Z_N x Z_M orientifolds with and without discrete torsion

We discuss compact four-dimensional Z_N x Z_M type IIB orientifolds. We take a systematic approach to classify the possible models and construct them explicitely. The supersymmetric orientifolds of this type have already been constructed some time ago. We find that there exist several consistent orientifolds for each of the discrete groups Z_2 x Z_2, Z_2 x Z_4, Z_4 x Z_4, Z_2 x Z_6, Z_2 x Z_6' and Z_6 x Z_6 if anti-D5-branes are introduced. Supersymmetry is broken by the open strings ending on antibranes. The rank of the gauge group is reduced by a factor two if the underlying orbifold space has discrete torsion.Comment: Latex, 61 page

Simulating and detecting artificial magnetic fields in trapped atoms

A Bose-Einstein condensate exhibiting a nontrivial phase induces an artificial magnetic field in immersed impurity atoms trapped in a stationary, ring-shaped optical lattice. We present an effective Hamiltonian for the impurities for two condensate setups: the condensate in a rotating ring and in an excited rotational state in a stationary ring. We use Bogoliubov theory to derive analytical formulas for the induced artificial magnetic field and the hopping amplitude in the limit of low condensate temperature where the impurity dynamics is coherent. As methods for observing the artificial magnetic field we discuss time of flight imaging and mass current measurements. Moreover, we compare the analytical results of the effective model to numerical results of a corresponding two-species Bose-Hubbard model. We also study numerically the clustering properties of the impurities and the quantum chaotic behavior of the two-species Bose-Hubbard model.Comment: 14 pages, 9 figures. Published versio

Kurtosis ordering of the generalized secant hyperbolic distribution: a technical note

Two major generalizations of the hyperbolic secant distribution have been proposed in the statistical literature which both introduce an additional parameter that governs the kurtosis of the generalized distribution. The generalized hyperbolic secant (GHS) distribution was introduced by Harkness and Harkness (1968) who considered the p-th convolution of a hyperbolic secant distribution. Another generalization, the so-called generalized secant hyperbolic (GSH) distribution was recently suggested by Vaughan 2002). In contrast to the GHS distribution, the cumulative and inverse cumulative distribution function of the GSH distribution are available in closedform expressions. We use this property to proof that the additional shape parameter of the GSH distribution is actually a kurtosis parameter in the sense of van Zwet (1964). --kurtosis ordering,hyperbolic secant distribution

Some results on weak and strong tail dependence coefficients for means of copulas

Copulas represent the dependence structure of multivariate distributions in a natural way. In order to generate new copulas from given ones, several proposals found its way into statistical literature. One simple approach is to consider convex-combinations (i.e. weighted arithmetic means) of two or more copulas. Similarly, one might consider weighted geometric means. Consider, for instance, the Spearman copula, defined as the geometric mean of the maximum and the independence copula. In general, it is not known whether weighted geometric means of copulas produce copulas, again. However, applying a recent result of Liebscher (2006), we show that every weighted geometric mean of extreme-value copulas produces again an extreme-value copula. The second contribution of this paper is to calculate extremal dependence measures (e.g. weak and strong tail dependence coe±cients) for (weighted) geometric and arithmetic means of two copulas. --Tail Dependence,Extreme-value copulas,arithmetic and geometric mean

Constructing symmetric generalized FGM copulas by means of certain univariate distributions

In this paper we focus on symmetric generalized Fairlie-Gumbel-Morgenstern (or symmetric Sarmanov) copulas which are characterized by means of so-called generator functions. In particular, we introduce a class of generator functions which is based on univariate distributions with certain properties. Some of the generator functions from the literature are recovered. Moreover two new generators are suggested, implying two new copulas. Finally, the opposite way around, it is exemplarily shown how to calculate the univariate distribution which belongs to a given copula generator function. --

Kurtosis transformation and kurtosis ordering

Leptokurtic distributions can be generated by applying certain non-linear transformations to a standard normal random variable. Within this work we derive general conditions for these transformations which guarantee that the generated distributions are ordered with respect to the partial ordering of van Zwet for symmetric distributions and the partial ordering of MacGillivray for arbitrary distributions. In addition, we propose a general power transformation which nests the H-, J- and K-transformations which have already been proposed in the literature. Within this class of power transformations the above mentioned condition can be easily verified and the power can be interpreted as parameter of leptokurtosis. --Power kurtosis transformation,leptokurtosis,kurtosis ordering