Variable selection in nonparametric additive models

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the sample size. The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component selection becomes that of selecting the groups of coefficients in the expansion. We apply the adaptive group Lasso to select nonzero components, using the group Lasso to obtain an initial estimator and reduce the dimension of the problem. We give conditions under which the group Lasso selects a model whose number of components is comparable with the underlying model, and the adaptive group Lasso selects the nonzero components correctly with probability approaching one as the sample size increases and achieves the optimal rate of convergence. The results of Monte Carlo experiments show that the adaptive group Lasso procedure works well with samples of moderate size. A data example is used to illustrate the application of the proposed method.Comment: Published in at http://dx.doi.org/10.1214/09-AOS781 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Remove-Win: a Design Framework for Conflict-free Replicated Data Collections

Internet-scale distributed systems often replicate data within and across data centers to provide low latency and high availability despite node and network failures. Replicas are required to accept updates without coordination with each other, and the updates are then propagated asynchronously. This brings the issue of conflict resolution among concurrent updates, which is often challenging and error-prone. The Conflict-free Replicated Data Type (CRDT) framework provides a principled approach to address this challenge. This work focuses on a special type of CRDT, namely the Conflict-free Replicated Data Collection (CRDC), e.g. list and queue. The CRDC can have complex and compound data items, which are organized in structures of rich semantics. Complex CRDCs can greatly ease the development of upper-layer applications, but also makes the conflict resolution notoriously difficult. This explains why existing CRDC designs are tricky, and hard to be generalized to other data types. A design framework is in great need to guide the systematic design of new CRDCs. To address the challenges above, we propose the Remove-Win Design Framework. The remove-win strategy for conflict resolution is simple but powerful. The remove operation just wipes out the data item, no matter how complex the value is. The user of the CRDC only needs to specify conflict resolution for non-remove operations. This resolution is destructed to three basic cases and are left as open terms in the CRDC design skeleton. Stubs containing user-specified conflict resolution logics are plugged into the skeleton to obtain concrete CRDC designs. We demonstrate the effectiveness of our design framework via a case study of designing a conflict-free replicated priority queue. Performance measurements also show the efficiency of the design derived from our design framework.Comment: revised after submissio

Kinematic properties of the dual AGN system J0038+4128 based on long-slit spectroscopy

The study of kiloparsec-scale dual active galactic nuclei (AGN) will provide important clues to understand the co-evolution between the host galaxies and their central supermassive black holes undergoing a merging process. We present long-slit spectroscopy of the J0038$+$4128, a kiloparsec-scale dual AGN candidate discovered by Huang et al. recently, using the Yunnan Faint Object Spectrograph and Camera (YFOSC) mounted on Li-Jiang 2.4-m telescope at Yunnan observatories. From the long-slit spectra, we find that the average relative line-of-sight (LOS) velocity between the two nuclei (J0038$+$4128N and J0038$+$4128S) is about 150 km s$^{-1}$. The LOS velocities of the emission lines from the gas ionized by the nuclei activities and of the absorption lines from stars governed by the host galaxies for different regions of the J0038$+$4128 exhibit the same trend. The same velocities trend indicates that the gaseous disks are co-rotating with the stellar disks in this ongoing merge system. We also find several knots/giant HII regions scattered around the two nuclei with strong star formation revealed by the observed line ratios from the spectra. Those regions are also detected clearly in HST $F336W/U$-band and HST $F555W/V$-band images.Comment: 12 pages, 5 figures, 3 tables, Research in Astronomy and Astrophysics accepte