Marc Barthelemy

Supply networks are essential for modern production, yet their critical properties remain understudied. We present a stochastic model with random production capacities to analyze material flow to a root node, focusing on topology and buffer stocks. The critical demand, where unsatisfied demand diverges, is examined mostly through numerical simulations. Without stocks, minimal production dictates behavior, making topology irrelevant. With stocks, memory effects arise, making topology crucial.

We introduce a metric to quantify the fragility of chess positions using the interaction graph of pieces. This fragility score captures the tension within a position and serves as a strong indicator of tipping points in a game. In well-known games, maximum fragility often aligns with decisive moments marked by brilliant moves. Analyzing a large dataset of games, we find that fragility typically peaks around move 15, with pawns () and knights () frequently involved in high-tension positions.

Abstract Recent studies show that rare and extreme domestic migration flows influence both population growth and the rise and fall of cities in urbanized countries such as the USA, Canada, the UK and France. This study examines the relationship between domestic net flows (inflows minus outflows) and city rank volatility across countries over time.