THE MAGNETIC FLOW ON THE MANIFOLD OF ORIENTED GEODESICS OF A THREE DIMENSIONAL SPACE FORM

Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical pseudo-Riemannian metric of signature (2,2)(2,2) and Kähler structure J. A smooth curve in L determines a ruled surface in M. We characterize the ruled surfaces of MM associated with the magnetic geodesics of LL, that is, those curves σσ in LL satisfying ∇σ˙σ˙=Jσ˙∇σ˙σ˙=Jσ˙. More precisely: a time-like (space-like) magnetic geodesic determines the ruled surface in M given by the binormal vector field along a helix with positive (negative) torsion. Null magnetic geodesics describe cones, cylinders or, in the hyperbolic case, also cones with vertices at infinity. This provides a relationship between the geometries of L and M.Fil: Godoy, Yamile Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaFil: Salvai, Marcos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentin

Marginally trapped submanifolds in Lorentzian space forms and in the Lorentzian product of a space form by the real line

We give local, explicit representation formulas for n-dimensional spacelike submanifolds which are marginally trapped in the Minkowski space, the de Sitter and anti de Sitter spaces and the Lorentzian products of the sphere and the hyperbolic space by the real line.Comment: 20 pages. Third version: a few corrections have been done. The bibliography has been update

The canonical contact structure on the space of oriented null geodesics of pseudospheres and products

Let Sk,m be the pseudosphere of signature (k,m). We show that the space ℒ0(Sk,m) of all oriented null geodesics in Sk,m is a manifold, and we describe geometrically its canonical contact distribution in terms of the space of oriented geodesics of certain totally geodesic degenerate hypersurfaces in Sk;m. Further, we find a contactomorphism with some standard contact manifold, namely, the unit tangent bundle of some pseudo-Riemannian manifold. Also, we express the null billiard operator on ℒ0(Sk,m) associated with some simple regions in Sk;m in terms of the geodesic flows of spheres. For the pseudo-Riemannian product N of two complete Riemannian manifolds, we give geometrical conditions on the factors for ℒ0(N) to be manifolds and exhibit a contactomorphism with some standard contact manifold.Fil: Godoy, Yamile Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; ArgentinaFil: Salvai, Marcos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentin

Outer billiards in the spaces of oriented geodesics of the three dimensional space forms

Let $M_{\kappa }$ be the three-dimensional space form of constant curvature $\kappa =0,1,-1$, that is, Euclidean space $\mathbb{R}^{3}$, the sphere $S^{3}$, or hyperbolic space $H^{3}$. Let $S$ be a smooth, closed, strictly convex surface in $M_{\kappa }$. We define an outer billiard map $B$ on the four dimensional space $\mathcal{G}_{\kappa }$ of oriented complete geodesics of $M_{\kappa }$, for which the billiard table is the subset of $\mathcal{G}_{\kappa }$ consisting of all oriented geodesics not intersecting $S$. We show that $B$ is a diffeomorphism when $S$ is quadratically convex. For $\kappa =1,-1$, $\mathcal{G}_{\kappa }$ has a K\"{a}hler structure associated with the Killing form of $\operatorname{Iso}(M_{\kappa })$. We prove that $B$ is a symplectomorphism with respect to its fundamental form and that $B$ can be obtained as an analogue to the construction of Tabachnikov of the outer billiard in $\mathbb{R}^{2n}$ defined in terms of the standard symplectic structure. We show that $B$ does not preserve the fundamental symplectic form on $\mathcal{G}_{\kappa }$ associated with the cross product on $M_{\kappa }$, for $\kappa =0,1,-1$. We initiate the dynamical study of this outer billiard in the hyperbolic case by introducing and discussing a notion of holonomy for periodic points.Comment: significant changes to exposition and presentation; new examples and figure

T Regulatory cells from non-obese diabetic mice show low responsiveness to IL-2 stimulation and exhibit differential expression of anergy-related and ubiquitination factors

