Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some "non-analytic" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \emph{degrees of the parameters}, while one has an exponential growth out of these subspaces. The analysis of our birational transformation in $CP_2$ is first carried out using Diller-Favre criterion in order to find the complexity reduction of the mapping. The integrable cases are found. The identification between the complexity growth and the topological entropy is, one more time, verified. We perform plots of the post-critical set, as well as calculations of Lyapunov exponents for many orbits, confirming that generically no meromorphic two-form can be preserved for this mapping. These birational transformations in $CP_2$, which, generically, do not preserve any meromorphic two-form, are extremely similar to other birational transformations we previously studied, which do preserve meromorphic two-forms. We note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned, but drastically different results as far as a more ``probabilistic'' approach of dynamical systems is concerned (Lyapunov exponents). With these examples we see that the existence of a preserved meromorphic two-form explains most of the (numerical) discrepancy between the topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure

Grids of stellar models with rotation VII : models from 0.8 to 300 M⊙ at supersolar metallicity (Z = 0.020)

We present a grid of stellar models at supersolar metallicity (Z = 0.020) extending the previous grids of Geneva models at solar and sub-solar metallicities. A metallicity of Z = 0.020 was chosen to match that of the inner Galactic disc. A modest increase of 43 per cent (= 0.02/0.014) in metallicity compared to solar models means that the models evolve similarly to solar models but with slightly larger mass-loss. Mass-loss limits the final total masses of the supersolar models to 35 M⊙ even for stars with initial masses much larger than 100 M⊙. Mass-loss is strong enough in stars above 20 M⊙ for rotating stars (25 M⊙ for non-rotating stars) to remove the entire hydrogen-rich envelope. Our models thus predict SNII below 20 M⊙ for rotating stars (25 M⊙ for non-rotating stars) and SNIb (possibly SNIc) above that. We computed both isochrones and synthetic clusters to compare our supersolar models to the Westerlund 1 (Wd1) massive young cluster. A synthetic cluster combining rotating and non-rotating models with an age spread between log10(age/yr) = 6.7 and 7.0 is able to reproduce qualitatively the observed populations of WR, RSG, and YSG stars in Wd1, in particular their simultaneous presence at log10(L/L⊙) = 5–5.5. The quantitative agreement is imperfect and we discuss the likely causes: synthetic cluster parameters, binary interactions, mass-loss and their related uncertainties. In particular, mass-loss in the cool part of the HRD plays a key role

Complexity analysis of the fetal heart rate variability: early identification of severe intrauterine growth-restricted fetuses

The main goal of this work is to suggest new indices for a correct identification of the intrauterine growth-restricted (IUGR) fetuses on the basis of fetal heart rate (FHR) variability analysis performed in the antepartum period. To this purpose, we analyzed 59 FHR time series recorded in early periods of gestation through a Hewlett Packard 1351A cardiotocograph. Advanced analysis techniques were adopted including the computation of the Lempel Ziv complexity (LZC) index and the multiscale entropy (MSE), that is, the entropy estimation with a multiscale approach. A multiparametric classifier based on k-mean cluster analysis was also performed to separate pathological and normal fetuses. The results show that the proposed LZC and the MSE could be useful to identify the actual IUGRs and to separate them from the physiological fetuses, providing good values of sensitivity and accuracy (Se = 77.8%, Ac = 82.4%)

Renin and angiotensinogen expression and functions in growth and apoptosis of human glioblastoma

The expression and function in growth and apoptosis of the renin-angiotensin system (RAS) was evaluated in human glioblastoma. Renin and angiotensinogen (AGT) mRNAs and proteins were found by in situ hybridisation and immunohistochemistry in glioblastoma cells. Angiotensinogen was present in glioblastoma cystic fluids. Thus, human glioblastoma cells produce renin and AGT and secrete AGT. Human glioblastoma and glioblastoma cells expressed renin, AGT, renin receptor, AT(2) and/or AT(1) mRNAs and proteins determined by RT-PCR and/or Western blotting, respectively. The function of the RAS in glioblastoma was studied using human glioblastoma cells in culture. Angiotensinogen, des(Ang I)AGT, tetradecapaptide renin substrate (AGT1-14), Ang I, Ang II or Ang III, added to glioblastoma cells in culture, did not modulate their proliferation, survival or death. Angiotensin-converting enzyme inhibitors did not diminish glioblastoma cell proliferation. However, the addition of selective synthetic renin inhibitors to glioblastoma cells decreased DNA synthesis and viable tumour cell number, and induced apoptosis. This effect was not counterbalanced by concomitant addition of Ang II. In conclusion, the complete RAS is expressed by human glioblastomas and glioblastoma cells in culture. Inhibition of renin in glioblastoma cells may be a potential approach to control glioblastoma cell proliferation and survival, and glioblastoma progression in combination therapy

