Are dreidels fair? In other words, does the average dreidel have an equal chance of turning up any one of its four sides? To explore this hypothesis, three different dreidels were each spun hundreds of times with the number of occurrences of each side recorded. It was found that all three dreidels tested --a cheap plastic dreidel, an old wooden dreidel, and a dreidel that came embossed with a picture of Santa Claus --were not fair. Statistically, for each dreidel, some sides came up significantly more often than others. Although an unfair dreidel does not necessarily make the game itself unfair, it is conjectured that hundreds of pounds of chocolate have been distributed during Chanukah under false pretenses.

We present a catalog of the redshift estimates and probability distributions for 1366 individual Long-duration Gamma-Ray Bursts (LGRBs) detected by the Burst And Transient Source Experiment (BATSE). This result is based on a careful classification and modeling of the population distribution of BATSE LGRBs in the 5-dimensional space of redshift as well as intrinsic prompt gamma-ray emission properties: the isotropic 1024ms peak luminosity (L iso ), the total isotropic emission (E iso ), the spectral peak energy (E pz ), as well as the intrinsic duration (T 90z ), while taking into account the complex detection mechanism of BATSE and sample incompleteness. The underlying assumption in our modeling approach is that LGRBs trace the Cosmic Star Formation Rate and that the joint 4-dimensional distribution of the aforementioned prompt gamma-ray emission properties follows a multivariate lognormal distribution. Our modeling approach enables us to constrain the redshifts of BATSE LGRBs to average uncertainty ranges of 0.7 and 1.7 at 50% and 90% confidence levels, respectively. We compare our predictions with the previous redshift estimates of BATSE GRBs based on the proposed phenomenological high-energy relations, including the lag-luminosity, the spectral peak energy-luminosity, and the variability-luminosity relations. Our predictions are almost entirely at odds with the previous estimates based on these phenomenological high-energy correlations, in particular with the estimates derived from the lag-luminosity and the variability-luminosity relations. There is, however, a weak but significant correlation of strength ∼ 0.26 between our predicted redshift estimates and those derived from the hardness-brightness relations. The discrepancies between the estimates can be explained by the strong influence of sample incompleteness in shaping the phenomenologically proposed highenergy correlations in the literature. The presented catalog here can be useful for demographic studies of LGRBs and studies of individual BATSE events.

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Effective techniques for organizing and visualizing large image collections are in growing demand as visual search gets increasingly popular. Targeting an online astronomy archive with thousands of images, we present our solution for image search and clustering based on the evaluation of image similarity using both visual and textual information. Time-consuming image similarity computation is accelerated using GPU. To lay out images, we introduce iMap, a treemap-based representation for visualizing and navigating image search and clustering results. iMap not only makes effective use of available display area to arrange images but also maintains stable update when images are inserted or removed during the query. We also develop an embedded visualization that integrates image tags for in-place search refinement. To show the effectiveness of our approach, we demonstrate experimental results, compare our iMap layout with a force-directed layout, and conduct a comparative user study. As a potential tool for astronomy education and outreach, we deploy our iMap to a large tiled display of nearly 50 million pixels.

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