Jun Wang

Jun Wang, Leslie Greengard

We present a hybrid asymptotic/numerical method for the accurate computation of single and double layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called "geometrically-induced stiffness," meaning that formally high-order accurate methods require excessively small time steps before the rapid convergence rate is observed. This can be overcome by analytic integration in time, requiring the evaluation of a collection of spatial boundary integral operators with non-physical, weakly singular kernels. In our hybrid scheme, we combine a local asymptotic approximation with the evaluation of a few boundary integral operators involving only Gaussian kernels, which are easily accelerated by a new version of the fast Gauss transform. This new scheme is robust, avoids geometrically-induced stiffness, and is easy to use in the presence of moving geometries. Its extension to three dimensions is natural and straightforward, and should permit layer heat potentials to become flexible and powerful tools for modeling diffusion processes.

Yingxin Lai, Zitong Yu, Jun Wang et al.

Face forgery detection faces a critical challenge: a persistent gap between offline benchmarks and real-world efficacy,which we attribute to the ecological invalidity of training data.This work introduces Agent4FaceForgery to address two fundamental problems: (1) how to capture the diverse intents and iterative processes of human forgery creation, and (2) how to model the complex, often adversarial, text-image interactions that accompany forgeries in social media. To solve this,we propose a multi-agent framework where LLM-poweredagents, equipped with profile and memory modules, simulate the forgery creation process. Crucially, these agents interact in a simulated social environment to generate samples labeled for nuanced text-image consistency, moving beyond simple binary classification. An Adaptive Rejection Sampling (ARS) mechanism ensures data quality and diversity. Extensive experiments validate that the data generated by our simulationdriven approach brings significant performance gains to detectors of multiple architectures, fully demonstrating the effectiveness and value of our framework.