The relative age of galaxies at different redshifts can be used to infer the Hubble parameter and put constraints on cosmological models. We select luminous red galaxies (LRGs) from the Sloan Digital Sky Survey Data Release 7 and then cross match it with the MPA/JHU catalog of galaxies to obtain a large sample of quiescent LRGs at redshift z ~ 0.03-0.39. The total number of quiescent LRGs, 23,883, is divided into four sub-samples according to their velocity dispersions and each sub-sample is further divided into 12 redshift bins. The spectra of the LRGs in each redshift and velocity bin are co-added in order to obtain a combined spectrum with a relatively high signal-to-noise ratio. Adopting the GalexEV/SteLib model, we estimate the mean ages of the LRGs from these combined spectra by using the full-spectrum fitting method. We check the reliability of the estimated age by using Monte Carlo simulations and find that the estimates are robust and reliable. Assuming that the LRGs in each sub-sample and each redshift bin were on average formed at the same time, the Hubble parameter at the present time H ₀ is estimated from the age-redshift relation obtained for each sub-sample, which is compatible with the H ₀ value measured by other methods. We demonstrate that a systematic bias (up to ~20%) may be introduced to the H ₀ estimation because of recent star formation in the LRGs due to the later major mergers at z 0.4, but this bias may be negligible for those sub-samples with large velocity dispersions. Using the age-redshift relations obtained from the sub-sample with the largest velocity dispersion or the two sub-samples with high velocity dispersions, we find H ₀ = 65⁺⁷ _–3 km s^–1 Mpc^–1 or H ₀ = 74⁺⁵ _–4 km s^–1 Mpc^–1 by assuming a spatially flat ΛCDM cosmology. With upcoming surveys, such as the Baryon Oscillation Spectroscopic Survey, even larger samples of quiescent massive LRGs may be obtained, and thus the Hubble parameter can be measured with high accuracy usimg the age-redshift relation.

Sheep face recognition technology is critical in key areas such as individual sheep identification and behavior monitoring. Existing sheep face recognition models typically require high computational resources. When these models are deployed on mobile or embedded devices, problems such as reduced model recognition accuracy and increased recognition time arise. To address these problems, an improved Parameter Fusion Lightweight You Only Look Once (PFL-YOLO) sheep face recognition model based on YOLOv8n is proposed. In this study, the Efficient Hybrid Conv (EHConv) module is first integrated to enhance the extraction capability of the model for sheep face features. At the same time, the Residual C2f (RC2f) module is introduced to facilitate the effective fusion of multi-scale feature information and improve the information processing capability of the model; furthermore, the Efficient Spatial Pyramid Pooling Fast (ESPPF) module was used to fuse features of different scales. Finally, parameter fusion optimization work was carried out for the detection head, and the construction of the Parameter Fusion Detection (PFDetect) module was achieved, which significantly reduced the number of model parameters and computational complexity. The experimental results show that the PFL-YOLO model exhibits an excellent performance–efficiency balance in sheep face recognition tasks: mAP@50 and mAP@50:95 reach 99.5% and 87.4%, respectively, and the accuracy is close to or equal to the mainstream benchmark model. At the same time, the number of parameters is only 1.01 M, which is reduced by 45.1%, 83.7%, 66.6%, 71.4%, and 61.2% compared to YOLOv5n, YOLOv7-tiny, YOLOv8n, YOLOv9-t, and YOLO11n, respectively. The size of the model was compressed to 2.1 MB, which was reduced by 44.7%, 82.5%, 65%, 72%, and 59.6%, respectively, compared to similar lightweight models. The experimental results confirm that the PFL-YOLO model maintains high accuracy recognition performance while being lightweight and can provide a new solution for sheep face recognition models on resource-constrained devices.