https://scholar.korea.ac.kr/handle/2021.sw.korea/324 Sun, 05 Apr 2026 15:53:18 GMT 2026-04-05T15:53:18Z https://scholar.korea.ac.kr/handle/2021.sw.korea/271404 Title: A fast and accurate 3D lung tumor segmentation algorithm Authors: Wang, Jian; Han, Ziwei; Chen, Xinlei; Kim, Junseok Abstract: In this article, we propose a lung tumor segmentation algorithm based on the Allen-Cahn (AC) energy equation. The novelty lies in the fact that, when extracting the energy matrix using the AC energy equation, we employ a sliding window algorithm for feature extraction on the data without neglecting local features. After obtaining the energy matrix, we construct constraint conditions based on the minimum and maximum values in the matrix, forming an arithmetic progression. Due to the flexibility in setting the sliding window size and constraint conditions, we can achieve segmentation results according to different requirements. In the numerical experiments, we conduct segmentation experiments of varying difficulty in both two-dimensional (2D) and three-dimensional (3D) spaces to verify the effectiveness of the proposed method. When addressing the lung tumor segmentation problem, we compare the maximum diameter of 3D lung tumors segmented by our proposed segmentation algorithm with the maximum diameter of lung tumors in the original 2D CT images to validate the segmentation accuracy and significance of the proposed method. By conducting more detailed and precise measurements and segmentations of tumors in 3D space, this approach contributes to advancements in medical science and enhances patient treatment outcomes. We also conduct tumor segmentation experiments on the MSD and LIDC-IDRI datasets, setting up comparison metrics to further verify the method's effectiveness. Sun, 01 Jun 2025 00:00:00 GMT https://scholar.korea.ac.kr/handle/2021.sw.korea/271404 2025-06-01T00:00:00Z https://scholar.korea.ac.kr/handle/2021.sw.korea/271391 Title: A normalized time-fractional Korteweg-de Vries equation Authors: Lee, Hyun Geun; Kwak, Soobin; Jyoti; Nam, Yunjae; Kim, Junseok Abstract: A novel normalized time-fractional Korteweg-de Vries (KdV) equation is presented to investigate the effects of fractional time derivatives on nonlinear wave dynamics. The classical KdV model is extended by incorporating a fractional-order derivative, which captures memory and inherited properties in the evolution of solitonlike structures. Computational studies of the equation's nonlinear dynamics use a numerical scheme designed for the fractional temporal dimension. Simulations show that as the fractional parameter alpha decreases from 1 (the classical case) to smaller values, soliton dynamics change significantly. The soliton amplitude decreases, and its width increases. These changes are interpreted as dispersive or dissipative effects introduced by the fractional time component. At lower values of alpha, the soliton becomes broader and flatter, and its propagation is slowed. At intermediate values of alpha, multiple peaks and broader waveforms are observed, which implies more complex nonlinear interactions under fractional time evolution. The importance of fractional time derivatives in modifying the behavior of soliton solutions is highlighted, which demonstrates their potential in modeling physical systems where memory effects play a crucial role. The computational results provide insights into fractional partial differential equations and create new opportunities for future research in nonlinear wave propagation under fractional dynamics. Sun, 01 Jun 2025 00:00:00 GMT https://scholar.korea.ac.kr/handle/2021.sw.korea/271391 2025-06-01T00:00:00Z https://scholar.korea.ac.kr/handle/2021.sw.korea/270783 Title: A Finite Difference Method for a Normalized Time-Fractional Black–Scholes Equation Authors: Nam, Yunjae; Wang, Jian; Lee, Chaeyoung; Choi, Yongho; Bang, Minjoon; Li, Zhengang; Kim, Junseok Abstract: In this article, we propose a normalized time-fractional Black–Scholes (TFBS) equation. The proposed model uses a normalized time-fractional derivative which has a distinctive feature wherein a weight function possesses the property that its integral with respect to time is always equal to one. This feature ensures a well-balanced integration over time and provides a fair comparison between different fractional orders. An implicit finite difference method is used for the numerical solution of the TFBS equation. We perform several standard numerical tests to examine the effect of the fractional parameter on the option pricing. These experiments are designed to investigate how variations in the fractional parameter influence pricing outcomes and provide valuable insights into the model’s behavior under different conditions. The computational results demonstrate the model’s potential for capturing more intricate market dynamics, which makes the proposed model a promising tool for financial analysis. In the appendix, we provide a computer program that implements the numerical methods discussed in the paper for interested readers. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2025. Sun, 01 Jun 2025 00:00:00 GMT https://scholar.korea.ac.kr/handle/2021.sw.korea/270783 2025-06-01T00:00:00Z https://scholar.korea.ac.kr/handle/2021.sw.korea/269497 Title: Computational analysis of a normalized time-fractional Fokker-Planck equation Authors: Wang, Jian; Chen, Keyong; Kim, Junseok Abstract: We propose a normalized time-fractional Fokker-Planck equation (TFFPE). A finite ence method is used to develop a computational method for solving the equation, system's dynamics are investigated through computational simulations. The proposed demonstrates accuracy and efficiency in approximating analytical solutions. Numerical validate the method's effectiveness and highlight the impact of various fractional the dynamics of the normalized time-fractional Fokker-Planck equation. The numerical emphasize the significant impact of different fractional orders on the temporal evolution the system. Specifically, the computational results demonstrate how varying the order influences the diffusion process, with lower orders exhibiting stronger memory and slower diffusion, while higher orders lead to faster propagation and a transition classical diffusion behavior. This work contributes to the understanding of fractional and provides a robust tool for simulating time-fractional systems. Thu, 01 May 2025 00:00:00 GMT https://scholar.korea.ac.kr/handle/2021.sw.korea/269497 2025-05-01T00:00:00Z