We use an asymmetric Nash bargaining model between worker and firms, under the assumption of firm-specific human capital (FSHC), to argue that city size influences the proportion of the rent received by labor (i.e., the magnitude of labor share of rent). We argue that an increase in city size generates both a positive effect (the “FSHC-autonomy effect”) on the bargaining power of labor as well as a negative effect (the division-of-labor effect) on the bargaining power of labor. Our empirical exploration found that labor share of the rent (in percent) increases with city size, suggesting that the FSHC-autonomy effect is greater than the division of labor effect.

Rapid and accurate multi-class fault diagnosis is essential for high-end equipment because different fault categories require different maintenance responses. This study aims to develop a lightweight and discriminative diagnostic framework that can identify multiple fault categories from non-stationary vibration signals while reducing redundant computation. High-frequency vibration signals provide direct condition information, but long sequences, noise, nonlinear dynamics, and non-stationary behavior make raw-signal classification unreliable. From an entropy-based information-processing perspective, the key issue is to separate informative fault modes from redundant fluctuations and enlarge inter-class distinctions in the probabilistic decision space. This study proposes Fastformer, an integrated framework for vibration-based fault identification. Empirical Mode Decomposition first converts each signal into Intrinsic Mode Functions to reduce modal mixing and preserve fault-related oscillatory components. The resulting components are processed by an encoder-oriented Q/K/V dot-product scoring mechanism, which constructs compact spatiotemporal embeddings without adopting a complete Transformer architecture. Validation-guided pruning removes low-contribution attention responses, while a Margin-Enhanced Fault Softmax classifier optimized with a cross-entropy-based objective strengthens category separation. By combining stable decomposition, lightweight attention scoring, pruning, and probabilistic margin learning, Fastformer achieves faster and more stable convergence. On the XJTU-SpurGear dataset, Fastformer obtains precision, recall, F1-score, and AUC values of 1.000. Additional validation on the HUST bearing dataset further shows that Fastformer achieves the best overall performance among the compared methods, with an AUC value of 0.9596.