Geometric maximal operators and BMO on product bases

We consider the problem of the boundedness of maximal operators on BMO on shapes in $\mathbb{R}^n$. We prove that for bases of shapes with an engulfing property, the corresponding maximal function is bounded from BMO to BLO, generalising a known result of Bennett for the basis of cubes. When the basis of shapes does not possess an engulfing property but exhibits a product structure with respect to lower-dimensional shapes coming from bases that do possess an engulfing property, we show that the corresponding maximal function is bounded from BMO to a space we define and call rectangular BLO

Copy number aberrations of BCL2 and CDKN2A/B identified by array-CGH in thymic epithelial tumors

The molecular pathology of thymic epithelial tumors (TETs) is largely unknown. Using array comparative genomic hybridization (CGH), we evaluated 59 TETs and identified recurrent patterns of copy number (CN) aberrations in different histotypes. GISTIC algorithm revealed the presence of 126 significant peaks of CN aberration, which included 13 cancer-related genes. Among these peaks, CN gain of BCL2 and CN loss of CDKN2A/B were the only genes in the respective regions of CN aberration and were associated with poor outcome. TET cell lines were sensitive to siRNA knockdown of the anti-apoptotic molecules BCL2 and MCL1. Gx15-070, a pan-BCL2 inhibitor, induced autophagy-dependent necroptosis in TET cells via a mechanism involving mTOR pathways, and inhibited TET xenograft growth. ABT263, an inhibitor of BCL2/BCL-XL/BCL-W, reduced proliferation in TET cells when administered in combination with sorafenib, a tyrosine kinase inhibitor able to downregulate MCL1. Immunohistochemistry on 132 TETs demonstrated that CN loss of CDKN2A correlated with lack of expression of its related protein p16(INK4) and identified tumors with poor prognosis. The molecular markers BCL2 and CDKN2A may be of potential value in diagnosis and prognosis of TETs. Our study provides the first preclinical evidence that deregulated anti-apoptotic BCL2 family proteins may represent suitable targets for TET treatment