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.
Nutrient scarcity is pervasive for natural microbial communities, affecting species reproduction and co-existence. However, it remains unclear whether there are general rules of how microbial species abundances are shaped by biotic and abiotic factors. Here we show that the ribosomal RNA gene operon (rrn) copy number, a genomic trait related to bacterial growth rate and nutrient demand, decreases from the abundant to the rare biosphere in the nutrient-rich coastal sediment but exhibits the opposite pattern in the nutrient-scarce pelagic zone of the global ocean. Both patterns are underlain by positive correlations between community-level rrn copy number and nutrients. Furthermore, inter-species co-exclusion inferred by negative network associations is observed more in coastal sediment than in ocean water samples. Nutrient manipulation experiments yield effects of nutrient availability on rrn copy numbers and network associations that are consistent with our field observations. Based on these results, we propose a “hunger games” hypothesis to define microbial species abundance rules using the rrn copy number, ecological interaction, and nutrient availability.
As a stereo odor cue, internostril odor influx could help us in many spatial tasks, including localization and navigation. Studies have also revealed that this benefit could be modulated by the asymmetric concentrations of both influxes (left nose vs right nose). The interaction between olfaction and vision, such as in object recognition and visual direction judgment, has been documented; however, little has been revealed about the impact of odor cues on sound localization. Here we adopted the ventriloquist paradigm in auditory-odor interactions and investigated sound localization with the concurrent unilateral odor influx. Specifically, we teased apart both the "nature" of the odors (pure olfactory stimulus vs. mixed olfactory/trigeminal stimulus) and the location of influx (left nose vs. right nose) and examined sound localization with the method of constant stimuli. Forty-one participants, who passed the Chinese Smell Identification Test, perceived sounds with different azimuths (0°, 5°, 10°, and 20° unilaterally deflected from the sagittal plane by head-related transfer function) and performed sound localization (leftward or rightward) tasks under concurrent, different unilateral odor influxes (10% v/v phenylethyl alcohol, PEA, as pure olfactory stimulus, 1% m/v menthol as mixed olfactory/trigeminal stimulus, and propylene glycol as the control). Meanwhile, they reported confidence levels of the judgments. Results suggested that unilateral PEA influx did not affect human sound localization judgments. However, unilateral menthol influx systematically biased the perceived sound localization, shifting toward the odor source. Our study provides evidence that unilateral odor influx could bias perceived sound localization only when the odor activates the trigeminal nerves.
This paper discusses a widely accepted emendation to an earlier version of IG X 2.1 137. Early draft copies of the Herennia announcement show that Antoninus Pius was hailed as Σωτήρ by the city of Thessalonike, a rare epithet for this emperor. This reading was later replaced due to an expert’s claim that σωτῆρος has to be read σωτηρίας. Since this seems to conform to a well-known salutary formula, the emendation was adopted from then on. This paper suggests that the reading of σωτῆρος is based on reliable and published reports instead, and ought to be preferred over the expert claim. Empirical evidence is given to support reading σωτῆρος.