/|N| for all i≥ N, however, this cannot be guaranteed due to the presence of faulty agents. In fact, the maximum number of nonzero weights (αi's) that can be guaranteed is |N|-f, where f is the maximum number of Byzantine faulty agents.We present an iterative distributed algorithm that achieves optimal fault-tolerance. Specifically, it ensures that at least |N|-f agents have weights that are bounded away from 0 (in particular, lower bounded by 1/2|N|-f}). The proposed distributed algorithm has a simple iterative structure, with each agent maintaining only a small amount of local state. We show that the iterative algorithm ensures two properties as time goes to ∞: consensus (i.e., output of non-faulty agents becomes identical in the time limit), and optimality (in the sense that the output is the optimum of a suitably defined global cost function).

Abstract: Phase retrieval is a long-standing problem in imaging when only the intensity of the wavefield can be recorded. Coherent diffraction imaging is a lensless technique that uses iterative algorithms to recover amplitude and phase contrast images from diffraction intensity data. For general samples, phase retrieval from a single-diffraction pattern has been an algorithmic and experimental challenge. Here we report a method of phase retrieval that uses a known modulation of the sample exit wave. This coherent modulation imaging method removes inherent ambiguities of coherent diffraction imaging and uses a reliable, rapidly converging iterative algorithm involving three planes. It works for extended samples, does not require tight support for convergence and relaxes dynamic range requirements on the detector. Coherent modulation imaging provides a robust method for imaging in materials and biological science, while its single-shot capability will benefit the investigation of dynamical processes with pulsed sources, such as X-ray free-electron lasers.

Abstract: Channel estimation and precoding in hybrid analog-digital millimeter-wave (mmWave) MIMO systems is a fundamental problem that has yet to be addressed, before any of the promised gains can be harnessed. For that matter, we propose a method (based on the well-known Arnoldi iteration) exploiting channel reciprocity in TDD systems and the sparsity of the channel’s eigenmodes, to estimate the right (resp. left) singular subspaces of the channel, at the BS (resp. MS). We first describe the algorithm in the context of conventional MIMO systems, and derive bounds on the estimation error in the presence of distortions at both BS and MS. We later identify obstacles that hinder the application of such an algorithm to the hybrid analog-digital architecture, and address them individually. In view of fulfilling the constraints imposed by the hybrid analog-digital architecture, we further propose an iterative algorithm for subspace decomposition, whereby the above estimated subspaces, are approximated by a cascade of analog and digital precoder/combiner. Finally, we evaluate the performance of our scheme against the perfect CSI, fully digital case (i.e., an equivalent conventional MIMO system), and conclude that similar performance can be achieved, especially at medium-to-high SNR (where the performance gap is less than 5%), however, with a drastically lower number of RF chains ( ${\sim}4$ to 8 times less).

Abstract: We denoise Poisson images with an iterative algorithm that progressively improves the effectiveness of variance-stabilizing transformations (VST) for Gaussian denoising filters. At each iteration, a combination of the Poisson observations with the denoised estimate from the previous iteration is treated as scaled Poisson data and filtered through a VST scheme. Due to the slight mismatch between a true scaled Poisson distribution and this combination, a special exact unbiased inverse is designed. We present an implementation of this approach based on the BM3D Gaussian denoising filter. With a computational cost at worst twice that of the noniterative scheme, the proposed algorithm provides significantly better quality, particularly at low signal-to-noise ratio, outperforming much costlier state-of-the-art alternatives.

Abstract: Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical physics computations, and proven in few specific cases. Here, we show how to rigorously prove the conjectured formula for the symmetric rank-one case. This allows to express the minimal mean-square-error and to characterize the detectability phase transitions in a large set of estimation problems ranging from community detection to sparse PCA. We also show that for a large set of parameters, an iterative algorithm called approximate message-passing is Bayes optimal. There exists, however, a gap between what currently known polynomial algorithms can do and what is expected information theoretically. Additionally, the proof technique has an interest of its own and exploits three essential ingredients: the interpolation method introduced in statistical physics by Guerra, the analysis of the approximate message-passing algorithm and the theory of spatial coupling and threshold saturation in coding. Our approach is generic and applicable to other open problems in statistical estimation where heuristic statistical physics predictions are available.

Abstract: This work concerns linearization methods for efficiently solving the Richards equation, a degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous media. The discretization of Richards’ equation is based on backward Euler in time and Galerkin finite elements in space. The most valuable linearization schemes for Richards’ equation, i.e. the Newton method, the Picard method, the Picard/Newton method and the L-scheme are presented and their performance is comparatively studied. The convergence, the computational time and the condition numbers for the underlying linear systems are recorded. The convergence of the L-scheme is theoretically proved and the convergence of the other methods is discussed. A new scheme is proposed, the L-scheme/Newton method which is more robust and quadratically convergent. The linearization methods are tested on illustrative numerical examples.

Abstract: In this paper, we investigate simultaneous wireless information and power transfer systems for multiuser multiple-input single-output secure broadcasting channels. Considering imperfect channel state information, we introduce a robust secure beamforming design, where the transmit power is minimized subject to the secrecy rate outage probability constraint for legitimate users and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is non-convex due to the presence of the probabilistic constraints. With the aid of Bernstein-type inequalities, we transform the outage constraints into the deterministic forms. Based on a successive convex approximation (SCA) method, we propose a low-complexity approach, which reformulates the original problem as a second-order cone programming problem. Also, we prove the convergence of the SCA-based iterative algorithm. Simulation shows that the proposed scheme outperforms the conventional method with lower complexity.

