A method for the reconstruction of unknown non-monotonic growth functions in the chemostat

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out (reconstruct) the whole graph of the growth function. The process of tracing out the graph can be performed either continuously or step-wise. We present and compare both approaches. Even in the case of two species in competition, which is not directly accessible with our approach due to lack of controllability, feedback control improves identifiability of the non-dominant growth rate.Comment: expansion of ideas from proceedings paper (17 pages, 8 figures), proceedings paper is version v

Renewed and emerging concerns over the production and emission of ozone-depleting substances

Stratospheric ozone depletion, first observed in the 1980s, has been caused by the increased production and use of substances such as chlorofluorocarbons (CFCs), halons and other chlorine-containing and bromine-containing compounds, collectively termed ozone-depleting substances (ODSs). Following controls on the production of major, long-lived ODSs by the Montreal Protocol, the ozone layer is now showing initial signs of recovery and is anticipated to return to pre-depletion levels in the mid-to-late twenty-first century, likely 2050–2060. These return dates assume widespread compliance with the Montreal Protocol and, thereby, continued reductions in ODS emissions. However, recent observations reveal increasing emissions of some controlled (for example, CFC-11, as in eastern China) and uncontrolled substances (for example, very short-lived substances (VSLSs)). Indeed, the emissions of a number of uncontrolled VSLSs are adding significant amounts of ozone-depleting chlorine to the atmosphere. In this Review, we discuss recent emissions of both long-lived ODSs and halogenated VSLSs, and how these might lead to a delay in ozone recovery. Continued improvements in observational tools and modelling approaches are needed to assess these emerging challenges to a timely recovery of the ozone layer

Testing non-correlation and non-causality between two multivariate ARMA time series

Haugh [Journal of the American Statistical Association (1976) Vol. 71, pp. 378–85] developed an approach to the problem of testing non-correlation (at all leads and lags) between two univariate time series. Haugh's tests however have low power against two series which are related over a long distributed lag when individual lag coefficients are relatively small. As a remedy, Koch and Yang [Journal of the American Statistical Association (1986) Vol. 8, pp. 533–44] proposed an alternative method that performs better than Haugh's under such dependencies. A multivariate extension of Haugh's procedure was proposed by El Himdi and Roy [The Canadian Journal of Statistics (1997) Vol. 25, pp. 233–56], but suffers the same weaknesses as the original univariate method. We develop here an asymptotic test generalizing Koch and Yang's method to the multivariate case. Our method includes El Himdi and Roy's as a special case. Based on the same idea, we also suggest a generalization of the El Himdi and Roy procedure for testing causality in the sense of Granger [Econometrica (1969) Vol. 37, pp. 424–38] between two multivariate series. A Monte Carlo study is conducted, which indicates that our approach performs better than El Himdi and Roy's for a wide range of models. Both procedures are applied to the problem of testing the absence of correlation between Canadian and US economic indicators, and to a brief study of causality between money and income in Canada.FLWINinfo:eu-repo/semantics/publishe