Implementation of the LDA+U method using the full potential linearized augmented plane wave basis

We provide a straightforward and efficient procedure to combine LDA+U total energy functional with the full potential linearized augmented plane wave method. A detailed derivation of the LDA+U Kohn-Sham type equations is presented for the augmented plane wave basis set, and a simple ``second-variation'' based procedure for self-consistent LDA+U calculations is given. The method is applied to calculate electronic structure and magnetic properties of NiO and Gd. The magnetic moments and band eigenvalues obtained are in very good quantitative agreement with previous full potential LMTO calculations. We point out that LDA+U reduces the total d charge on Ni by 0.1 in NiO

Radio interferometric gain calibration as a complex optimization problem

Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss-Newton, Levenberg-Marquardt, etc.) into the domain of complex functions of a complex variable. This employs a formalism called the Wirtinger derivative, and derives a full-complex Jacobian counterpart to the conventional real Jacobian. We apply these developments to the problem of radio interferometric gain calibration, and show how the general complex Jacobian formalism, when combined with conventional optimization approaches, yields a whole new family of calibration algorithms, including those for the polarized and direction-dependent gain regime. We further extend the Wirtinger calculus to an operator-based matrix calculus for describing the polarized calibration regime. Using approximate matrix inversion results in computationally efficient implementations; we show that some recently proposed calibration algorithms such as StefCal and peeling can be understood as special cases of this, and place them in the context of the general formalism. Finally, we present an implementation and some applied results of CohJones, another specialized direction-dependent calibration algorithm derived from the formalism.Comment: 18 pages; 6 figures; accepted by MNRA

First-principles calculation of x-ray dichroic spectra within the full-potential linearized augmented planewave method: An implementation into the Wien2k code

X-ray absorption and its dependence on the polarization of light is a powerful tool to investigate the orbital and spin moments of magnetic materials and their orientation relative to crystalline axes. Here, we present a program for the calculation of dichroic spectra from first principles. We have implemented the calculation of x-ray absorption spectra for left and right circularly polarized light into the Wien2k code. In this package, spin-density functional theory is applied in an all-electron scheme that allows to describe both core and valence electrons on the same footing. The matrix elements, which define the dependence of the photo absorption cross section on the polarization of light and on the sample magnetization, are computed within the dipole approximation. Results are presented for the L2,3 and M4,5 egdes of CeFe2 and compared to experiments

Semi-supervised sequence tagging with bidirectional language models

Pre-trained word embeddings learned from unlabeled text have become a standard component of neural network architectures for NLP tasks. However, in most cases, the recurrent network that operates on word-level representations to produce context sensitive representations is trained on relatively little labeled data. In this paper, we demonstrate a general semi-supervised approach for adding pre- trained context embeddings from bidirectional language models to NLP systems and apply it to sequence labeling tasks. We evaluate our model on two standard datasets for named entity recognition (NER) and chunking, and in both cases achieve state of the art results, surpassing previous systems that use other forms of transfer or joint learning with additional labeled data and task specific gazetteers.Comment: To appear in ACL 201

A penalty method for PDE-constrained optimization in inverse problems

Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal, then, is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand-sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the paramaters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the non-linearity of the problem and is less sensitive the initial iterate