Nitrogen (N) is a major ingredient of the atmosphere, but a trace component in the silicate Earth. Its initial inventory in these reservoirs during Earth's early differentiation requires knowledge of N speciation in magmas, for example, whether it outgasses as N 2 or is sequestered in silicate melts as N 3− , which remains largely unconstrained over the entire mantle regime. Here we examine N species in anhydrous and hydrous pyrolitic melts at varying P‐T‐redox conditions by ab‐initio calculations, and find N‐N bonding under oxidizing conditions from ambient to lower mantle pressures. Under reducing conditions, N interacts with the silicate network or forms N‐H bonds, depending on the availability of hydrogen. Redox control of N speciation is demonstrated valid over a P‐T space encompassing probable magma ocean depths. Finally, if the Earth accreted from increasingly oxidized materials toward the end of its accretion, an N‐enriched secondary atmosphere might be produced and persist until later impacts.
Quantile regression is a method of fundamental importance. How to efficiently conduct quantile regression for a large dataset on a distributed system is of great importance. We show that the popularly used one-shot estimation is statistically inefficient if data are not randomly distributed across different workers. To fix the problem, a novel one-step estimation method is developed with the following nice properties. First, the algorithm is communication efficient. That is the communication cost demanded is practically acceptable. Second, the resulting estimator is statistically efficient. That is its asymptotic covariance is the same as that of the global estimator. Third, the estimator is robust against data distribution. That is its consistency is guaranteed even if data are not randomly distributed across different workers. Numerical experiments are provided to corroborate our findings. A real example is also presented for illustration.