Present and Future Prospects for GRB Standard Candles

Following our previous work, we conclude that a GRB standard candle constructed from the Ghirlanda et al. power-law relation between the geometry-corrected energy (E_gamma) and the peak of the rest-frame prompt burst spectrum (E_p) is not yet cosmographically useful, despite holding some potential advantages over SNe Ia. This is due largely to the small sample of \~20 GRBs with the required measured redshifts, jet-breaks, and peak energies, and to the strong sensitivity of the goodness-of-fit of the power-law to input assumptions. The most important such finding concerns the sensitivity to the generally unknown density (and density profile), of the circumburst medium. Although the E_p-E_gamma relation is a highly significant correlation over many cosmologies, until the sample expands to include many low-z events, it will be most sensitive to Omega_M but essentially insensitive to Omega_Lambda and w, with some hope of constraining dw/dt with high-z GRB data alone. The relation clearly represents a significant improvement in the search for an empirical GRB standard candle, but is further hindered by an unknown physical basis for the relation, the lack of a low-z training set to calibrate the relation in a cosmology-independent way, and several major potential systematic uncertainties and selection effects. Until these concerns are addressed, a larger sample is acquired, and attempts are made to marginalize or perform Monte Carlo simulations over the unknown density distribution, we urge caution concerning claims of the utility of GRBs for cosmography and especially the attempts to combine GRBs with SNe Ia.Comment: 5 pages, 2 figures, "Proceedings, Gamma-Ray Bursts in the Afterglow Era: 4th Workshop, Rome, Italy, Oct 18-22, 2004". Accepted to Il Nuovo Cimento. For more details, see astro-ph/0408413 (ApJ accepted), and other work from the cosmicbooms.net Team at http://www.cosmicbooms.net

Sustained Positive Effects on Graduation Rates Produced by New York City's Small Public High Schools of Choice

Evaluates how effectively small academically nonselective high schools that replaced large failing ones achieved sustained improvement in academic progress and graduation rates across variations in prior proficiency, family income, and demographics

Towards precision distances and 3D dust maps using broadband Period--Magnitude relations of RR Lyrae stars

We determine the period-magnitude relations of RR Lyrae stars in 13 photometric bandpasses from 0.4 to 12 {\mu}m using timeseries observations of 134 stars. The Bayesian formalism, extended from our previous work to include the effects of line-of-sight dust extinction, allows for the simultaneous inference of the posterior distribution of the mean absolute magnitude, slope of the period-magnitude power-law, and intrinsic scatter about a perfect power-law for each bandpass. In addition, the distance modulus and line-of-sight dust extinction to each RR Lyrae star in the calibration sample is determined, yielding a sample median fractional distance error of 0.66%. The intrinsic scatter in all bands appears to be larger than the photometric errors, except in WISE W1 (3.4 {\mu}m) and W2 (4.6 {\mu}m) where the photometric error ($\sigma \approx 0.05$ mag) is to be comparable or larger than the intrinsic scatter. Additional observations at these wavelengths could improve the inferred distances to these sources further. As an application of the methodology, we infer the distance to the RRc-type star RZCep at low Galactic latitude ($b = 5.5^\circ$) to be $\mu=8.0397\pm0.0123$ mag ($405.4\pm2.3$ pc) with colour excess $E(B-V)=0.2461\pm0.0089$ mag. This distance, equivalent to a parallax of $2467\pm14$ microarcsec, is consistent with the published HST parallax measurement but with an uncertainty that is 13 times smaller than the HST measurement. If our measurements (and methodology) hold up to scrutiny, the distances to these stars have been determined to an accuracy comparable to those expected with Gaia. As RR Lyrae are one of the primary components of the cosmic distance ladder, the achievement of sub-1% distance errors within a formalism that accounts for dust extinction may be considered a strong buttressing of the path to eventual 1% uncertainties in Hubble's constant.Comment: 21 pages, 29 figures, 2 tables, abstract abridged for arXiv. Comments solicited on referee report (received June 9, 2014) linked: https://gist.github.com/profjsb/c6c4e2f3a20ea02f1762 . Public archive of code used to generate results and figures: https://github.com/ckleinastro/period_luminosity_relation_fittin

Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments

Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study focuses on techniques for analyzing Single Particle Tracking (SPT) data experiencing abrupt state changes. We demonstrate the approach on GFP tagged chromatids experiencing metaphase in yeast cells and probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes are induced by factors such as microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, etc. Simulations are used to demonstrate the relevance of the approach in more general SPT data analyses. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One publication available freely as an open-access article at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763