Recovering the mass and the charge of a Reissner-Nordstr\"om black hole by an inverse scattering experiment

In this paper, we study inverse scattering of massless Dirac fields that propagate in the exterior region of a Reissner-Nordstr\"om black hole. Using a stationary approach we determine precisely the leading terms of the high-energy asymptotic expansion of the scattering matrix that, in turn, permit us to recover uniquely the mass of the black hole and its charge up to a sign

The Dirac system on the Anti-de Sitter Universe

We investigate the global solutions of the Dirac equation on the Anti-de-Sitter Universe. Since this space is not globally hyperbolic, the Cauchy problem is not, {\it a priori}, well-posed. Nevertheless we can prove that there exists unitary dynamics, but its uniqueness crucially depends on the ratio beween the mass $M$ of the field and the cosmological constant $\Lambda>0$ : it appears a critical value, $\Lambda/12$, which plays a role similar to the Breitenlohner-Freedman bound for the scalar fields. When $M^2\geq \Lambda/12$ there exists a unique unitary dynamics. In opposite, for the light fermions satisfying $M^2<\Lambda/12$, we construct several asymptotic conditions at infinity, such that the problem becomes well-posed. In all the cases, the spectrum of the hamiltonian is discrete. We also prove a result of equipartition of the energy.Comment: 33 page

Local energy decay of massive Dirac fields in the 5D Myers-Perry metric

We consider massive Dirac fields evolving in the exterior region of a 5-dimensional Myers-Perry black hole and study their propagation properties. Our main result states that the local energy of such fields decays in a weak sense at late times. We obtain this result in two steps: first, using the separability of the Dirac equation, we prove the absence of a pure point spectrum for the corresponding Dirac operator; second, using a new form of the equation adapted to the local rotations of the black hole, we show by a Mourre theory argument that the spectrum is absolutely continuous. This leads directly to our main result.Comment: 40 page

Symbiont Community Diversity is More Variable in Corals That Respond Poorly to Stress

Coral reefs are declining globally as climate change and local water quality press environmental conditions beyond the physiological tolerances of holobionts—the collective of the host and its microbial symbionts. To assess the relationship between symbiont composition and holobiont stress tolerance, community diversity metrics were quantified for dinoflagellate endosymbionts (Family: Symbiodiniaceae) from eight Acropora millepora genets that thrived under or responded poorly to various stressors. These eight selected genets represent the upper and lower tails of the response distribution of 40 coral genets that were exposed to four stress treatments (and control conditions) in a 10-day experiment. Specifically, four ‘best performer’ coral genets were analyzed at the end of the experiment because they survived high temperature, high pCO2, bacterial exposure, or combined stressors, whereas four ‘worst performer’ genets were characterized because they experienced substantial mortality under these stressors. At the end of the experiment, seven of eight coral genets mainly hosted Cladocopium symbionts, whereas the eighth genet was dominated by both Cladocopium and Durusdinium symbionts. Symbiodiniaceae alpha and beta diversity were higher in worst performing genets than in best performing genets. Symbiont communities in worst performers also differed more after stress exposure relative to their controls (based on normalized proportional differences in beta diversity), than did best performers. A generalized joint attribute model estimated the influence of host genet and treatment on Symbiodiniaceae community composition and identified strong associations among particular symbionts and host genet performance, as well as weaker associations with treatment. Although dominant symbiont physiology and function contribute to host performance, these findings emphasize the importance of symbiont community diversity and stochasticity as components of host performance. Our findings also suggest that symbiont community diversity metrics may function as indicators of resilience and have potential applications in diverse disciplines from climate change adaptation to agriculture and medicine

Factors of interrupting chemotherapy in patients with Advanced Non-Small-Cell Lung Cancer

<p>Abstract</p> <p>Background</p> <p>Little is known about prognosis of metastatic patients after receiving a first-line treatment and failure. Our group already showed in pre-treated patients enrolled in phase I clinical trials that a performance status (PS) > 2 and an LDH > 600 UI/L were independent prognostic factors. In this prospective study, which included 45 patients, we identified clinical and biological variables as outcome predictors in metastatic Non-Small Cell lung cancer after first line chemotherapy were identified.</p> <p>Findings</p> <p>Forty-five patients that were previously treated for metastatic disease from 12/2000 to 11/2005 in the comprehensive cancer centre (Centre Léon Bérard). Clinical assessment and blood parameters were recorded and considered. Patient prognostic factors for overall survival (OS) with a 0.05-significance level in univariate analysis were entered in a multivariate Cox model for further analysis.</p> <p>Patients' median age was 58.5 years (range: 37 - 76). Sixty two percent of the patients were PS = 0 or 1. After inclusion, nine patients received second-line (22.5%), and two received third-line chemotherapy (5%). Univariate analysis showed that the factors associated with reduced OS were: PS > 2, weight loss >10%, more than one line of chemotherapy treatment and abnormal blood parameters (hemoglobin (Hb), platelet and neutrophils counts). Multiple regression analysis confirmed that PS > 2 and abnormal hemoglobin were independent predictors for low overall survival. According to the presence of none (33%), 1 (37%) and 2 (30%) prognostic factors, median OS were 12, 5 and 2 months respectively.</p> <p>Conclusion</p> <p>From this prospective study, both PS and anemia were found as independent determinants of survival, we found that both PS and anemia were independent determinants of survival. The combination of poor PS and anemia is an effective strategy to predict survival in the case of patients with metastatic NSCLC receiving further treatment after the first line.</p

Bohr's Correspondence Principle and The Area Spectrum of Quantum Black Holes

During the last twenty-five years evidence has been mounting that a black-hole surface area has a {\it discrete} spectrum. Moreover, it is widely believed that area eigenvalues are {\it uniformally} spaced. There is, however, no general agreement on the {\it spacing} of the levels. In this letter we use Bohr's correspondence principle to provide this missing link. We conclude that the area spacing of a black-hole is $4\hbar \ln 3$. This is the unique spacing consistent both with the area-entropy {\it thermodynamic} relation for black holes, with Boltzmann-Einstein formula in {\it statistical physics} and with {\it Bohr's correspondence principle}.Comment: 10 page