Abstract: In this study, the authors introduce a new solution to the alternating current optimal power flow problem based on successive linear approximation of power flow equations. The polar coordination of the power flow equations is used to take advantage of the quasi-linear P– θ relationship. A mathematical transformation for the crossing term of voltage magnitude is used, which guarantees the accuracy of the linear approximation when the quality of initial points regarding voltage magnitude is relatively low in the first few iterations. As a result, the accuracy of the proposed approximation becomes very high in very few iterations. Linearisation method for the quadratic apparent branch flow limits is provided. Methods to recover the AC feasibility from the obtained optimal power flow solution and correct possible constraint violations are introduced. The proposed method is tested in several IEEE and Polish benchmark systems. The difference in objective functions relative to MATPOWER benchmark results is generally <0.1% when the algorithm terminates.

Abstract: An automatic, iterative method to determine the orientation relationship between parent austenite and martensite is described. The algorithm generates the orientation relationship from grain boundary misorientations through an iterative procedure based on correct symmetry operator assignment. The automatic method is demonstrated to work on both martensitic and bainitic steels and to provide comparable results to a manual grain selection method.

Abstract: Usually, direction-of-arrival (DOA) estimators are derived under the assumption of uniform white noise, whose covariance matrix is a scaled identity matrix. However, in practice, the noise can be nonuniform with an arbitrary unknown diagonal covariance matrix. In this situation, the performance of DOA estimators may be deteriorated considerably if the noise nonuniformity is ignored. To tackle this problem, iterative approaches to subspace estimation are developed and the corresponding subspace-based DOA estimators are addressed. In our proposed methods, the signal subspace and noise covariance matrix are first determined by maximizing the log-likelihood (LL) function or solving a least-squares (LS) minimization problem, both of which are accomplished in an iterative manner. Then, the DOAs are determined from the subspace estimate and/or noise covariance matrix estimate with the help of traditional DOA estimators. As the signal subspace and noise covariance matrix can be computed in closed-form in each iteration, the proposals are computationally attractive. Furthermore, the signal subspace is directly calculated without the requirement of the exact knowledge of the array manifold, enabling us to handle array uncertainties by incorporating conventional subspace-based calibration algorithms. Simulations and experimental results are included to demonstrate the superiority of the proposed approaches.

Abstract: Multiframe super-resolution algorithms reconstruct high-resolution images by exploiting complementary information in multiple low-resolution frames. However, despite their success under ideal conditions, most existing methods rely on simplistic approximations to the physics of image acquisition and show limited robustness in real-world applications. This paper proposes spatially adaptive Bayesian modeling and an iterative algorithm for robust super-resolution imaging. In particular, we introduce a weighted Gaussian observation model to consider space variant noise and weighted bilateral total variation to exploit sparsity of natural images. Based on this model, we develop a majorization–minimization algorithm implemented as iteratively re-weighted minimization. The proposed method simultaneously estimates model parameters and the super-resolved image in an iterative coarse-to-fine scheme. Compared to prior work, our approach combines the benefits of achieving robust and edge preserving image reconstruction with small amount of parameter tuning, while being flexible in terms of motion models, computationally efficient and easy to implement. Our experimental evaluation confirms that our approach outperforms state-of-the-art algorithms under various practical conditions, e.g., inaccurate geometric and photometric registration or invalid measurements.

Abstract: The model of nonlinear heat was generalized using the new trend of derivative with fractional order. The new definition of derivative with fractional order has no singular kernel thus allows a description of the variation on time or space from the lower to the upper boundaries within the space/time interval which the investigation is taken place for a given model. In detail, we presented the analysis of unique and existence of a solution for the nonlinear fractional equation. We present the derivation of a special solution using an iterative method.

Abstract: This brief addresses the energy management problem with the framework of receding horizon optimization. For power-split plug-in hybrid electric vehicles (HEVs), the real-time power-split decision is formulated as a nonlinear receding horizon optimization problem. Then, an online iterative algorithm to solve the optimization problem is proposed based on the continuation/generalized minimum residual algorithm. It should be noted that the proposed energy management strategy aims for optimality of the targeted horizon, but the solution is not optimal for the full driving route, unlike many solutions presented using the dynamic programming approaches. At each decision step, only the initial value of the optimal solution is implemented according to the receding horizon optimization approach. Finally, to demonstrate a comparison of the proposed scheme with other schemes, numerical validations conducted on a full-scale GT-SUITE HEV simulator are presented.

Abstract: This study applies the filtering technique to system identification to study the data filtering-based parameter estimation methods for multivariable systems, which are corrupted by correlated noise – an autoregressive moving average process. To solve the difficulty that the identification model contains the unmeasurable variables and noise terms in the information matrix, the authors present a hierarchical gradient-based iterative (HGI) algorithm by using the hierarchical identification principle. To improve the convergence rate, they apply the filtering technique to derive a filtering-based HGI algorithm and a filtering-based hierarchical least squares-based iterative (HLSI) algorithm. The simulation examples indicate that the filtering-based HLSI algorithm has the highest computational efficiency among these three algorithms.