This report highlights the latest developments in various research areas, including theoretical computer science, medical imaging, and artificial intelligence. A common theme among these areas is the increasing use of innovative approaches, such as homological invariants, categorical frameworks, and algebraic theories, to model and analyze complex systems. In theoretical computer science, researchers are exploring new perspectives on the evaluation of lambda terms and the verification of infinite-state systems. Noteworthy papers in this area include the introduction of Ohana trees for the λI-calculus and the development of a cyclic proof system for alternating parity automata. In medical imaging, advancements in machine learning and data-driven modeling are driving significant growth in document image rectification and digital twins in healthcare. Researchers are proposing novel rectification networks and developing end-to-end data-to-decisions methodologies for personalized medicine. The field of fuzzy logic and belief revision is also evolving, with a focus on improving the representation of rules and developing more principled and predictable methods for belief revision. In medical image analysis, researchers are adapting foundation models, such as the Segment Anything Model, for medical image classification and exploring weakly supervised pre-training frameworks for multi-instance learning. The development of innovative deep learning models and techniques is also advancing the field of medical image segmentation, with a focus on integrating multiple modalities and anatomical contexts to improve segmentation accuracy and robustness. Finally, the field of surgical video analysis is witnessing significant advancements, with the development of semi-supervised learning approaches and innovative methods for point tracking, disparity estimation, and surgical scene segmentation. Overall, these emerging trends demonstrate the potential for significant improvements in various fields, from theoretical computer science to medical imaging and artificial intelligence.