[2025 Spring Semester]
지정 날짜 수요일 13:30
운영위원 : 표성인 ( luinn27@ajou.ac.kr, 팔달관 426호 )
감독위원 : 장설( jangseol@ajou.ac.kr @ajou.ac.kr, 팔달관 426호 )
Title : Real toric spaces associated with Bier spheres
Abstract : We focus on particular classes of the full subcomplexes of the Bier sphere, and determine their topological types. Furthermore, we compute the Betti numbers of real toric spaces associated with Bier spheres.
Title : The cohomology rings of type B real permutohedral varieties
Abstract : We study type B real permutohedral varieties, which are real toric varieties associated with signed permutohedra.
These varieties can be seen as type B analogues of real permutohedral varieties, which are associated with permutohedra.
It is known that the rational cohomology of a real permutohedral variety can be fully described in terms of alternating permutations.
In this talk, we present an explicit description of the rational cohomology of a type B real permutohedral variety in terms of B-snakes, the type B analogues of alternating permutations.
Title : Classification of complete non-singular toric varieties with Picard number 4
Abstract : In toric geometry, classifyingf complete non-singular toric varieties with a fixed Picard number is a fundamental problem. Kleinschmidt and Batyrev classified those with Picard number 2 in 1988 and 3 in 1991.We extend their work to a complete classification of complete non-singular toric varieties with Picard number 4.
Title : DPEU-Net: Enhanced U-Net Architecture with a Dual Pooling Encoder for Retinal Vessel Segmentation
Abstract : Retinal vessel segmentation is crucial for diagnosing and monitoring systemic and retinal diseases. Various U-Net-based models have been widely used, but recent segmentation models have become increasingly complex. Here, we propose Dual Pooling Encoder U-Net (DPEU-Net), a simple and effective extension of U-Net that integrates Max Pooling and Average Pooling into a novel dual encoder design. By effectively merging encoder outputs through a Weighted Average Mechanism, DPEU-Net improves boundary feature extraction and preserves structural continuity. Evaluated on DRIVE, CHASE DB1, and STARE datasets, DPEU-Net generally outperformed baseline U-Net models across 5 metrics: accuracy, F1-score, sensitivity, specificity, and area under the curve (AUC). On the DRIVE dataset, it achieved an AUC of 0.9806, surpassing U-Net with Max Pooling (0.9784) and U-Net with Average Pooling (0.9782). DPEU-Net also demonstrated strong generalizability across datasets, as well as improvements in vessel boundary feature extraction, continuity, and false detection reduction. Furthermore, when the dual pooling encoder structure was applied, U-Net++, Attention U-Net, and Residual U-Net all demonstrated consistent performance gains. These results indicate that DPEU-Net has strong scalability and the potential to be effectively extended to other various U-Net-based models. With its simplicity and robust results, DPEU-Net shows a practical and effective solution for retinal vessel segmentation.
Title : Extending Self-Controlled Case Series to Handle Spontaneous Reporting Bias: Insights from Rotavirus Vaccine Data
Abstract : This study proposes an extension of the self-controlled case series (SCCS) method to analyze spontaneous reports of adverse events after vaccination, accounting for time-dependent underreporting. Using global data on intussusception following Rotarix vaccination, both nonparametric and parametric models were developed to adjust for variations in reporting over time and between doses. Results showed a significantly increased risk during days 3–7 after the first dose, even after correcting for reporting biases. Simulation studies confirmed good control of type I error and high power under various conditions. This extended SCCS approach provides a timely and flexible tool for early vaccine safety signal detection from spontaneous reporting systems.
Title : Considering intersections among clusters in Latent Dirichlet Allocation Topic Modeling
Abstract : Traditional LDA (Latent Dirichlet Allocation) topic modeling does not allow overlaps among topics. As a result, when certain crucial keywords affect multiple topics, restricting them to just one topic can be problematic. In this talk, we introduce an extended LDA approach that permits topic intersections using several methods, thereby providing a more flexible framework for handling widely influential keywords in topic modeling.
