Although stem cell therapy holds promise as a potential treatment in a number of diseases, the tumorigenicity of embryonic stem cells (ESC) and induced pluripotent stem cells remains a major obstacle. <i>In vitro</i> predifferentiation of ESCs can help prevent the risk of teratoma formation, yet proliferating neural progenitors can generate tumors, especially in the presence of immunosuppressive therapy. In this study, we investigated the effects of the microenvironment on stem cell growth and teratoma development using undifferentiated ESCs. Syngeneic ESC transplantation triggered an inflammatory response that involved the recruitment of bone marrow (BM)derived macrophages. These macrophages differentiated into an M2 or angiogenic phenotype that expressed multiple angiogenic growth factors and proteinases, such as macrophage migration inhibitory factor (MIF), VEGF, and matrix metalloproteinase 9

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In this paper, we establish the global C^{2,α} and W^{2,p} regularity for the Monge-Amp`ere equation det D^2u = f subject to boundary condition Du(Ω) = Ω^∗, where Ω and Ω^∗ are bounded convex domains in the Euclidean space R^n with C^{1,1} boundaries, and f is a Ho ̈lder continuous function. This boundary value problem arises naturally in optimal transportation and many other applications.

Mean curvature ows of hypersurfaces have been extensively studied and there are various dierent approaches and many beautiful results. However, relatively little is known about mean curvature ows of submanifolds of higher codimensions. This notes starts with some basic materials on submanifold geometry, and then introduces mean curvature ows in general dimensions and co-dimensions. The related techniques in the so called \blow-up" analysis are also discussed. At the end, we present some global existence and convergence results for mean curvature ows of two-dimensional surfaces in four-dimensional ambient spaces.

We consider a regularization method for mean curvature flow of a submanifold of arbitrary codimension in the Euclidean space,through higher order equations. We prove that the regularized problems converge to the mean curvature flow for all times before the first singularity.