Kernel Selection for Gaussian Process in Cosmology: with Approximate Bayesian Computation Rejection and Nested Sampling

Gaussian Process (GP) has gained much attention in cosmology due to its ability to reconstruct cosmological data in a model-independent manner. In this study, we compare two methods for GP kernel selection: Approximate Bayesian Computation (ABC) Rejection and nested sampling. We analyze three types of data: cosmic Chronometer data (CC), Type Ia Supernovae (SNIa), and Gamma Ray Burst (GRB), using five kernel functions. To evaluate the differences between kernel functions, we assess the strength of evidence using Bayes factors. Our results show that, for ABC Rejection, the Mat\'ern kernel with $\nu$=5/2 (M52 kernel) outperformes the commonly used Radial Basis Function (RBF) kernel in approximating all three datasets. Bayes factors indicate that the M52 kernel typically supports the observed data better than the RBF kernel, but with no clear advantage over other alternatives. However, nested sampling gives different results, with the M52 kernel losing its advantage. Nevertheless, Bayes factors indicate no significant dependence of the data on each kernel.Comment: 15 pages, 4 tables, 6 figures, accepted for publication in ApJS. We draw a new conclusion which is different from the standard ABC-related methods(e.g. ABC-SMC) in kernel selection for Gaussian Proces

THE KINEMATICS CHAIN OF INSTEP KICKING OF SOCCER WITH UPPERBODY CONSTRAINED: A PILOT STUDY

The purpose of this study was to understand the kicking performance when the upperbody motion has been limited. One player in the college cup level A volunteered to participate in this study (Aged: 20 years, Height: 172 cm, Body mass: 65 kg). A VICON motion capture system (200 Hz) was used to capture the kicking motion. The participant was asked to kick the ball both using an arm swing and not using an arm swing. The Visual3D was used to calculate the segment velocity, angular velocity, and kinetic chain. The results indicated that kicking with arm swing had a greater ball and lower-extrimity segment velocity. The main effect for lower ball velocity during kicking without arm swing is the decreased angular velocity at the ankle joint. When arm motion has been limited, players should noticed that the ankle joint needs to follow through after foot-ball contact

Iterative Online Image Synthesis via Diffusion Model for Imbalanced Classification

Accurate and robust classification of diseases is important for proper diagnosis and treatment. However, medical datasets often face challenges related to limited sample sizes and inherent imbalanced distributions, due to difficulties in data collection and variations in disease prevalence across different types. In this paper, we introduce an Iterative Online Image Synthesis (IOIS) framework to address the class imbalance problem in medical image classification. Our framework incorporates two key modules, namely Online Image Synthesis (OIS) and Accuracy Adaptive Sampling (AAS), which collectively target the imbalance classification issue at both the instance level and the class level. The OIS module alleviates the data insufficiency problem by generating representative samples tailored for online training of the classifier. On the other hand, the AAS module dynamically balances the synthesized samples among various classes, targeting those with low training accuracy. To evaluate the effectiveness of our proposed method in addressing imbalanced classification, we conduct experiments on the HAM10000 and APTOS datasets. The results obtained demonstrate the superiority of our approach over state-of-the-art methods as well as the effectiveness of each component. The source code will be released upon acceptance