Gamma-Ray Bursts (GRBs) have been conventionally bifurcated into two distinct categories dubbed "short" and "long", depending on whether their durations are less than or greater than two seconds respectively. However, many authors have pointed to the existence of a third class of GRBs with mean durations intermediate between the short and long GRBs. Here, we apply multiple model comparison techniques to verify these claims. For each category, we obtain the best-fit parameters by maximizing a likelihood function based on a weighted superposition of two (or three) lognormal distributions. We then do model-comparison between each of these hypotheses by comparing the chi-square probabilities, Akaike Information criterion (AIC), and Bayesian Information criterion (BIC). We uniformly apply these techniques to GRBs from Swift (both observer and intrinsic frame), BATSE, BeppoSAX, and Fermi-GBM. We find that the Swift GRB distributions (in the observer frame) for the entire dataset favor three categories at about 2.4σ from difference in chi-squares, and show decisive evidence in favor of three components using both AIC and BIC. However, when the same analysis is done for the subset of Swift GRBs with measured redshifts, two components are favored with marginal significance. For all the other datasets, evidence for three components is either very marginal or disfavored.

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Recently, Odrzywolek and Rafelski [1] have found three distinct categories of exoplanets, when they are classified based on density. We first carry out a similar classification of exoplanets according to their density using the Gaussian Mixture Model, followed by information theoretic criterion (AIC and BIC) to determine the optimum number of components. Such a one-dimensional classification favors two components using AIC and three using BIC, but the statistical significance from both the tests is not significant enough to decisively pick the best model between two and three components. We then extend this GMM-based classification to two dimensions by using both the density and the Earth similarity index [2], which is a measure of how similar each planet is compared to the Earth. For this two-dimensional classification, both AIC and BIC provide decisive evidence in favor of three components.

This paper describes a novel, to the best of our knowledge, approach to build ultrastable interferometers using commercial mirror mounts anchored in an ultralow expansion (ULE) base. These components will play a critical role in any light particle search (ALPS) and will also be included in ground testing equipment for the upcoming laser interferometer space antenna (LISA) mission. Contrary to the standard ultrastable designs where mirrors are bonded to the spacers, ruling out any later modifications and alignments, our design remains flexible and allows the alignment of optical components at all stages to be optimized and changed. Here we present the dimensional stability and angular stability of two commercial mirror mounts characterized in a cavity setup. The long-term length change in the cavity did not exceed 30 nm and the relative angular stability was within 2 µrad, which meet the requirements for ALPS. We were also able to demonstrate 1 p m / H z   length noise stability, which is a critical requirement for various subsystems in LISA. These results have led us to design similar opto-mechanical structures, which will be used in ground verification to test the LISA telescope.

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