Foxp3+ Regulatory T cells (Tregs) are pivotal for the maintenance of tolerance. Alterations in their number and/or function have been proposed to occur in the autoimmune-prone non-obese diabetic (NOD) mouse. Comparing the frequencies and absolute numbers of CD4+Foxp3+CD25+ Tregs among 4 to 6-week old NOD, B6, and BALB/c mice, we observed differences in counts and Foxp3 expression in Tregs from secondary lymphoid organs, but not in the thymus. Upon TCR and IL-2 stimulation, NOD Tregs showed lower responses than Tregs from B6 and BALB/c mice. Indeed, NOD Tregs responded with less proliferation and with smaller increments in the expression of CD25, LAP-1, CD39, PD-1, PD-L1, and LAG-3, when in vitro cultured for 3 days with anti-CD3/CD28 in the absence or presence of IL-2, Tregs from NOD mice showed to be highly dependent on IL-2 to maintain Foxp3 expression. Moreover, NOD Tregs become producers of IL-17 and INF-gamma more easily than Tregs from the other strains. In addition, NOD Tregs showed lower responsiveness to IL-2, with significantly reduced levels of pSTAT5, even at high IL-2 doses, with respect to B6 and BALB/c Tregs. Interestingly, NOD Tregs exhibit differences in the expression of SOCS3, GRAIL, and OTUB1 when compared with Tregs from B6 and BALB/c mice. Both, at steady state conditions and also after activation, Tregs from NOD mice showed increased levels of OTUB1 and low levels of GRAIL. In addition, NOD Tregs had differences in the expression of ubiquitin related molecules that play a role in the maintenance of Foxp3 cellular pools. Indeed, significantly higher STUB1/USP7 ratios were detected in NOD Tregs, both at basal conditions and after stimulation, compared to in B6 and BALB/c Tregs. Moreover, the addition of a proteasome inhibitor to cell cultures, conferred NOD Tregs the ability to retain Foxp3 expression. Herein, we provide evidence indicating a differential expression of SOCS3, GRAIL, and STUB1/USP7 in Tregs from NOD mice, factors known to be involved in IL-2R signaling and to affect Foxp3 stability. These findings add to the current knowledge of the immunobiology of Tregs and may be related to the known insufficiency of Tregs from NOD mice to maintain self-tolerance.Fil: Godoy, Gloria Janet. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; Argentina. Universidad Nacional de Córdoba; ArgentinaFil: Olivera, Carolina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; Argentina. Universidad Nacional de Córdoba; ArgentinaFil: Paira, Daniela Andrea. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; ArgentinaFil: Salazar, Florencia. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; ArgentinaFil: Ana, Yamile. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; ArgentinaFil: Stempin, Cinthia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; Argentina. Universidad Nacional de Córdoba; ArgentinaFil: Motrich, Ruben Dario. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; ArgentinaFil: Rivero, Virginia Elena. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; Argentin

Creencias y conocimientos de los médicos generales sobre el trastorno depresivo en instituciones públicas de Bogotá

Objetivo. Se buscó establecer si los conocimientos y las creencias que los médicos generales tienen sobre el trastorno depresivo, pueden constituir una barrera para que los pacientes accedan a un diagnóstico y tratamiento oportunos.Metodología. Se utilizó una metodología cuantitativa de tipo descriptivo, implementada en dos instituciones del sector público de Bogotá, D.C, cuya población objeto fueron los médicos generales de consulta externa del primer nivel de atención.Resultados. El conocimiento de los médicos generales sobre los trastornos asociados a los cuadros depresivos es limitado en lo que tiene que ver con la etiología, el diagnóstico y el tratamiento. Entre sus creencias, la mayoría de los médicos entrevistados consideró que los mecanismos bioquímicos son importantes para la instauración de los síntomas depresivos y que, frente al ciclo vital, deprimirse es natural en la edad adulta.Conclusiones. Los médicos generales tuvieron dificultades en los conocimientos del trastorno depresivo, en lo relacionado con la posible etiología, el diagnóstico y el tratamiento, lo cual limita las posibilidades de su detección y manejo, así como de la promoción de la salud y prevención del trastorno mental