Evolutes of curves in the Lorentz-Minkowski plane

We can use a moving frame, as in the case of regular plane curves in the Euclidean plane, in order to define the arc-length parameter and the Frenet formula for non-lightlike regular curves in the Lorentz-Minkowski plane. This leads naturally to a well defined evolute associated to non-lightlike regular curves without inflection points in the Lorentz-Minkowski plane. However, at a lightlike point the curve shifts between a spacelike and a timelike region and the evolute cannot be defined by using this moving frame. In this paper, we introduce an alternative frame, the lightcone frame, that will allow us to associate an evolute to regular curves without inflection points in the Lorentz-Minkowski plane. Moreover, under appropriate conditions, we shall also be able to obtain globally defined evolutes of regular curves with inflection points. We investigate here the geometric properties of the evolute at lightlike points and inflection points

The hyperbolic Gauss-Bonnet type theorem

We show that the Gauss-Bonnet type theorem holds for the hyperbolic Gauss-Kronecker curvature of a closed orientable even dimensional hypersurface in hyperbolic space. We also give detailed studies for surfaces

The horospherical geomoetry of submanifolds in hyperbolic space

We study some geometrical properties associated to the contact of submanifolds with hyperhorospheres in hyperbolic $n$-space as an application of the theory of Legendrian singularities

Conformal invariants interpreted in the sitter space

[EN] We give a new interpretation of the conformally invariant differential 1-forms along the curvature lines of hypersurfaces in IRn+1, obtained in [10], in terms of the infinitesimal arc-length of conveniently chosen curves in the (n + 2)-dimensional de Sitter space.Work of both authors is partially supported by DGCYT and FEDER grant no. MTM2006-06027Romero Fuster, MC.; Sanabria Codesal, E. (2008). Conformal invariants interpreted in the sitter space. Matemática Contemporânea. 35(2):205-220. http://hdl.handle.net/10251/52667S20522035

The horospherical geometry of surfaces in Hyperbolic 4-space

We study some geometrical properties associated to the contacts of surfaces with hyperhorospheres in Ht ( -1). We introduce the concepts of osculating hyperhorospheres, horobinormals, horoasymptotic directions and horospherical points and provide conditions ensuring their existence. We show that totally semiumbilical surfaces have orthogonal horoasymp­totic directions

The lightcone Gauss map of a spacelike surface in Minkowski 4-space

We study the geometry of the spacclike surfaces in Minkowski 4-space through their generic contact with lightlike hyperplanes

Development Refractoriness of MLL-Rearranged Human B Cell Acute Leukemias to Reprogramming into Pluripotency

Induced pluripotent stem cells (iPSCs) are a powerful tool for disease modeling. They are routinely generated from healthy donors and patients from multiple cell types at different developmental stages. However, reprogramming leukemias is an extremely inefficient process. Few studies generated iPSCs from primary chronic myeloid leukemias, but iPSC generation from acute myeloid or lymphoid leukemias (ALL) has not been achieved. We attempted to generate iPSCs from different subtypes of B-ALL to address the developmental impact of leukemic fusion genes. OKSM(L)-expressing mono/polycistronic-, retroviral/lentiviral/episomal-, and Sendai virus vector-based reprogramming strategies failed to render iPSCs in vitro and in vivo. Addition of transcriptomic-epigenetic reprogramming ‘‘boosters’’ also failed to generate iPSCs from B cell blasts and B-ALL lines, and when iPSCs emerged they lacked leukemic fusion genes, demonstrating non-leukemic myeloid origin. Conversely, MLL-AF4-overexpressing hematopoietic stem cells/B progenitors were successfully reprogrammed, indicating that B cell origin and leukemic fusion gene were not reprogramming barriers. Global transcriptome/DNA methylome profiling suggested a developmental/differentiation refractoriness of MLL-rearranged B-ALL to reprogramming into pluripotency

Study of Leading Hadrons in Gluon and Quark Fragmentation

The study of quark jets in e+e- reactions at LEP has demonstrated that the hadronisation process is reproduced well by the Lund string model. However, our understanding of gluon fragmentation is less complete. In this study enriched quark and gluon jet samples of different purities are selected in three-jet events from hadronic decays of the Z collected by the DELPHI experiment in the LEP runs during 1994 and 1995. The leading systems of the two kinds of jets are defined by requiring a rapidity gap and their sum of charges is studied. An excess of leading systems with total charge zero is found for gluon jets in all cases, when compared to Monte Carlo Simulations with JETSET (with and without Bose-Einstein correlations included) and ARIADNE. The corresponding leading systems of quark jets do not exhibit such an excess. The influence of the gap size and of the gluon purity on the effect is studied and a concentration of the excess of neutral leading systems at low invariant masses (<~ 2 GeV/c^2) is observed, indicating that gluon jets might have an additional hitherto undetected fragmentation mode via a two-gluon system. This could be an indication of a possible production of gluonic states as predicted by QCD.Comment: 19 pages, 6 figures, Accepted by Phys. Lett.