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Identifiability of directed-cycle and catenary linear compartment models

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Pith's one-line read A directed-cycle compartment model is generically locally identifiable exactly when its leaks interlace with its inputs and outputs, with one exceptional configuration set aside.

desk verdict Completes the directed-cycle identifiability classification with a genuinely new leak-interlacing criterion, but the sufficiency proof has a fixable gap when an input segment contains no output. read the letter →

arxiv 2412.05283 v3 pith:56PZZMRT submitted 2024-11-15 math.CO math.AGmath.DS

Saber Ahmed , Natasha Crepeau , Paul R. Dessauer Jr. , Alexis Edozie , Odalys Garcia-Lopez , Tanisha Grimsley , Jordy Lopez Garcia , Viridiana Neri
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Anne Shiu
This is my paper · ORCID
classification math.COmath.AGmath.DS MSC 93B3037N2592C4534A3034A5505C50
keywords linearcompartmentalmodelstructuralidentifiabilitydirected-cyclecatenaryleak-interlacinginput-outputequationscoefficientmapsingularlocus
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper resolves a question about when the rate constants in a cyclic compartment model can be recovered from noiseless input-output data. Its main theorem states that a directed-cycle model with at least one input and one output is generically locally identifiable exactly when it is leak-interlacing: between any two leak compartments along the cycle there is an input or an output, with one explicit exceptional family set aside. The proof works through the coefficients of input-output equations, reducing the question to whether the Jacobian of the coefficient map has full rank, and then showing this happens precisely for leak-interlacing models. For the companion class of catenary models, the paper gives an explicit formula for all coefficients of the input-output equations, which is expected to support future identifiability analysis of those models. The result gives a simple graph-theoretic test that decides identifiability without solving any differential equations.

What carries the argument

The engine of the proof is the coefficient map c of the model, the vector of coefficients of the input-output equations, together with the rank criterion that a strongly connected linear compartmental model is generically locally identifiable exactly when the Jacobian of c has full column rank at a generic parameter point. For directed cycles the coefficient map has an explicit form (Lemma 3.10): in the one-input, one-output case it is built from elementary symmetric polynomials e_j of edge-plus-leak sums, the path product κ from input to output, and products e*_j κ from the output back to the input; Proposition 2.14 extends these coefficients to models with multiple inputs and outputs by restricting to one-input, one-output submodels. The identifiability proof separates into a failure direction, where two leak columns of the Jacobian are shown to be linearly dependent, and a success direction, where a block-triangular submatrix with nonzero diagonal blocks is exhibited for leak-interlacing models. For catenary models the corresponding coefficient-map formula is derived from the spanning-incoming-forest expansion of input-output equation coefficients, using elementary symmetric polynomials on sets of outgoing sums.

What would settle it

For the 4-compartment directed-cycle model with In={1}, Out={3}, and Leak={1,3} — a leak-interlacing model that Theorem 3.6 declares identifiable — evaluate the Jacobian matrix of the coefficient map (four edge parameters k21,k32,k43,k14 plus two leak parameters k01,k03) at a generic parameter point. If its determinant is the zero polynomial, or a computer algebra system yields two distinct parameter vectors with identical input-output coefficients, then the classification is false.

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Extended reading notes

Core claim

On the paper's terms, the central discovery is the equivalence in Theorem 3.6: an n-compartment directed-cycle model is generically locally identifiable if and only if it is leak-interlacing, meaning it is not exceptional (the only obstruction is the configuration In={i}, Out={i-1}, |Leak|=2, with i-1 in Leak) and every arc of the cycle from one leak to the next contains at least one input or output compartment, counting endpoints. This covers any number of inputs, outputs, and leaks, extending earlier one-input/one-output results. A direct corollary is that any directed-cycle model with |Leak| at least |In|+|Out|+1 is unidentifiable. The paper also identifies several hyperplanes that always lie in the singular locus of an identifiable directed-cycle model (Theorems 4.3 and 4.5), and, for catenary models, proves a closed coefficient-map formula (Theorem 5.1) expressed through elementary symmetric polynomials and products of edge parameters along paths.

Load-bearing premise

The load-bearing premise is that generic local identifiability is exactly the full-rank condition on the Jacobian of the coefficient map of the input-output equations, and that the cited coefficient-map formula for directed cycles is correct for every leak configuration; if either fails for some model, the leak-interlacing criterion would not decide identifiability.

