The odd side of torsion geometry

We introduce and study a notion of `Sasaki with torsion structure' (ST) as an odd-dimensional analogue of K\"ahler with torsion geometry (KT). These are normal almost contact metric manifolds that admit a unique compatible connection with 3-form torsion. Any odd-dimensional compact Lie group is shown to admit such a structure; in this case the structure is left-invariant and has closed torsion form. We illustrate the relation between ST structures and other generalizations of Sasaki geometry, and explain how some standard constructions in Sasaki geometry can be adapted to this setting. In particular, we relate the ST structure to a KT structure on the space of leaves, and show that both the cylinder and the cone over an ST manifold are KT, although only the cylinder behaves well with respect to closedness of the torsion form. Finally, we introduce a notion of `G-moment map'. We provide criteria based on equivariant cohomology ensuring the existence of these maps, and then apply them as a tool for reducing ST structures.Comment: 34 pages; v2: added a small generalization (Proposition 3.6) of the cone construction; two references added. To appear on Ann. Mat. Pura App

New Techniques for Analysing Axisymmetric Gravitational Systems. 1. Vacuum Fields

A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These equations are under-determined. Restricting the Weyl tensor to type D produces a set of equations which can be solved, and a range of new techniques are introduced to simplify the problem. Imposing the further condition that the solution is asymptotically flat yields the Kerr solution uniquely. The implications of this result for the no-hair theorem are discussed. The techniques developed here have many other applications, which are described in the conclusions.Comment: 30 pages, no figure

On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories

The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between k-symplectic field theories and the so-called autonomous k-cosymplectic field theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between k-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian field theories (those where the configuration bundle of the theory is trivial).Comment: 25 page

Singularity free dilaton-driven cosmologies and pre-little-bang

There are no reasons why the singularity in the growth of the dilaton coupling should not be regularised, in a string cosmological context, by the presence of classical inhomogeneities. We discuss a class of inhomogeneous dilaton-driven models whose curvature invariants are all bounded and regular in time and space. We prove that the non-space-like geodesics of these models are all complete in the sense that none of them reaches infinity for a finite value of the affine parameter. We conclude that our examples represent truly singularity-free solutions of the low energy beta functions. We discuss some symmetries of the obtained solutions and we clarify their physical interpretation. We also give examples of solutions with spherical symmetry. In our scenario each physical quantity is everywhere defined in time and space, the big-bang singularity is replaced by a maximal curvature phase where the dilaton kinetic energy reaches its maximum. The maximal curvature is always smaller than one (in string units) and the coupling constant is also smaller than one and it grows between two regimes of constant dilaton, implying, together with the symmetries of the solutions, that higher genus and higher curvature corrections are negligible. We argue that our examples describe, in a string cosmological context, the occurrence of ``little bangs''(i.e. high curvature phases which never develop physical singularities). They also suggest the possibility of an unexplored ``pre-little-bang'' phase.Comment: 25 pages in LaTex style, 3 encapsulated figure

T-Duality and Penrose limits of spatially homogeneous and inhomogeneous cosmologies

Penrose limits of inhomogeneous cosmologies admitting two abelian Killing vectors and their abelian T-duals are found in general. The wave profiles of the resulting plane waves are given for particular solutions. Abelian and non-abelian T-duality are used as solution generating techniques. Furthermore, it is found that unlike in the case of abelian T-duality, non-abelian T-duality and taking the Penrose limit are not commutative procedures.Comment: 16 pages, 4 figures. Discussion on non-abelian T-duality expande

Thrombopoietin Receptor Agonists for Severe Thrombocytopenia after Allogeneic Stem Cell Transplantation : Experience of the Spanish Group of Hematopoietic Stem Cell Transplant

