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Yazhou Han

Publications and source records attributed to Yazhou Han.

12 recordsLinked to original sources

Learning to Generate and Extract: A Multi-Agent Collaboration Framework For Zero-shot Document-level Event Arguments Extraction

Document-level event argument extraction (DEAE) is essential for knowledge acquisition, aiming to extract participants of events from documents . In the zero-shot setting, existing methods employ LLMs to generate synthetic data to address the challenge posed by the scarcity of annotated data. However, relying solely on Event-type-only prompts makes it difficult for the generated content to accurately capture the contextual and structural relationships of unseen events. Moreover, ensuring the reliability and usability of synthetic data remains a significant challenge due to the absence of quality evaluation mechanisms. To this end, we introduce a multi-agent collaboration framework for zero-shot document-level event argument extraction (ZS-DEAE), which simulates the human collaborative cognitive process of "Propose-Evaluate-Revise." Specifically, the framework comprises a generation agent and an evaluation agent. The generation agent synthesizes data for unseen events by leveraging knowledge from seen events, while the evaluation agent extracts arguments from the synthetic data and assesses their semantic consistency with the context. The evaluation results are subsequently converted into reward signals, with event structure constraints incorporated into the reward design to enable iterative optimization of both agents via reinforcement learning.In three zero-shot scenarios constructed from the RAMS and WikiEvents datasets, our method achieves improvements both in data generation quality and argument extraction performance, while the generated data also effectively enhances the zero-shot performance of other DEAE models.

cs.CL

Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary

In this paper, we establish a sharp Onofri trace inequality on the upper half space $\overline{\mathbb R_+^n} (n\geq 2)$ by considering the limiting case of Sobolev trace inequality and classify its extremal functions on a suitable weighted Sobolev space. For this aim, by the Serrin-Zou type identity and the Pohozaev type identity, we show the classification of the solutions for a quasi-linear Liouville equation with Neumann boundary which is closely related to the Euler-Lagrange equation of the Onofri trace inequality and it has independent research value. The regularity and asymptotic estimates of solutions to the above equation are essential to discuss.

math.AP

Reversed Hardy-Littlewood-Sobolev inequality on Heisenberg group $\mathbb{H}^n$ and CR sphere $\mathbb{S}^{2n+1}$

This paper is mainly devoted to the study of the reversed Hardy-Littlewood-Sobolev (HLS) inequality on Heisenberg group $\mathbb{H}^n$ and CR sphere $\mathbb{S}^{2n+1}$. First, we establish the roughly reversed HLS inequality and give a explicitly lower bound for the sharp constant. Then, the existence of the extremal functions with sharp constant is proved by subcritical approach and some compactness techniques. Our method is rearrangement free and can be applied to study the classical HLS inequality and other similar inequalities.

math.AP

Paley's inequality for nonabelian groups

This article studies Paley's theory for lacunary Fourier series on (nonabelian) discrete groups. The results unify and generalize the work of Rudin for abelian discrete groups and the work of Lust-Piquard and Pisier for operator valued functions, and provide new examples of Paley sequences and $\Lambda(p)$ sets on free groups.

math.FA

Logarithmic submajorisations inequalities for operators in a finite von Neumann algebra

The aim of this paper is to study the logarithmic submajorisations inequalities for operators in a finite von Neumann algebra. Firstly, some logarithmic submajorisations inequalities due to Garg and Aulja are extended to the case of operators in a finite von Neumann algebra. As an application, we get some new Fuglede-Kadison determinant inequalities of operators in that circumstance. Secondly, we improve and generalize to the setting of finite von Neumann algebras, a generalized H\"{o}lder type generalized singular numbers inequality.

math.OA

Harnack type inequalities for operators in logarithmic submajorisation

The aim of this paper is to study the Harnack type logarithmic submajorisation and Fuglede-Kadison determinant inequalities for operators in a finite von Neumann algebra. In particular, the Harnack type determinant inequalities due to Lin-Zhang [15] and Yang-Zhang [27] are extended to the case of operators in a finite von Neumann algebra.

