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Xiamen University (Malaysia Campus)

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Research library17linked papers
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Selected work

Representative Papers

Formalizing Scarf, Brouwer, and Nash in Lean

Jul 07, 2026

This work presents the first unified formalization in Lean 4 that seamlessly connects Scarf’s theorem, Brouwer’s fixed-point theorem, and the existence of mixed Nash equilibria in finite games within a single combinatorial proof framework. By leveraging an indexed-order formulation of Scarf’s theorem, room–door structures, parity arguments, and explicit embedding–projection constructions—combined with compactness and continuity reasoning—the study establishes a rigorous derivation from triangulated simplices to product spaces of simplices. The project not only delivers fully formalized combinatorial proofs of these three foundational results but also introduces BrouwerBench, a benchmark comprising 80 tasks designed to evaluate formal proof systems’ capacity to understand and reason about deep mathematical structures.

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STEPS: A Temporal Smooth Error Propagation Solver on the Manifolds for Test-Time Adaptation in Time Series Forecasting

May 08, 2026

This work addresses the challenges of time series forecasting under test-time distribution shifts, where sparse or noisy observation prefixes lead to weak identifiability, error accumulation, and unstable long-term correction. To this end, it formulates test-time adaptation for the first time as a Dirichlet boundary value problem on a temporal manifold. By treating known prefix errors as boundary conditions, the approach combines a local solver for error propagation with a global solver that retrieves cross-window error memory, and introduces Spatio-Temporal Manifold Fusion (SMF) to generate a smooth, bounded correction field. Evaluated across six benchmark datasets and four frozen backbones, the method achieves an average 26.82% relative reduction in MSE over standard baselines and improves upon the strongest baseline by 12.77%, demonstrating remarkable robustness under sparse and corrupted prefix conditions.

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Edge-specific signal propagation on mature chromophore-region 3D mechanism graphs for fluorescent protein quantum-yield prediction

May 07, 2026

This study addresses the challenge of modeling how the quantum yield of fluorescent proteins is governed by their chromophore and its local three-dimensional microenvironment, a task hindered by the difficulty of capturing region-specific physical signals with existing methods. To overcome this, the authors propose a chromophore-centered, typed 3D residue graph representation that incorporates spatial partitioning and a channel–signal–region propagation mechanism, enabling interpretable modeling of edge-specific physical signals and directly revealing wavelength-dependent interaction mechanisms. Coupled with non-identity feature filtering and ExtraTrees regression, the approach achieves a cross-validated R value of 0.772 on a benchmark set of 531 proteins, significantly outperforming current state-of-the-art methods—particularly excelling in tasks involving distantly related homologs (<50% sequence identity) and high-brightness screening.

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Recent publications

Latest Papers

Formalizing Scarf, Brouwer, and Nash in Lean

Jul 07, 2026

This work presents the first unified formalization in Lean 4 that seamlessly connects Scarf’s theorem, Brouwer’s fixed-point theorem, and the existence of mixed Nash equilibria in finite games within a single combinatorial proof framework. By leveraging an indexed-order formulation of Scarf’s theorem, room–door structures, parity arguments, and explicit embedding–projection constructions—combined with compactness and continuity reasoning—the study establishes a rigorous derivation from triangulated simplices to product spaces of simplices. The project not only delivers fully formalized combinatorial proofs of these three foundational results but also introduces BrouwerBench, a benchmark comprising 80 tasks designed to evaluate formal proof systems’ capacity to understand and reason about deep mathematical structures.

0 citationsRead paper

STEPS: A Temporal Smooth Error Propagation Solver on the Manifolds for Test-Time Adaptation in Time Series Forecasting

May 08, 2026

This work addresses the challenges of time series forecasting under test-time distribution shifts, where sparse or noisy observation prefixes lead to weak identifiability, error accumulation, and unstable long-term correction. To this end, it formulates test-time adaptation for the first time as a Dirichlet boundary value problem on a temporal manifold. By treating known prefix errors as boundary conditions, the approach combines a local solver for error propagation with a global solver that retrieves cross-window error memory, and introduces Spatio-Temporal Manifold Fusion (SMF) to generate a smooth, bounded correction field. Evaluated across six benchmark datasets and four frozen backbones, the method achieves an average 26.82% relative reduction in MSE over standard baselines and improves upon the strongest baseline by 12.77%, demonstrating remarkable robustness under sparse and corrupted prefix conditions.

0 citationsRead paper

Edge-specific signal propagation on mature chromophore-region 3D mechanism graphs for fluorescent protein quantum-yield prediction

May 07, 2026

This study addresses the challenge of modeling how the quantum yield of fluorescent proteins is governed by their chromophore and its local three-dimensional microenvironment, a task hindered by the difficulty of capturing region-specific physical signals with existing methods. To overcome this, the authors propose a chromophore-centered, typed 3D residue graph representation that incorporates spatial partitioning and a channel–signal–region propagation mechanism, enabling interpretable modeling of edge-specific physical signals and directly revealing wavelength-dependent interaction mechanisms. Coupled with non-identity feature filtering and ExtraTrees regression, the approach achieves a cross-validated R value of 0.772 on a benchmark set of 531 proteins, significantly outperforming current state-of-the-art methods—particularly excelling in tasks involving distantly related homologs (<50% sequence identity) and high-brightness screening.

0 citationsRead paper