Sparse Moments of Univariate Step Functions and Allele Frequency Spectra

We study the univariate moment problem of piecewise-constant density functions on interval [0,1] and its consequences for an inference in population genetics. show that, up to closure, any collection n moments is achieved by a step function with at most ? 1 breakpoints that this bound tight. use point th coalescence manifold genetics can be attained piecewise constant history 2 changes. Both cones are projected spectrahedra we describe finding nearest them as semidefinite program.