Embossed Paper Platform for Whole Blood Collection, Room Temperature Storage, and Direct Analysis by Pinhole Paper Spray Mass Spectrometry
- Award ID(s):
- 1900271
- PAR ID:
- 10338485
- Date Published:
- Journal Name:
- Analytical Chemistry
- Volume:
- 94
- Issue:
- 10
- ISSN:
- 0003-2700
- Page Range / eLocation ID:
- 4417 to 4425
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph onnvertices, on each turn Proposer proposes a potential edge and Decider simultaneously decides (without knowing Proposer's choice) whether to add it to the graph. Proposer cannot propose an edge which would create a triangle in the graph. The game ends when Proposer has no legal moves remaining, and Proposer wins if the final graph has independence number at leasts. We prove a threshold phenomenon exists for this game by exhibiting randomized strategies for both players that are optimal up to constants. Namely, there exist constants 0 < A < Bsuch that (under optimal play) Proposer wins with high probability if, while Decider wins with high probability if. This is a factor oflarger than the lower bound coming from the off‐diagonal Ramsey numberr(3,s).more » « less
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