Abstract: An important tool for proving the safety of dynamical systems is the notion of a barrier certificate. In this paper, we prove that every robustly safe ordinary differential equation has a ...

Abstract: In this article, we consider a linear-quadratic optimal control problem of mean-field stochastic differential equation with jump diffusion, which is also called as an mean-field ...

An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and ...

In August 1944, with the German army poised for destruction, the citizens of Paris did not wait for liberation—they seized it. This is the gripping story of how schoolteachers, shopkeepers, and ...

Every day, viewers across the country send photos to the investigative NBC Bay Area Responds team — highlighting real consumer problems that demand attention. From worthless windows, faulty fridges, ...

Can you chip in? This year we’ve reached an extraordinary milestone: 1 trillion web pages preserved on the Wayback Machine. This makes us the largest public repository of internet history ever ...