Non-uniform continuous dependence on initial data of solutions to the Euler-Poincar\'{e} system

In this paper, we investigate the continuous dependence on initial data of solutions to the Euler-Poincar\'{e} system. By constructing a sequence approximate solutions and calculating the error terms, we show that the data-to-solution map is not uniformly continuous in Sobolev space $H^s(\mathbb{R}^d)$ for $s>1+\frac d2$.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1505.00086 by other author

Quenching depends on morphologies: implications from the ultraviolet-optical radial color distributions in Green Valley Galaxies

In this Letter, we analyse the radial UV-optical color distributions in a sample of low redshift green valley (GV) galaxies, with the Galaxy Evolution Explorer (GALEX)+Sloan Digital Sky Survey (SDSS) images, to investigate how the residual recent star formation distribute in these galaxies. We find that the dust-corrected $u-r$ colors of early-type galaxies (ETGs) are flat out to $R_{90}$, while the colors turn blue monotonously when $r>0.5R_{50}$ for late-type galaxies (LTGs). More than a half of the ETGs are blue-cored and have remarkable positive NUV$-r$ color gradients, suggesting that their star formation are centrally concentrated; the rest have flat color distributions out to $R_{90}$. The centrally concentrated star formation activity in a large portion of ETGs is confirmed by the SDSS spectroscopy, showing that $\sim$50 % ETGs have EW(H$\rm \alpha$)$>6.0$ \AA. For the LTGs, 95% of them show uniform radial color profiles, which can be interpreted as a red bulge plus an extended blue disk. The links between the two kinds of ETGs, e.g., those objects having remarkable "blue-cored" and those having flat color gradients, are less known and require future investigations. It is suggested that the LTGs follow a general picture that quenching first occur in the core regions, and then finally extend to the rest of the galaxy. Our results can be re-examined and have important implications for the IFU surveys, such as MaNGA and SAMI.Comment: ApJ Letter, accepted. Five figure

From outside-in to inside-out: galaxy assembly mode depends on stellar mass

In this Letter, we investigate how galaxy mass assembly mode depends on stellar mass $M_{\ast}$, using a large sample of $\sim$10, 000 low redshift galaxies. Our galaxy sample is selected to have SDSS R_{90}>5\arcsec.0, which allows the measures of both the integrated and the central NUV$-r$ color indices. We find that: in the $M_{\ast}-($ NUV$-r$) green valley, the M_{\ast}<10^{10}~M_{\sun} galaxies mostly have positive or flat color gradients, while most of the M_{\ast}>10^{10.5}~M_{\sun} galaxies have negative color gradients. When their central $D_{n}4000$ index values exceed 1.6, the M_{\ast}<10^{10.0}~M_{\sun} galaxies have moved to the UV red sequence, whereas a large fraction of the M_{\ast}>10^{10.5}~M_{\sun} galaxies still lie on the UV blue cloud or the green valley region. We conclude that the main galaxy assembly mode is transiting from "the outside-in" mode to "the inside-out" mode at M_{\ast} 10^{10.5}~M_{\sun}. We argue that the physical origin of this is the compromise between the internal and the external process that driving the star formation quenching in galaxies. These results can be checked with the upcoming large data produced by the on-going IFS survey projects, such as CALIFA, MaNGA and SAMI in the near future.Comment: Accepted for publication in ApJL,6 pages, 5 figure

Telepath: Understanding Users from a Human Vision Perspective in Large-Scale Recommender Systems

Designing an e-commerce recommender system that serves hundreds of millions of active users is a daunting challenge. From a human vision perspective, there're two key factors that affect users' behaviors: items' attractiveness and their matching degree with users' interests. This paper proposes Telepath, a vision-based bionic recommender system model, which understands users from such perspective. Telepath is a combination of a convolutional neural network (CNN), a recurrent neural network (RNN) and deep neural networks (DNNs). Its CNN subnetwork simulates the human vision system to extract key visual signals of items' attractiveness and generate corresponding activations. Its RNN and DNN subnetworks simulate cerebral cortex to understand users' interest based on the activations generated from browsed items. In practice, the Telepath model has been launched to JD's recommender system and advertising system. For one of the major item recommendation blocks on the JD app, click-through rate (CTR), gross merchandise value (GMV) and orders have increased 1.59%, 8.16% and 8.71% respectively. For several major ads publishers of JD demand-side platform, CTR, GMV and return on investment have increased 6.58%, 61.72% and 65.57% respectively by the first launch, and further increased 2.95%, 41.75% and 41.37% respectively by the second launch.Comment: 8 pages, 11 figures, 1 tabl