[2025 Fall Semester]
지정 날짜 목요일 13:30
운영위원 : 표성인 ( luinn27@ajou.ac.kr, 팔달관 426호 )
감독위원 : 장설( jangseol@ajou.ac.kr @ajou.ac.kr, 팔달관 426호 )
Title : On the full subcomplexes of Bier spheres
Abstract : In 1992, Thomas Bier introduced a combinatorial construction that yields many simplicial (m-2)-dimensional PL-spheres on 2m vertices. The study of full subcomplexes of a simplicial complex is important for understanding the structure of simplicial complexes, or its associated topological spaces. In this talk, we will discuss the homological types of full subcomplexes of Bier spheres.
Title : Real toric varieties from nested fans
Abstract : While complex toric varieties have been extensively studied, the geometric and topological properties of their real loci remain much less understood. In this talk, I will discuss real toric varieties arising from nested fans, focusing on their topological invariants. In particular, I will show that when the nested fan is chordal or graphical, the associated real toric variety exhibits rich combinatorial structures and intriguing topological phenomena.
Title : Sparse FEONet: Neural Networks with FEM-Based Local Connections
Abstract : Partial differential equations (PDEs) are central to modeling physical and engineering systems, yet traditional solvers such as FEM and FDM become costly in high dimensions and complex domains. Neural operators, including DeepONet and the Fourier Neural Operator, address this by learning solution operators that generalize across inputs. FEONet extends this idea by embedding FEM-inspired locality into neural operator architectures, integrating numerical structure with data-driven learning. Building on FEONet, Sparse FEONet incorporates FEM-derived sparsity through stiffness-matrix connectivity, achieving comparable accuracy to dense models with a significantly smaller number of parameters. This demonstrates the effectiveness of combining locality and sparsity in operator learning and points toward more efficient and interpretable neural PDE solvers.
Title : Exact Post-Selection Inference with Application to the LASSO
Abstract : We develop a general approach to valid inference after model selection. At the core of our framework is a result that characterizes the distribution of a post-selection estimator conditioned on the selection event. We specialize the approach to model selection by the lasso to form valid confidence intervals for the selected coefficients and test whether all relevant variables have been included in the model.
Title : A Systematic Review and Meta-Analysis of Self-Controlled Case Series Studies on Vaccine-Associated Stroke
Abstract : Vaccination is essential for public health, but rare adverse events such as stroke require close evaluation. We performed the first systematic review and meta-analysis of self-controlled case series (SCCS) studies assessing stroke risk after BNT162b2 vaccination. Literature searches were conducted in PubMed and Embase through March 2025, and study quality was evaluated using a modified Newcastle–Ottawa Scale. Random-effects meta-analysis (REML with Knapp–Hartung adjustment) produced a pooled incidence rate ratio of 1.04 (95% CI: 0.84–1.27), indicating no significant increase in short-term stroke risk. Although substantial heterogeneity was observed (I² = 84.2%), sensitivity analyses confirmed robustness, and no publication bias was detected. These findings support the overall safety of BNT162b2 while underscoring the need for standardized methodologies in future vaccine safety studies.
Title : Universality of Cokernels for p-adic Random Matrices under Inhomogeneous Conditions
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Title : Fairness-Aware Score Adjustment for Optimizing the λ value in Recommendation Systems
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Title : TDA in Longitudinal Time Series Clustering
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Title : Subsurface Utility Detection through Integrated Analysis of Electrical Resistivity and GPR Using Kriging, Topological Data Analysis, and Deep Learning
Abstract : Ground Penetrating Radar (GPR) and Electrical Resistivity (ER) are widely used geophysical techniques for subsurface exploration, but each method has inherent limitations when applied independently. To address this, we propose an integrated framework that combines ER analysis via Kriging-based spatial interpolation with GPR interpretation enhanced by Topological Data Analysis (TDA) and deep learning models. The ER data provide continuous resistivity distributions through Kriging, while GPR B-scan images are processed with TDA to extract shape-aware topological descriptors that are further utilized in deep learning networks for buried object detection. Experimental results using both simulated and field datasets demonstrate that this integrated approach achieves higher accuracy and robustness than single-modality analyses, offering a novel pathway for reliable subsurface utility detection and contributing to improved safety in civil infrastructure and excavation practices.
Title : Flux Reconstruction in the Raviart–Thomas Space for the HDG Method
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Title: Physics-Informed Convolutional Operator Network for Efficient PDE Solvers
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