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A dynamic model is structurally identifiable if it is possible to infer its unknown parameters by observing its output. Structural identifiability depends on the system dynamics, output, and input, as well as on the specific values of initial conditions and parameters. Here we present a symbolic method that characterizes the input that a model requires to be structurally identifiable. It determines which derivatives must be non-zero in order to have a sufficiently exciting input. Our approach considers structural identifiability as a generalization of nonlinear observability and incorporates extended Lie derivatives. The methodology assesses structural identifiability for time-varying inputs and, additionally, it can be used to determine the input profile that is required to make the parameters structurally locally identifiable. Furthermore, it is sometimes possible to replace an experiment with time-varying input with multiple experiments with constant inputs. We implement the resulting method as a MATLAB toolbox named STRIKE-GOLDD2. This tool can assist in the design of new experiments for the purpose of parameter estimation

A parameter is structurally identifiable if its value can theoretically be estimated by observing the model output. Structural identifiability is a desirable property in biological modelling: if a parameter is structurally unidentifiable, its estimated numerical value is meaningless, and model predictions of unmeasured state variables can be wrong, compromising the ability of the model to provide biological insight. Structural identifiability depends on the system dynamics, observation function (model output), initial conditions, and external inputs. In this paper we focus on the last factor. Methods for structural identifiability analysis typically classify a model as identifiable provided that it is fed with sufficiently exciting inputs. For example, a given model may require a time-varying input to be structurally identifiable, while for another model a constant non-zero input may be enough. Here we present a method that determines how sufficiently exciting an input should be. The approach builds on the STRIKE-GOLDD toolbox, which considers structural identifiability as generalized observability. The approach incorporates extended Lie derivatives, which correctly assess structural identifiability in the case of time-varying inputs. The procedure can also be used to determine the type of input profile that is required to make the parameters identifiable. This capability is helpful when designing new experiments for the purpose of parameter estimation

Analysis of the identifiability of a given model system is an essential prerequisite to the determination of model parameters from physical data. However, the tools available for the analysis of non-linear systems can be limited both in applicability and by computational intractability for any but the simplest of models. The input-output relation of a model summarises the input-output structure of the whole system and as such provides the potential for an alternative approach to this analysis. In order for this approach to be valid it is necessary to determine whether the monomials of a differential polynomial are linearly independent. A simple test for this property is presented in this work. The derivation and analysis of this relation can be implemented symbolically within Maple either using the built-in Rosenfeld_Groebner algorithm or via the observability normal form, an alternative representation of the model derived from observability criteria. These techniques are applied to analyse models of two reaction schemes. Such systems form the building blocks of metabolic pathway models which are increasingly used in drug discovery and development.

This dissertation is an examination of community as it exists in selected Ramblers, Rasselas, the Dictionary, and the Lives of the Poets. My readings of Johnson's texts challenge the valuation of Johnson as little more than a Christian moralist, as well as question the notion of Johnson's authoritarianism. Indeed, Johnson continually subverts his own authority by placing it in the hands of other speakers (as in the female Ramblers and Rasselas) and in other writers (as in the Dictionary and the Lives of the Poets). As Johnson explores various facets of community, he argues against the increased impact of commercialization, consumerism, imperialism, colonial exploitation, and examines the social roles allotted to women and men in England. Underlying the ethical arguments in the Rambler, the search for “the choice of life” in Rasselas, the construction of the Dictionary, and the interactions of authors in the Lives of the Poets is community in many forms and manifestations. The primary impulse for community derives from a desire to counterbalance the rise of self-interest and social fragmentation caused by changes in the socioeconomic structure of eighteenth-century England. Though he is pleased that the rise of a capital-based economic system has made more wealth available to more Englishmen, he also sees the devastation this economic system brings with it. In the end, Johnson critiques the morality underlying the rush for individual wealth and personal satisfaction, which he finds at odds with the concerns of the commonwealth and with communal good. I examine four types of community in Johnson's texts. These communities are centered around women's roles in society in selected Ramblers , the conflicts within and alternatives to families in Rasselas , the linguistic communities existing in the Dictionary, and a large literary community in the Lives of the Poets. By reading Johnson's texts as meditations on community, we open up Johnson's ideas to interpretations of br