论文标题
单变量步骤功能和等位基因频率光谱的稀疏力矩
Sparse moments of univariate step functions and allele frequency spectra
论文作者
论文摘要
我们研究了分段恒定密度功能在间隔$ [0,1] $上的单变量力矩问题及其对人群遗传学的推论问题的后果。我们表明，要关闭，任何$ n $矩的集合都是通过最多$ n-1 $断点来实现的，并且这种界限很紧。我们用它来表明，人口遗传学的$ n $ th结合歧管中的任何一点都可以通过分段恒定的人口历史来实现，最多$ n-2 $变化。力矩锥和聚结的歧管都投影了谱图，我们描述了在它们上找到最近的一点作为半限定程序的问题。
We study the univariate moment problem of piecewise-constant density functions on the interval $[0,1]$ and its consequences for an inference problem in population genetics. We show that, up to closure, any collection of $n$ moments is achieved by a step function with at most $n-1$ breakpoints and that this bound is tight. We use this to show that any point in the $n$th coalescence manifold in population genetics can be attained by a piecewise constant population history with at most $n-2$ changes. Both the moment cones and the coalescence manifold are projected spectrahedra and we describe the problem of finding a nearest point on them as a semidefinite program.
