The real-time monitoring of animal postures through computer vision techniques has become essential for modern precision livestock management. To overcome the limitations of current behavioral analysis systems in balancing computational efficiency and detection accuracy, this study develops an optimized deep learning framework named YOLOv8-BCD specifically designed for ovine posture recognition. The proposed architecture employs a multi-level lightweight design incorporating enhanced feature fusion mechanisms and spatial-channel attention modules, effectively improving detection performance in complex farm environments with occlusions and variable lighting. Our methodology introduces three technical innovations: (1) Adaptive multi-scale feature aggregation through bidirectional cross-layer connections. (2) Context-aware attention weighting for critical region emphasis. (3) Streamlined detection head optimization for resource-constrained devices. The experimental dataset comprises 1476 annotated images capturing three characteristic postures (standing, lying, and side lying) under practical farming conditions. Comparative evaluations demonstrate significant improvements over baseline models, achieving 91.7% recognition accuracy with 389 FPS processing speed while maintaining 19.2% parameter reduction and 32.1% lower computational load compared to standard YOLOv8. This efficient solution provides technical support for automated health monitoring in intensive livestock production systems, showing practical potential for large-scale agricultural applications requiring real-time behavioral analysis.

In this paper, we study direct and inverse problems for a spatial-fractional Black–Scholes equation with space-dependent volatility. For the direct problem, we provide CN-WSGD (Crank–Nicholson and the weighted and shifted Grünwald difference) scheme to solve the initial boundary value problem. The latter aims to recover the implied volatility via observable option prices. Using a linearization technique, we rigorously derive a mathematical formulation of the inverse problem in terms of a Fredholm integral equation of the first kind. Based on an integral equation, an efficient numerical reconstruction algorithm is proposed to recover the coefficient. Numerical results for both problems are provided to illustrate the validity and effectiveness of proposed methods.