In this letter we propose a new and model-independent cosmological test for the distance-duality (DD) relation, η = D L (z)(1 + z) −2 /D A (z) = 1, where D L and D A are, respectively, the luminosity and angular diameter distances. For D L we consider two sub-samples of SNe type Ia taken from Constitution data (2009) whereas D A distances are provided by two samples of galaxy clusters compiled by De Fillipis et al. (2005) and Bonamente et al. (2006) by combining Sunyaev-Zeldovich effect (SZE) and X-ray surface brightness. The SNe Ia redshifts of each sub-sample were carefully chosen to coincide with the ones of the associated galaxy cluster sample (∆z < 0.005) thereby allowing a direct test of DD relation. Since for very low redshifts, D A (z) ≅ D L (z), we have tested the DD relation by assuming that η is a function of the redshift parametrized by two different expressions: η(z) = 1 + η 0 z and η(z) = 1 + η 0 z/(1 + z), where η 0 is a constant parameter quantifying a possible departure from the strict validity of the reciprocity relation (η 0 = 0). In the best scenario (linear parametrization) we obtain η 0 = −0.28 +0.44 −0.44 (2σ, statistical + systematic errors) for de Fillipis et al. sample (elliptical geometry), a result only marginally compatible with the DD relation. However, for Bonamente et al. sample (spherical geometry) the constraint is η 0 = −0.42 +0.34 −0.34 (3σ, statistical + systematic errors) which is clearly incompatible with the duality-distance relation.

Context. Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, η = D L (z)(1 + z) 2 /D A (z) = 1, an exact result required by the Etherington reciprocity theorem where D L (z) and D A (z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts D A (z) = D L (z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine D A (z) from galaxy clusters. This combination offers the possibility of testing the validity of the DD relation, as well as determining which physical processes occur in galaxy clusters via their shapes. Aims. We use WMAP (7 years) results by fixing the conventional ΛCDM model to verify the consistence between the validity of DD relation and different assumptions about galaxy cluster geometries usually adopted in the literature. Methods. We assume that η is a function of the redshift parametrized by two different relations: η(z) = 1+η 0 z, and η(z) = 1+η 0 z/(1+z), where η 0 is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of η 0 , we consider the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical (isothermal) and spherical (non-isothermal) β models. The strict validity of the DD relation will occur only if the maximum value of η 0 PDF is centered on η 0 = 0. Results. It was found that the elliptical β model is in good agreement with the data, showing no violation of the DD relation (PDF peaked close to η 0 = 0 at 1σ), while the spherical (non-isothermal) one is only marginally compatible at 3σ. Conclusions. The present results derived by combining the SZE and X-ray surface brightness data from galaxy clusters with the latest WMAP results (7-years) favors the elliptical geometry for galaxy clusters. It is remarkable that a local property like the geometry of galaxy clusters might be constrained by a global argument provided by the cosmic DD relation.

The two-point correlation function for the dust distribution in the unperturbed Einsteinde Sitter cosmological model is studied along the past light cone. It was found that the two-point correlation function seems unable to represent the theoretical distribution of dust along the backward null cone of this unperturbed model, which has already been determined in a previous paper as being apparently inhomogeneous at ranges usually considered as local. Such result was revisited in order to determine more precisely the quantitative limits where, in theory, we can detect apparent homogeneity, and it was found that this may only happen up to z ∼ 10 −2 . A different statistical analysis proposed by Pietronero is used, and it appears to be able to represent more accurately the theoretical distribution of dust in this cosmology. In the light of these results, it is argued that the usual practice of disregarding relativistic effects in studies of distribution of galaxies, by considering them as being placed on local regions, seems to be valid only on much closer scales than it is commonly believed, if the Einstein-de Sitter model is used as a theoretical framework for studying such distributions. In this cosmology with H 0 = 75 Km s −1 Mpc −1 , that may only happen in redshifts as low as z ≈ 0.04, which means that the local approximation seems to be valid up to zeroth order of approximation only. As at present there are many redshift surveys which have already probed at deeper ranges, it seems that in order to compare the Friedmann models with observations we have to be very careful when ignoring the past light cone problem in observational cosmology, either in theoretical calculations or in data analysis, due to relativistic effects which produce observable inhomogeneity even in spatially homogeneous cosmological models.

Background: The aim of the present study was to investigate whether adipose-derived stem cells could contribute to skeletal muscle-healing. Methods: Adipose-derived stem cells of male rats were cultured and injected into the soleus muscles of female rats. Two and four weeks after injections, muscles were tested fortetanic force (50 Hz). Histological analysis was performed to evaluate muscle collagen deposition and the number of centronucleated muscle fibers. In orderto track donor cells, chimerism was detected with use of real-time polymerase chain reaction targeting the male sex-determining region Y (SRY) gene. Results: Two weeks after cell injection, tetanus strength and the number of centronucleated regenerating myofibers, as well as the number of centronucleated regenerating myofibers, were higher in the treated group than they were in the control group (mean and standard error of the mean, 79.2 ± 5.0% versus 58.3 ± 8.1%, respectively [p < 0.05]; and 145 ± 36 versus 273 ± 18 per 103 myofibers, respectively [p < 0.05]). However, there were no significant differences at four weeks. Treatment did not decrease collagen deposition. Male gene was not detected in female host tissue at two and four weeks after engraftment by polymerase chain reaction analysis. Conclusions: Adipose-derived stem-cell therapy increased muscle repair and force at two weeks, but not four weeks, after injection, suggesting that adipose-derived stem-cell administration may accelerate muscle repair; however, the rapid disappearance of injected cells suggests a paracrine mechanism of action. Disclosure: One or more of the authors received payments or services, either directly or indirectly (i.e., via his or her institution), from a third party in support of an aspect of this work. None of the authors, or their institution(s), have had any financial relationship, in the thirty-six months prior to submission of this work, with any entity in the biomedical arena that could be perceived to influence or have the potential to influence what is written in this work. Also, no author has had any other relationships, or has engaged in any other activities, that could be perceived to influence or have the potential to influence what is written in this work. The complete Disclosures of Potential Conflicts of Interest submitted by authors are always provided with the online version of the article.

This paper presents numerical solutions of particular Tolman models approximating a fractal behaviour along the past light cone. The initial conditions of the numerical problem are discussed and the algorithm used to carry out the numerical integrations is presented. It was found that the numerical solutions are stiff across the flat-curved interface necessary to obtain the initial conditions of the problem. The spatially homogeneous Friedmann models are treated as special cases of the Tolman solution and solved numerically. Extending the results of paper II on the Einstein-de Sitter model, to the K = ±1 models, it was found that the open and closed Friedmann models also do not appear to remain homogeneous along the backward null cone, with a vanishing volume (average) density as one approaches the big bang singularity hypersurface. Fractal solutions, that is, solutions representing an averaged and smoothed-out single fractal, were obtained in