The Hitchin--Kobayashi Correspondence for Quiver Bundles over Generalized K\"ahler Manifolds

In this paper, we establish the Hitchin--Kobayashi correspondence for the $I_\pm$-holomorphic quiver bundle $\mathcal{E}=(E,\phi)$ over a compact generalized K\"{a}hler manifold $(X, I_+,I_-,g, b)$ such that $g$ is Gauduchon with respect to both $I_+$ and $I_-$, namely $\mathcal{E}$ is $(\alpha,\sigma,\tau)$-polystable if and only if $\mathcal{E}$ admits an $(\alpha,\sigma,\tau)$-Hermitian--Einstein metric.Comment: To appear in The Journal of Geometric Analysi

Flat λ\lambda-Connections, Mochizuki Correspondence and Twistor Spaces

In this paper, we first collect some basic results for $\lambda$-flat bundles, and then get an estimate for the norm of $\lambda$-flat sections, which leads to some vanishing theorem. Mochizuki correspondence provides a homeomorphism between the moduli space of (poly-)stable $\lambda$-flat bundles and that of (poly-)stable Higgs bundles, and provides a dynamical system on the later moduli space (the Dolbeault moduli space). We investigate such dynamical system, in particular, we discuss the corresponding first variation and asymptotic behavior. We generalize the Deligne's twistor construction for any element $\gamma$ of the outer automorphism group of the fundamental group of Riemann surface to obtain the $\gamma$-twistor space, and we apply the twistor theory to study a Lagrangian submanifold of the de Rham moduli space. As an application, we prove a Torelli-type theorem for the twistor spaces, and meanwhile, we prove that the oper stratum in the oper stratification of the de Rham moduli space is the unique closed stratum of minimal dimension, which partially confirms a conjecture by Simpson.Comment: Simpson pointed out a mistake on the Moishezon property for the twistor space in the last version, we delete it and add a section on the study of oper stratification of the de Rham moduli space as an applicatio

Color Superconductivity at Moderate Density

The effect of color breaking on colored quarks' chiral condensates has been investigated at zero temperature and moderate baryon density. It is found that the influence of the diquark condensate on different colored quarks is very small.Comment: 4 pages, 1 figure in eps, talk given at XXXI International Symposium on Multiparticle Dynamics, Sept 1-7, 2001, Datong China. See http://ismd31.ccnu.edu.cn

Adversarial Multi-task Learning for Text Classification

Neural network models have shown their promising opportunities for multi-task learning, which focus on learning the shared layers to extract the common and task-invariant features. However, in most existing approaches, the extracted shared features are prone to be contaminated by task-specific features or the noise brought by other tasks. In this paper, we propose an adversarial multi-task learning framework, alleviating the shared and private latent feature spaces from interfering with each other. We conduct extensive experiments on 16 different text classification tasks, which demonstrates the benefits of our approach. Besides, we show that the shared knowledge learned by our proposed model can be regarded as off-the-shelf knowledge and easily transferred to new tasks. The datasets of all 16 tasks are publicly available at \url{http://nlp.fudan.edu.cn/data/}Comment: Accepted by ACL201

Dynamic Compositional Neural Networks over Tree Structure

Tree-structured neural networks have proven to be effective in learning semantic representations by exploiting syntactic information. In spite of their success, most existing models suffer from the underfitting problem: they recursively use the same shared compositional function throughout the whole compositional process and lack expressive power due to inability to capture the richness of compositionality. In this paper, we address this issue by introducing the dynamic compositional neural networks over tree structure (DC-TreeNN), in which the compositional function is dynamically generated by a meta network. The role of meta-network is to capture the metaknowledge across the different compositional rules and formulate them. Experimental results on two typical tasks show the effectiveness of the proposed models.Comment: Accepted by IJCAI 201