Persistent thrombocytopenia is a common complication after allogeneic hematopoietic stem cell transplantation (allo-SCT). Romiplostim and eltrombopag are the currently available thrombopoietin receptor agonists (TPO-RAs), and some studies with very small numbers of cases have reported their potential efficacy in the allo-SCT setting. The present retrospective study evaluated the safety and efficacy of TPO-RAs in 86 patients with persistent thrombocytopenia after allo-HSCT. Sixteen patients (19%) had isolated thrombocytopenia (PT), and 71 (82%) had secondary failure of platelet recovery (SFPR). TPO-RA therapy was started at a median of 127 days (range, 27 to 1177 days) after allo-SCT. The median initial and maximum administered doses were 50 mg/day (range, 25 to 150 mg/day) and 75 mg/day (range, 25 to 150 mg/day), respectively, for eltrombopag and 1 µg/kg (range, 1 to 7 µg/kg) and 5 µg/kg (range, 1 to 10 µg/kg), respectively, for romiplostin. The median platelet count before initiation of TPO-RA therapy was 14,000/µL (range, 1000 to 57,000/µL). Platelet recovery to ≥50,000/µL without transfusion support was achieved in 72% of patients at a median time of 66 days (range, 2 to 247 days). Eighty-one percent of the patients had a decreased number of megakaryocytes before treatment, showing a slower response to therapy (P =.011). The median duration of treatment was 62 days (range, 7 to 700 days). Grade 3-4 adverse events (hepatic and asthenia) were observed in only 2% of the patients. At last follow-up, 81% of patients had discontinued TPO-RAs and maintained response, and 71% were alive. To our knowledge, this is the largest series analyzing the use of TPO-RAs after allo-SCT reported to date. Our results support the efficacy and safety in this new setting. Further prospective trials are needed to increase the level of evidence and to identify predictors of response

Lower-order ODEs to determine new twisting type N Einstein spaces via CR geometry

In the search for vacuum solutions, with or without a cosmological constant, of the Einstein field equations of Petrov type N with twisting principal null directions, the CR structures to describe the parameter space for a congruence of such null vectors provide a very useful tool. A work of Hill, Lewandowski and Nurowski has given a good foundation for this, reducing the field equations to a set of differential equations for two functions, one real, one complex, of three variables. Under the assumption of the existence of one Killing vector, the (infinite-dimensional) classical symmetries of those equations are determined and group-invariant solutions are considered. This results in a single ODE of the third order which may easily be reduced to one of the second order. A one-parameter class of power series solutions, g(w), of this second-order equation is realized, holomorphic in a neighborhood of the origin and behaving asymptotically as a simple quadratic function plus lower-order terms for large values of w, which constitutes new solutions of the twisting type N problem. The solution found by Leroy, and also by Nurowski, is shown to be a special case in this class. Cartan's method for determining equivalence of CR manifolds is used to show that this class is indeed much more general. In addition, for a special choice of a parameter, this ODE may be integrated once, to provide a first-order Abel equation. It can also determine new solutions to the field equations although no general solution has yet been found for it.Comment: 28 page

Effects of Subthalamic Nucleus Lesions and Stimulation upon Corticostriatal Afferents in the 6-Hydroxydopamine-Lesioned Rat

Abnormalities of striatal glutamate neurotransmission may play a role in the pathophysiology of Parkinson's disease and may respond to neurosurgical interventions, specifically stimulation or lesioning of the subthalamic nucleus (STN). The major glutamatergic afferent pathways to the striatum are from the cortex and thalamus, and are thus likely to be sources of striatal neuronally-released glutamate. Corticostriatal terminals can be distinguished within the striatum at the electron microscopic level as their synaptic vesicles contain the vesicular glutamate transporter, VGLUT1. The majority of terminals which are immunolabeled for glutamate but are not VGLUT1 positive are likely to be thalamostriatal afferents. We compared the effects of short term, high frequency, STN stimulation and lesioning in 6-hydroxydopamine (6OHDA)-lesioned rats upon striatal terminals immunolabeled for both presynaptic glutamate and VGLUT1. 6OHDA lesions resulted in a small but significant increase in the proportions of VGLUT1-labeled terminals making synapses on dendritic shafts rather than spines. STN stimulation for one hour, but not STN lesions, increased the proportion of synapses upon spines. The density of presynaptic glutamate immuno-gold labeling was unchanged in both VGLUT1-labeled and -unlabeled terminals in 6OHDA-lesioned rats compared to controls. Rats with 6OHDA lesions+STN stimulation showed a decrease in nerve terminal glutamate immuno-gold labeling in both VGLUT1-labeled and -unlabeled terminals. STN lesions resulted in a significant decrease in the density of presynaptic immuno-gold-labeled glutamate only in VGLUT1-labeled terminals. STN interventions may achieve at least part of their therapeutic effect in PD by normalizing the location of corticostriatal glutamatergic terminals and by altering striatal glutamatergic neurotransmission

