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Shapelet is a discriminative subsequence of time series. An advanced shapelet-based method is to embed shapelet into accurate and fast random forest. However, it shows several limitations. First, random shapelet forest requires a large training cost for split threshold searching. Second, a single shapelet provides limited information for only one branch of the decision tree, resulting in insufficient accuracy and interpretability. Third, randomized ensemble causes interpretability declining. For that, this paper presents Random Pairwise Shapelets Forest (RPSF). RPSF combines a pair of shapelets from different classes to construct random forest. It omits threshold searching to be more efficient, includes more information for each node of the forest to be more effective. Moreover, a discriminability metric, Decomposed Mean Decrease Impurity (DMDI), is proposed to identify influential region for every class. Extensive experiments show RPSF improves the accuracy and training speed of shapelet-based forest. Case studies demonstrate the interpretability of our method., Comment: There is some misunderstanding between authors when this manuscript is submitted. Some of authors disagree to submit this manuscript. So we decide to withdraw the article

The metallicity and its relationship with other galactic properties is a fundamental probe of the evolution of galaxies. In this work, we select about 750,000 star-forming spatial pixels from 1122 blue galaxies in the MaNGA survey to investigate the global stellar mass - local stellar mass surface density - gas-phase metallicity ($M_*$ - $\Sigma_*$ - $Z$ ) relation. At a fixed $M_*$, the metallicity increases steeply with increasing $\Sigma_*$. Similarly, at a fixed $\Sigma_*$, the metallicity increases strongly with increasing $M_*$ at low mass end, while this trend becomes less obvious at high mass end. We find the metallicity to be more strongly correlated to $\Sigma_*$ than to $M_*$. Furthermore, we construct a tight (0.07 dex scatter) $M_*$ - $\Sigma_*$ - $Z$ relation, which reduces the scatter in the $\Sigma_*$ - $Z$ relation by about 30$\%$ for galaxies with $7.8 < {\rm log}(M_*/M_\odot) < 11.0$, while the reduction of scatter is much weaker for high-mass galaxies. This result suggests that, especially for low-mass galaxies, the $M_*$ - $\Sigma_*$ - $Z$ relation is largely more fundamental than the $M_*$ - $Z$ and $\Sigma_*$ - $Z$ relations, meaning that both $M_*$ and $\Sigma_*$ play important roles in shaping the local metallicity. We also find that the local metallicity is probably independent on the local star formation rate surface density at a fixed $M_*$ and $\Sigma_*$. Our results are consistent with the scenario that the local metallicities in galaxies are shaped by the combination of the local stars formed in the history and the metal loss caused by galactic winds., Comment: 14 pages, 8 figures; accepted by ApJ

We investigate the spatially-resolved star formation main sequence in star-forming galaxies (SFGs) using Integral Field Spectroscopic (IFS) observations from the Mapping Nearby Galaxies at the Apache Point Observatory (MaNGA) survey. We demonstrate that the correlation between the stellar mass surface density ($\Sigma_*$) and star formation rate surface density ($\Sigma_{\mathrm{SFR}}$) holds down to sub-galactic scale, leading to the Sub-Galactic Main Sequence (SGMS). By dividing galaxies into two populations based on their recent mass assembly modes, we find the resolved main sequence in galaxies with 'outside-in' mode is steeper than that in galaxies with 'inside-out' mode. This is also confirmed on a galaxy-by-galaxy level, where we find the distributions of SGMS slopes for individual galaxies are clearly separated for the two populations. When normalizing and stacking the SGMS of individual galaxies on one panel for the two populations, we find the inner regions of galaxies with 'inside-out' mode statistically exhibit a suppression in star formation, with a less significant trend in the outer regions of galaxies with 'outside-in' mode. In contrast, the inner regions of galaxies with 'outside-in' mode and the outer regions of galaxies with 'inside-out' mode follow a slightly sub-linear scaling relation with a slope $\sim$0.9, which is in good agreement with previous findings, suggesting that they are experiencing a universal regulation without influences of additional physical processes., Comment: 11 pages, 9 figures, accepted for publication in ApJ