Mammary gland involution is characterized by extensive apoptosis of the epithelial cells. At the onset of involution, Stat3 is specifically activated. To address the function of this signaling molecule in mammary epithelial apoptosis, we have generated a conditional knockout of Stat3 using the Cre-lox recombination system. Following weaning, a decrease in apoptosis and a dramatic delay of invol...

During mammary gland involution, the epithelial mesenchymal transition (EMT) process plays an important role in tissue remodelling and in the termination of milk production. Transforming growth factor β (TGFβ) has been known as a central inducer to EMT and contributor to the mammary gland involution. However, the whole mechanism has accomplished the EMT process in mammary gland is still unclear...

In this paper we investigate the Lipschitz equivalence of dust-like self-similar sets in Rd. One of the fundamental results by Falconer and Marsh [On the Lipschitz equivalence of Cantor sets, Mathematika, 39 (1992), 223– 233] establishes conditions for Lipschitz equivalence based on the algebraic properties of the contraction ratios of the self-similar sets. In this paper we extend the study by...

We introduce Lipschitz continuity of set-valued maps with respect to a given set difference. The existence of Lipschitz selections that pass through any point of the graph of the map and inherit its Lipschitz constant is studied. We show that the Lipschitz property of the set-valued map with respect to the Demyanov difference with a given constant is characterized by the same property of its ge...

We characterize the variation functions of computable Lipschitz functions. We show that a real z is computably random if and only if every computable Lipschitz function is differentiable at z. Furthermore, a real z is Schnorr random if and only if every Lipschitz function with L1-computable derivative is differentiable at z. For the implications from left to right we rely on literature results....

Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure m. We prove that the set of of real valued Lipschitz function with non zero point-wise Lipschitz constant m-almost everywhere is residual, and hence dense, in the Banach space of Lipschitz and bounded functions. The result is the metric analogous of a result proved for real valued Lipschitz maps...

Strong convergence results on tamed Euler schemes, which approximate stochastic differential equations with superlinearly growing drift coefficients that are locally one-sided Lipschitz continuous, are presented in this article. The diffusion coefficients are assumed to be locally Lipschitz continuous and have at most linear growth. Furthermore, the classical rate of convergence, i.e. one–half,...

We show that the odd-indexed derived Witt groups of a semilocal ring with trivial involution vanish. We show that this is wrong when the involution is not trivial and we provide examples.