Editorial extensions

If this is right

  • For any directed-cycle model, the leak-interlacing condition gives a purely combinatorial check of generic local identifiability: list the leaks around the cycle and confirm each gap contains an input or an output, after excluding the single exceptional family.
  • Directed-cycle models with at least |In|+|Out|+1 leaks are always unidentifiable, so adding leaks beyond the number of inputs plus outputs cannot preserve identifiability.
  • The previous characterization for one-input, one-output directed-cycle models becomes a special case of Theorem 3.6, and the same theorem covers models with several inputs and outputs for the first time.
  • For identifiable directed-cycle models, Theorems 4.3 and 4.5 show the singular locus contains explicit hyperplanes; in the single-leak case with input and output at compartment 1, the full singular locus is the product of edge parameters times a Vandermonde factor in the leak-shifted edge parameters.
  • For catenary models with one input and one output, Theorem 5.1 gives an explicit coefficient-map formula usable in later identifiability computations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the same interlacing idea is a natural conjecture for other strongly connected compartmental graphs, replacing the directed cycle by requiring that between any two leaks along every directed path there is an input or output.
  • Beyond the paper: combining the catenary coefficient formula with the paper's reduction from multiple inputs and outputs to one-input/one-output submodels yields an explicit coefficient map for all catenary models, so a full leak-interlacing-style classification for bidirected paths is a testable next step.
  • Beyond the paper: the block-triangular structure used to prove the identifiable direction suggests that for leak-interlacing models the Jacobian of the coefficient map is sparse and triangular after column operations; if true, this would give a direct way to compute identifiable parameter combinations, not just the yes/no answer.
  • Beyond the paper: the singular-locus hyperplanes found for small leak-interlacing cycles suggest the singular locus in the full leak-interlacing family is a hyperplane arrangement; checking the n=4 and n=5 cases in the paper's database would test this.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. The paper studies generic local identifiability of linear compartmental models whose underlying graph is a directed cycle or a bidirected path (catenary model). The main result, Theorem 3.6, states that a directed-cycle model is generically locally identifiable if and only if it is leak-interlacing: outside a small exceptional family, every directed path between consecutive leaks contains at least one input or output. The proof uses the rank of the Jacobian of the input-output coefficient map, the coefficient-map formula of Gerberding-Obatake-Shiu for one-input/one-output cycles, and a reduction (Proposition 2.14) from multi-input/multi-output models to one-input/one-output submodels. Section 4 identifies hyperplanes contained in the singular locus of identifiable directed-cycle models and gives the full singular locus for the case In=Out=Leak={1}. Section 5 states and proves a formula for the input-output equations of catenary models with one input and one output. Appendices contain SIAN-generated identifiability databases for small directed-cycle and catenary models.

Significance. If Theorem 3.6 is correct, it gives a complete and very simply checkable combinatorial characterization of generic local identifiability for all directed-cycle compartmental models, with arbitrary numbers of inputs, outputs, and leaks. This goes well beyond the earlier one-input/one-output results and is the first such classification for a family of models allowing any number of inputs and outputs, as the authors note. The catenary coefficient-map formula in Theorem 5.1 is a potentially useful new tool for future identifiability and singular-locus analyses, and the singular-locus results add explicit information about the measure-zero non-identifiable set. Strengths of the manuscript include worked examples with explicit Jacobians, the clear statements of the combinatorial conditions, and the reproducible SIAN databases in the appendices. The necessity direction and the catenary formula appear sound; however, the sufficiency proof of the main theorem has a load-bearing gap in the construction of the block matrix in Proposition 3.25, as detailed below.

