A generalisation of the Hopf Construction and harmonic morphisms into \s^2

In this paper we construct a new family of harmonic morphisms \varphi:V^5\to\s^2, where $V^5$ is a 5-dimensional open manifold contained in an ellipsoidal hypersurface of \c^4=\r^8. These harmonic morphisms admit a continuous extension to the completion ${V^{\ast}}^5$, which turns out to be an explicit real algebraic variety. We work in the context of a generalization of the Hopf construction and equivariant theory.Comment: 10 page

Properties of biharmonic submanifolds in spheres

In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature submanifolds in spheres.Comment: 10 pages; contribution to the Proceedings of the 11-th International Conference on Geometry, Integrability and Quantization, Varna 2009, Bulgari

Classification results for biharmonic submanifolds in spheres

We classify biharmonic submanifolds with certain geometric properties in Euclidean spheres. For codimension 1, we determine the biharmonic hypersurfaces with at most two distinct principal curvatures and the conformally flat biharmonic hypersurfaces. We obtain some rigidity results for pseudo-umbilical biharmonic submanifolds of codimension 2 and for biharmonic surfaces with parallel mean curvature vector field. We also study the type, in the sense of B-Y. Chen, of compact proper biharmonic submanifolds with constant mean curvature in spheres.Comment: Dedicated to Professor Vasile Oproiu on his 65th birthday, 14 page

Helix surfaces in the special linear group

We characterize helix surfaces (constant angle surfaces) in the special linear group $\mathrm{SL}(2,\r)$. In particular, we give an explicit local description of these surfaces in terms of a suitable curve and a 1-parameter family of isometries of $\mathrm{SL}(2,\r)$.Comment: Minor corrections. To appear in Annali di Matematica Pura e Applicata. arXiv admin note: substantial text overlap with arXiv:1206.127

SILAC labeling coupled to shotgun proteomics analysis of membrane proteins of liver stem/hepatocyte allows to candidate the inhibition of TGF-beta pathway as causal to differentiation

Background: Despite extensive research on hepatic cells precursors and their differentiated states, much remains to be learned about the mechanism underlying the self-renewal and differentiation.Results: We apply the SILAC (stable isotope labeling by amino acids in cell culture) approach to quantitatively compare the membrane proteome of the resident liver stem cells (RLSCs) and their progeny spontaneously differentiated into epithelial/hepatocyte (RLSCdH). By means of nanoLC-MALDI-TOF/TOF approach, we identified and quantified 248 membrane proteins and 57 of them were found modulated during hepatocyte differentiation. Functional clustering of differentially expressed proteins by Ingenuity Pathway Analysis revealed that the most of membrane proteins found to be modulated are involved in cell-to-cell signaling/interaction pathways. Moreover, the upstream prediction analysis of proteins involved in cell-to-cell signaling and interaction unveiled that the activation of the mesenchymal to epithelial transition (MET), by the repression of TGFB1/Slug signaling, may be causal to hepatocyte differentiation.Conclusions: Taken together, this study increases the understanding of the underlying mechanisms modulating the complex biological processes of hepatic stem cell proliferation and differentiation. © 2014 Montaldo et al.; licensee BioMed Central Ltd