The effect of projections on dimension in the Heisenberg group

We prove analogs of classical almost sure dimension theorems for Euclidean projection mappings in the first Heisenberg group, equipped with a sub-Riemannian metric.

Bright moonlight triggers natal dispersal departures

Upon leaving their natal area, dispersers are confronted with unknown terrains. Species-specific perceptual ranges (i.e. the maximum distance from which an individual can perceive landscape features) play a crucial role in spatial movement decisions during such wanderings. In nocturnal animals that rely on vision, perceptual range is dramatically enhanced during moonlight, compared to moonless conditions. This increase of the perceptual range is an overlooked element that may be responsible for the successful crossing of unfamiliar areas during dispersal. The information gathered from 143 radio-tagged eagle owl Bubo bubo juveniles in Spain, Finland and Switzerland shows that, although the decision to initiate dispersal is mainly an endogenous phenomenon determined by the attainment of a given age (∼6 months), dispersers leave their birthplace primarily under the best light conditions at night, i.e. when most of the lunar disc is illuminated. This sheds new light into the mechanisms that may trigger dispersal from parental territory.

Inherited susceptibility to uterine leiomyomas and renal cell cancer

Herein we report the clinical, histopathological, and molecular features of a cancer syndrome with predisposition to uterine leiomyomas and papillary renal cell carcinoma. The studied kindred included 11 family members with uterine leiomyomas and two with uterine leiomyosarcoma. Seven individuals had a history of cutaneous nodules, two of which were confirmed to be cutaneous leiomyomatosis. The four kidney cancer cases occurred in young (33- to 48-year-old) females and displayed a unique natural history. All these kidney cancers displayed a distinct papillary histology and presented as unilateral solitary lesions that had metastasized at the time of diagnosis. Genetic-marker analysis mapped the predisposition gene to chromosome 1q. Losses of the normal chromosome 1q were observed in tumors that had occurred in the kindred, including a uterine leiomyoma. Moreover, the observed histological features were used as a tool to diagnose a second kindred displaying the phenotype. We have shown that predisposition to uterine leiomyomas and papillary renal cell cancer can be inherited dominantly through the hereditary leiomyomatosis and renal cell cancer (HLRCC) gene. The HLRCC gene maps to chromosome 1q and is likely to be a tumor suppressor. Clinical, histopathological, and molecular tools are now available for accurate detection and diagnosis of this cancer syndrome.