major comments (1)
  1. [§3.3, Proposition 3.25 and inequality (27)] The construction of the D block is undefined when an input segment contains no output, i.e. when j_s=0 for some s. The D rows are specified as κ(i_s,p_{s,1}),...,κ(i_s,p_{s,j_s}), κ(i_s,ν(p_{s,j_s})) for s<x, and the proof states that "at least one coefficient exists in each list, namely ... κ(i_s,ν(p_{s,j_s}))". But the discussion immediately after (27) explicitly allows j_s=0 and says that in that case p_{s,1} does not exist, so ν(p_{s,0}) is undefined. A concrete minimally leak-interlacing model realizing this is n=6, In={1,3}, Out={5}, Leak={2,4,6}; here x=2, y=1, j_1=0, and the s=1 block would require the undefined coefficient κ(1,ν(p_{1,0})), while the corresponding column list is also not well-formed. Since Proposition 3.25 is the sufficiency half of Theorem 3.6, the written proof does not cover a nonempty family of leak-interlacing models. The gap appears repairable—for example, by defining ν(p_{s,0}) to be the first output in the next segment, the n=6 example does satisfy the intended lower-triangular form—but the proof as written is incomplete.
minor comments (4)
  1. [§3.3, Proposition 3.25, Case 1] In the discussion of the upper-right zero block, the last row is said to correspond to the coefficient "e*_1(ix,pβ)", but no pβ has been defined; this should be e*_1(ix,px1).
  2. [§3.3, Proposition 3.25, Case 2] The displayed 2×2 matrix D appears to contain sign and index errors relative to the column order defined immediately before it. With columns J_{k0ℓ}-J_{kℓ+1,ℓ} and J_{k0n}-J_{k1n} and the row order κ(1,n), en-∏k_{i+1,i}, the first diagonal entry should be -κ/k_{ℓ+1,ℓ} and the second should be κ, rather than the displayed values; also the subscript k_{ℓ+2,ℓ} should presumably be k_{ℓ+2,ℓ+1}.
  3. [§5, Theorem 5.1 and equation (39)] Theorem 5.1 states n≥1, but the definition of OutM(ℓ) in (39)-(40) refers to k21 for ℓ=1, which does not exist when n=1. The n=1 case should be treated separately or the theorem should assume n≥2.
  4. [Appendix A] Several rows of the database tables in Appendix A appear garbled or truncated in the typeset version, with parameter lists cut off mid-sentence. The authors should check the final typeset tables for completeness.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the leak-interlacing theorem is a new combinatorial rank proof; prior self-citations are parameter-free lemmas, not the conclusion.

full rationale

The central claim (Theorem 3.6) is a combinatorial equivalence: a directed-cycle model is generically locally identifiable iff its leaks interlace with inputs/outputs. Leak-interlacing is defined without reference to identifiability or coefficient maps, and the proof establishes full rank of the coefficient-map Jacobian via linear algebra. The imported ingredients—the rank criterion (Proposition 2.16, from [19,21]), the one-input/one-output coefficient-map formula (Lemma 3.10, from [12]), and the known tree and at-most-one-leak cycle classifications (Propositions 2.21 and 2.22, from [2,12])—are stated parameter-free with assumptions that do not include the full classification, and the paper derives the multi-input/output and multi-leak cases from them rather than assuming them. The citation of [12, proof of Theorem 3.10] in Lemma 3.19 and of [2, Theorem 3.1] in Lemma 5.5 is normal use of prior theorems; although some authors overlap with the present paper, these are published results, not an unverified self-supporting chain. The only substantive concern in the manuscript is an internal indexing/gap issue in Proposition 3.25 when an input segment contains no output (j_s=0), which is a correctness matter, not circularity: it does not make the theorem an input to itself. No fitted parameter is renamed as a prediction, and no equation is equivalent to its input by construction. Accordingly, no circular step is present.

Assumptions & free parameters 0 free parameters · 8 assumptions · 0 invented entities

The central claim rests on published identifiability theory for linear compartmental models ([2, 12, 14, 19, 21]) plus standard results on symmetric polynomials; the paper's new work is the derivation layered on top. No free parameters are fitted, and no new physical entities are introduced. The most load-bearing imported item is Lemma 3.10 (coefficient map for one-input/one-output directed-cycle models), on which the entire analysis of Section 3 is built.

