Ranking and Selection under Input Uncertainty: Fixed Confidence and Fixed Budget

In stochastic simulation, input uncertainty (IU) is caused by the error in estimating the input distributions using finite real-world data. When it comes to simulation-based Ranking and Selection (R&S), ignoring IU could lead to the failure of many existing selection procedures. In this paper, we study R&S under IU by allowing the possibility of acquiring additional data. Two classical R&S formulations are extended to account for IU: (i) for fixed confidence, we consider when data arrive sequentially so that IU can be reduced over time; (ii) for fixed budget, a joint budget is assumed to be available for both collecting input data and running simulations. New procedures are proposed for each formulation using the frameworks of Sequential Elimination and Optimal Computing Budget Allocation, with theoretical guarantees provided accordingly (e.g., upper bound on the expected running time and finite-sample bound on the probability of false selection). Numerical results demonstrate the effectiveness of our procedures through a multi-stage production-inventory problem

Topological mechanics in quasicrystals

We study topological mechanics in two-dimensional quasicrystalline parallelogram tilings. Topological mechanics has been studied intensively in periodic lattices in the past a few years, leading to the discovery of topologically protected boundary floppy modes in Maxwell lattices. In this paper we extend this concept to quasicrystalline parallelogram tillings and we use the Penrose tiling as our example to demonstrate how these topological boundary floppy modes arise with a small geometric perturbation to the tiling. The same construction can also be applied to disordered parallelogram tilings to generate topological boundary floppy modes. We prove the existence of these topological boundary floppy modes using a duality theorem which relates floppy modes and states of self stress in parallelogram tilings and fiber networks, which are Maxwell reciprocal diagrams to one another. We find that, due to the unusual rotational symmetry of quasicrystals, the resulting topological polarization can exhibit orientations not allowed in periodic lattices. Our result reveals new physics about the interplay between topological states and quasicrystalline order, and leads to novel designs of quasicrystalline topological mechanical metamaterials.Comment: 16 pages, 8 figure