Triangular flow in event-by-event ideal hydrodynamics in Au+Au collisions at √SNN = 200A GeV

The first calculation of triangular flow ν3 in Au+Au collisions at √sNN = 200A GeV from an event-by-event (3 + 1) d transport+hydrodynamics hybrid approach is presented. As a response to the initial triangularity Ie{cyrillic, ukrainian}3 of the collision zone, ν3 is computed in a similar way to the standard event-plane analysis for elliptic flow ν2. It is found that the triangular flow exhibits weak centrality dependence and is roughly equal to elliptic flow in most central collisions. We also explore the transverse momentum and rapidity dependence of ν2 and ν3 for charged particles as well as identified particles. We conclude that an event-by-event treatment of the ideal hydrodynamic evolution startingwith realistic initial conditions generates the main features expected for triangular flow. © 2010 The American Physical Society.

PenPC: A two-step approach to estimate the skeletons of high-dimensional directed acyclic graphs.

Estimation of the skeleton of a directed acyclic graph (DAG) is of great importance for understanding the underlying DAG and causal effects can be assessed from the skeleton when the DAG is not identifiable. We propose a novel method named PenPC to estimate the skeleton of a high-dimensional DAG by a two-step approach. We first estimate the nonzero entries of a concentration matrix using penalized regression, and then fix the difference between the concentration matrix and the skeleton by evaluating a set of conditional independence hypotheses. For high-dimensional problems where the number of vertices p is in polynomial or exponential scale of sample size n, we study the asymptotic property of PenPC on two types of graphs: traditional random graphs where all the vertices have the same expected number of neighbors, and scale-free graphs where a few vertices may have a large number of neighbors. As illustrated by extensive simulations and applications on gene expression data of cancer patients, PenPC has higher sensitivity and specificity than the state-of-the-art method, the PC-stable algorithm.