Angiopoietin 2 Alters Pancreatic Vascularization in Diabetic Conditions

Islet vascularization, by controlling beta-cell mass expansion in response to increased insulin demand, is implicated in the progression to glucose intolerance and type 2 diabetes. We investigated how hyperglycaemia impairs expansion and differentiation of the growing pancreas. We have grafted xenogenic (avian) embryonic pancreas in severe combined immuno-deficient (SCID) mouse and analyzed endocrine and endothelial development in hyperglycaemic compared to normoglycaemic conditions. 14 dpi chicken pancreases were grafted under the kidney capsule of normoglycaemic or hyperglycaemic, streptozotocin-induced, SCID mice and analyzed two weeks later. Vascularization was analyzed both quantitatively and qualitatively using either in situ hybridization with both mouse- and chick-specific RNA probes for VEGFR2 or immunohistochemistry with an antibody to nestin, a marker of endothelial cells that is specific for murine cells. To inhibit angiopoietin 2 (Ang2), SCID mice were treated with 4 mg/kg IP L1-10 twice/week. In normoglycaemic condition, chicken-derived endocrine and exocrine cells developed well and intragraft vessels were lined with mouse endothelial cells. When pancreases were grafted in hyperglycaemic mice, growth and differentiation of the graft were altered and we observed endothelial discontinuities, large blood-filled spaces. Vessel density was decreased. These major vascular anomalies were associated with strong over-expression of chick-Ang2. To explore the possibility that Ang2 over-expression could be a key step in vascular disorganization induced by hyperglycaemia, we treated mice with L1-10, an Ang-2 specific inhibitor. Inhibition of Ang2 improved vascularization and beta-cell density. this work highligghted an important role of Ang2 in pancreatic vascular defects induced by hyperglycemia

Impact of Population III homogeneous stellar evolution on early cosmic reionisation

Context. Population III (Pop III) stars may be fast rotating. An expected consequence of fast rotation is strong internal mixing that deeply affects their evolutionary tracks in the Hertzsprung-Russell diagram and hence their ionising power. Aims. We investigate the impact on the ionising power of Pop III stars in an extreme case of internal mixing, the one leading to chemically homogeneous evolution (CHE). In that situation, during the main sequence phase, the star keeps the same chemical composition from its centre to its surface. Homogeneous stars have larger effective temperatures and luminosities than stars evolving non-homogeneously and thus are stronger ionising sources. Methods. The stellar evolution models are based on n = 3 polytropes with a time-varying mass fraction of hydrogen. The ionisation model employs the self-similar champagne flow solution from Shu et al. (2002, ApJ, 580, 969) and numerical simulations for the stochastic treatment of star clusters over a grid of redshifts and halo masses. Results. We find that haloes containing chemically homogeneous stars have an escape fraction of ionising photons up to twice that of haloes containing classical Pop III stars. By extrapolating the high-z ionisation history powered by Pop III stars (at z ≳ 15) to the post-reionisation epoch, we derived the Thomson scattering optical depth τ, which is compared with the value measured by Planck. We find that τ is overproduced by ∼1.5 − 5σ when all Pop III stars evolve homogeneously. This indicates that CHE is unlikely to be realised in the majority of Pop III stars, although the present study cannot exclude that a fraction of them undergo CHE. Conclusions. Fast rotation might have a significant impact on the ionising budget of Pop III stars and thus on early cosmic reionisation. The impact is stronger for less top-heavy initial mass functions of Pop III stars