Quiver Bundles and Wall Crossing for Chains

Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural C*-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundle to the Hom-complex of two chains, and prove that stability of the chains implies stability of this new quiver bundle. Our approach uses the Hitchin-Kobayashi correspondence for quiver bundles. Moreover, we use our result to give a new proof of a key lemma on chains (due to \'Alvarez-C\'onsul, Garc\'ia-Prada and Schmitt), which has been important in the study of Higgs bundle moduli; this proof relies on stability and thus avoids the direct use of the chain vortex equations

Comparison of classification performance of XGBoost by sports types: PR curve.

Comparison of classification performance of XGBoost by sports types: PR curve.</p

Results of analyzing essential physical fitness of male adolescent athletes across sports types using feature importance method of XGBoost.

The red bar plot represents essential elements of physical fitness. (TIF)</p

Comparative results of essential physical fitness analysis: 1st Principal Component Analysis (PCA), XGBoost feature importance, and SHAP value.

Comparative results of essential physical fitness analysis: 1st Principal Component Analysis (PCA), XGBoost feature importance, and SHAP value.</p

Results of analyzing the essential physical fitness of male adolescent athletes between sports types using SHAP value method.

Each dot represents the influence of the physical fitness factor between sports types, where the red color of the dot indicates higher values and the blue color indicates lower values. A positive SHAP value corresponds to sports types listed vertically (football, baseball, swimming, and badminton), Negative SHAP value corresponds to sports types listed horizontally (track & field, football, baseball, and swimming) The plotted dots represent the characteristics of each individual.</p

Physical characteristic of the participants.

Physical fitness (PF) includes various factors that significantly impacts athletic performance. Analyzing PF is critical in developing customized training methods for athletes based on the sports in which they compete. Previous approaches to analyzing PF have relied on statistical or machine learning algorithms that focus on predicting athlete injury or performance. In this study, six machine learning algorithms were used to analyze the PF of 1,489 male adolescent athletes across five sports, including track & field, football, baseball, swimming, and badminton. Furthermore, the machine learning models were utilized to analyze the essential elements of PF using feature importance of XGBoost, and SHAP values. As a result, XGBoost represents the highest performance, with an average accuracy of 90.14, an area under the curve of 0.86, and F1-score of 0.87, demonstrating the similarity between the sports. Feature importance of XGBoost, and SHAP value provided a quantitative assessment of the relative importance of PF in sports by comparing two sports within each of the five sports. This analysis is expected to be useful in analyzing the essential PF elements of athletes in various sports and recommending personalized exercise methods accordingly.</div

Quantitative comparison of similarity and essential elements of physical fitness between sports types using SHAP value of XGBoost.

The darker the blue line between the sports types, the lower the similarity. The top 3 essential elements of physical fitness for each sports type were shown in a pie chart.</p

Description of physical fitness measurement.

Physical fitness (PF) includes various factors that significantly impacts athletic performance. Analyzing PF is critical in developing customized training methods for athletes based on the sports in which they compete. Previous approaches to analyzing PF have relied on statistical or machine learning algorithms that focus on predicting athlete injury or performance. In this study, six machine learning algorithms were used to analyze the PF of 1,489 male adolescent athletes across five sports, including track & field, football, baseball, swimming, and badminton. Furthermore, the machine learning models were utilized to analyze the essential elements of PF using feature importance of XGBoost, and SHAP values. As a result, XGBoost represents the highest performance, with an average accuracy of 90.14, an area under the curve of 0.86, and F1-score of 0.87, demonstrating the similarity between the sports. Feature importance of XGBoost, and SHAP value provided a quantitative assessment of the relative importance of PF in sports by comparing two sports within each of the five sports. This analysis is expected to be useful in analyzing the essential PF elements of athletes in various sports and recommending personalized exercise methods accordingly.</div

Comparison of confusion matrix of XGboost by sports types.

Comparison of confusion matrix of XGboost by sports types.</p

Comparison of classification performance of XGBoost by sports types: ROC curve.

Comparison of classification performance of XGBoost by sports types: ROC curve.</p