Applied Sciences

(1) Background: The midsole hardness (i.e., cushioning) of running shoes has received significant attention as a crucial element influencing both performance and injury prevention. This research aimed to examine how variations in midsole hardness affect the biomechanical responses of the lower extremities during running. (2) Methods: Twenty-five male recreational runners in their 20 s with no history of musculoskeletal injuries (age: 23.3 ± 4.24 years) were recruited. Custom-made shoes with four different midsole hardness levels (Asker-C 70, 60, 50, and 40) were used, and the mechanical properties of the midsoles were analyzed. Participants ran on an instrumented treadmill at speeds of 2.3 m/s and 3.3 m/s. Ground reaction forces and motion data were collected during the trials. A one-way repeated-measures ANOVA was conducted to compare groups. (3) Results: In the running trials, a decrease in midsole hardness increased the impact peak (IP) while loading rate (LR) decreased significantly (p < 0.05). In addition, runners wearing shoes with greater cushioning exhibited higher ankle joint stiffness than those wearing harder shoes (p < 0.05). (4) Conclusion: Adjusting joint stiffness appears to be a key strategy employed by runners in response to softer or cushioned running environments (i.e., shoe and surface), ultimately contributing to greater dynamic stability during movement.

This interdisciplinary study presents a novel questionnaire analysis methodology using Artificial Intelligence (AI) and Machine Learning (ML). The framework is broadly applicable to all areas of research using questionnaire data analysis, including health sciences and physical education. Our predictive modeling was based on the XG-Boost algorithm, which classified individuals into three distinct groups—employees and two cohorts of retirees—based on their demographic profiles and responses to the WHOQOL-BREF survey. In order to ensure the credibility and reliability of the predictions, the model building process used the implementation of cross-validation. This procedure produced a model with a resultant accuracy of 0.8038 ($95\%$ confidence interval: 0.7551–0.8908). To go beyond conventional performance metrics, we implemented the SHapley Additive exPlanations (SHAP) method, providing a transparent and detailed interpretation of the model’s decision-making process. This explainable AI analysis clarifies both the magnitude and direction of the impact of key factors such as age and various predictors of quality of life, providing detailed, data-driven insights into what differentiates groups.

Accurate, scalable, and outlier-robust state estimation (SE) is critical for large AC power systems with mixed SCADA and PMU measurements. This paper proposes D-BSE-L1, a distributed robust state estimator for the bilinear AC model. The method combines the bilinear state estimation framework with a convex weighted least absolute value (WLAV) loss so that all area subproblems become convex linear or quadratic programs coordinated by ADMM, and a cache-enabled Cholesky factorization is used to accelerate the third-stage linear solves. Simulations on the IEEE 14-, 118-, and 1062-bus systems show that D-BSE-L1 achieves estimation accuracy comparable to its centralized bilinear counterpart. Under severe bad-data conditions, its advantage over weighted least squares with the largest normalized residual test (WLS + LNRT) is pronounced: with 10% 1.5× bad data, the voltage magnitude and angle MAEs are about 62% and 54% of those of WLS + LNRT, and with 5% 5× bad data, they further drop to roughly 43% and 51%, while requiring only about one-tenth of the CPU time. On the 1062-bus system, D-BSE-L1 maintains the MAE of the centralized estimator but reduces runtime from 2.46 s to 0.72 s, providing a scalable, hyperparameter-free, and robust solution for partitioned state estimation in large-scale power grids.