论文标题
热带小组测试
Tropical Group Testing
论文作者
论文摘要
聚合酶链反应（PCR）测试是诊断Covid-19的金标准。 PCR将病毒DNA扩增40次，以产生跨越七个数量级的病毒载荷测量。不幸的是，这些测试的输出不精确，因此依赖于精确测量的定量组测试方法不适用。由于识别感染SARS-COV-19的个体的不断增长的需求，我们提出了一个新模型，该模型利用热带算术来表征PCR测试过程。我们提出的框架称为热带小组测试，通过允许不精确的测试测量来克服定量组测试的现有局限性。在许多情况下，其中一些在这项工作中强调了，热带组测试比传统的二进制组测试更强大，因为它所需的测试比经典方法更少，同时还提供了一种机制来识别每个受感染者的病毒负荷。它在经验上也比试图结合PCR，定量组测试和压缩感测的相关工作更强大。
Polymerase chain reaction (PCR) testing is the gold standard for diagnosing COVID-19. PCR amplifies the virus DNA 40 times to produce measurements of viral loads that span seven orders of magnitude. Unfortunately, the outputs of these tests are imprecise and therefore quantitative group testing methods, which rely on precise measurements, are not applicable. Motivated by the ever-increasing demand to identify individuals infected with SARS-CoV-19, we propose a new model that leverages tropical arithmetic to characterize the PCR testing process. Our proposed framework, termed tropical group testing, overcomes existing limitations of quantitative group testing by allowing for imprecise test measurements. In many cases, some of which are highlighted in this work, tropical group testing is provably more powerful than traditional binary group testing in that it require fewer tests than classical approaches, while additionally providing a mechanism to identify the viral load of each infected individual. It is also empirically stronger than related works that have attempted to combine PCR, quantitative group testing, and compressed sensing.
