Few-shot Text Classification with Dual Contrastive Consistency

In this paper, we explore how to utilize pre-trained language model to perform few-shot text classification where only a few annotated examples are given for each class. Since using traditional cross-entropy loss to fine-tune language model under this scenario causes serious overfitting and leads to sub-optimal generalization of model, we adopt supervised contrastive learning on few labeled data and consistency-regularization on vast unlabeled data. Moreover, we propose a novel contrastive consistency to further boost model performance and refine sentence representation. After conducting extensive experiments on four datasets, we demonstrate that our model (FTCC) can outperform state-of-the-art methods and has better robustness.Comment: 8 pages, 2 figures, under revie

Time-periodic solution to nonhomogeneous isentropic compressible Euler equations with time-periodic boundary conditions

In this paper, we study one-dimensional nonhomogeneous isentropic compressible Euler equations with time-periodic boundary conditions. With the aid of the energy methods, we prove the existence and uniqueness of the time-periodic supersonic solutions after some certain time

Global existence and stability of subsonic time-periodic solution to the damped compressible Euler equations in a bounded domain

In this paper, we consider the one-dimensional isentropic compressible Euler equations with source term $\beta(t,x)\rho|u|^{\alpha}u$ in a bounded domain, which can be used to describe gas transmission in a nozzle.~The model is imposed a subsonic time-periodic boundary condition.~Our main results reveal that the time-periodic boundary can trigger an unique subsonic time-periodic smooth solution and this unique periodic solution is stable under small perturbations on initial and boundary data.~To get the existence of subsonic time-periodic solution, we use the linear iterative skill and transfer the boundary value problem into two initial value ones by using the hyperbolic property of the system. Then the corresponding linearized system can be decoupled.~The uniqueness is a direct by-product of the stability. There is no small assumptions on the damping coefficient

Multi-symplectic discontinuous Galerkin methods for the stochastic Maxwell equations with additive noise

One- and multi-dimensional stochastic Maxwell equations with additive noise are considered in this paper. It is known that such system can be written in the multi-symplectic structure, and the stochastic energy increases linearly in time. High order discontinuous Galerkin methods are designed for the stochastic Maxwell equations with additive noise, and we show that the proposed methods satisfy the discrete form of the stochastic energy linear growth property and preserve the multi-symplectic structure on the discrete level. Optimal error estimate of the semi-discrete DG method is also analyzed. The fully discrete methods are obtained by coupling with symplectic temporal discretizations. One- and two-dimensional numerical results are provided to demonstrate the performance of the proposed methods, and optimal error estimates and linear growth of the discrete energy can be observed for all cases

Relation Strength-Aware Clustering of Heterogeneous Information Networks with Incomplete Attributes

With the rapid development of online social media, online shopping sites and cyber-physical systems, heterogeneous information networks have become increasingly popular and content-rich over time. In many cases, such networks contain multiple types of objects and links, as well as different kinds of attributes. The clustering of these objects can provide useful insights in many applications. However, the clustering of such networks can be challenging since (a) the attribute values of objects are often incomplete, which implies that an object may carry only partial attributes or even no attributes to correctly label itself; and (b) the links of different types may carry different kinds of semantic meanings, and it is a difficult task to determine the nature of their relative importance in helping the clustering for a given purpose. In this paper, we address these challenges by proposing a model-based clustering algorithm. We design a probabilistic model which clusters the objects of different types into a common hidden space, by using a user-specified set of attributes, as well as the links from different relations. The strengths of different types of links are automatically learned, and are determined by the given purpose of clustering. An iterative algorithm is designed for solving the clustering problem, in which the strengths of different types of links and the quality of clustering results mutually enhance each other. Our experimental results on real and synthetic data sets demonstrate the effectiveness and efficiency of the algorithm.Comment: VLDB201