Three Body Interactions, Angular Momentum and Black Hole Moduli Spaces

We investigate the dynamics of a pair of (4+1)-dimensional black holes in the moduli approximation and with fixed angular momentum. We find that spinning black holes at small separations are described by the de Alfaro, Fubini and Furlan model. For more than two black holes, we find an explicit expression for the three-body interactions in the moduli metric by associating them with the one-loop three-point amplitude of a four-dimensional $\phi^3$ theory. We also investigate the dynamics of a three black hole system in various approximations.Comment: 20 pages, phyzz

Getting the Measure of the Flatness Problem

The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of probability for such problems and stress the connection between probability and information which this approach makes explicit. This connection is important even when information is ``minimal'' or, in other words, when we need to argue from a state of maximum ignorance. We use the transformation group method of Jaynes to assign minimally--informative prior probability measure for cosmological parameters in the simple example of a dust Friedman model, showing that the usual statements of the cosmological flatness problem are based on an inappropriate choice of prior. We further demonstrate that, in the framework of a classical cosmological model, there is no flatness problem.Comment: 11 pages, submitted to Classical and Quantum Gravity, Tex source file, no figur

Extreme events and event size fluctuations in biased random walks on networks

Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the context of complex networks. This was motivated by the occurrence of rare events such as traffic jams, floods, and power black-outs which take place on networks. In this work, we study extreme events in a generalized random walk model in which the walk is preferentially biased by the network topology. The walkers preferentially choose to hop toward the hubs or small degree nodes. In this setting, we show that extremely large fluctuations in event-sizes are possible on small degree nodes when the walkers are biased toward the hubs. In particular, we obtain the distribution of event-sizes on the network. Further, the probability for the occurrence of extreme events on any node in the network depends on its 'generalized strength', a measure of the ability of a node to attract walkers. The 'generalized strength' is a function of the degree of the node and that of its nearest neighbors. We obtain analytical and simulation results for the probability of occurrence of extreme events on the nodes of a network using a generalized random walk model. The result reveals that the nodes with a larger value of 'generalized strength', on average, display lower probability for the occurrence of extreme events compared to the nodes with lower values of 'generalized strength'

Bias and Hierarchical Clustering

It is now well established that galaxies are biased tracers of the distribution of matter, although it is still not known what form this bias takes. In local bias models the propensity for a galaxy to form at a point depends only on the overall density of matter at that point. Hierarchical scaling arguments allow one to build a fully-specified model of the underlying distribution of matter and to explore the effects of local bias in the regime of strong clustering. Using a generating-function method developed by Bernardeau & Schaeffer (1992), we show that hierarchical models lead one directly to the conclusion that a local bias does not alter the shape of the galaxy correlation function relative to the matter correlation function on large scales. This provides an elegant extension of a result first obtained by Coles (1993) for Gaussian underlying fields and confirms the conclusions of Scherrer & Weinberg (1998) obtained using a different approach. We also argue that particularly dense regions in a hierarchical density field display a form of bias that is different from that obtained by selecting such peaks in Gaussian fields: they are themselves hierarchically distributed with scaling parameters $S_p=p^{(p-2)}$. This kind of bias is also factorizable, thus in principle furnishing a simple test of this class of models.Comment: Latex, accepted for publication in ApJL; moderate revision

Theory of Parabolic Arcs in Interstellar Scintillation Spectra

Our theory relates the secondary spectrum, the 2D power spectrum of the radio dynamic spectrum, to the scattered pulsar image in a thin scattering screen geometry. Recently discovered parabolic arcs in secondary spectra are generic features for media that scatter radiation at angles much larger than the rms scattering angle. Each point in the secondary spectrum maps particular values of differential arrival-time delay and fringe rate (or differential Doppler frequency) between pairs of components in the scattered image. Arcs correspond to a parabolic relation between these quantities through their common dependence on the angle of arrival of scattered components. Arcs appear even without consideration of the dispersive nature of the plasma. Arcs are more prominent in media with negligible inner scale and with shallow wavenumber spectra, such as the Kolmogorov spectrum, and when the scattered image is elongated along the velocity direction. The arc phenomenon can be used, therefore, to constrain the inner scale and the anisotropy of scattering irregularities for directions to nearby pulsars. Arcs are truncated by finite source size and thus provide sub micro arc sec resolution for probing emission regions in pulsars and compact active galactic nuclei. Multiple arcs sometimes seen signify two or more discrete scattering screens along the propagation path, and small arclets oriented oppositely to the main arc persisting for long durations indicate the occurrence of long-term multiple images from the scattering screen.Comment: 22 pages, 11 figures, submitted to the Astrophysical Journa

Wall Street Trading Firms as Securities Insiders

The purpose of this article is to examine this view of the Blau case, the implications of the SEC\u27s decision In The Matter of Cady, Roberts and Co. and the possible ramifications of this view and of the Cady, Roberts decision on the future trading activities of investment banking firms