A continuous movement version of the Banach—Tarski paradox: A solution to de Groot's Problem

In 1924 Banach and Tarski demonstrated the existence of a paradoxical decomposition of the 3-ball B, i.e., a piecewise isometry from B onto two copies of B. This article answers a question of de Groot from 1958 by showing that there is a paradoxical decomposition of B in which the pieces move continuously while remaining disjoint to yield two copies of B. More generally, we show that if n ≥ 2, any two bounded sets i

Phenotypic Characterization of Chicken Thymic Stromal Elements

Phenotypic profiles of the thymic stromal components provide an excellent approach to elucidating the nature of the microenvironment of this organ. To address this issue in chickens, we have produced an extensive panel of 18 mAb to the thymic stroma. These mAb have been extensively characterized with respect to their phenotypic specificities and reveal that the stromal cells are equally as complex as the T cells whose maturation they direct. They further demonstrate that, in comparison to the mammalian thymus, there is a remarkable degree of conservation in thymic architecture between phylogenetically diverse species. Eleven mAb reacted with thymic epithelial cells: MUI-73 was panepithelium, MUI-54 stained all cortical and medullary epithelium but only a minority of the subcapsule, MUI-52 was specific for isolated stellate cortical epithelial cells, MUI-62, -69, and -71 were specific for the medulla (including Hassall’s corpusclelike structures), MUI-51, -53, -70, and -75 reacted only with the type-I epithelium, or discrete regions therein, lining the subcapsular and perivascular regions and MUI-58 demonstrated the antigenic similarity between the subcapsule and the medulla. Seven other mAb identified distinct isolated stromal cells throughout the cortex and medulla. Large thymocyte-rich regions, which often spanned from the outer cortex to medulla, lacked epithelial cells. These mAb should prove invaluable for determining the functional significance of thymic stromal-cell subsets to thymopoiesis

Myc Cooperates with Ras by Programming Inflammation and Immune Suppression.

The two oncogenes KRas and Myc cooperate to drive tumorigenesis, but the mechanism underlying this remains unclear. In a mouse lung model of KRasG12D-driven adenomas, we find that co-activation of Myc drives the immediate transition to highly proliferative and invasive adenocarcinomas marked by highly inflammatory, angiogenic, and immune-suppressed stroma. We identify epithelial-derived signaling molecules CCL9 and IL-23 as the principal instructing signals for stromal reprogramming. CCL9 mediates recruitment of macrophages, angiogenesis, and PD-L1-dependent expulsion of T and B cells. IL-23 orchestrates exclusion of adaptive T and B cells and innate immune NK cells. Co-blockade of both CCL9 and IL-23 abrogates Myc-induced tumor progression. Subsequent deactivation of Myc in established adenocarcinomas triggers immediate reversal of all stromal changes and tumor regression, which are independent of CD4+CD8+ T cells but substantially dependent on returning NK cells. We show that Myc extensively programs an immune suppressive stroma that is obligatory for tumor progression