Symmetry

This paper introduces the Topp–Leone Heavy-Tailed Odd Burr X-G (TL-HT-OBX-G) family of distributions (FOD), designed to model diverse data patterns. The new distribution is an infinite linear combination of the established exponentiated-G distributions. We used the established properties of the exponentiated-G distribution to infer the properties of the new FOD. The properties considered include the quantile function, moments and moment generating functions, probability-weighted moments, order statistics, stochastic orderings, and Rényi entropy. Parameter estimation is performed using multiple techniques, such as maximum likelihood, least squares, weighted least squares, Anderson–Darling, Cramér–von Mises, and Right-Tail Anderson–Darling. The maximum likelihood estimation method produced superior results in the Monte Carlo simulation studies. A special case of the developed model was applied to three real-world datasets. The model parameters were estimated using the maximum likelihood method. The selected special model was compared to other competing models, and goodness-of-fit was evaluated by the use of several goodness-of-fit statistics. The developed model fit the selected real-world datasets better than all the selected competing models. The new FOD provides a new framework for data modeling in health sciences and reliability datasets.

Rhythm disturbances during human exercise represent a critical challenge for both physiological monitoring and athlete safety. To address this, a structure-enhanced β-TCVAE framework was proposed that derives a Rhythm Disturbance Index (RDI) from multimodal wearable sensor signals. RDI demonstrated a strong correlation with bilateral imbalance (r = 0.838, R² = 0.702) and achieved high discriminative performance (ROC-AUC = 0.823). Importantly, its weak and non-significant correlation with heart rate (r = 0.0569, p > 0.05) supported independence from cardiovascular load, underscoring its specificity to motor rhythm rather than systemic exertion. Analyses conducted on multimodal datasets further validated the robustness of this correlation, showing that RDI consistently aligns with disruptions in locomotor symmetry even after controlling for heart rate. This quantifiable coupling between rhythmic instability and symmetry loss positions RDI as a dual correlational indicator, sensitively reflecting both neuromuscular rhythm irregularities and axial imbalance. Such dual insight enables continuous and objective monitoring of locomotor quality, empowering coaches, clinicians, and sports scientists to tailor training strategies, optimize performance, and reduce the risk of injury. By integrating advanced variational reasoning with real-time wearable sensing, the proposed framework offers an evidence-based step forward in precision monitoring and risk assessment for athletes.

Subway stations are enclosed spaces with high passenger density and complex evacuation conditions. Fires in such environments can escalate rapidly and cause severe consequences. This study proposes a dynamic risk assessment model grounded in dual symmetries. The first symmetry is a balanced “Human–Machine–Environment–Management” analytical structure. The second is a coherent model transformation from a Fault Tree (FT) to a Bayesian Network (BN). Shuanggang Station on Nanchang Metro Line 1 serves as a case study. This work establishes a comprehensive evaluation system based on 4 first-level indicators of man–machine–environment–management, 9 secondary indicators, and 27 tertiary indicators. FT analysis identified 117 minimal cuts and 14 minimal paths, pinpointing core risk nodes such as flammable materials and oxidizers, electrical equipment overheating, and fire management deficiencies. The model was then symmetrically converted into a BN using GeNle Academic 4.1 software to support dynamic probability inference. The results show that prevention measures at Shuanggang Station reduce the fire occurrence probability from 0.000249 to 0.00007 (a 71.9% reduction). The probability importance of rescue escape routes is 0.00223. This indicates that the accessibility of rescue routes constitutes a highly sensitive hazard. The symmetric framework and modeling approach offer a scientific basis for targeted fire prevention, control, and evacuation management in the Nanchang Metro and similar stations. The findings support improvements in the safety and resilience of metro operations.