math.FA

Sharp Sobolev inequalities on the complex sphere

This paper is devoted to establish a class of sharp Sobolev inequalities on the unit complex sphere as follows: 1) Case $0<d<Q=2n+2$: for any $f\in C^\infty$ and $2\leq q \leq \frac{2Q}{Q-d}$, \begin{equation*} \|f\|_q^2\leq \frac{8(q-2)}{d(Q-d)} \frac{Γ^2((Q-d)/4+1)} {Γ^2((Q+d)/4)}\left( \int_{\mathbb{S}^{2n+1}} f\mathcal{A}_df dξ -\frac{Γ^2((Q+d)/4)} {Γ^2((Q-d)/4)} \int_{\mathbb{S}^{2n+1}} |f|^2 dξ\right) +\int_{\mathbb{S}^{2n+1}} |f|^2 dξ; \end{equation*} 2) Case $d=Q$: for any $f\in C^\infty \cap\mathbb{R}\mathcal{P}$ and $2\leq q< +\infty$, \begin{equation*} \|f\|_q^2\leq \frac{q-2}{(n+1)!} \int_{\mathbb{S}^{2n+1}} f \mathcal{A}'_Q f dξ+\int_{\mathbb{S}^{2n+1}} |f|^2 dξ, \end{equation*} where $\mathcal{A}_d(0<d<Q)$ are the intertwining operator, $\mathcal{A}'_Q$ is the conditional intertwinor introduced in \cite{BFM2013}, and $dξ$ is the normalized surface measure of $\mathbb{S}^{2n+1}$.

math.AP

Sharp Hardy-Littlewood-Sobolev inequalities on compact CR manifold

Assume that $M$ is a CR compact manifold without boundary and CR Yamabe invariant $\mathcal{Y}(M)$ is positive. Here, we devote to study a class of sharp Hardy-Littlewood-Sobolev inequality as follows \begin{equation*} \Bigl| \int_M\int_M [G_\xi^\theta(\eta)]^{\frac{Q-\alpha}{Q-2}} f(\xi) g(\eta) dV_\theta(\xi) dV_\theta(\eta) \Bigr| \leq \mathcal{Y}_\alpha(M) \|f\|_{L^{\frac{2Q}{Q+\alpha}}(M)} \|g\|_{L^{\frac{2Q}{Q+\alpha}}(M)}, \end{equation*} where $G_\xi^\theta(\eta)$ is the Green function of CR conformal Laplacian $\mathcal{L_\theta}=b_n\Delta_b+R$, $\mathcal{Y}_\alpha(M)$ is sharp constant, $\Delta_b$ is Sublaplacian and $R$ is Tanaka-Webster scalar curvature. For the diagonal case $f=g$, we prove that $\mathcal{Y}_\alpha(M)\geq \mathcal{Y}_\alpha(\mathbb{S}^{2n+1})$ (the unit complex sphere of $\mathbb{C}^{n+1}$) and $\mathcal{Y}_\alpha(M)$ can be attained if $\mathcal{Y}_\alpha(M)> \mathcal{Y}_\alpha(\mathbb{S}^{2n+1})$. Particular, if $\alpha=2$, the previous extremal problem is closely related to the CR Yamabe problem. Hence, we can study the CR Yamabe problem by integral equations.

math.AP

An integral type Brezis-Nirenberg problem on the Heisenberg group

This paper is devoted to study a class of integral type Brezis-Nirenbreg problem on the Heisenberg group. It is a class of new nonlinear integral equations on the bounded domains of Heisenberg group and related to the CR Yamabe problems on the CR manifold. Based on the sharp Hardy-Littlewood-Sobolev inequalities, the nonexistence and existence results are obtained by Pohozaev type identity, variational method and blow-up analysis, respectively.

math.AP

Pattern formation for a volume-filling chemotaxis model with logistic growth

This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform steady-state solution. Then, weakly nonlinear analysis with multi-scales is used to deal with the emerging process of patterns near the bifurcation point. For the single unstable mode case, we derive the Stuart-Landau equations describing the evolution of the amplitude, and thus the asymptotic expressions of patterns are obtained in both supercritical case and subcritical case. While for the case of multiple unstable modes, we also derive coupled amplitude equations to study the competitive behavior between two unstable modes through the phase plane analysis. In particular, we find that the initial data play a dominant role in the competition. All the theoretical and numerical results are in excellently qualitative agreement and better quantitative agreement than that in [1]. Moreover, in the subcritical case, we confirm the existence of stationary patterns with larger amplitudes when the bifurcation parameter is less than the first bifurcation point, which gives an positive answer to the open problem proposed in [2].

math.AP

Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications

In this paper we extend Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds for dimension $n\ne 2$. As one application, we solve a generalized Yamabe problem on locally conforamlly flat manifolds via a new designed energy functional and a new variational approach. Even for the classic Yamabe problem on locally conformally flat manifolds, our approach provides a new and relatively simpler solution.

math.AP