论文标题
通过残留和部分几何测试进行小组测试
Group testing via residuation and partial geometries
论文作者
论文摘要
本文的动机来自正在进行的SARS-COV-2大流行。它的目标是提出一种先前被忽视的非自适应组测试的方法，并用部分有序的集合中的残留对来描述它。我们的调查具有优势，因为它自然会为任何给定的测试方案产生有效的决策方案（解码器）。该解码器允许检测大量的感染模式。除此之外，我们还设计了基于有限部分线性空间的发病率矩阵的良好组测试方案的结构。关键思想是利用这些矩阵的结构，并使它们可作为用于组测试的测试矩阵。这些矩阵通常可以针对不同估计的疾病患病率量身定制。例如，我们讨论了基于广义四边形的组测试方案。在手头的上下文中，我们仅针对到目前为止的无错误案例陈述结果。希望伸展到噪声方案，并将在该主题的后续帐户中对待。
The motivation for this paper comes from the ongoing SARS-CoV-2 Pandemic. Its goal is to present a previously neglected approach to non-adaptive group testing and describes it in terms of residuated pairs on partially ordered sets. Our investigation has the advantage, as it naturally yields an efficient decision scheme (decoder) for any given testing scheme. This decoder allows to detect a large amount of infection patterns. Apart from this, we devise a construction of good group testing schemes that are based on incidence matrices of finite partial linear spaces. The key idea is to exploit the structure of these matrices and make them available as test matrices for group testing. These matrices may generally be tailored for different estimated disease prevalence levels. As an example, we discuss the group testing schemes based on generalized quadrangles. In the context at hand, we state our results only for the error-free case so far. An extension to a noisy scenario is desirable and will be treated in a subsequent account on the topic.
