Tim Dunne

Modelling fire-return interval T: Stochasticity and censoring in the two-parameter Weibull model

Abstract Biologists are heavily reliant on the characterisation and description of disturbance phenomena and disturbance regimes. This dependency is well illustrated within research on fire recurrence and models of fire-frequency. It is well understood that the process of fire-return is subject to stochastic variation. However, a deterministic paradigm underlies many contemporary studies of fire-frequency to the possible detriment of robust ecological description. It is also commonplace for data on historical fire processes to contain some degree of either partial or missing data. Yet the parameter estimators of the prevailing two-parameter Weibull model of fire-recurrence are rarely seen to account for incomplete data structuring. The consequences of ignoring the structure of incomplete data will likely lead to misrepresentation of predicted fire frequencies and trends. In this paper, we introduce methods for incorporating parameter stochasticity into the two-parameter Weibull model under different degrees of data censoring. Both the explicit handling of censored fire observations and the intrusion of variability about the average predicted patterns in inter-fire interval recurrence are obligatory to any modelling that admits an effective ecological and evolutionary interpretation. These points are well illustrated through a worked example on modelling the fire-return interval regime within the Cape of Good Hope Nature Reserve, South Africa. Here, the observed process of fire recurrence is seen to include a substantial stochastic component about the trends predicted from the two-parameter Weibull model. The implications of a stochastic fire-regime interpretation to both management practises and to the evolutionary understanding of fynbos vegetation are discussed.

Spinal Cord Protection in the Absence of Collateral Circulation: Meta‐Analysis of Mortality and Paraplegia

A meta‐analysis of paraplegia complicating aortic surgery on patients having neither intercostal nor spinal collaterals, epitomized by patients with acute traumatic aortic rupture, was done. Index Medicus and Medline were searched for all suitable English publications between 1972 and 1992. New paraplegia occurred in 9.9% of 1492 patients who underwent surgery. However, 19.2% of patients undergoing surgery with only simple aortic cross‐clamping developed paraplegla, in contrast to 6.1% if distal aortic perfusion was augmented by either “passive” or “active” methods (p < 0.00001). The risk of paraplegia increased progressively as cross‐clamp times lengthened if simple aortic cross‐clamping was used (p < 0.00001), but only once did the cross‐clamp time exceed 30 minutes (p < 0.05). Paraplegia occurred in 8.2% of patients with “passive” shunts from the ascending aorta (p < 0.001 vs simple cross‐clamping). Shunts from the left ventricular apex, however, had an incidence of paraplegia of 26.1% and, therefore, did not decrease the risk of paraplegia. “Active” augmentation of distal perfusion had the lowest risk of paraplegia: 2.3% (p < 0.00001 vs simple cross‐clamping or “passive” shunts). Mortality, however, was higher in these potentially polytraumatized patients when they were perfused distally using methods requiring full systemic heparinization (18.2%), compared to mortality with methods not requiring heparin (11.9%; p < 0.01). In conclusion, simple aortic cross‐clamping has a high risk of paraplegia if the cross‐clamp time extends beyond 30 minutes. “Active” modalities of augmenting distal perfusion provide optimal spinal protection. (J Card Surg 1994;9:685–691)

Morphine Suppresses the Oxytocin Response in Breast-Feeding Women

The activity of opiate-mediated regulatory mechanisms of oxytocin secretion during breast-feeding was studied by the administration of either morphine, naloxone or placebo to women prior to the commencement of breast-feeding. Seventeen healthy women in the first week after delivery who had established lactation were ramdomized to receive either intravenous morphine 5 mg (n = 6), naloxone 2.4 mg (n = 6) or a placebo, sterile water (n = 5), which was given prior to commencement of breast-feeding. Oxytocin levels were measured by radioimmunoassay prior to initiation of breast-feeding and then at 2-min intervals until the feed was complete. Breast-feeding produced a significant rise in oxytocin levels in the control and naloxone groups but no significant rise in the patients given morphine. There was a significant reduction in oxytocin response following morphine administration when compared to placebo but not between naloxone and placebo. In conclusion, oxytocin secretion to breast-feeding is inhibited by exogenous morphine when compared to a control group but the administration of naloxone did not produce a significant difference from control.

Textbooks, teaching and learning in primary mathematics classrooms

Abstract This paper describes a research project that was undertaken to explore the impact of a textbook, Maths for all, in primary mathematics classrooms. A quasi-experimental design was used, and a random sample of 14 classrooms from ex-DET primary schools in Cape Town was selected, 10 of which were given class sets of the textbook at the start of the project, and 4 were given these sets only after the project was completed. Data from interviews, questionnaires, classroom observation and pre-and post-tests were collected. An analysis of aspects of the textbook was undertaken, and of its use by teachers in classrooms. It is argued that the inductive style prioritised by the textbook is in tension with the preferred deductive style of most of the teachers, resulting in the fragmenting of its semantic structure. Statistical analysis of pre- and post-tests revealed no educationally significant differences between students with access to the textbook and those without access. The majority of learners (n=538) performed very poorly on the test. While the data analysis does not allow strong claims to be made about the impact of the textbook on learner performance, it raises important pedagogic issues about the contexts into which textbooks are inserted, especially with respect to the specialisation of time.

