A reconstruction and extension of Maple’s assume facility via constraint contextual rewriting

Armando, Alessandro; Ballarin, Clemens

doi:10.1016/j.jsc.2004.12.010

Cited by 4 publications

(7 citation statements)

References 6 publications

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“…Often this is a commercial product, such as Maple™, Mathematica, or MATLAB. However, as for all complex computer code, one cannot necessarily guarantee that results produced by a CAS will be correct in all situations (see, for example, [2] noting a limitation of certain versions of Maple™). As such, it is good practice for us to check that results obtained from one CAS agree with those from another.…”

Section: Reproducibility Of Analysismentioning

confidence: 99%

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Model structures and structural identifiability: What? Why? How?

Whyte

2021

Preprint

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We may attempt to encapsulate what we know about a physical system by a model structure, S. This collection of related models is defined by parametric relationships between system features; say observables (outputs), unobservable variables (states), and applied inputs. Each parameter vector in some parameter space is associated with a completely specified model in S. Before choosing a model in S to predict system behaviour, we must estimate its parameters from system observations. Inconveniently, multiple models (associated with distinct parameter estimates) may approximate data equally well. Yet, if these equally valid alternatives produce dissimilar predictions of unobserved quantities, then we cannot confidently make predictions. Thus, our study may not yield any useful result.We may anticipate the non-uniqueness of parameter estimates ahead of data collection by testing S for structural global identifiability (SGI). Here we will provide an overview of the importance of SGI, some essential theory and distinctions, and demonstrate these in testing some examples.

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Section: Reproducibility Of Analysismentioning

confidence: 99%

“…We expect to anticipate the non-uniqueness of parameter estimates when scrutiny of our structure shows that it is not structurally globally identifiable (SGI). 2 The concept was first formalised for state-space structures in Bellman and Åström [4] with reference to compartmental structures similar to that shown in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Model structures and structural identifiability: What? Why? How?

Whyte

2021

Preprint

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“…An uncontrolled positive LTI state-space structure with indices n, k ∈ N is a ULTI state-space structure having representative system of the form given in (1), where states and outputs are restricted to non-negative values. That is, the structure has X = Rn + and Y = Rk + .…”

Section: Linear Time-invariant Structuresmentioning

confidence: 99%

“…We demonstrate key concepts through a consideration of continuous-time, uncontrolled, linear time-invariant state-space (henceforth, for brevity, ULTI) structures. 1 More particularly, we consider the "compartmental" (that is, subject to conservation of mass conditions) subclass of ULTI structures, which arise in various modelling applications. Some standard test methods may not be appropriate for compartmental structures, which guides our choice of test method here.…”

Section: Introductionmentioning

confidence: 99%

“…We note recent concerns around reproducibility in computational biology (see, for example, Laubenbacher and Hastings [6]). Reproducibility is impeded when symbolic algebra packages behave inconsistently (as noted for Maple's assume command by Armando and Ballarin [1]). We intend that our routines will facilitate the checking of SGI test results obtained from either an alternative testing method, or from code written in another language.…”

Section: Introductionmentioning

confidence: 99%

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Branching out into Structural Identifiability Analysis with Maple: Interactive Exploration of Uncontrolled Linear Time-Invariant Structures

Whyte

2021

Preprint

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Suppose we wish to predict the behaviour of a physical system. We may choose to represent the system by model structure S (a set of related mathematical models defined by parametric relationships between system variables), and a parameter set Θ. Each parameter vector in Θ is associated with a completely specified model in S. We use S with system observations in estimating the "true" (unknown) parameter vector. Inconveniently, multiple parameter vectors may cause S to approximate the data equally well. If we cannot distinguish between such alternatives, and these lead to dissimilar predictions, we cannot confidently use S in decision making. This result may render efforts in data collection and modelling fruitless. This outcome occurs when S lacks the property of structural global identifiability (SGI). Fortunately, we can test various classes of structures for SGI prior to data collection. A non-SGI result may guide changes to our structure or experimental design towards obtaining a better outcome. We aim to assist the testing of structures for SGI through bespoke Maple 2020 procedures. We consider continuous-time, uncontrolled, linear timeinvariant state-space structures. Here, the time evolution of the statevariable vector x is modelled by a system of constant-coefficient, ordinary differential equations. We utilise the "transfer function" approach, which is also applicable to the "compartmental" subclass (mass is conserved). Our use of Maple's "Explore" enables an interactive consideration of a parent structure and its variants, obtained as the user changes which components of x are observed, or have non-zero initial conditions. Such changes may influence the information content of the idealised output available for the SGI test, and hence, its result. Our approach may inform the interactive analysis of structures from other classes.

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Model Structures and Structural Identifiability: What? Why? How?

Whyte

2021

2019-20 MATRIX Annals

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A reconstruction and extension of Maple’s assume facility via constraint contextual rewriting

Cited by 4 publications

References 6 publications

Model structures and structural identifiability: What? Why? How?

Model structures and structural identifiability: What? Why? How?

Branching out into Structural Identifiability Analysis with Maple: Interactive Exploration of Uncontrolled Linear Time-Invariant Structures

Model Structures and Structural Identifiability: What? Why? How?

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