Funder Restrictions on Application Numbers Lead to Chaos.

Restricting application rates is an attractive way for funders to reduce time and money wasted evaluating uncompetitive applications. However, mathematical models show that this could induce chaotic cycles in total application numbers, increasing uncertainty in the funding process. One emergent property is that smaller institutions spend disproportionally more time unfunded.

The input-output relationship approach to structural identifiability analysis.

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. However 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. These techniques are applied to analyse classical models from biomedical systems modelling and those of enzyme catalysed reaction schemes.