Given a coherent ideal sheaf J we construct locally a vector-valued residue current R whose annihilator is precisely the given sheaf. In case J is a complete intersection, R is just the classical Coleff-Herrera product. By means of these currents we can extend various results, previously known for a complete intersection, to general ideal sheaves. Combining with integral formulas we obtain a residue version of the Ehrenpreis-Palamodov fundamental principle. © 2007 Elsevier Masson SAS RÉSUMÉ.-Soit J un faisceau cohérent d'idéaux. Nous construisons localement un courant résiduel R à valeurs vectorielles dont l'annihilateur est J. Au cas où J serait une intersection complète, R est simplement le produit classique de Coleff-Herrera. Ces courants permettent d'étendre au cas général des résultats divers, déjà connus dans le cas d'une intersection complète. En utilisant ces courants résiduels et des formules intégrales, nous obtenons ainsi une version résiduelle du Principe Fondamental d'Ehrenpreis-Palamodov.

Let X be a complex space of pure dimension. We introduce fine sheaves A X q of (0, q)-currents, which coincides with the sheaves of smooth forms on the regular part of X, so that the associated Dolbeault complex yields a resolution of the structure sheaf O X . Our construction is based on intrinsic and quite explicit semi-global Koppelman formulas.

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Multiangle light scattering (MALS) is a well-established technique used to determine the size of macromolecules and particles. In this study, different extrapolation procedures used in MALS were investigated with regard to accuracy and robustness in the obtained molar mass and rms radius. Three different mathematical transformations of the light scattering function referred to as the Debye, Zimm, and Berry methods for constructing the Debye plot were investigated for two idealized polymer shapes, homogeneous spheres and random coils, with radii from 25 to 250 nm. The effect of the angular interval used for the extrapolation was investigated, as was the robustness of the different transformations toward errors in the measured light scattering intensity at low angles. For an rms radius less than 50 nm, the relative error in molar mass due to extrapolation was less than 1% independent of the method used. For larger radii, the error increased and the extrapolation procedure became more critical. For random coil polymers, the Berry method was superior in terms of accuracy and robustness. For spheres, the Debye method was superior. The Zimm method was inferior to the others. The different extrapolation methods were evaluated and compared on experimental data from a size exclusion chromatography-MALS analysis of an ultrahigh molar mass poly(ethylene oxide) (PEO). The PEO data qualitatively verified the calculations and stressed the importance of optimizing the extrapolation procedure after careful evaluation of the experimental data. A discussion of how to detect erroneous data in an experimental Debye plot is given.

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We present the new computerized Human Brain Atlas (HBA) for anatomical and functional mapping studies of the human brain. The HBA is based on many high-resolution magnetic resonance images of normal subjects and provides continuous updating of the mean shape and position of anatomical structures of the human brain. The structures are transformable by linear and nonlinear global and local transformations applied anywhere in 3-D pictures to fit the anatomical structures of individual brains, which, by reformatting, are transformed into a high-resolution standard anatomical format. The power of the HBA to reduce anatomical variations was evaluated on a randomized selection of anatomical landmarks in brains of 27 young normal male volunteers who were different from those on whom the standard brain was selected. The HBA, even when based only on standard brain surface and central structures, reduced interindividual anatomical variance to the level of the variance in structure position between the right and left hemisphere in individual brains. © 1994 Wiley-Liss, Inc.

The validity of parametric functional magnetic resonance imaging (fMRI) analysis has only been reported for simulated data. Recent advances in computer science and data sharing make it possible to analyze large amounts of real fMRI data. In this study, 1484 rest datasets have been analyzed in SPM8, to estimate true familywise error rates. For a familywise significance threshold of 5%, significant activity was found in 1% -70% of the 1484 rest datasets, depending on repetition time, paradigm and parameter settings. This means that parametric significance thresholds in SPM both can be conservative or very liberal. The main reason for the high familywise error rates seems to be that the global AR(1) auto correlation correction in SPM fails to model the spectra of the residuals, especially for short repetition times. The findings that are reported in this study cannot be generalized to parametric fMRI analysis in general, other software packages may give different results. By using the computational power of the graphics processing unit (GPU), the 1484 rest datasets were also analyzed with a random permutation test. Significant activity was then found in 1% -19% of the datasets. These findings speak to the need for a better model of temporal correlations in fMRI timeseries.

Estimation of local spatial structure has a long history and numerous analysis tools have been developed. A concept that is widely recognized as fundamental in the analysis is the structure tensor. However, precisely what it is taken to mean varies within the research community. We present a new method for structure tensor estimation which is a generalization of many of it's predecessors. The method uses filter sets having Fourier directional responses being monomials of the normalized frequency vector, one odd order subset and one even order subset. It is shown that such filter sets allow for a particularly simple way of attaining phase invariant, positive semi-definite, local structure tensor estimates. We continue to compare a number of known structure tensor algorithms by formulating them in monomial filter set terms. In conclusion we show how higher order tensors can be estimated using a generalization of the same simple formulation.