The Rising Stellar Velocity Dispersion of M87 from Integrated Starlight

We have measured the line-of-sight velocity distribution from integrated stellar light at two points in the outer halo of M87 (NGC 4486), the second-rank galaxy in the Virgo Cluster. The data were taken at R = 480" ($\sim 41.5$ kpc) and R = 526" ($\sim 45.5$ kpc) along the SE major axis. The second moment for a non-parametric estimate of the full velocity distribution is $420 \pm 23$ km/s and $577 \pm 35$ km/s respectively. There is intriguing evidence in the velocity profiles for two kinematically distinct stellar components at the position of our pointing. Under this assumption we employ a two-Gaussian decomposition and find the primary Gaussian having rest velocities equal to M87 (consistent with zero rotation) and second moments of $383 \pm 32$ km/s and $446 \pm 43$ km/s respectively. The asymmetry seen in the velocity profiles suggests that the stellar halo of M87 is not in a relaxed state and confuses a clean dynamical interpretation. That said, either measurement (full or two component model) shows a rising velocity dispersion at large radii, consistent with previous integrated light measurements, yet significantly higher than globular cluster measurements at comparable radial positions. These integrated light measurements at large radii, and the stark contrast they make to the measurements of other kinematic tracers, highlight the rich kinematic complexity of environments like the center of the Virgo Cluster and the need for caution when interpreting kinematic measurements from various dynamical tracers.Comment: 16 pages, 5 figures; accepted for publication in The Astrophysical Journa

Signal Detection Theory and Single Observation Designs: Methods and Indices for Advertising Recognition Testing

Two simulations assessed the statistical bias, consistency, and efficiency of 4 different signal detection theory (SDT) sensitivity measures; a corrected-hit probability, the traditional d′ statistic, and 2 nonparametric measures collected from a collapsed-data procedure. Overall, results reinforce evidence that collapsed procedures produce relatively unbiased and efficient estimators. Recommendations for the best approach to using SDT for advertisement recognition testing are offered

Multicriterion Clusterwise Regression for Joint Segmentation Settings: An Application to Customer Value

The authors present a multicriterion clusterwise linear regression model that can be applied to a joint segmentation setting. The model enables the consideration of segment homogeneity, as well as multiple dependent variables (segmentation bases), in a weighted objective function. The authors propose a heuristic solution strategy based on simulated annealing and examine trade-offs in the recovery of multiple true cluster structures for several synthetic data sets. They also propose an application of the model to a joint segmentation problem in the telecommunications industry, which addresses important issues pertaining to the selection of the objective function weights and the number of clusters