Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.     

On applicability of PCA,voxel-wise variance normalization and dimensionality assumptions for sliding temporal window sICA in resting-state fMRI

Subject-level resting-state fMRI (RS-fMRI) spatial independent component analysis (sICA) may provide new ways to analyze the data when performed in the sliding time window. However, whether principal component analysis (PCA) and voxel-wise variance normalization (VN) are applicable pre-processing procedures in the sliding-window context, as they are for regular sICA, has not been addressed so far. Also model order selection requires further studies concerning sliding-window sICA. In this paper we have addressed these concerns. First, we compared PCA-retained subspaces concerning overlapping parts of consecutive temporal windows to answer whether in-window PCA and VN can confound comparisons between sICA analyses in consecutive windows. Second, we compared the PCA subspaces between windowed and full data to assess expected comparability between windowed and full-data sICA results. Third, temporal evolution of dimensionality estimates in RS-fMRI data sets was monitored to identify potential challenges in model order selection in a sliding-window sICA context. Our results illustrate that in-window VN can be safely used, in-window PCA is applicable with most window widths and that comparisons between windowed and full data should not be performed from a subspace similarity point of view. In addition, our studies on dimensionality estimates demonstrated that there are sustained, periodic and very case-specific changes in signal-to-noise ratio within RS-fMRI data sets. Consequently, dimensionality estimation is needed for well-founded model order determination in the sliding-window case. The observed periodic changes correspond to a frequency band of ≤ 0.1 Hz, which is commonly associated with brain activity in RS-fMRI and become on average most pronounced at window widths of 80 and 60 time points (144 and 108 s, respectively). Wider windows provided only slightly better comparability between consecutive windows, and 60 time point or shorter windows also provided the best comparability with full-data results. Further studies are needed to determine the cause for dimensionality variations.     

ChemInform Abstract: X-Ray Structural Studies of the Polymorphic Elpasolites K2LiAlF6 and Rb2LiGaF6.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Fluctuating lattice-Boltzmann model for complex fluids

We develop and test numerically a lattice-Boltzmann (LB) model for nonideal fluids that incorporates thermal fluctuations. The fluid model is a momentum-conserving thermostat, for which we demonstrate how the temperature can be made equal at all length scales present in the system by having noise both locally in the stress tensor and by shaking the whole system in accord with the local temperature. The validity of the model is extended to a broad range of sound velocities. Our model features a consistent coupling scheme between the fluid and solid molecular dynamics objects, allowing us to use the LB fluid as a heat bath for solutes evolving in time without external Langevin noise added to the solute. This property expands the applicability of LB models to dense, strongly correlated systems with thermal fluctuations and potentially nonideal equations of state. Tests on the fluid itself and on static and dynamic properties of a coarse-grained polymer chain under strong hydrodynamic interactions are used to benchmark the model. The model produces results for single-chain diffusion that are in quantitative agreement with theory.     

Analytical gradients of a state average MCSCF state and a state average diagnostic

An efficient method for calculating the Lagrange multipliers and the analytical gradients of one state included in a state average MCSCF wave function is presented. It is demonstrated that the state average energy of an ‘equal-weight’ scheme is invariant to rotations within the state average subspace and that the corresponding rotations should be eliminated from the Lagrangian equations. Finally, a diagnostic is presented, which gauges the energy difference between a state defined by a state average calculation and the corresponding fully variational multi-configurational SCF state.     

Structure and morphology of the reaction fronts during the formation of MgAl2O4 thin films by solid state reaction between R-cut sapphire substrates and MgO films

The thin-film spinel-forming solid state reaction between Al₂O₃ and MgO has been studied under initially non-coherent conditions. MgO films in (001) orientation on -cut sapphire single crystals were heated at 1100°C for 30 min or 1h. The film/substrate reaction proceeds via cation counterdiffusion as was revealed by a marker experiment. The MgAl₂O₄ films formed were predominantly (001) oriented, with an additional systematic tilt of about 5° of the spinel lattice around the [010] axis. The structure of the Al₂O₃ /MgAl₂O₄(001) and MgAl₂O₄(001)/MgO(001) reaction fronts has been investigated on cross section samples by high-resolution electron microscopy. It appeared that after starting from an incoherent interface, the Al₂O₃ /MgAl₂O₄(001) front assumes an almost fully coherent structure during the reaction. As a result the lattice misfit is reduced to 1%, and interfacial ledges are formed. The latter most probably play an active role in the necessary c.p.h. f.c.c. reconstruction of the oxygen sublattice. The MgAl₂O₄(001)/MgO(001) reaction front consists of coherent regions divided by misfit dislocations. During the reaction the former run ahead whereas the latter lag behind. As a result the morphology of the reaction front is bowed. The results confirm earlier observations of Carter and Schmalzried of the semicoherent Al₂O₃(00.1)/CoAl₂O₄(111) interface, thus strongly supporting the conclusion of a fundamental new phase transformation mechanism specific to oxide systems.Presented at the workshop on High-Voltage and High-Resolution Electron Microscopy, February 21–24, 1994, Stuttgart, Germany.     

Optimal Recovery of the Derivative of Bounded Analytic Functions

Given (–1, 0), n N, we discuss the optimal recoveryof (), for analytic and bounded in < 1, from the knowledge of the values of at n points z1,.zm[0,l),where these points are chosen to produce the least possibleintrinsic error. The optimal algorithms are explicitly determined.     

Computer program for neutron activation analysis with the SLOWPOKE reactor

A FORTRAN computer program for automatic neutron activation analysis is presented. The program locates and identifies peaks in a gamma-ray spectrum, calculates peak areas and the concentrations of the elements of interest in the sample. This program was specifically designed for the SLOWPOKE reactor, it uses a semi-absolute method and does not need standards or flux monitors. The program was written so as to minimize the computation time, and a typical 4096-channel spectrum is processed in five seconds by an IBM 360/75 computer.