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Transformers have been widely applied in text classification. Unfortunately, real-world data contain anomalies and noisy labels that cause challenges for state-of-art Transformers. This paper proposes Protoformer, a novel self-learning framework for Transformers that can leverage problematic samples for text classification. Protoformer features a selection mechanism for embedding samples that allows us to efficiently extract and utilize anomalies prototypes and difficult class prototypes. We demonstrated such capabilities on datasets with diverse textual structures (e.g., Twitter, IMDB, ArXiv). We also applied the framework to several models. The results indicate that Protoformer can improve current Transformers in various empirical settings., Comment: Advances in Knowledge Discovery and Data Mining (PAKDD 2022)

The temperatures of observed protoplanetary disks are not sufficiently high to produce the accretion rate needed to form stars, nor are they sufficient to explain the volatile depletion patterns in CM, CO, and CV chondrites and terrestrial planets. We revisit the role that stellar outbursts, caused by high accretion episodes, play in resolving these two issues. These outbursts provide the necessary mass to form the star during the disk lifetime, and provide enough heat to vaporize planet-forming materials. We show that these outbursts can reproduce the observed chondrite abundances at distances near one AU. These outbursts would also affect the growth of calcium-aluminum-rich inclusions (CAIs) and the isotopic compositions of carbonaceous and non-carbonaceous chondrites., Comment: 20 pages, 13 figures, accepted to ApJ

The gravitational instabilities are important to the evolution of the disks and the planet formation in the disks. We calculate the evolution of the disks which form from the collapse of the molecular cloud cores. By changing the properties of the cloud cores and the hydrodynamical viscosity parameters, we explore their effects on the properties of the gravitational instabilities. We find that the disk is unstable when the angular velocity of the molecular cloud core is larger than a critical value. The time duration of the instability increases as the angular velocity of the core increases. The increase of the hydrodynamical viscosity parameter hardly affects the stability of the disk, but decreases the time duration of the critical state of the gravitational instability in the disk. The instability of the disks can happen at very early time of evolution of the disk, which is consistent with the observations., Comment: 10 pages, 9 figures, accepted by PASP

We calculate the cross-correlation function $\langle (\Delta T/T)(\mathbf{v}\cdot \mathbf{n}/\sigma_{v}) \rangle$ between the kinetic Sunyaev-Zeldovich (kSZ) effect and the reconstructed peculiar velocity field using linear perturbation theory, to constrain the optical depth $\tau$ and peculiar velocity bias of central galaxies with Planck data. We vary the optical depth $\tau$ and the velocity bias function $b_{v}(k)=1+b(k/k_{0})^{n}$, and fit the model to the data, with and without varying the calibration parameter $y_{0}$ that controls the vertical shift of the correlation function. By constructing a likelihood function and constraining $\tau$, $b$ and $n$ parameters, we find that the quadratic power-law model of velocity bias $b_{v}(k)=1+b(k/k_{0})^{2}$ provides the best-fit to the data. The best-fit values are $\tau=(1.18 \pm 0.24) \times 10^{-4}$, $b=-0.84^{+0.16}_{-0.20}$ and $y_{0}=(12.39^{+3.65}_{-3.66})\times 10^{-9}$ ($68\%$ confidence level). The probability of $b>0$ is only $3.12 \times 10^{-8}$ for the parameter $b$, which clearly suggests a detection of scale-dependent velocity bias. The fitting results indicate that the large-scale ($k \leq 0.1\,h\,{\rm Mpc}^{-1}$) velocity bias is unity, while on small scales the bias tends to become negative. The value of $\tau$ is consistent with the stellar mass--halo mass and optical depth relation proposed in the previous literatures, and the negative velocity bias on small scales is consistent with the peak background-split theory. Our method provides a direct tool to study the gaseous and kinematic properties of galaxies., Comment: 13 pages, 13 figures, 3 tables

In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We find that, due to coarse-graining, the entropy is a monotonic increasing function of the bin width for histogram or bandwidth for kernel estimation, which seems to be difficult to select an optimal bin width/bandwidth for computing the entropy. Fortunately, we notice that there exists a minimum of the first derivative of entropy for both histogram and kernel estimation, and this minimum point of the first derivative asymptotically points to the optimal bin width or bandwidth. We have verified these findings by large amounts of numerical experiments. Hence, we suggest that the minimum of the first derivative of entropy be used as a selector for the optimal bin width or bandwidth of density estimation. Moreover, the optimal bandwidth selected by the minimum of the first derivative of entropy is purely data-based, independent of the unknown underlying probability density distribution, which is obviously superior to the existing estimators. Our results are not restricted to one-dimensional, but can also be extended to multivariate cases. It should be emphasized, however, that we do not provide a robust mathematical proof of these findings, and we leave these issues with those who are interested in them., Comment: 8 pages, 6 figures, MNRAS, in the press