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Scientific analysis often relies on the ability to make accurate predictions of a system’s dynamics. Mechanistic models, parameterized by a number of unknown parameters, are often used for this purpose. Accurate estimation of the model state and parameters prior to prediction is necessary, but may be complicated by issues such as noisy data and uncertainty in parameters and initial conditions. At the other end of the spectrum exist nonparametric methods, which rely solely on data to build their predictions. While these nonparametric methods do not require a model of the system, their performance is strongly influenced by the amount and noisiness of the data. In this article, we consider a hybrid approach to modeling and prediction which merges recent advancements in nonparametric analysis with standard parametric methods. The general idea is to replace a subset of a mechanistic model’s equations with their corresponding nonparametric representations, resulting in a hybrid modeling and prediction scheme. Overall, we find that this hybrid approach allows for more robust parameter estimation and improved short-term prediction in situations where there is a large uncertainty in model parameters. We demonstrate these advantages in the classical Lorenz-63 chaotic system and in networks of Hindmarsh-Rose neurons before application to experimentally collected structured population data. [ABSTRACT FROM AUTHOR]

From time to time, novel ways of interpreting and modifying ageing mechanisms are proposed. Occasionally, these lead to a conceptual dead end, whereas at other times new and vital insights into basic ageing mechanisms are gained. This review concentrates on one such way of interpreting and manipulating ageing processes, based on chaos (dynamical systems) theory. One prediction of this theory is that a wide-ranging loss of physiological complexity from molecular to cellular, and from tissue to organismic levels accompanies ageing and age-related diseases. Although this view has been criticised, and arguments have been put forward to claim that there is also an increase of complexity during ageing and dysfunction, this review holds that the interpretation of ageing as a simplification of physiological dynamical complexity offers clear advantages. Ageing changes can be quantified and the results of treatment monitored. Clinical benefits can be predicted and intervention strategies improved. Two main practical suggestions for achieving successful ageing at the clinical level are examined. First, chaos theory challenges the traditional pharmacological regimes and implies that, for maximum benefit, medication aimed at modifying some of the signs of ageing should be given at irregular, pulsed or multiple intervals, and at constantly changing dosage strengths. Second, for preventing age-related disability, it is necessary to introduce and maintain a multiplicity of external and internal physiological stimuli, such as variable physical and mental exercise regimes. [ABSTRACT FROM AUTHOR]