Diagnostics for Regression-Arma Time Series

In the context of ARMA time series, two types of outlier have been treated in the literature. These are the observation (type I) and the innovation (type II) outlier. Commonly these outliers have been modelled as mean-shift outliers, but variance-shift outliers may also be considered. In this paper we formulate the resulting 4 outlier types (mean-shift observation outlier, variance-shift observation outlier, mean-shift innovation outlier, and variance-shift innovation outlier) as perturbation schemes, in the manner of Cook(1986). Then we propose 3 types of diagnostics for these perturbation schemes, namely residuals, which will indicate the size of the perturbation in question, diagnostics for the potential influence of a perturbation, and diagnostics for the actual or observed influence of a perturbation.

Pre-school follow-up of a cohort of children with myelomeningocele in Cape Town, South Africa.

A cohort of South African children with myelomeningocele was followed for 5 years. Fifty-three were from metropolitan Cape Town and 65 from rural areas including the tribal region of Transkei. The mean general developmental quotient (GQ) at 5 years of age was lower than that previously reported. Black and coloured children had lower GQs than white children, but there were no significant differences between those from the urban and the rural areas. Early closure of the lesion and delivery by caesarean section were associated with higher levels of general developmental functioning. Central nervous system infections and the placement of more than one shunt for hydrocephalus resulted in lower GQs. Lesions above L2 were associated with non-ambulation. Ambulation was more likely in children in Cape Town than in rural children. Urinary incontinence occurred more frequently in rural children and among those in lower socio-economic circumstances.

Numerical recipes for disaster: changing hazard and the stand-origin-map

The quantitative study of predictable temporal characteristics of disturbance phenomena is of tremendous consequence for both an effective understanding of biological process and for successful implementation of sustainable practices. This reliance is well demonstrated in both pure (e.g. biodiversity research) and applied (e.g. forestry sciences) research into patterns of fire-recurrence and its consequent interpretation and management implications. Much of fire-frequency prediction is dependent on the data manifest in a stand-origin-map. In this paper, we review the statistical methods for fire-frequency estimation from a stand-origin-map, where fire-recurrence is governed by an underlying probabilistic process that changes with time since last occurrence (i.e. non-constant hazard). We argue that both patterns of fire-recurrence that change with time are likely to be commonplace biological phenomena and that the conventionally prescribed methods for non-constant hazard fire-recurrence estimation from a stand-origin-map are erroneous. Even modified maximum-likelihood techniques that account for different degrees of data censoring are likely to be severely restrained in their capacity for rigorous estimation. We propose a novel formulation whereby the two-parameter Weibull distribution can be fitted retrospectively to the data in a stand-origin-map. This formulation is explored through an example from the Canadian Rockies.

The effect of morphine and naloxone administration on maternal oxytocin concentration in late pregnancy

OBJECTIVE Modification of the inhibitory control of oxytocin secretion by endogenous opiates in late pregnancy may be one of the factors involved in the onset of labour. The interrelationships between exogenously administered opioids and oxytocin may demonstrate activity of this control mechanism.

Health Belief Model Interpretation of Compliance Factors in a Weight Loss and Cardiac Rehabilitation Programme

The aim of the research was to establish the common and/or different factors associated with compliance or noncompliance in either a weight loss or a cardiac rehabilitation programme. A questionnaire was designed from a revised formulation of the original Health Belief Model and a pilot study was run on 22 weight loss and 13 cardiac subjects. The modified questionnaire was then completed by 37 compliers and 19 noncompliers with a weight loss programme and 11 compliers and 19 noncompliers with a cardiac rehabilitation programme. Compliance was associated with exercise enjoyment, self-motivation, and the need to stay on the programme. The major reasons for noncompliance were the complexity of the required behaviour changes, inconvenience, time constraints, and the ability to cope independently of the programmes. Particularly regarding the weight loss programme, noncompliance arising from the required simultaneous changes to eating and exercise patterns could be reduced by teaching alternative coping skills and realistic goal setting. Cardiac patients are faced with the life-threatening nature of their disease, but there is a lack of overt disease symptoms among weight loss subjects. This results in a need to inform obese subjects, preferably using a multi-disciplinary approach, about the health risks resulting from noncompliance.

Applying Rasch Measurement in Mathematics Education Research: Steps towards a Triangulated Investigation into Proficiency in the Multiplicative Conceptual Field.

Educational measurement is generally thought of as empirical, quantitative, and large-scale, whose purpose is to monitor educational systems. Sociocognitive studies, on the other hand, are associated with small-scale, theoretical, and qualitative studies, the purpose of which is to conduct fine-grained analysis of learning or teaching, or to comprehend in depth the development of a mathematical topic. This article describes an application of the Rasch model in mathematics education in which theory and measurement are used interactively to provide greater understanding of a constellation of mathematical concepts within the multiplicative conceptual field. It is affirmed here that Rasch measurement provides the basis for a coherent research model based on principles of measurement, while giving consideration to the theoretical construct. Challenges to educational measurement demand that researchers provide substantive theoretical models to support, firstly, educational measurement and, secondly, the level of inference that can be made from the measurement outcomes.