[2024 Fall Semester]
지정 날짜 목요일 13:30
운영위원 : 표성인 ( luinn27@ajou.ac.kr, 팔달관 426호 )
감독위원 : 유성현( yoosh0319 @ajou.ac.kr, 팔달관 622호 )
Title : Stability Analysis of the HDG Method for Elliptic Equations
Abstract : This study combines Hybrid Discontinuous Galerkin (HDG) and Finite Element Method (FEM) to solve elliptic equations. The analysis focuses on the stability conditions and the computation of stability, ensuring the stability of the proposed method.
Title : Seeds with maximal Buchstaber numbers
Abstract : A PL sphere is called a seed if it is not obtained by simplicial wedge operation, which preserves Buchstaber numbers. For a seed of dimension n − 1 with n + p vertices, Choi and Park proved that the inequality n + p ≤ p^2 - 1 holds if p ≥ 3, and as a corollary, the number of seeds is finite for each fixed number p. We introduce a method to generate a new seed from an original seed as preserving its Buchstaber number, and apply to show that for all integers n ≥ 2, p ≥ 3 satisfying the inequality, there exists a seed of dimension n−1 with n+p vertices whose Buchstaber number is maximal, particularly, the inequality is tight.
This is joint work with Suyoung Choi.
Title : Venustus building sets
Abstract : In this talk, we introduce the concept of venustus building sets, which is derived from toric topology. We will also present some conjectures related to venustus building sets.
Title : Chest X-Ray Multi-Label Classification
Abstract : Chest X-ray images often present multiple diseases simultaneously, necessitating the use of multi-label classification methods for effective diagnosis. This study proposes a hybrid model that utilizes the NIH Chest X-ray 14 dataset for accurate disease classification. The hybrid model combines Convolutional Neural Networks (CNN) with Transformers and evaluates its performance compared to standalone CNN and Transformer models.
Title : Special graded Betti numbers of 3-dimensional irreducible simplicial polytopes
Abstract : It is well known that the bigraded betti numbers explain the characters of polytope such as the number of vertices, the number of faces, etc. However, it is not enough to explain their own characters. Because of that, in general, we cannot distinguish polytopes by comparing only their bigraded Betti numbers.
In this talk, we discuss the special graded Betti numbers and show the cases that we can distinguish them by comparing their special graded Betti numbers. It is well known problem as combinatorial rigidity problem.
Title : Unsupervised Sentiment Analysis
Abstract : Most of sentiment analysis is worked on large-sized, labeled data or pre-trained and fine-tuned model enviornment. Sentiment analysis have been designed by deep-learning model due to its dimension of size. Hence, based on such characteristics, interpretation of result is uncomfortable and analysis have to rely on the pre-defined features. In this talk, i will organize the unsupervised sentiment analysis using statistical methods.
Title : Prediction of Underground Utility Locations Using TDA and YOLO
Abstract : Non-destructive testing is crucial for maintaining and inspecting infrastructure. Among the various methods, Ground Penetrating Radar (GPR) stands out for its effectiveness. This study aims to detect the location of underground utility, epically for pipes. We use Topological Data Analysis (TDA) and the YOLO (You Only Look Once) algorithm. TDA is employed to extract essential features from the GPR data, while YOLO is utilized for object detection and localization. This study reveals features extracted by TDA can improve the accuracy of the predicting the location of underground utilities. The analysis revealed that the integration of TDA and YOLO provides a robust and effective approach for detecting the underground utilities.
Title : Introduction to the Arithmetic of Elliptic Curves
Abstract : Elliptic curves are curves of genus one having a specified base point.. The set of points on an elliptic curve, including the point at infinity, forms an abelian group under a well-defined geometric operation. This group structure is central to the study of elliptic curves and has profound implications in various areas, including cryptography, number theory, and complex multiplication. In this talk, I will introduce the group structure on elliptic curves and explore some of their remarkable arithmetic properties.
Title : Introduction to Self-Controlled Case Series Studies
Abstract : Self-Controlled Case Series (SCCS) is an epidemiological method that assesses the relationship between a time-varying exposure and an outcome by comparing periods within the same individual. This design controls for fixed confounders, such as genetic factors, and is particularly useful for studying transient exposures like vaccines or medications. Key assumptions include exposure variation over time and potential modifications due to age or seasonality. Recent advancements in SCCS address these factors, making it a valuable tool for analyzing safety in public health contexts with minimal confounding.
Title : GPU-Accelerated JAX-FEM: Enhancing Computational Efficiency for Large-Scale Finite Element Analysis
Abstract : This seminar presents the development and application of a GPU-accelerated finite element method (FEM) solver, implemented using the JAX framework. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, our FEM is implemented with pure Python while scalable to solve problems with moderate to large sizes efficiently. The solver also integrates higher-order approximation methods, allowing for more precise solutions in complex simulations. By utilizing higher-order elements and automatic differentiation, our FEM achieves superior accuracy and efficiency in handling nonlinear problems and optimization tasks.