On the stratication of secant varieties of Veronese varieties via symmetric rank.

When considering $\sigma_r(X)$, the variety of r-secant \PP {r-1} to a projective variety $X$, one question which arises is what are the possible values of the $X$-rank of points on $\sigma_r(X)$, apart from the generic value $r$? This geometric problem is of particular relevance (also for Applied Math) when $X$ is a variety parameterizing some kind of tensors. We study here the case when $X$ is a Veronese variety (i.e. the case of symmetric tensors). We find the complete description of the rank strata in some cases, and we give algorithms which compute the symmetric rank

Approximating the 2-dimensional matching distance

Some new approximation results about the 2-dimensional matching distance are presented, leading to the formulation of an algorithm for its computation (up to an arbitrary input error)

Data about the role of RXRγ in T3-mediated oligodendrocyte precursor cell differentiation

This dataset contains data describing the effect of the knock-out of the Rxrg gene in neral stem cell (NSC)-derived oligodendrocyte precursor cells (OPCs) differentiation and maturation. Data has been obtained by transcriptomic analysis using RNAseq in cells isolated by WT and Rxrg-/- animals cultured as indifferentiated precursors and 24 hours after the differentiation induction by triiodotironine (T3) exposure, mimiking the physiologic differentiation/maturation molecular machinery. RNAseq data has been validated using morphological analysis. Molecular tools has been used to inhibit (cyclopamine, GANT61) or activate (SAG, purmorphamine) the sonic hadgehog (SHH) pathway in differentiating WT and Rxrg-/- OPC cultures. Specific markers (NG2, MBP) have been used to quantify the differentiation/maturation of the OPC culture, measuring the percentage of precursors and mature oligodendrocytes