Title : The distribution of cokernel of random matrix
Abstract : Universality refers to the phenomenon where different mathematical models converge to the same limiting behavior as a parameter $n$ tends to infinity.
The cokernels of random $\mathbb{Z}_{p}$ matrices originating from a seemingly unrelated probabilistic model converge to the same distribution predicted by Cohen and Lenstra.
A key method to verify this kind of universality is through solving the moment problem.
In this talk, I will introduce the number theoretic setting of moment problem and the Cohen–Lenstra heuristics, which predict a natural probability distribution on finite abelian groups arising in number theory, such as class groups of number fields.
Title : HDG Method for Elliptic Problems Using Patch-Based Meshes
Abstract : We present a modified Hybrid Discontinuous Galerkin (HDG) method for solving elliptic problems. Unlike the traditional HDG approach, which relies on triangulated meshes, our method employs rectangular patches, each subdivided into triangles. Within each patch, standard finite element methods (FEM) are applied, while HDG is used for inter-patch communication. We implement this approach in MATLAB and compare the resulting error with the traditional HDG method. Our results highlight the differences in accuracy and computational efficiency between the two approaches.
Title : Machine Learning Fairness – Current Solutions and Challenges
Abstract : As AI and machine learning technologies are increasingly applied across various industries, ensuring fairness in data-driven decision-making models has become a critical research topic. Machine learning models used in areas such as loan approvals, hiring evaluations, medical diagnoses, and judicial systems can lead to serious social issues if they make biased predictions against certain groups (e.g., gender, race, age). These biases often stem from imbalanced datasets and underlying biases in the data, which traditional machine learning models tend to learn and reinforce. This seminar will introduce existing methodologies for ensuring fairness and discuss their limitations.
Title : A novel approach for GPR data analysis based on topological data analysis
Abstract : This study explores a novel method for analyzing Ground Penetrating Radar (GPR) data using Topological Data Analysis (TDA). GPR is widely used in subsurface investigations, yet conventional methods often struggle with noise and complex data structures. TDA provides a robust framework to capture the intrinsic topological features of GPR data. We present a workflow using topological data analysis for object detective.
Title : Reformulating land-use regression method as sign-constrained regularized regressions: Advantages and improvements
Abstract : Land-use regression is a popular method for predicting ambient pollutant concentrations at points of interest where no measurements are taken. However, the model-building process is complicated, and systematically understanding when and how the process works is difficult. To overcome these limitations, we reformulate the existing land use regression method as a sign-constrained regression problem with an explicit objective function to be minimized. This novel formulation always leads to estimated regression coefficients that satisfy the predefined direction based on subject matter knowledge while simultaneously substantially improving the prediction performance of the existing land-use regression method. The advantages of the proposed sign-constrained regression method are confirmed through a numerical study and real data analysis.
Title: Integrating Classical Numerical Methods into Deep Operator Networks
Abstract: We propose an operator learning framework for solving parametric Poisson equations using convolutional neural networks trained with unsupervised loss functions derived from classical numerical formulations. Our method supports both finite difference and finite element discretizations and directly enforces the governing PDE and boundary conditions without requiring ground-truth solutions. Leveraging the linearity of the problem, we introduce a decomposition strategy that separates the original problem into two subproblems with disjoint input components. The solutions from independently trained submodels are linearly combined to reconstruct the full solution, enabling efficient training and improved accuracy. Numerical experiments show that the decomposition approach achieves lower prediction errors than solving the original problem, even though each subproblem is trained using only the square root of the total number of samples. This setup highlights the potential for enhanced data efficiency through structural decomposition, while also offering benefits in modularity, interpretability, and scalability. Furthermore, our method scales favorably with grid resolution, maintaining compact model size and low inference time even when classical solvers become impractical due to memory or speed constraints. These results suggest that CNN-based operator learning provides a scalable and practical alternative to classical solvers.