An analysis is presented of the generalized weighted mean of a set of quantities, some or all of which may be correlated, and the variance associated with that mean. The cases covered specifically are (a) two correlated quantities, (b) a general number of quantities, two of which are correlated and (c) a general number of quantities, all of which are correlated. For (c), two instances are treated, namely where the quantity variances are equal and unequal. Consistency of the data representing realizations of the quantities concerned is shown to be important in terms of appreciating the results obtained.

This paper focuses on the mathematical modelling required to support the development of new primary standard systems for traceable calibration of dynamic pressure sensors. We address two fundamentally different approaches to realising primary standards, specifically the shock tube method and the drop-weight method. Focusing on the shock tube method, the paper presents first results of system identification and discusses future experimental work that is required to improve the mathematical and statistical models. We use simulations to identify differences between the shock tube and drop-weight methods, to investigate sources of uncertainty in the system identification process and to assist experimentalists in designing the required measuring systems. We demonstrate the identification method on experimental results and draw conclusions.

Columnar cell lesions of the breast are increasingly recognized at mammography for their tendency to calcify. We studied 392 vacuum-assisted core biopsies performed solely for calcifications to evaluate the frequency of columnar cell lesions, their relationship with radiological risk, appearance of calcifications, and clinical data. Management and follow-up of columnar cell lesions without and with atypia (flat epithelial atypia) was analyzed. Cases with architectural atypia (cribriform spaces and/or micropapillae) were excluded from flat epithelial atypia. Calcifications were within the lumen of acini affected by columnar cell lesions in 137 out of 156 biopsies diagnosed with some columnar cell lesions. These represented 37% of vacuum-assisted core biopsies and 62% of low radiological risk (BI-RADS3) calcifications. High-risk (BI-RADS5) calcifications were never associated with columnar cell lesions. Age and menopausal status were comparable in columnar and in not-columnar cell lesions. Atypia was associated with long-term hormone replacement therapy in both lesions. Surgical biopsy was recommended for all cases with atypia. Flat epithelial atypia, as the only histological findings on vacuum-assisted core biopsies, was never associated with malignancy at surgery. In conclusion, we suggest that surgical excision is not mandatory when flat epithelial atypia is found as the most advanced lesion on vacuum-assisted core biopsy performed for low radiological risk calcifications, and that women should be advised of the possible hormone dependency of this entity. Modern Pathology ( Keywords: columnar cell lesions; flat epithelial lesion; calcifications Stereotactic vacuum-assisted core biopsy is currently used to diagnose indeterminate or suspicious breast calcifications that are histologically related to a spectrum of breast lesions encompassing ductal carcinomas in situ and preneoplastic and benign lesions. Often this type of calcification resides in so-called 'columnar cell lesions', 1 entities characterized by the presence of columnar epithelial cells lining the terminal duct lobular units that typically show flocculant or secretory material and microcalcifications in the lumen. The Breast Imaging Reporting and Data System (BI-RADS) 2 has standardized the description and management of findings identified on mammograms, thereby facilitating communication between radiologists and referring physicians. However, to our knowledge, there are no specific studies evaluating whether specific calcification descriptors are associate with columnar cell lesions.Columnar cell lesions have been described under a variety of names. [3][4][5][6][7] According to Schnitt and Vincent-Salomon, 1 columnar cell lesions have been grouped into the categories of columnar cell change and columnar cell hyperplasia without or with atypia. Other authors 8 have proposed a subcategorization of columnar cell lesions depending on the presence of architectural and/or cytological atypia. The unifying term 'flat epithelial atypia' has been proposed by ...

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An algorithm able to deal with any desired fitting model was developed for regression problems with uncertain and correlated variables. A typical application concerns the determination of calibration curves, especially (i) in those cases in which the uncertainties on the independent variables xi cannot be considered negligible with respect to those associated with the dependent variables yi, and (ii) when correlations exist among xi and yi. In the metrological field, several types of software have already been dedicated to the determination of calibration curves, some being focused just on problem (i) and a few others considering also problem (ii) but only for a straight-line fitting model. The proposed algorithm is able to deal with problems (i) and (ii) at the same time, for a generic fitting model. The tool was developed in the MATLAB® environment and validated on several benchmark data sets, fitted with linear and non-linear regression models. A review of the most commonly applied approximations to the parameter uncertainty is also presented, together with a Monte Carlo method proposed for comparison purposes with the results provided by the formula for the uncertainty evaluation which is implemented in the software.