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Context. Gravitational lensing is one of the leading tools in understanding the dark side of the Universe. The need for accurate, efficient and effective methods which are able to extract this information along with other cosmological parameters from cosmic shear data is ever growing. COSEBIs, Complete Orthogonal Sets of E-/B-Integrals, is a recently developed statistical measure that encompasses the complete E-/B-mode separable information contained in the shear correlation functions measured on a finite angular range. Aims. The aim of the present work is to test the properties of this newly developed statistics for a higher-dimensional parameter space and to generalize and test it for shear tomography. Methods. We use Fisher analysis to study the effectiveness of COSEBIs. We show our results in terms of figure-of-merit quantities, based on Fisher matrices. Results. We find that a relatively small number of COSEBIs modes is always enough to saturate to the maximum information level. This number is always smaller for 'logarithmic COSEBIs' than for 'linear COSEBIs', and also depends on the number of redshift bins, the number and choice of cosmological parameters, as well as the survey characteristics. Conclusions. COSEBIs provide a very compact way of analyzing cosmic shear data, i.e., all the E-/B-mode separable second-order statistical information in the data is reduced to a small number of COSEBIs modes. Furthermore, with this method the arbitrariness in data binning is no longer an issue since the COSEBIs modes are discrete. Finally, the small number of modes also implies that covariances, and their inverse, are much more conveniently obtainable, e.g., from numerical simulations, than for the shear correlation functions themselves., Comment: 17 pages, 15 figures

Purpose:Dose‐volume histograms (DVH) are commonly used for quality appraisal of treatment plans. However, since each volume of interest is treated as functionally and histologically uniform, the DVH reflects no information about the underlying anatomy. This simplification, while often reasonable, is excessive when applied to the lung. It has been frequently suggested that weighting dose distributions in thorax according to the relative functional integrity of the irradiated regions may provide better information for risk assessment of pneumonitis. We investigate the utility of dose‐density‐corrected histograms, and other potential dose‐functional metrics, in treatment plan evaluation, risk assessment of the treatment complications, and clinical decision‐making. Method and Materials: In the first approximation, the tissue density, estimated from CT data, can serve as a surrogate measure of lung perfusion, ventilation, or both. Potentially, the dose‐function histograms may be created based on more direct measurements of lung perfusion: e.g., with SPECT, helical CT with IV‐contrast, while ventilation may be estimated from point density changes between the extreme phases in respiratory‐correlated CT. For this study, clinical lungIMRT plans were analyzed using in‐house software, and DVH were compared to histograms corrected for tissue density (standard CT) and tissue‐density variations (respiratory‐correlated CT). Results: Generally, the DVH and density‐corrected histograms differ wherever density variations are present within the volumes of interest: e.g., in radiotherapy of tumors in the lung, paranasal sinuses. Substantial changes in certain histogram metrics were observed, e.g., the relative difference of over 20% between the dose to 60% of volume (D60) and that to 60% of the lung mass. Conclusion: The adjustments to the shape of the histogram, resulting from density‐correlated weighting of the dose, will result in a different data binning in the outcome analysis, which may, in its turn, lead to refinements in the risk assessment models. Supported by NIH grants R01‐CA103904, RO1‐CA118200.

Local linear density estimators achieve automatic boundary corrections and enjoy some typical optimal properties. Proper choice of the smoothing parameters is crucial for their performance. A data-based bandwidth selector is developed in the spirit of plug-in rules. Consistency and asymptotic normality of the selected bandwidth are demonstrated. The bandwidth is very efficient regardless of whether there are non-smooth boundaries in the support of the density or not.

Wind field observations by means of spaceborne scatterometers are of tremendous interest for oceanographic and meteorological applications. In order to best accomplish such a task the relationship between the radar cross section and the wind field, i.e. the geophysical model function, must be properly calibrated. Within such a framework a radar cross section data grouping is usually accomplished and it is referred to as binning. The authors revisit the radar cross section data binning step as a stochastic estimation procedure.