How does one plan a space mission that involves visiting multiple celestial bodies which are constantly moving? Researchers at Bielefeld University have, for the first time, developed a precise mathematical approach to this problem. The publication in a leading international journal demonstrates that decision-support methods at the interface between economics and mathematics can advance space travel and transport planning – with implications extending far beyond space missions.

Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly challenging class of mathematical problems with broad implications for understanding the natural world. The advance, which the researchers call “Mollifier Layers,” could benefit fields as varied as genetics and weather forecasting, because inverse PDEs help scientists work backward from observable patterns to infer the hidden dynamics that produced them.

Researchers from The University of Osaka, Kyushu University, and the University of Victoria have developed MV-SZZ, a new method that accurately identifies defect-inducing software commits. By combining detailed code tracking with a majority voting system, the approach reduces false positives and outperforms existing techniques. This improvement could help developers debug software more efficiently and build more reliable systems.