This research develops mathematical models to understand how honeybee clusters survive extreme cold without their hive. Using temperature and density equations, the model predicts how bees move, generate heat, and form insulating layers. Accurate simulations could reduce harmful field experiments and provide biologists with a powerful tool for studying bee behaviour.

This research quantifies the uncertainty in chaotic systems, showing why long-term predictions — from planetary motion to weather patterns — become unreliable. By developing mathematical models that capture chaotic behaviour, the work supports applications in traffic flow, wireless communication, climate forecasting, and disease spread, revealing why some systems are inherently more predictable than others.

This research explores how to secure low-power Internet of Things devices using physical-layer security. Instead of relying on computational cryptography, it harnesses randomness in wireless communication channels to achieve strong or even perfect security. As 5G expands device numbers, understanding these mathematical limits is essential for protecting future networks.