assumptions (8)
  • domain assumption Input-output equation formula: det(dI-A)y_i = sum_j (-1)^(i+j) det((dI-A)_{j,i}) u_j (Prop 2.10, from [19, Theorem 2]).
    The coefficient maps that all identifiability analysis is based on are derived from this cited formula.
  • domain assumption Rank criterion: generic local identifiability is equivalent to generic full rank of the coefficient-map Jacobian for strongly connected models with at least one input (Prop 2.16, from [19, Prop 2] and [21, Main Result 3]).
    This equivalence converts the differential-algebraic notion into linear algebra; the entire proof of Theorem 3.6 operates through it.
  • domain assumption Coefficient-map formula for one-input/one-output directed-cycle models with leaks: c = (e1,...,e_{n-1}, e_n-Pi, kappa, e*_1 kappa, ..., e*_{n-p} kappa) (Lemma 3.10, from [12, Prop 3.8]).
    All of Section 3 builds on this formula; it was cross-checked here against Example 2.13 and is consistent.
  • domain assumption Classification of directed-cycle models with at most one leak, and of the In={i}, Out={i-1} configuration (Prop 2.22, from [12]).
    Used for the |Leak| <= 1 case and for the exceptional models in Theorem 3.6.
  • domain assumption Adding inputs or outputs preserves identifiability (Prop 2.20, from [14]).
    Bridges minimally leak-interlacing submodels to the full model in Proposition 3.25.
  • domain assumption Spanning-incoming-forest formula for input-output equation coefficients (Lemma 5.5, from [2, Theorem 3.1], corrected in Remark 5.6).
    The engine for the catenary coefficient-map formula (Theorem 5.1).
  • domain assumption Assumption 2.2: every model has at least one input and one output, and models considered are strongly connected.
    Satisfied by directed cycles and bidirected paths; required for the coefficient-map definition of identifiability.
  • standard math Algebraic independence of elementary symmetric polynomials (Lemma 2.26(1), from [18]).
    Used with Lemma 2.18 to show the A-block of the Jacobian has nonzero determinant.

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Pith. "Pith review of Identifiability of directed-cycle and catenary linear compartment models." pith.science (2026). https://pith.science/paper/56PZZMRT

@misc{pith2026241205283,
  author       = {Pith},
  title        = {Pith review of: Identifiability of directed-cycle and catenary linear compartment models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/56PZZMRT}},
  note         = {Machine review of arXiv:2412.05283}
}
read the original abstract

A parameter of a mathematical model is structurally identifiable if it can be determined from noiseless experimental data. Here, we examine the identifiability properties of two important classes of linear compartmental models: directed-cycle models and catenary models (models for which the underlying graph is a directed cycle or a bidirected path, respectively). Our main result is a complete characterization of the directed-cycle models for which every parameter is (generically locally) identifiable. Additionally, for catenary models, we give a formula for their input-output equations. Such equations are used to analyze identifiability, so we expect our formula to support future analyses into the identifiability of catenary models. Our proofs rely on prior results on input-output equations, and we also use techniques from linear algebra and graph theory.

Figures

Figures reproduced from arXiv: 2412.05283 by the authors.

Figure 1
Figure 1. A catenary model (left), and a directed-cycle model (right). Output (p) Leaks Result Reference (any) |Leak| ≤ 1 identifiable [12, Theorem 3.4] p = 1 or p = n (see result) identifiable ⇔ |Leak| ≤ 1 [12, Theorem 3.7 and Corollary 3.11] 2 ≤ p ≤ n − 1 (see result) identifiable ⇔ leak-interlacing condition Theorem 3.6 (any) |Leak| ≥ 3 unidentifiable Corollary 3.9 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. A linear compartmental model. Definition 2.1. A linear compartmental model, denoted by (G,In, Out, Leak), consists of a finite, directed graph G = (V, E), where each vertex (or node) i ∈ V represents a compartment of the model, with three sets In, Out, Leak ⊆ V denoting the sets of input, output, and leak compartments, respectively. In a linear compartmental model, a directed edge j → i represents the flow or transf… view at source ↗
Figure 3
Figure 3. A catenary model. Example 2.5. Directed-cycle models are shown in Figures 1 and 2, while catenary models are depicted in Figures 1 and 3. 2.2. ODEs and input-output equations. To define the ODEs arising from a linear compartmental model, we use the following matrix. Definition 2.6. The compartmental matrix of a linear compartmental model (G,In, Out, Leak) with n compartments, where G = (V, E), is the n × n matrix A … view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Two exceptional models. Remark 3.2. Exceptional models are so named, because they must be excluded from the “leak-interlacing” condition (Definition 3.3 below) in order for the classification result (Theorem 3.6 below) to hold. Indeed, by part (2) of Proposition 2.22, …
Figure 5
Figure 5. Figure 5: A directed-cycle model that is not leak-interlacing. An immediate consequence of Theorem 3.6 concerns directed-cycle models with too many leaks (cf. [3, Theorem 6.1]). Corollary 3.9 (Directed-cycle models with too many leaks). If M = (G,In, Out, Leak) is a directed-cyc…
Figure 6
Figure 6. Figure 6: A leak-interlacing directed-cycle model with In = {1}, Out = {3}, and Leak = {1, 3}. For directed-cycle models with In = Out = Leak = {1}, part (2) of Theorem 4.3 implies that the singular locus contains the n − 1 coordinate hyperplanes defined by, respectively, k32 = …
Figure 7
Figure 7. Figure 7: Identifiable catenary models with three compartments, one input, one output, and zero or one leaks. SIAN code for these models is available in a supplementary data file and also accessible via the GitHub repository [11] [PITH_FULL_IMAGE:figures/full_fig_p037_7.png]
Figure 8
Figure 8. Figure 8: Catenary models with three compartments, one input, and one output. SIAN code for these models is available in a supplementary data file [PITH_FULL_IMAGE:figures/full_fig_p039_8.png]
Figure 9
Figure 9. Figure 9: Catenary models with three compartments, one input, and one output (page 2) [PITH_FULL_IMAGE:figures/full_fig_p040_9.png]
Figure 10
Figure 10. Figure 10: Catenary models with three compartments, one input, and one output (page 3) [PITH_FULL_IMAGE:figures/full_fig_p041_10.png]
Figure 11
Figure 11. Figure 11: Catenary models with three compartments, one input, and one output (page 4) [PITH_FULL_IMAGE:figures/full_fig_p042_11.png]
Figure 12
Figure 12. Figure 12: Catenary models with three compartments, one input, and one output (page 5) [PITH_FULL_IMAGE:figures/full_fig_p043_12.png]

