A Grid of Relativistic, non-LTE Accretion Disk Models for Spectral Fitting of Black Hole Binaries

Self-consistent vertical structure models together with non-LTE radiative transfer should produce spectra from accretion disks around black holes which differ from multitemperature blackbodies at levels which may be observed. High resolution, high signal-to-noise observations warrant spectral modeling which both accounts for relativistic effects, and treats the physics of radiative transfer in detail. In Davis et al. (2005) we presented spectral models which accounted for non-LTE effects, Compton scattering, and the opacities due to ions of abundant metals. Using a modification of this method, we have tabulated spectra for black hole masses typical of Galactic binaries. We make them publicly available for spectral fitting as an Xspec model. These models represent the most complete realization of standard accretion disk theory to date. Thus, they are well suited for both testing the theory's applicability to observed systems and for constraining properties of the black holes, including their spins.Comment: 7 pages, emulate ApJ, accepted to Ap

The finite-sample effects of VAR dimensions on OLS bias, OLS variance, and minimum MSE estimators: Purely nonstationary case

Vector autoregressions (VARs) are an important tool in time series analysis. However, relatively little is known about the nite-sample behaviour of parameter estimators. We address this issue, by investigating ordinary least squares (OLS) estimators given a data generating process that is a purely nonstationary rst-order VAR. Specically, we use Monte Carlo simulation and numerical optimization to derive response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct and (several types of) over-parameterization of the model: we include a constant, and a constant and trend, and introduce excess lags. We then examine the correction factors required for the least squares estimator to attain minimum mean squared error (MSE). Our results improve and extend one of the main nite-sample analytical bias results of Abadir, Hadri and Tzavalis (Econometrica 67 (1999) 163), generalize the univariate variance and MSE ndings of Abadir (Econ. Lett. 47 (1995) 263), and complement various asymptotic studies

Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery

This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for non-negativity and full-additivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images

Asymptotic enumeration and limit laws for graphs of fixed genus

It is shown that the number of labelled graphs with n vertices that can be embedded in the orientable surface S_g of genus g grows asymptotically like $c^{(g)}n^{5(g-1)/2-1}\gamma^n n!$ where $c^{(g)}>0$, and $\gamma \approx 27.23$ is the exponential growth rate of planar graphs. This generalizes the result for the planar case g=0, obtained by Gimenez and Noy. An analogous result for non-orientable surfaces is obtained. In addition, it is proved that several parameters of interest behave asymptotically as in the planar case. It follows, in particular, that a random graph embeddable in S_g has a unique 2-connected component of linear size with high probability

Effects of Thermal Discharge Upon a Subarctic Stream: Completion Report

The work upon which this report is based was supported in part by funds provided by the United States Department of Interior, Office of Water Research and Technology (Project B-020-ALAS), as authorized by the Water Resources Research Act of 1964, Public Law 88-279, as amended; in part by funds provided by the Municipal Utility System of the City of Fairbanks, Alaska; and in part by funds provided by the University of Alaska, Fairbanks

The Variance Gamma Scaled Self-Decomposable Process in Actuarial Modelling

A scaled self-decomposable stochastic process put forward by Carr, Geman, Madan and Yor (2007) is used to model long term equity returns and options prices. This parsimonious model is compared to a number of other one-dimensional continuous time stochastic processes (models) that are commonly used in finance and the actuarial sciences. The comparisons are conducted along three dimensions: the models ability to fit monthly time series data on a number of different equity indices; the models ability to fit the tails of the times series and the models ability to calibrate to index option prices across strike price and maturities. The last criteria is becoming increasingly important given the popularity of capital gauranteed products that contain long term imbedded options that can be (at least partially) hedged by purchasing short term index options and rolling them over or purchasing longer term index options. Thus we test if the models can reproduce a typical implied volatility surface seen in the market.Variance gamma, regime switching lognormal, long term equity returns.