https://scholarworks.unist.ac.kr/handle/201301/56 2026-04-08T00:34:14Z https://scholarworks.unist.ac.kr/handle/201301/91244 Title: Some applications of the traces of Frobenius of elliptic curves in a certain family Author(s): Cho, Peter J.; Yoo, Jinjoo Abstract: Let J = {a, b} be an unordered pair of elements of Fq and EJ the associated elliptic curve of the form y 3 = (x − a)(x − b) over Fq. Using its trace of Frobenius, we obtain several applications. We first compute the average analytic rank of elliptic curves for our family and generate elliptic curves with designated extremal primes. Furthermore, we determine explicit and average values on class numbers of every constant field extension of KJ := Fq(T, p3 (T − a)(T − b)). Finally, we estimate the exact values and average values on Euler-Kronecker constants of KJ . 2026-07-31T15:00:00Z https://scholarworks.unist.ac.kr/handle/201301/90577 Title: Valid oversampling schemes to handle imbalance Author(s): Kim, Young-geun; Kwon, Yongchan; Paik, Myunghee Cho Abstract: An imbalance is one of the problems in machine learning. When data are not balanced, the correct specification rate for the minor class suffers even if accuracy is high. The oversampling method has been used to address the issue without consideration about the sacrifice of accuracy. In addition, an arbitrary oversampling scheme may introduce bias. In this paper, we propose principled methods of handling imbalance under user-specified constraints on the sensitivity and specificity. Our work consists of three elements of contributions. First, we provide an optimized target proportion that minimizes the maximum error rate under user-specified constraints on sensitivity and specificity. Second, we introduce the notion of resampling at random (RAR) under which the limit of the estimator is not altered from the original sample. These two elements are relevant to any classification methods. Third, we derive asymptotic properties of selected classifiers when we apply RAR oversampling with the target proportion. Finally, we implement the proposed method in an image recognition context using the extracted feature from the last layer of deep convolutional neural networks (CNNs). We present an analysis of fundus data to classify diabetic retinopathy using the proposed method. (C) 2019 Elsevier B.V. All rights reserved. 2019-06-30T15:00:00Z https://scholarworks.unist.ac.kr/handle/201301/90576 Title: Conditional Wasserstein Generator Author(s): Kim, Young-geun; Lee, Kyungbok; Paik, Myunghee Cho Abstract: The statistical distance of conditional distributions is an essential element of generating target data given some data as in video prediction. We establish how the statistical distances between two joint distributions are related to those between two conditional distributions for three popular statistical distances: f-divergence, Wasserstein distance, and integral probability metrics. Such characterization plays a crucial role in deriving a tractable form of the objective function to learn a conditional generator. For Wasserstein distance, we show that the distance between joint distributions is an upper bound of the expected distance between conditional distributions, and derive a tractable representation of the upper bound. Based on this theoretical result, we propose a new conditional generator, the conditional Wasserstein generator. Our proposed algorithm can be viewed as an extension of Wasserstein autoencoders (Tolstikhin et al. 2018) to conditional generation or as a Wasserstein counterpart of stochastic video generation (SVG) model by Denton and Fergus (Denton et al. 2018). We apply our algorithm to video prediction and video interpolation. Our experiments demonstrate that the proposed algorithm performs well on benchmark video datasets and produces sharper videos than state-of-the-art methods. 2023-05-31T15:00:00Z https://scholarworks.unist.ac.kr/handle/201301/90575 Title: Explaining deep learning-based representations of resting state functional connectivity data: focusing on interpreting nonlinear patterns in autism spectrum disorder Author(s): Kim, Young-geun; Ravid, Orren; Zheng, Xinyuan; Kim, Yoojean; Neria, Yuval; Lee, Seonjoo; He, Xiaofu; Zhu, Xi Abstract: Background Resting state Functional Magnetic Resonance Imaging fMRI (rs-fMRI) has been used extensively to study brain function in psychiatric disorders, yielding insights into brain organization. However, the high dimensionality of the rs-fMRI data presents significant challenges for data analysis. Variational autoencoders (VAEs), a type of neural network, have been instrumental in extracting low-dimensional latent representations of resting state functional connectivity (rsFC) patterns, thereby addressing the complex nonlinear structure of rs-fMRI data. Despite these advances, interpreting these latent representations remains a challenge. This paper aims to address this gap by developing explainable VAE models and testing their utility using rs-fMRI data in autism spectrum disorder (ASD).Methods One-thousand one hundred and fifty participants (601 healthy controls [HC] and 549 patients with ASD) were included in the analysis. RsFC correlation matrices were extracted from the preprocessed rs-fMRI data using the Power atlas, which includes 264 regions of interest (ROIs). Then VAEs were trained in an unsupervised manner. Lastly, we introduce our latent contribution scores to explain the relationship between estimated representations and the original rs-fMRI brain measures.Results We quantified the latent contribution scores for both the ASD and HC groups at the network level. We found that both ASD and HC groups share the top network connectivitives contributing to all estimated latent components. For example, latent 0 was driven by rsFC within ventral attention network (VAN) in both the ASD and HC. However, we found significant differences in the latent contribution scores between the ASD and HC groups within the VAN for latent 0 and the sensory/somatomotor network for latent 2.Conclusion This study introduced latent contribution scores to interpret nonlinear patterns identified by VAEs. These scores effectively capture changes in each observed rsFC feature as the estimated latent representation changes, enabling an explainable deep learning model that better understands the underlying neural mechanisms of ASD. 2024-04-30T15:00:00Z