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Structural Identifiability of Compartmental Models: Recent Progress and Future Directions

    stat.ME 2025-07 accept

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Reference graph

Works this paper leans on

23 extracted references · 15 canonical work pages · cited by 1 Pith paper

  1. [1]

    Villaverde

    Xabier Rey Barreiro and Alejandro F. Villaverde. On the origins and rarity of locally but not globally identifiable parameters in biological modeling. IEEE Access, 11:65457–65467, 2023

    2023

  2. [2]

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

    Cashous Bortner, Elizabeth Gross, Nicolette Meshkat, Anne Shiu, and Seth Sullivant. Identifiability of linear compartmental tree models and a general formula for input-output equations. Adv. in Appl. Math., 146:102490, 2023

    2023

  3. [3]

    Identifiable paths and cycles in linear compartmental models

    Cashous Bortner and Nicolette Meshkat. Identifiable paths and cycles in linear compartmental models. Bull. Math. Biol., 84(5):Paper No. 53, 43, 2022

    2022

  4. [4]

    Graph-based sufficient conditions for indistinguishability of linear compartmental models

    Cashous Bortner and Nicolette Meshkat. Graph-based sufficient conditions for indistinguishability of linear compartmental models. SIAM J. Appl. Dyn. Syst., 23(3):2179–2207, 2024

    work page 2024

  5. [5]

    Identifiability of linear compart- mental models: The impact of removing leaks and edges

    Patrick Chan, Katherine Johnston, Anne Shiu, Aleksandra Sobieska, and Clare Spinner. Identifiability of linear compart- mental models: The impact of removing leaks and edges. Preprint, arXiv:2102.04417, 2021

    arXiv 2021

  6. [6]

    Linear n-compartment catenary models: Formulas to describe tracer amount in any compartment and identification of parameters from a concentration-time curve

    Nguyen Phong Chau. Linear n-compartment catenary models: Formulas to describe tracer amount in any compartment and identification of parameters from a concentration-time curve. Math. Biosci., 76(2):185–206, 1985

    work page 1985

  7. [7]

    Compartmental analysis of dynamic nuclear medicine data: models and identifiability

    Fabrice Delbary, Sara Garbarino, and Valentina Vivaldi. Compartmental analysis of dynamic nuclear medicine data: models and identifiability. Inverse Probl., 32(12):125010, 2016

    work page 2016

  8. [8]

    Harrington, and Gleb Pogudin

    Ruiwen Dong, Christian Goodbrake, Heather A. Harrington, and Gleb Pogudin. Differential elimination for dynamical models via projections with applications to structural identifiability. SIAM Journal on Applied Algebra and Geometry, 7(1):194–235, 2023

    work page 2023

Show all 23 references
  1. [9]

