2019/10/29 by Seth Gerberding, Gerberding, Seth, Nida Obatake +3 · 1 citation
Computer Science · #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Formal Methods in Verification
paper · pdf · doi:10.48550/arxiv.1910.13549
openalex publication_date 2019/10/29 · openalex created_date 2022/07/22 · openalex updated_date 2026/07/28
A mathematical model is identifiable if its parameters can be recovered from\ndata. Here we investigate, for linear compartmental models, whether (local,\ngeneric) identifiability is preserved when parts of the model -- specifically,\ninputs, outputs, leaks, and edges -- are moved, added, or deleted. Our results\nare as follows. First, for certain catenary, cycle, and mammillary models,\nmoving or deleting the leak preserves identifiability. Next, for cycle models\nwith up to one leak, moving inputs or outputs preserves identifiability. Thus,\nevery cycle model with up to one leak (and at least one input and at least one\noutput) is identifiable. Next, we give conditions under which adding leaks\nrenders a cycle model unidentifiable. Finally, for certain cycle models with no\nleaks, adding specific edges again preserves identifiability. Our proofs, which\nare algebraic and combinatorial in nature, rely on results on elementary\nsymmetric polynomials and the theory of input-output equations for linear\ncompartmental models.\n