Equity market interdependence: the relationship between European and US stock markets.

In this article, the degree of interdependence between European and US stock markets is measured by the conditional correlation between stock returns: the correlation coefficient is estimated using a model describing the variations over time in a number of variables (returns and volatility, for example), and its estimate takes account of all available information at a given time. We estimate conditional variance in the same way. Moreover, two statistical tools, recently introduced in applied finance, are combined. The first, developed by Engle in 2001 – an original specification of the conditional correlations in multivariate models – enables us to describe time-varying correlations between two or more assets. The second tool, copula functions, allows us to apply distributions that are more consistent with the stylised facts observed on financial markets than those commonly used. The approach used in this study is original in that it combines both the above tools. Using a multivariate model implies rejecting the two assumptions traditionally adopted in empirical studies in finance: correlations between assets are presumed to be constant; asymmetry or the presence of rare events are not taken into account in asset price distributions. Consequently, our empirical findings corroborate the assumption that correlations vary over time and validate the choice of an asymmetric joint distribution integrating the presence of rare events. We also observe the presence of periods of strong and weak correlations and similar periods for volatility. Furthermore, our results highlight a close link between the correlations and volatilities observed on the different equity markets: in phases of high volatility, the correlation tends to rise above its medium-term average; inversely, in phases of low volatility, markets seem to display greater independence. Lastly, the correlation coefficient of close to 1 confirms that French and German stock market indices have been converging in recent years. This may reflect the growing integration of these two markets and of the economies of these two countries within Economic and Monetary Union.

The specific entropy of elliptical galaxies: an explanation for profile-shape distance indicators?

Dynamical systems in equilibrium have a stationary entropy; we suggest that elliptical galaxies, as stellar systems in a stage of quasi-equilibrium, may have a unique specific entropy. This uniqueness, a priori unknown, should be reflected in correlations between the parameters describing the mass (light) distribution in galaxies. Following recent photometrical work (Caon et al. 1993; Graham & Colless 1997; Prugniel & Simien 1997), we use the Sersic law to describe the light profile of elliptical galaxies and an analytical approximation to its three dimensional deprojection. The specific entropy is calculated supposing that the galaxy behaves as a spherical, isotropic, one-component system in hydrostatic equilibrium, obeying the ideal gas state equations. We predict a relation between the 3 parameters of the Sersic, defining a surface in the parameter space, an `Entropic Plane', by analogy with the well-known Fundamental Plane. We have analysed elliptical galaxies in Coma and ABCG 85 clusters and a group of galaxies (associated with NGC 4839). We show that the galaxies in clusters follow closely a relation predicted by the constant specific entropy hypothesis with a one-sigma dispersion of 9.5% around the mean value of the specific entropy. Assuming that the specific entropy is also the same for galaxies of different clusters, we are able to derive relative distances between the studied clusters. If the errors are only due to the determination of the specific entropy (about 10%), then the error in the relative distance determination should be less than 20% for rich clusters. We suggest that the unique specific entropy may provide a physical explanation for the distance indicators based on the Sersic profile put forward by Young & Currie (1994, 1995) and discussed by Binggeli & Jerjen (1998).Comment: Submitted to MNRAS (05/05/99), 15 pages, 10 figure

Superconducting states of pure and doped graphene

We study the superconducting phases of the two-dimensional honeycomb lattice of graphene. We find two spin singlet pairing states, s-wave and an exotic $p+ip$ that is possible because of the special structure of the honeycomb lattice. At half filling, the $p+ip$ phase is gapless and superconductivity is a hidden order. We discuss the possibility of a superconducting state in metal coated graphene.Comment: 4 pages, 6 figure

Comments on "Growth of Covariant Perturbations in the Contracting Phase of a Bouncing Universe" by A. Kumar

A recent paper by Kumar (2012) (hereafter K12) claimed that in a contracting model, described by perturbations around a collapsing Friedmann model containing dust or radiation, the perturbations can grow in such a way that the linearity conditions would become invalid. This conclusion is not correct due to the following facts: first, it is claimed that the linearity conditions are not satisfied, but nowhere in K12 the amplitudes of the perturbations were in fact estimated. Therefore, without such estimates, the only possible conclusion from this work is the well known fact that the perturbations indeed grow during contraction, which, per se, does not imply that the linearity conditions become invalid. Second, some evaluations of the linearity conditions are incorrect because third other terms, instead of the appropriate second order ones, are mistakenly compared with first order terms, yielding artificially fast growing conditions. Finally, it is claimed that the results of K12 are in sharp contrast with the results of the paper by Vitenti and Pinto-Neto (2012) (hereafter VPN12), because the former was obtained in a gauge invariant way. However, the author of K12 did not realized that the evolution of the perturbations were also calculated in a gauge invariant way in VPN12, but some of the linearity conditions which are necessary to be checked cannot be expressed in terms of gauge invariant quantities. In the present work, the incorrect or incomplete statements of K12 are clarified and completed, and it is shown that all other correct results of K12 were already present in VPN12, whose conclusions remain untouched, namely, that cosmological perturbations of quantum mechanical origin in a bouncing model can remain in the linear regime all along the contracting phase and at the bounce itself for a wide interval of energy scales of the bounce. (Abstract abridged)Comment: 7 pages, revtex4-1, accepted for publication in PR

Large Adiabatic Scalar Perturbations in a Regular Bouncing Universe

It has been shown that a contracting universe with a dust-like ($w \approx 0$) fluid may provide an almost scale invariant spectrum for the gravitational scalar perturbations. As the universe contracts, the amplitude of such perturbations are amplified. The gauge invariant variable $\Phi$ develops a growing mode which becomes much larger than the constant one around the bounce phase. The constant mode has its amplitude fixed by Cosmic Background Explorer (COBE) normalization, thus the amplitude of the growing mode can become much larger than 1. In this paper, we first show that this is a general feature of bouncing models, since we expect that general relativity should be valid in all scales away from the bounce. However, in the Newtonian gauge, the variable $\Phi$ gives the value of the metric perturbation $\phi$, raising doubts on the validity of the linear perturbative regime at the bounce. In order to address this issue, we obtain a set of necessary conditions for the perturbative series to be valid along the whole history of the model, and we show that there is a gauge in which all these conditions are satisfied, for a set of models, if the constant mode is fixed by COBE normalization. As a by-product of this analysis, we point out that there are sets of solutions for the perturbation variables where some gauge-fixing conditions are not well defined, turning these gauges prohibited for those solutions.Comment: 10 pages, revtex4, minor revision, version to appear in PR

Wave polarizations for a beam-like gravitational wave in quadratic curvature gravity

We compute analytically the tidal field and polarizations of an exact gravitational wave generated by a cylindrical beam of null matter of finite width and length in quadratic curvature gravity. We propose that this wave can represent the gravitational wave that keep up with the high energy photons produced in a gamma ray burst (GRB) source.Comment: 5 pages, 3 figures, minor corrections, to appear in CQ

Reply to Comment on "Quantum phase transition in the four-spin exchange antiferromagnet"

We argue that our analysis of the J-Q model, presented in Phys. Rev. B 80, 174403 (2009), and based on a field-theory description of coupled dimers, captures properly the strong quantum fluctuations tendencies, and the objections outlined by L. Isaev, G. Ortiz, and J. Dukelsky, arXiv:1003.5205, are misplaced