Interpreting the Distance Correlation Results for the COMBO-17 Survey

The accurate classification of galaxies in large-sample astrophysical databases of galaxy clusters depends sensitively on the ability to distinguish between morphological types, especially at higher redshifts. This capability can be enhanced through a new statistical measure of association and correlation, called the {\it distance correlation coefficient}, which has more statistical power to detect associations than does the classical Pearson measure of linear relationships between two variables. The distance correlation measure offers a more precise alternative to the classical measure since it is capable of detecting nonlinear relationships that may appear in astrophysical applications. We showed recently that the comparison between the distance and Pearson correlation coefficients can be used effectively to isolate potential outliers in various galaxy datasets, and this comparison has the ability to confirm the level of accuracy associated with the data. In this work, we elucidate the advantages of distance correlation when applied to large databases. We illustrate how the distance correlation measure can be used effectively as a tool to confirm nonlinear relationships between various variables in the COMBO-17 database, including the lengths of the major and minor axes, and the alternative redshift distribution. For these outlier pairs, the distance correlation coefficient is routinely higher than the Pearson coefficient since it is easier to detect nonlinear relationships with distance correlation. The V-shaped scatterplots of Pearson versus distance correlation coefficients also reveal the patterns with increasing redshift and the contributions of different galaxy types within each redshift range.Comment: 5 pages, 2 tables, 3 figures; published in Astrophysical Journal Letters, 784, L34 (2014

All for One and One for All! Disparity Between Overall Crew’s and Individual Rowers’ Pacing Strategies During Rowing

Purpose: This study examined individual contributions to overall pacing strategy during 2- and 5-km rowing trials in a cox-less-4 boat. Methods: A crew of 4 male rowers performed maximal-effort on-water trials over 2 and 5 km, and power output during every individual stroke was measured for each crew member. Mean overall boat and individual rower stroke power were calculated for each 25% epoch (25% of total strokes taken), and power for each individual epoch was calculated as a percentage of mean power maintained over the entire distance. The coefficient of variation was used to determine stroke-to-stroke and epoch-to-epoch variability for individual rowers and the overall boat. Results: In both trials, the overall pacing strategy consisted of a high power output in the initial 25% that decreased in the middle 50% and increased again in the final 25%. However, individual rower data indicate wide variation in individual power profiles that did not always mimic the overall boat profile. Conclusions: This study demonstrates that overall boat power profiles during 2- and 5-km rowing trials are similar to velocity profiles previously reported for individual ergometry and on-water racing events. However, this over-all profile is achieved despite considerable variation in individual rower profiles. Further research is warranted to determine the mechanisms through which individual contributions to overall pacing strategy are regulated and the effectiveness or oth-erwise of seemingly disparate individual strategies on overall performance

Exact ZF Analysis and Computer-Algebra-Aided Evaluation in Rank-1 LoS Rician Fading

We study zero-forcing detection (ZF) for multiple-input/multiple-output (MIMO) spatial multiplexing under transmit-correlated Rician fading for an N_R X N_T channel matrix with rank-1 line-of-sight (LoS) component. By using matrix transformations and multivariate statistics, our exact analysis yields the signal-to-noise ratio moment generating function (m.g.f.) as an infinite series of gamma distribution m.g.f.'s and analogous series for ZF performance measures, e.g., outage probability and ergodic capacity. However, their numerical convergence is inherently problematic with increasing Rician K-factor, N_R , and N_T. We circumvent this limitation as follows. First, we derive differential equations satisfied by the performance measures with a novel automated approach employing a computer-algebra tool which implements Groebner basis computation and creative telescoping. These differential equations are then solved with the holonomic gradient method (HGM) from initial conditions computed with the infinite series. We demonstrate that HGM yields more reliable performance evaluation than by infinite series alone and more expeditious than by simulation, for realistic values of K , and even for N_R and N_T relevant to large MIMO systems. We envision extending the proposed approaches for exact analysis and reliable evaluation to more general Rician fading and other transceiver methods.Comment: Accepted for publication by the IEEE Transactions on Wireless Communications, on April 7th, 2016; this is the final revision before publicatio