Unbiased flux calibration methods for spectral-line radio observations

Position and frequency switching techniques used for the removal of the bandpass dependence of radio astronomical spectra are presented and discussed in detail. Both methods are widely used, although the frequency dependence of the system temperature and/or noise diode is often neglected. This leads to systematic errors in the calibration that potentially have a significant impact on scientific results, especially when using large-bandwidth receivers or performing statistical analyses. We present methods to derive an unbiased calibration using a noise diode, which is part of many heterodyne receivers. We compare the proposed methods and describe the advantages and bottlenecks of the various approaches. Monte Carlo simulations are used to qualitatively investigate both systematics and the error distribution of the reconstructed flux estimates about the correct flux values for the new methods but also the 'classical' case. Finally, the determination of the frequency-dependent noise temperature of the calibration diode using hot-cold measurements or observations of well-known continuum sources is also briefly discussed.Comment: 25 pages, 30 figures. Accepted for publication in A&

Vietnam: A War with Two Fronts

The Vietnam War is viewed by many historians as a turning point in American war memory. Never before had there been such an outstanding opposition to a military endeavor by the United States\u27 own citizens, government officials, soldiers, and veterans. Drawing from the first hand accounts of PFC Steven Warner and the work of numerous historians, this paper offers an examination into the ways in which some high profile events of the Vietnam War (such as the Cambodia Campaign and the Kent State Shootings) created an environment that negatively impacted United States soldiers and veterans of the Vietnam War

Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions

We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford's sequence of alpha model trees in the continuum tree which we identified in a previous article as a distributional scaling limit of Ford's trees. In general, the Markov branching trees induced by the two-parameter growth rule are not sampling consistent, so the existence of compact limiting trees cannot be deduced from previous work on the sampling consistent case. We develop here a new approach to establish such limits, based on regenerative interval partitions and the urn-model description of sampling from Dirichlet random distributions.Comment: Published in at http://dx.doi.org/10.1214/08-AOP445 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Invariance principles for pruning processes of Galton-Watson trees

Pruning processes $(\mathcal{F}(\theta),\theta\geq 0)$ have been studied separately for Galton-Watson trees and for L\'evy trees/forests. We establish here a limit theory that strongly connects the two studies. This solves an open problem by Abraham and Delmas, also formulated as a conjecture by L\"ohr, Voisin and Winter. Specifically, we show that for any sequence of Galton-Watson forests $\mathcal{F}_n$, $n\geq 1$, in the domain of attraction of a L\'evy forest $\mathcal{F}$, suitably scaled pruning processes $(\mathcal{F}_n(\theta),\theta\geq 0)$ converge in the Skorohod topology on cadlag functions with values in the space of (isometry classes of) locally compact real trees to limiting pruning processes. We separately treat pruning at branch points and pruning at edges. We apply our results to study ascension times and Kesten trees and forests.Comment: 33 page

The Robustness of Least-Squares Frequency Switching (LSFS)

Least-squares frequency switching (LSFS) is a new method to reconstruct signal and gain function (known as bandpass or baseline) from spectral line observations using the frequency switching method. LSFS utilizes not only two but a set of three or more local oscillator (LO) frequencies. The reconstruction is based on a least squares fitting scheme. Here we present a detailed investigation on the stability of the LSFS method in a statistical sense and test the robustness against radio frequency interference (RFI), receiver gain instabilities and continuum sources. It turns out, that the LSFS method is indeed a very powerful method and is robust against most of these problems. Nevertheless, LSFS fails in presence of RFI signals or strong line emission. We present solutions to overcome these limitations using a flagging mechanism or remapping of measured signals, respectively.Comment: 17 pages, 21 figures, 1 table, accepted for publication in ApJS (November 2007, v173n1

Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees

We introduce the notion of a restricted exchangeable partition of $\mathbb{N}$. We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In particular, we deduce from the general theory developed here a limit result conjectured previously for Ford's alpha model and its extension, the alpha-gamma model, where restricted exchangeability arises naturally.Comment: 35 pages, 5 figure