Identifiability of linear compartmental tree models and a general formula for input-output equations

Bortner, Cashous; Gross, Elizabeth; Meshkat, Nicolette; Shiu, Anne; Sullivant, Seth

doi:10.1016/j.aam.2023.102490

Cited by 3 publications

(2 citation statements)

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“…output, the number of nontrivial coefficients on the right-hand side of the corresponding input-output equation according the Corollary 3.4 of [3] is:…”

Section: Example 36 [Moving Leak Does Not Always Results In Indisting...mentioning

confidence: 99%

“…The original inspiration for this study of indistinguishability was the recent work of the authors of this text and collaborators on a novel graphical characterization of the coefficients of linear compartmental model input-output equations [4]. From this graphical understanding of the input-output equations, as discussed in Section 3.1, we had an immediate understanding of the necessary conditions for indistinguishability.…”

Section: Discussionmentioning

confidence: 99%

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Identifiable Paths and Cycles in Linear Compartmental Models

Bortner

Meshkat

2022

Bull Math Biol

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We introduce a class of linear compartmental models called identifiable path/cycle models which have the property that all of the monomial functions of parameters associated to the directed cycles and paths from input compartments to output compartments are identifiable and give sufficient conditions to obtain an identifiable path/cycle model. Removing leaks, we then show how one can obtain a locally identifiable model from an identifiable path/cycle model. These identifiable path/cycle models yield the only identifiable models with certain conditions on their graph structure and thus we provide necessary and sufficient conditions for identifiable models with certain graph properties. A sufficient condition based on the graph structure of the model is also provided so that one can test if a model is an identifiable path/cycle model by examining the graph itself. We also provide some necessary conditions for identifiability based on graph structure. Our proofs use algebraic and combinatorial techniques.

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“…output, the number of nontrivial coefficients on the right-hand side of the corresponding input-output equation according the Corollary 3.4 of [3] is:…”

Section: Example 36 [Moving Leak Does Not Always Results In Indisting...mentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%