Random variables with moment-matching staircase density functions.

This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal log-likelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.

Areolar sebaceous hyperplasia with underlying primary duct carcinoma of the breast in a woman with Donohue syndrome (leprechaunism).

Areolar hyperplasia is only reported when exaggerated, and even so, exaggerated areolar sebaceous hyperplasia is rare. We have recently seen a case of areolar sebaceous hyperplasia in a 32-year-old woman with Donohue syndrome (leprechaunism), who also had an invasive ductal carcinoma in the same breast. The patient showed typical "elfin-like" face with wide nostrils and thick lips, large and low-set ears, and dysplastic nails. The areola showed a yellowish thickened plaque of 5-cm diameter that corresponded to a hyperplasia of the sebaceous glands. Immunohistochemistry for the mismatch repair proteins (MLH1, MSH2, MSH6, and PMS2) was performed on the sebaceous hyperplasia and on the breast carcinoma, and no lack of expression of the markers was evidenced. We have found no other reported case of areolar sebaceous hyperplasia either in cases of breast carcinoma or in cases of leprechaunism.

Granulomatous response due to anabolic steroid injections.

Injected corticosteroids can sometimes lead to a granulomatous reaction. This is apparently also true for anabolic steroids, which are often used by bodybuilders, although we have not found any histologic report on such a phenomenon. We report a case of a granulomatous reaction in a 30-year-old male bodybuilder having undergone anabolic steroid injections. Foreign bodies typical of steroids were found, together with areas of calcification and ossification with lamellar bone. Multivacuolated macrophages were found in the fibrous tissue close to these areas of calcification and ossification.

Immunohistochemical phenotype of cutaneous cribriform carcinoma with a panel of 15 antibodies.

We report a cribriform carcinoma of the left fossa poplitea in a 62-year-old woman. The patient did not present any symptoms, and the only complaint was the nodule, which was resected for diagnosis. After considering different diagnostic options, we decided that the most appropriate one was cribriform carcinoma, which is an entity described in 1998. The diagnostic criteria, which were provided in the few publications that refer to this entity, helped us to distinguish it from the main mimicker: cystic adenoid carcinoma. Owing to the cribriform pattern of the tumor, we also looked for a metastasis from other sites, mainly breast, vulva, and salivary glands, but all these were clinically excluded. The tumoral cells showed secretion by decapitation, as well as a positive stain of the luminal secretion by histochemical techniques of Alcian blue and periodic acid-Schiff. The tumor was negative for iron stain. In spite of these characteristics, which are, for some authors, indicative of an apocrine phenotype, the immunohistochemical study revealed some differences with the profile that has been described in cases of apocrine adenocarcinoma. The tumor did not express GCDFP-15 or CD 15. It was also negative for SMA, CEA, and PR. The pattern of cytokeratins expressed by our case was positive for AE1-AE3, CAM 5.2, and CK7, without any expression for CK20. Other markers expressed by the tumor were EMA, ER, c-erbB-2, p53, and S-100.