在竞争性微生物系统中达成一致
Reaching Agreement in Competitive Microbial Systems
AI总结：
研究在随机种群动态和竞争交互下分布式协议达成一致的问题，分析直接竞争对多数共识的影响，提出竞争动态在高概率下能达成多数共识，而无竞争需大初始差距。
摘要：
我们研究了在随机种群动态和竞争交互下的分布式协议达成一致问题。受合成生物学应用启发，我们探讨了直接竞争对微生物物种达成多数共识能力的影响。在该问题中，两种物种被指定为输入物种，目标是确保最终只有初始数量最高的输入物种占优。我们证明直接竞争动态在初始差距较小时（即Ω(√(n log n))）能以高概率达成多数共识。相比之下，无直接竞争的情况不稳健：要以常数概率解决多数共识问题，需要初始差距为Ω(n)。为验证分析结果，我们通过模拟显示这些共识动态在实际生物时间尺度内发生。
英文摘要：
We study distributed agreement in microbial distributed systems under stochastic population dynamics and competitive interactions. Motivated by recent applications in synthetic biology, we examine how the presence and absence of direct competition among microbial species influences their ability to reach majority consensus. In this problem, two species are designated as input species, and the goal is to guarantee that eventually only the input species which had the highest initial count prevails. We show that direct competition dynamics reach majority consensus with high probability even when the initial gap between the species is small, i.e., $Ω(\sqrt{n\log n})$, where $n$ is the initial population size. In contrast, we show that absence of direct competition is not robust: solving majority consensus with constant probability requires a large initial gap of $Ω(n)$. To corroborate our analytical results, we use simulations to show that these consensus dynamics occur within practical biological time scales.
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