Coexpression of vesicular glutamate transporters 1 and 2, glutamic acid decarboxylase and calretinin in rat entorhinal cortex

We studied the distribution and coexpression of vesicular glutamate transporters (VGluT1, VGluT2), glutamic acid decarboxylase (GAD) and calretinin (CR, calcium-binding protein) in rat entorhinal cortex, using immunofluorescence staining and multichannel confocal laser scanning microscopy. Images were computer processed and subjected to automated 3D object recognition, colocalization analysis and 3D reconstruction. Since the VGluTs (in contrast to CR and GAD) occurred in fibers and axon terminals only, we focused our attention on these neuronal processes. An intense, punctate VGluT1-staining occurred everywhere in the entorhinal cortex. Our computer program resolved these punctae as small 3D objects. Also VGluT2 showed a punctate immunostaining pattern, yet with half the number of 3D objects per tissue volume compared with VGluT1, and with statistically significantly larger 3D objects. Both VGluTs were distributed homogeneously across cortical layers, with in MEA VGluT1 slightly more densely distributed than in LEA. The distribution pattern and the size distribution of GAD 3D objects resembled that of VGluT2. CR-immunopositive fibers were abundant in all cortical layers. In double-stained sections we noted ample colocalization of CR and VGluT2, whereas coexpression of CR and VGluT1 was nearly absent. Also in triple-staining experiments (VGluT2, GAD and CR combined) we noted coexpression of VGluT2 and CR and, in addition, frequent coexpression of GAD and CR. Modest colocalization occurred of VGluT2 and GAD, and incidental colocalization of all three markers. We conclude that the CR-containing axon terminals in the entorhinal cortex belong to at least two subpopulations of CR-neurons: a glutamatergic excitatory and a GABAergic inhibitory

Formin homology 2 domains occur in multiple contexts in angiosperms

BACKGROUND: Involvement of conservative molecular modules and cellular mechanisms in the widely diversified processes of eukaryotic cell morphogenesis leads to the intriguing question: how do similar proteins contribute to dissimilar morphogenetic outputs. Formins (FH2 proteins) play a central part in the control of actin organization and dynamics, providing a good example of evolutionarily versatile use of a conserved protein domain in the context of a variety of lineage-specific structural and signalling interactions. RESULTS: In order to identify possible plant-specific sequence features within the FH2 protein family, we performed a detailed analysis of angiosperm formin-related sequences available in public databases, with particular focus on the complete Arabidopsis genome and the nearly finished rice genome sequence. This has led to revision of the current annotation of half of the 22 Arabidopsis formin-related genes. Comparative analysis of the two plant genomes revealed a good conservation of the previously described two subfamilies of plant formins (Class I and Class II), as well as several subfamilies within them that appear to predate the separation of monocot and dicot plants. Moreover, a number of plant Class II formins share an additional conserved domain, related to the protein phosphatase/tensin/auxilin fold. However, considerable inter-species variability sets limits to generalization of any functional conclusions reached on a single species such as Arabidopsis. CONCLUSIONS: The plant-specific domain context of the conserved FH2 domain, as well as plant-specific features of the domain itself, may reflect distinct functional requirements in plant cells. The variability of formin structures found in plants far exceeds that known from both fungi and metazoans, suggesting a possible contribution of FH2 proteins in the evolution of the plant type of multicellularity