Empirical likelihood confidence intervals for complex sampling designs

We define an empirical likelihood approach which gives consistent design-based confidence intervals which can be calculated without the need of variance estimates, design effects, resampling, joint inclusion probabilities and linearization, even when the point estimator is not linear. It can be used to construct confidence intervals for a large class of sampling designs and estimators which are solutions of estimating equations. It can be used for means, regressions coefficients, quantiles, totals or counts even when the population size is unknown. It can be used with large sampling fractions and naturally includes calibration constraints. It can be viewed as an extension of the empirical likelihood approach to complex survey data. This approach is computationally simpler than the pseudoempirical likelihood and the bootstrap approaches. The simulation study shows that the confidence interval proposed may give better coverages than the confidence intervals based on linearization, bootstrap and pseudoempirical likelihood. Our simulation study shows that, under complex sampling designs, standard confidence intervals based on normality may have poor coverages, because point estimators may not follow a normal sampling distribution and their variance estimators may be biased.<br/

Evaporation of (quantum) black holes and energy conservation

We consider Hawking radiation as due to a tunneling process in a black hole were quantum corrections, derived from Quantum Einstein Gravity, are taken into account. The consequent derivation, satisfying conservation laws, leads to a deviation from an exact thermal spectrum. The non-thermal radiation is shown to carry information out of the black hole. Under the appropriate approximation, a quantum corrected temperature is assigned to the black hole. The evolution of the quantum black hole as it evaporates is then described by taking into account the full implications of energy conservation as well as the back-scattered radiation. It is shown that, as a critical mass of the order of Planck's mass is reached, the evaporation process decelerates abruptly while the black hole mass decays towards this critical mass.Comment: 16 pages, 2 figure

The mechanism why colliders could create quasi-stable black holes

It has been postulated that black holes could be created in particle collisions within the range of the available energies for nowadays colliders (LHC). In this paper we analyze the evaporation of a type of black holes that are candidates for this specific behaviour, namely, small black holes on a brane in a world with large extra-dimensions. We examine their evolution under the assumption that energy conservation is satisfied during the process and compare it with the standard evaporation approach. We claim that, rather than undergoing a quick total evaporation, black holes become quasi-stable. We comment on the (absence of) implications for safety of this result. We also discuss how the presence of black holes together with the correctness of the energy conservation approach might be experimentally verified.Comment: 16 pages, 3 figure

The GeV-TeV Connection in Galactic gamma-ray sources

Recent observations with atmospheric Cherenkov telescope systems such as H.E.S.S. and MAGIC have revealed a large number of new sources of very-high-energy (VHE) gamma-rays from 100 GeV - 100 TeV, mostly concentrated along the Galactic plane. At lower energies (100 MeV - 10 GeV) the satellite-based instrument EGRET revealed a population of sources clustering along the Galactic Plane. Given their adjacent energy bands a systematic correlation study between the two source catalogues seems appropriate. Here, the populations of Galactic sources in both energy domains are characterised on observational as well as on phenomenological grounds. Surprisingly few common sources are found in terms of positional coincidence and spectral consistency. These common sources and their potential counterparts and emission mechanisms will be discussed in detail. In cases of detection only in one energy band, for the first time consistent upper limits in the other energy band have been derived. The EGRET upper limits are rather unconstraining due to the sensitivity mismatch to current VHE instruments. The VHE upper limits put strong constraints on simple power-law extrapolation of several of the EGRET spectra and thus strongly suggest cutoffs in the unexplored energy range from 10 GeV - 100 GeV. Physical reasons for the existence of cutoffs and for differences in the source population at GeV and TeV energies will be discussed. Finally, predictions will be derived for common GeV - TeV sources for the upcoming GLAST mission bridging for the first time the energy gap between current GeV and TeV instruments.Comment: (1) Kavli Institute for Particle Astrophysics and Cosmology (KIPAC), Stanford, USA (2) Stanford University, W.W. Hansen Experimental Physics Lab (HEPL) and KIPAC, Stanford, USA (3) ICREA & Institut de Ciencies de l'Espai (IEEC-CSIC) Campus UAB, Fac. de Ciencies, Barcelona, Spain. (4) School of Physics and Astronomy, University of Leeds, UK. Paper Submitted to Ap

A Compound model for the origin of Earth's water

One of the most important subjects of debate in the formation of the solar system is the origin of Earth's water. Comets have long been considered as the most likely source of the delivery of water to Earth. However, elemental and isotopic arguments suggest a very small contribution from these objects. Other sources have also been proposed, among which, local adsorption of water vapor onto dust grains in the primordial nebula and delivery through planetesimals and planetary embryos have become more prominent. However, no sole source of water provides a satisfactory explanation for Earth's water as a whole. In view of that, using numerical simulations, we have developed a compound model incorporating both the principal endogenous and exogenous theories, and investigating their implications for terrestrial planet formation and water-delivery. Comets are also considered in the final analysis, as it is likely that at least some of Earth's water has cometary origin. We analyze our results comparing two different water distribution models, and complement our study using D/H ratio, finding possible relative contributions from each source, focusing on planets formed in the habitable zone. We find that the compound model play an important role by showing more advantage in the amount and time of water-delivery in Earth-like planets.Comment: Accepted for publication in The Astrophysical Journa

Discrete-Time Fractional Variational Problems

We introduce a discrete-time fractional calculus of variations on the time scale $h\mathbb{Z}$, $h > 0$. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of the discrete-derivatives are integer values, and that they converge to the fractional continuous-time solutions when $h$ tends to zero. Our Legendre type condition is useful to eliminate false candidates identified via the Euler-Lagrange fractional equation.Comment: Submitted 24/Nov/2009; Revised 16/Mar/2010; Accepted 3/May/2010; for publication in Signal Processing