    Apolarity and canonical forms for homogeneous polynomials

    Richard Ehrenborg and Gian-Carlo Rota. Apolarity and canonical forms for homogeneous polynomials. Eur. J. Combin., 14(3):157–181, 1993

    1993

  2. [10]

    A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study

    Marisa C Eisenberg and Harsh V Jain. A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study. J. Theor. Biol., 431:63–78, 2017

    2017

  3. [11]

    Identifiability of directed cycle and catenary linear compartmental models github repo

    Odalys Garcia-Lopez. Identifiability of directed cycle and catenary linear compartmental models github repo. https://github.com/odalys-garcia/Identifiability-of-Directed-Cycle-and-Catenary-Linear-Compartmental- Models

  4. [12]

    Identifiability of linear compartmental models: the effect of moving inputs, outputs, and leaks

    Seth Gerberding, Nida Obatake, and Anne Shiu. Identifiability of linear compartmental models: the effect of moving inputs, outputs, and leaks. Linear Multilinear A., 70(14):2782–2803, 2020. 32 AHMED, CREPEAU, DESSAUER, EDOZIE, GARCIA-LOPEZ, GRIMSLEY, LOPEZ, NERI, AND SHIU

    2020

  5. [13]

    Database for identifiability properties of linear compartmental models

    Natali Gogishvili. Database for identifiability properties of linear compartmental models. Preprint, arXiv:2406.16132, 2024

    2024 arXiv

  6. [14]

    Linear compartmental models: input-output equations and operations that preserve identifiability

    Elizabeth Gross, Heather Harrington, Nicolette Meshkat, and Anne Shiu. Linear compartmental models: input-output equations and operations that preserve identifiability. SIAM J. Appl. Math., 79(4):1423–1447, 2019

    2019

  7. [15]

    Identifiability of linear compartmental models: The singular locus

    Elizabeth Gross, Nicolette Meshkat, and Anne Shiu. Identifiability of linear compartmental models: The singular locus. Adv. Appl. Math., 133(C), 2022

    2022

  8. [16]

    Global identifiability of differential models

    Hoon Hong, Alexey Ovchinnikov, Gleb Pogudin, and Chee Yap. Global identifiability of differential models. Comm. Pure Appl. Math., 73(9):1831 – 1879, 2018

    2018

  9. [17]

    SIAN: software for structural identifiability analysis of ode models

    Hoon Hong, Alexey Ovchinnikov, Gleb Pogudin, and Chee Yap. SIAN: software for structural identifiability analysis of ode models. Bioinformatics, 35(16):2873–2874, 2019

    2019

  10. [18]

    I. G. Macdonald. Symmetric Functions and Hall Polynomials. Oxford University Press, 1995

    1995

  11. [19]

    Identifiability results for several classes of linear compartment models

    Nicolette Meshkat, Seth Sullivant, and Marisa Eisenberg. Identifiability results for several classes of linear compartment models. B. Math. Biol., 77(8):1620–1651, 2015

    2015

  12. [20]

    An investigation of the sources of nonuniqueness in deterministic identifiability

    JP Norton. An investigation of the sources of nonuniqueness in deterministic identifiability. Math. Biosci., 60(1):89–108, 1982

    1982

  13. [21]

    Input-output equations and identifiability of linear ode models

    Alexey Ovchinnikov, Gleb Pogudin, and Peter Thompson. Input-output equations and identifiability of linear ode models. IEEE T. Automat. Contr., 68(2):812–824, 2023

    2023

  14. [22]

    A physiology-based para- metric imaging method for FDG–PET data

    Mara Scussolini, Sara Garbarino, Gianmario Sambuceti, Giacomo Caviglia, and Michele Piana. A physiology-based para- metric imaging method for FDG–PET data. Inverse Probl., 33(12):125010, 2017

    2017

  15. [23]

    Identifiability and interval identifiability of mammillary and catenary compartmental models with some known rate constants

    Paolo Vicini, Hsiao-Te Su, and Joseph J Distefano III. Identifiability and interval identifiability of mammillary and catenary compartmental models with some known rate constants. Math. Biosci., 167(2):145–161, 2000. IDENTIFIABILITY OF DIRECTED-CYCLE AND CATENARY LINEAR COMPAR...

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