If the three active neutrinos mix with a sterile one, i.e., in 3+1 scenarios, they may modify the flavor composition of high-energy astrophysical neutrinos. We analytically derived boundaries in flavor space to avoid having to sample over unknown mixing and help boost searches for new physics (we provided them in nice downloadable data tables, too):

Flavors of Astrophysical Neutrinos with Active-Sterile Mixing
Markus Ahlers, Mauricio Bustamante, Niels Gustav Nortvig Willesen
https://arxiv.org/abs/2009.01253

The solid lines are the new 3+1 boundaries, computed for the three benchmark production scenarios (three different colors), compared to the boundaries that we computed for three-flavor mixing (dashed lines) in our earlier paper (1810.00893):