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{"Abstract":["We investigate prophet inequalities with competitive ratios approaching 1, seeking to generalize k-uniform matroids. We first show that large girth does not suffice: for all k, there exists a matroid of girth ≥ k and a prophet inequality instance on that matroid whose optimal competitive ratio is 1/2. Next, we show k-fold matroid unions do suffice: we provide a prophet inequality with competitive ratio 1-O(√{(log k)/k}) for any k-fold matroid union. Our prophet inequality follows from an online contention resolution scheme.\r\nThe key technical ingredient in our online contention resolution scheme is a novel bicriterion concentration inequality for arbitrary monotone 1-Lipschitz functions over independent items which may be of independent interest. Applied to our particular setting, our bicriterion concentration inequality yields "Chernoff-strength" concentration for a 1-Lipschitz function that is not (approximately) self-bounding."]} 

Abstract The interaction between metal nanoparticles (NPs) and their substrate plays a critical role in determining the particle morphology, distribution, and properties. The pronounced impact of a thin oxide coating on the dispersion of metal NPs on a carbon substrate is presented. Al₂O₃‐supported Pt NPs are compared to the direct synthesis of Pt NPs on bare carbon surfaces. Pt NPs with an average size of about 2 nm and a size distribution ranging between 0.5 nm and 4.0 nm are synthesized on the Al₂O₃coated carbon nanofiber, a significant improvement compared to those directly synthesized on a bare carbon surface. First‐principles modeling verifies the stronger adsorption of Pt clusters on Al₂O₃than on carbon, which attributes the formation of ultrafine Pt NPs. This strategy paves the way towards the rational design of NPs with enhanced dispersion and controlled particle size, which are promising in energy storage and electrocatalysis.