Modified theories of gravity with non-minimal curvature-matter coupling

In this contribution one examines the generalization of the $f(R)$ theories of gravity where one introduces a non-minimal coupling between curvature and matter. This model has new and interesting features. %, specially concerning the energy exchange between the matter fields and the curvature. However, as any modified gravity theories, these may give origin to anomalies which might turn the theory physically meaningless. In this respect, one undertakes a study on the energy conditions and the Dolgov-Kawasaki criterion specific of this new model.Comment: 6 pages, 1 table. Talk present by O. B. at the "Invisible Universe International Conference", Paris, Palais de l'UNESCO June 29- July 3. To appear in the Proceeding

Digging Out the PPP Hypothesis: an Integrated Empirical Coverage

We use several popular tests to test the validity of the Purchasing Power Parity (PPP) hypothesis. In particular, we analyze four classes of tests { standard univariate unit root tests, co-integration, panel unit root tests and unit root tests for nonlinear frameworks {, for a dataset consisting of 20 bilateral exchange rates. Through this approach, we ascertain the eectiveness of each methodology in assessing the validity of PPP. Overall, our results suggest little evidence to support PPP. Among the conducted tests, the panel analysis of nonstationarity idiosyncratic and common components provides the richest insights by disentangling the possible sources of non-stationarity of real exchange rates. The relevance of using price indexes with dierent characteristics is also pinpointed.PPP; Real exchange rate; Unit roots; Co-integration; Panel; Nonlinear models; Cross-sectional dependence

Extremal Dependence in International Output Growth: Tales from the Tails

The statistical modelling of extreme values has recently received substantial attention in a broad spectrum of sciences. Given that in a wide variety of scenarios, one is mostly concerned with explaining tail events (say, an economic recession) than central ones, the need to rely on statistical methods well qualified for modelling extremes arises. Unfortunately, several classical tools regularly applied in the analysis of central events, are simply innapropriate for the analysis of extreme values. In particular, Pearson correlation is not a proper measure for assessing the level of agreement of two variables when one is concerned with tail events. This paper explores the comovement of the economic activity of several OECD countries during periods of large positive and negative growth (right and left tails, respectively). Extremal measures are here applied as means to assess the degree of cross-country tail dependence of output growth rates. Our main empirical findings are: (i) the comovement is much stronger in left tails than in right tails; (ii) asymptotic independence is claimed by the data; (iii) the dependence in the tails is considerably stronger than the one arising from a Gaussian dependence model. In addition, our results suggest that, among the typical determinants for explaining international output growth synchronization, only economic specialization similarity seems to play a role at extreme events.

A Euclidean likelihood estimator for bivariate tail dependence

The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based estimator for the spectral measure which is simple and explicitly defined, with its expression being free of Lagrange multipliers. Our estimator is shown to have the same limit distribution as the maximum empirical likelihood estimator of J. H. J. Einmahl and J. Segers, Annals of Statistics 37(5B), 2953--2989 (2009). Numerical experiments suggest an overall good performance and identical behavior to the maximum empirical likelihood estimator. We illustrate the method in an extreme temperature data analysis.Comment: 18 pages, 8 figure

Stabilization of vortex beams in Kerr media by nonlinear absorption

We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.Comment: Physical Review A, in press, 9 pages, 6 figure