A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.

A note on the local power of the LR, Wald, score and gradient tests

This paper examines the local power of the likelihood ratio, Wald, score and gradient tests under the presence of a scalar parameter, phi say, that is orthogonal to the remaining parameters. We show that some of the coefficients that define the local powers remain unchanged regardless of whether phi is known or needs to be estimated, where as the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if phi were known, and the second, an additional term yielded by the fact that phi is unknown. The contribution of each set of parameters on the local powers of the tests can then be examined. Various implications of our main result are stated and discussed. Several examples are presented for illustrative purposes

Muscle reorganisation through local injection of stem cells in the diaphragm of mdx mice

Background: The diaphragm is the major respiratory muscle affected by Duchenne muscular dystrophy (DMD) and is responsible for causing 80% of deaths. The use of mechanical forces that act on the body or intermittent pressure on the airways improves the quality of life of patients but does not prevent the progression of respiratory failure. Thus, diseases that require tissue repair, such as DMD, represent a group of pathologies that have great potential for cell therapy. The application of stem cells directly into the diaphragm instead of systemic application can reduce cell migration to other affected areas and increase the chances of muscle reorganisation. The mdx mouse is a suitable animal model for this research because its diaphragmatic phenotype is similar to human DMD. Therefore, the aim of this study was to assess the potential cell implantation in the diaphragm muscle after the xenotransplantation of stem cells. Methods: A total of 9 mice, including 3 control BALB/Cmice, 3 5-month-old mdx mice without stem cell injections and 3 mdx mice injected with stem cells, were used. The animals injected with stem cells underwent laparoscopy so that stem cells from GFP-labelled rabbit olfactory epithelium could be locally injected into the diaphragm muscle. After 8 days, all animals were euthanised, and the diaphragm muscle was dissected and subjected to histological and immunohistochemical analyses. Results: Both the fresh diaphragm tissue and immunohistochemical analyses showed immunopositive GFP labelling of some of the cells and immunonegativity of myoblast bundles. In the histological analysis, we observed a reduction in the inflammatory infiltrate as well as the presence of a few peripheral nuclei and myoblast bundles. Conclusion: We were able to implant stem cells into the diaphragm via local injection, which promoted moderate muscle reorganisation. The presence of myoblast bundles cannot be attributed to stem cell incorporation because there was no immunopositive labelling in this structure. It is believed that the formation of the bundles may have been stimulated by cellular signalling mechanisms that have not yet been elucidated.

Local Injections of Adipose-Derived Mesenchymal Stem Cells Modulate Inflammation and Increase Angiogenesis Ameliorating the Dystrophic Phenotype in Dystrophin-Deficient Skeletal Muscle

The effects of adipose-derived mesenchymal stem cells (ADMSC) transplantation on degeneration, regeneration and skeletal muscle function were investigated in dystrophin-deficient mice (24-week-old). ADMSC transplantation improved muscle strength and, resistance to fatigue. An increase in fiber cross-sectional area and in the number of fibers with centralized nuclei and augment of myogenin content were observed. In ADMSC-treated muscles a decrease in muscle content of TNF-alpha, IL-6 and oxidative stress measured by Amplex(A (R)) reagent were observed. The level of TGF-beta 1 was lowered whereas that of VEGF, IL-10 and IL-4 were increased by ADMSC treatment. An increase in markers of macrophage M1 (CD11 and F4-80) and a decrease in T lymphocyte marker (CD3) and arginase-1 were also observed in ADMSCs-treated dystrophic muscle. No change was observed in iNOS expression. Increased phosphorylation of Akt, p70S6k and 4E-BP1 was found in dystrophic muscles treated with ADMSC. These results suggest that ADMSC transplantation modulates inflammation and improves muscle tissue regeneration, ameliorating the dystrophic phenotype in dystrophin-deficient mice.

A new local variety of Crepidomanes minutum (Hymenophyllaceae) in the Mascarene Archipelago (Indian Ocean) and a new record for Mauritius

Crepidomanes minutum (Hymenophyllaceae) is here identified and recorded from Mauritius for the first time. The Mauritian specimens, in addition to those of La Reunion observed at low to middle elevations, are easily distinguished from populations observed outside the Mascarene Archipelago by their dwarfed size and rarity of the stipe proliferation that usually characterizes this species. We thus describe a new variety in this species for the Mascarene Islands.

Dental pulp stem cells express proteins involved in the local invasiveness of odontogenic myxoma

Little is known about the histogenesis of the odontogenic myxoma (OM). Dental pulp stem cells could be candidate precursors of OM because both OM and the dental pulp share the same embryological origin: the dental papilla. For the purpose of comparing OM and stem cells, this study analyzed the expression of two proteins related to OM invasiveness (MMP-2 and hyaluronic acid) in human immature dental pulp stern cells (hIDPSCs). Three lineages of hIDPSCs from deciduous and permanent teeth were used in this study. Immunofluorescence revealed positive reactions for MMP-2 and hyaluronic acid (HA) in all hIDPSCs. MMP-2 appeared as dots throughout the cytoplasm, whereas HA appeared either as diffuse and irregular dots or as short fibrils throughout the cytoplasm and outside the cell bodies. The gene expression profile of each cell lineage was evaluated using RT-PCR analysis, and HA was expressed more intensively than MMP-2. HA expression was similar among the three hIDPSCs lineages, whereas MMP-2 expression was higher in DL-1 than in the other cell lines. The expression of proteins related to OM invasiveness in hIDPSCs could indicate that OM originates from dental pulp stem cells.

The local environment of Co2+ ions intercalated in vanadium oxide/hexadecylamine nanotubes

Vanadium oxide nanotubes constitute promising materials for applications in nanoelectronics as cathode materials, in sensor technology and in catalysis. In this work we present a study on hybrid vanadium oxide/hexadecylamine multiwall nanotubes doped with Co ions using state of the art x-ray diffraction and absorption techniques, to address the issue of the dopant location within the nanotubes' structure. The x-ray absorption near-edge structure analysis shows that the Co ions in the nanotubes are in the 2+ oxidation state, while extended x-ray absorption fine structure spectroscopy reveals the local environment of the Co2+ ions. Results indicate that Co atoms are exchanged at the interface between the vanadium oxide's layers and the hexadecylamines, reducing the amount of amine chains and therefore the interlayer distance, but preserving the tubular shape. The findings in this work are important for describing Co2+ interaction with vanadium oxide nanotubes at the molecular level and will help to improve the understanding of their physicochemical behavior, which is desired in view of their promising applications.

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n(-1/2), n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.

Figures of equilibrium for tidally deformed non-homogeneous celestial bodies

Abstract (2,250 Maximum Characters): Several theories of tidal evolution, since the theory developed by Darwin in the XIX century, are based on the figure of equilibrium of the tidally deformed body. Frequently the adopted figure is a Jeans prolate spheroid. In some case, however, the rotation is important and Roche ellipsoids are used. The main limitations of these models are (a) they refer to homogeneous bodies; (b) the rotation axis is perpendicular to the plane of the orbit. This communication aims at presenting several results in which these hypotheses are not done. In what concerns the non-homogeneity, the presented results concerns initially bodies formed by N homogeneous layers and we study the non sphericity of each layer and relate them to the density distribution. The result is similar to the Clairaut figure of equilibrium, often used in planetary sciences, but taking into full account the tidal deformation. The case of the rotation axis non perpendicular to the orbital plane is much more complex and the study has been restricted for the moment to the case of homogeneous bodies.