Kening Wang

Kening Wang, Di Wen, Yufan Chen et al.

Automatic sleep staging is a multimodal learning problem involving heterogeneous physiological signals such as EEG and EOG, which often suffer from domain shifts across institutions, devices, and populations. In practice, these data are also affected by noisy annotations, yet label-noise-robust multi-source domain generalization remains underexplored. We present the first benchmark for Noisy Labels in Multi-Source Domain-Generalized Sleep Staging (NL-DGSS) and show that existing noisy-label learning methods degrade substantially when domain shifts and label noise coexist. To address this challenge, we propose FF-TRUST, a domain-invariant multimodal sleep staging framework with Joint Time-Frequency Early Learning Regularization (JTF-ELR). By jointly exploiting temporal and spectral consistency together with confidence-diversity regularization, FF-TRUST improves robustness under noisy supervision. Experiments on five public datasets demonstrate consistent state-of-the-art performance under diverse symmetric and asymmetric noise settings. The benchmark and code will be made publicly available at https://github.com/KNWang970918/FF-TRUST.git.

Susanne C. Brenner, Eun-Hee Park, Li-Yeng Sung et al.

We develop a nonoverlapping domain decomposition preconditioner for the $C^0$ interior penalty method, a discontinuous Galerkin method, for the biharmonic problem. The preconditioner is based on balancing domain decomposition by constraints (BDDC). We prove that the condition number of the preconditioned system is bounded by $C (1+\ln (H/h))^2$, where $h$ is the mesh size of the triangulation, $H$ is the typical diameter of subdomains, and the positive constant $C$ is independent of $h$ and $H$. Numerical experiments are also represented to corroborate the theoretical result.

SeongHee Jeong, Seulip Lee, Kening Wang

This paper presents a $C^0$ weak Galerkin ($C^0$-WG) method combined with an additive Schwarz preconditioner for solving optimal control problems (OCPs) governed by partial differential equations with general tracking cost functionals and pointwise state constraints. These problems pose significant analytical and numerical challenges due to the presence of fourth-order variational inequalities and the reduced regularity of solutions. Our first contribution is the design of a $C^0$-WG method based on globally continuous quadratic Lagrange elements, enabling efficient elementwise stiffness matrix assembly and parameter-free implementation while maintaining accuracy, as supported by a rigorous error analysis. As a second contribution, we develop an additive Schwarz preconditioner tailored to the $C^0$-WG method to improve solver performance for the resulting ill-conditioned linear systems. Numerical experiments confirm the effectiveness and robustness of the proposed method and preconditioner for both biharmonic and optimal control problems.