A pentagonal surface patch for computer-aided geometric design

A vector valued interpolation scheme for a pentagon is described which is compatible with surface patches which have a rectangular domain of definition. Such a scheme could be useful in computer- aided geometric design problems, where a pentagonal patch occurs within a rectangular patch framework

Low HER2 expression in normal breast epithelium enables dedifferentiation and malignant transformation via chromatin opening.

Overexpression of the HER2 protein in breast cancer patients is a predictor of poor prognosis and resistance to therapies. We used an inducible breast cancer transformation system that allows investigation of early molecular changes. HER2 overexpression to similar levels as those observed in a subtype of HER2-positive breast cancer patients induced transformation of MCF10A cells and resulted in gross morphological changes, increased anchorage-independent growth of cells, and altered the transcriptional programme of genes associated with oncogenic transformation. Global phosphoproteomic analysis during HER2 induction predominantly detected an increase in protein phosphorylation. Intriguingly, this correlated with chromatin opening, as measured by ATAC-seq on acini isolated from 3D cell culture. HER2 overexpression resulted in opening of many distal regulatory regions and promoted reprogramming-associated heterogeneity. We found that a subset of cells acquired a dedifferentiated breast stem-like phenotype, making them likely candidates for malignant transformation. Our data show that this population of cells, which counterintuitively enriches for relatively low HER2 protein abundance and increased chromatin accessibility, possesses transformational drive, resulting in increased anchorage-independent growth in vitro compared to cells not displaying a stem-like phenotype

Surrogacy tourism: the ethical and legal challenges

Although surrogacy seemed to have been practised since ancient times, its resurgence in the contemporary era has been nothing short of phenomenal. With advances made in reproductive technology, it is now possible to fertilise eggs and sperms in laboratories and have the embryo transferred into the womb of a surrogate mother for gestation. Through a combination of push and pull factors, this possibility of gestational surrogacy has led to the meteoric rise of cross-border surrogacy. This paper seeks to highlight the ethical and legal challenges associated with the practice, and calls for better legal oversight at international level

The use of triangular and pentagonal patches in the numerical representation of surfaces

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