Chaoran Liu

Gang Chen, Chaoran Liu, Yangwen Zhang

Nitsche's method is a standard device for weakly imposing Dirichlet boundary conditions, but for the stabilized nonsymmetric formulation the available $L^2$-error analysis for Poisson's equation still predicts a half-order loss, whereas numerical evidence indicates optimal convergence. We prove that, for conforming $k$th-order finite elements on quasi-uniform triangulations of convex polygonal domains in two dimensions, the stabilized nonsymmetric Nitsche approximation satisfies \[ \|{u-u_h}\|_{L^2(Ω)} \le C h^{k+1}\|{u}\|_{W^{k+1,\infty}(Ω)}. \] The proof compares the Nitsche solution with an auxiliary conforming finite element solution with strongly imposed projected boundary data and combines three ingredients: a two-layer boundary-strip lifting, an exact boundary identity on the one-dimensional boundary mesh, and localized residual estimates. In addition, we isolate the auxiliary $W^{1,\infty}$ estimate needed in the argument and provide a revised proof based on the $L^\infty$-stability of the boundary $L^2$-projection together with a weak discrete maximum principle for discrete harmonic functions. The analysis is intrinsically two-dimensional and clarifies why the stronger assumption $u\in W^{k+1,\infty}(Ω)$ enters the proof.

Ha-Thanh Nguyen, Chaoran Liu, Qianying Liu et al.

We present BIS Reasoning 1.0, the first large-scale Japanese dataset of syllogistic reasoning problems explicitly designed to evaluate belief-inconsistent reasoning in large language models (LLMs). Unlike prior datasets such as NeuBAROCO and JFLD, which focus on general or belief-aligned reasoning, BIS Reasoning 1.0 introduces logically valid yet belief-inconsistent syllogisms to uncover reasoning biases in LLMs trained on human-aligned corpora. We benchmark state-of-the-art models - including GPT models, Claude models, and leading Japanese LLMs - revealing significant variance in performance, with GPT-4o achieving 79.54% accuracy. Our analysis identifies critical weaknesses in current LLMs when handling logically valid but belief-conflicting inputs. These findings have important implications for deploying LLMs in high-stakes domains such as law, healthcare, and scientific literature, where truth must override intuitive belief to ensure integrity and safety.

Dongsheng Yang, Qianying Liu, Wataru Sato et al.

Automatic robotic facial expression generation is crucial for human-robot interaction, as handcrafted methods based on fixed joint configurations often yield rigid and unnatural behaviors. Although recent automated techniques reduce the need for manual tuning, they tend to fall short by not adequately bridging the gap between human preferences and model predictions-resulting in a deficiency of nuanced and realistic expressions due to limited degrees of freedom and insufficient perceptual integration. In this work, we propose a novel learning-to-rank framework that leverages human feedback to address this discrepancy and enhanced the expressiveness of robotic faces. Specifically, we conduct pairwise comparison annotations to collect human preference data and develop the Human Affective Pairwise Impressions (HAPI) model, a Siamese RankNet-based approach that refines expression evaluation. Results obtained via Bayesian Optimization and online expression survey on a 35-DOF android platform demonstrate that our approach produces significantly more realistic and socially resonant expressions of Anger, Happiness, and Surprise than those generated by baseline and expert-designed methods. This confirms that our framework effectively bridges the gap between human preferences and model predictions while robustly aligning robotic expression generation with human affective responses.