General Relativistic Scalar Field Models in the Large

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the hyperboloidal initial value problem for those scalar fields has an unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exist a smooth future null infinity and a regular future timelike infinity.Comment: 22 pages, latex, AGG 1

Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Markets

Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the distribution of fluctuations in returns. Empirical studies conducted over the last decade have reported that they arenon-Gaussian, scale in time, and have power-law(or fat) tails. However, because they use sliding interval methods of analysis, these studies implicitly assume that the underlying process has stationary increments. We explicitly show that this assumption is not valid for the Euro-Dollar exchange rate between 1999-2004. In addition, we find that fluctuations in returns of the exchange rate are uncorrelated and scale as power-laws for certain time intervals during each day. This behavior is consistent with a diffusive process with a diffusion coefficient that depends both on the time and the price change. Within scaling regions, we find that sliding interval methods can generate fat-tailed distributions as an artifact, and that the type of scaling reported in many previous studies does not exist.Comment: 12 pages, 4 figure

A Method for Calculating the Structure of (Singular) Spacetimes in the Large

A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity (\Scri{}^+) and future timelike infinity ($i^+$) are mapped to grid points on the numerical grid. The determination of the causal structure of singularities, the localization of event horizons, the extraction of radiation, and the avoidance of unphysical reflections at the outer boundary of the grid, are demonstrated with calculations of spherically symmetric models with a scalar field as matter and radiation model.Comment: 29 pages, AGG2

First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields

First-order hyperbolic systems are promising as a basis for numerical integration of Einstein's equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed independently. This can be expensive computationally, especially if the prescription involves solving elliptic equations. Therefore, including the lapse and shift in the hyperbolic system could be advantageous for numerical work. In this paper, two first-order symmetrizable hyperbolic systems are presented that include the lapse and shift as dynamical fields and have only physical characteristic speeds.Comment: 11 page

Localization of NG2 immunoreactive neuroglia cells in the rat locus coeruleus and their plasticity in response to stress

The locus coeruleus (LC) nucleus modulates adaptive behavioural responses to stress and dysregulation of LC neuronal activity is implicated in stress-induced mental illnesses. The LC is composed primarily of noradrenergic neurons together with various glial populations. A neuroglia cell-type largely unexplored within the LC is the NG2 cell. NG2 cells serve primarily as oligodendrocyte precursor cells throughout the brain. However, some NG2 cells are in synaptic contact with neurons suggesting a role in information processing. The aim of this study was to neurochemically and anatomically characterise NG2 cells within the rat LC. Furthermore, since NG2 cells have been shown to proliferate in response to traumatic brain injury, we investigated whether such NG2 cells plasticity also occurs in response to emotive insults such as stress. Immunohistochemistry and confocal microscopy revealed that NG2 cells were enriched within the pontine region occupied by the LC. Close inspection revealed that a sub-population of NG2 cells were located within unique indentations of LC noradrenergic somata and were immunoreactive for the neuronal marker NeuN whilst NG2 cell processes formed close appositions with clusters immunoreactive for the inhibitory synaptic marker proteins gephyrin and the GABA-A receptor alpha3-subunit, on noradrenergic dendrites. In addition, LC NG2 cell processes were decorated with vesicular glutamate transporter 2 immunoreactive puncta. Finally, ten days of repeated restraint stress significantly increased the density of NG2 cells within the LC. The study demonstrates that NG2 IR cells are integral components of the LC cellular network and they exhibit plasticity as a result of emotive challenges

Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen

A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor l(l+1) is replaced by (l+1/2)^2, are avoided. The semiclassical energy levels are shown to be exact to first order in $\hbar$ with all higher order contributions vanishing. The wave functions and dipole matrix elements are also discussed.Comment: 5 pages, to appear in Phys. Rev.

Persistence of Problematic Sexual Behaviors in Children

The purpose of this study was to identify personal and family predictors and correlates of persistence of problematic sexual behaviors (PSB) in children. Participants were the families of 49 children (ages 4–11 years) referred by Child Protective Services in 4 administrative districts of Quebec. Caregivers completed interviews and questionnaires twice at a 1-year interval. Results showed that 43% of children persisted with PSB. When age was controlled, greater exposure to sexualized behaviors in the family proved both a correlate and a predictor of PSB persistence in children 12 months later.\ud Externalizing problems and somatic complaints emerged as correlates of PSB as well. Maltreatment subtypes did not predict PSB persistence

On smoothness-asymmetric null infinities

We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past and a future null infinity of different smoothness. For simplicity, the analysis is restricted to the class of conformally flat, axially symmetric initial data sets. It is shown how the free parameters in the second fundamental form of the data can be used to satisfy certain obstructions to the smoothness of null infinity. The resulting initial data sets could be interpreted as those of some sort of (non-linearly) distorted Schwarzschild black hole. Its developments would be so that they admit a peeling future null infinity, but at the same time have a polyhomogeneous (non-peeling) past null infinity.Comment: 13 pages, 1 figur