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    Berger, Stanley A. This behavior seems to be inconsistent with the strong time-like axial evolution of the flow, as expressed explicitly, for example, by the quasi-cylindrical approximate equations for this flow. An order-of-magnitude analysis of the equations of motion near breakdown leads to a modified set of governing equations, analysis of which demonstrates that the interplay between radial inertial, pressure, and viscous forces gives an elliptic character to these concentrated swirling flows.

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    Analytical, asymptotic, and numerical solutions of a simplified non-linear equation are presented; these qualitatively exhibit the features of vortex onset and location noted above. It may well be that some of these parameters cannot be derived from observed data via regression techniques.

    Such parameters are said to be unidentifiable, the remaining parameters being identifiable.

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    Closely related to this idea is that of redundancy, that a set of parameters can be expressed in terms of some smaller set. Before data is analysed it is critical to determine which model parameters are identifiable or redundant to avoid ill-defined and poorly convergent regression.

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    These are based on local properties of the likelihood, in particular the rank of the Hessian matrix. We relate these to the notions of parameter identifiability and redundancy previously introduced by Rothenberg Econometrica 39 and Catchpole and Morgan Biometrika 84 Within the widely used exponential family, parameter irredundancy, local identifiability, gradient weak local identifiability and weak local identifiability are shown to be largely equivalent.

    We consider applications to a recently developed Vladislav Gilka binary options of cancer models of Little and Wright Math Biosciences and Little et al.

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    J Theoret Biol that generalize a large number of other recently used quasi-biological cancer models.