31,929 research outputs found
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
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