Relativistic corrections in magnetic systems

We present a weak-relativistic limit comparison between the Kohn-Sham-Dirac equation and its approximate form containing the exchange coupling, which is used in almost all relativistic codes of density-functional theory. For these two descriptions, an exact expression of the Dirac Green's function in terms of the non-relativistic Green's function is first derived and then used to calculate the effective Hamiltonian, i.e., Pauli Hamiltonian, and effective velocity operator in the weak-relativistic limit. We point out that, besides neglecting orbital magnetism effects, the approximate Kohn-Sham-Dirac equation also gives relativistic corrections which differ from those of the exact Kohn-Sham-Dirac equation. These differences have quite serious consequences: in particular, the magnetocrystalline anisotropy of an uniaxial ferromagnet and the anisotropic magnetoresistance of a cubic ferromagnet are found from the approximate Kohn-Sham-Dirac equation to be of order $1/c^2$, whereas the correct results obtained from the exact Kohn-Sham-Dirac equation are of order $1/c^4$ . We give a qualitative estimate of the order of magnitude of these spurious terms

Theory of strongly correlated f and d-electron systems. I. Exact Hamiltonian, Hubbard-Anderson models and perturbation theory near atomic limit within non-orthogonal basis set

The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is transformed into a correlated form. In order to elucidate the microscopical origin of the parameters of the periodical Hubbard-Anderson model (PHAM) the terms of the full Hamiltonian which have the operator structure of PHAM are separated. It is found that the matrix element of mixing interaction includes ion-configuration and number-of-particles dependent contributions from the Coulomb interaction. In a second step the diagram technique (DT) is developed by means of generalization of the Baym-Kadanoff method for correlated systems.Comment: 40 pages, 6 figure

Importance of Correlation Effects on Magnetic Anisotropy in Fe and Ni

We calculate magnetic anisotropy energy of Fe and Ni by taking into account the effects of strong electronic correlations, spin-orbit coupling, and non-collinearity of intra-atomic magnetization. The LDA+U method is used and its equivalence to dynamical mean-field theory in the static limit is emphasized. Both experimental magnitude of MAE and direction of magnetization are predicted correctly near U=4 eV for Ni and U=3.5 eV for Fe. Correlations modify one-electron spectra which are now in better agreement with experiments.Comment: 4 pages, 2 figure

A Bayesian hierarchical approach to multirater correlated ROC analysis

In a common ROC study design, several readers are asked to rate diagnostics of the same cases processed under different modalities. We describe a Bayesian hierarchical model that facilitates the analysis of this study design by explicitly modelling the three sources of variation inherent to it. In so doing, we achieve substantial reductions in the posterior uncertainty associated with estimates of the differences in areas under the estimated ROC curves and corresponding reductions in the mean squared error (MSE) of these estimates. Based on simulation studies, both the widths of coverage intervals and MSE of estimates of differences in the area under the curves appear to be reduced by a factor that often exceeds five. Thus, our methodology has important implications for increasing the power of analyses based on ROC data collected from an available study population. Copyright © 2005 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34862/1/2314_ftp.pd

A self-interaction corrected pseudopotential scheme for magnetic and strongly-correlated systems

Local-spin-density functional calculations may be affected by severe errors when applied to the study of magnetic and strongly-correlated materials. Some of these faults can be traced back to the presence of the spurious self-interaction in the density functional. Since the application of a fully self-consistent self-interaction correction is highly demanding even for moderately large systems, we pursue a strategy of approximating the self-interaction corrected potential with a non-local, pseudopotential-like projector, first generated within the isolated atom and then updated during the self-consistent cycle in the crystal. This scheme, whose implementation is totally uncomplicated and particularly suited for the pseudopotental formalism, dramatically improves the LSDA results for a variety of compounds with a minimal increase of computing cost.Comment: 18 pages, 14 figure

Evaluating computer‐aided detection algorithms

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134784/1/mp6289.pd

Systematic theoretical study of the spin and orbital magnetic moments of 4d and 5d interfaces with Fe films

Results of ab initio calculations using the relativistic Local Spin Density theory are presented for the magnetic moments of periodic 5d and 4d transition metal interfaces with bcc Fe(001). In this systematic study we calculated the layer-resolved spin and orbital magnetic moments over the entire series. For the Fe/W(001) system, the Fe spin moment is reduced whilst its orbital moment is strongly enhanced. In the W layers a spin moment is induced, which is antiparallel to that of Fe in the first and fourth W layers but parallel to Fe in the second and third W layers. The W orbital moment does not follow the spin moment. It is aligned antiparallel to Fe in the first two W layers and changes sign in the third and fourth W layers. Therefore, Hund's third rule is violated in the first and third W layers, but not in the second and fourth W layers. The trend in the spin and orbital moments over the 4d and 5d series for multilayers is quite similar to previous impurity calculations. These observations strongly suggest that these effects can be seen as a consequence of the hybridization between 5d (4d) and Fe which is mostly due to band filling, and to a lesser extent geometrical effects of either single impurity or interface

Flexible regression models for ROC and risk analysis, with or without a gold standard

A novel semiparametric regression model is developed for evaluating the covariate-specific accuracy of a continuous medical test or biomarker. Ideally, studies designed to estimate or compare medical test accuracy will use a separate, flawless gold-standard procedure to determine the true disease status of sampled individuals. We treat this as a special case of the more complicated and increasingly common scenario in which disease status is unknown because a gold-standard procedure does not exist or is too costly or invasive for widespread use. To compensate for missing data on disease status, covariate information is used to discriminate between diseased and healthy units. We thus model the probability of disease as a function of 'disease covariates'. In addition, we model test/biomarker outcome data to depend on 'test covariates', which provides researchers the opportunity to quantify the impact of covariates on the accuracy of a medical test. We further model the distributions of test outcomes using flexible semiparametric classes. An important new theoretical result demonstrating model identifiability under mild conditions is presented. The modeling framework can be used to obtain inferences about covariate-specific test accuracy and the probability of disease based on subject-specific disease and test covariate information. The value of the model is illustrated using multiple simulation studies and data on the age-adjusted ability of soluble epidermal growth factor receptor - a ubiquitous serum protein - to serve as a biomarker of lung cancer in men. SAS code for fitting the model is provided. Copyright © 2015 John Wiley & Sons, Ltd