Rejoinder to James Hamilton

Hamilton (2001) makes a number of comments on our paper (Harding and Pagan, 2002b). The objectives of this rejoinder are, firstly, to note the areas in which we agree; secondly, to define with greater clarity the areas in which we disagree; and, thirdly, to point to other papers, including a longer version of this response, where we have dealt with some of the issues that he raises. The core of our debate with him is whether one should use an algorithm with a specified set of rules for determining the turning points in economic activity or whether one should use a parametric model that features latent states. Hamilton begins his criticism by stating that there is a philosophical distinction between the two methods for dating cycles and concludes that the method we use “leaves vague and intuitive exactly what this algorithm is intended to measure”. Nothing is further from the truth. When seeking ways to decide on whether a turning point has occurred it is always useful to ask the question, what is a recession? Common usage suggests that it is a decline in the level of economic activity that lasts for some time. For this reason it has become standard to describe a recession as a decline in GDP that lasts for more than two quarters. Finding periods in which quarterly GDP declined for two periods is exactly what our approach does. What is vague about this?

Elucidating the links between UV radiation and vitamin D synthesis : using an in vitro model

Ultraviolet radiation (UV) is the carcinogen that causes the most common malignancy in humans – skin cancer. However, moderate UV exposure is essential for producing vitaminDin our skin. VitaminDincreases the absorption of calcium from the diet, and adequate calcium is necessary for the building and maintenance of bones. Thus, low levels of vitamin D can cause osteomalacia and rickets and contribute to osteoporosis. Emerging evidence also suggests vitamin D may protect against falls, internal cancers, psychiatric conditions, autoimmune diseases and cardiovascular diseases. Since the dominant source of vitamin D is sunlight exposure, there is a need to understand what is a “balanced” level of sun exposure to maintain an adequate level of vitamin D but minimise the risks of eye damage, skin damage and skin cancer resulting from excessive UV exposure. There are many steps in the pathway from incoming solar UV to the eventual vitamin D status of humans (measured as 25-hydroxyvitamin D in the blood), and our knowledge about many of these steps is currently incomplete. This project begins by investigating the levels of UV available for synthesising vitamin D, and how these levels vary across seasons, latitudes and times of the day. The thesis then covers experiments conducted with an in vitro model, which was developed to study several aspects of vitamin D synthesis. Results from the model suggest the relationship between UV dose and vitamin D is not linear. This is an important input into public health messages regarding ‘safe’ UV exposure: larger doses of UV, beyond a certain limit, may not continue to produce vitamin D; however, they will increase the risk of skin cancers and eye damage. The model also showed that, when given identical doses of UV, the amount of vitamin D produced was impacted by temperature. In humans, a temperature-dependent reaction must occur in the top layers of human skin, prior to vitamin D entering the bloodstream. The hypothesis will be raised that cooler temperatures (occurring in winter and at high latitudes) may reduce vitamin D production in humans. Finally, the model has also been used to study the wavelengths of UV thought to be responsible for producing vitamin D. It appears that vitamin D production is limited to a small range of UV wavelengths, which may be narrower than previously thought. Together, these results suggest that further research is needed into the ability of humans to synthesise vitamin D from sunlight. In particular, more information is needed about the dose-response relationship in humans and to investigate the proposed impact of temperature. Having an accurate action spectrum will also be essential for measuring the available levels of vitamin D-effective UV. As this research continues, it will contribute to the scientific evidence-base needed for devising a public health message that will balance the risks of excessive UV exposure with maintaining adequate vitamin D.

Accurate series solutions for gravity-driven Stokes waves

In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

Exponential asymptotics with multiple stokes lines

When asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they are unable to demonstrate behaviour that occurs on a scale that is exponentially small compared to the algebraic terms of the asymptotic series. There are many examples of physical systems where behaviour on this scale has important effects and, as such, a range of techniques known as exponential asymptotic techniques were developed that may be used to examinine behaviour on this exponentially small scale. Many problems in applied mathematics may be represented by behaviour within the complex plane, which may subsequently be examined using asymptotic methods. These problems frequently demonstrate behaviour known as Stokes phenomenon, which involves the rapid switches of behaviour on an exponentially small scale in the neighbourhood of some curve known as a Stokes line. Exponential asymptotic techniques have been applied in order to obtain an expression for this exponentially small switching behaviour in the solutions to orginary and partial differential equations. The problem of potential flow over a submerged obstacle has been previously considered in this manner by Chapman & Vanden-Broeck (2006). By representing the problem in the complex plane and applying an exponential asymptotic technique, they were able to detect the switching, and subsequent behaviour, of exponentially small waves on the free surface of the flow in the limit of small Froude number, specifically considering the case of flow over a step with one Stokes line present in the complex plane. We consider an extension of this work to flow configurations with multiple Stokes lines, such as flow over an inclined step, or flow over a bump or trench. The resultant expressions are analysed, and demonstrate interesting implications, such as the presence of exponentially sub-subdominant intermediate waves and the possibility of trapped surface waves for flow over a bump or trench. We then consider the effect of multiple Stokes lines in higher order equations, particu- larly investigating the behaviour of higher-order Stokes lines in the solutions to partial differential equations. These higher-order Stokes lines switch off the ordinary Stokes lines themselves, adding a layer of complexity to the overall Stokes structure of the solution. Specifically, we consider the different approaches taken by Howls et al. (2004) and Chap- man & Mortimer (2005) in applying exponential asymptotic techniques to determine the higher-order Stokes phenomenon behaviour in the solution to a particular partial differ- ential equation.

Thinking Collaboratively about the Peer-Review Process for Journal- Article Publication

In this conversation, Kevin K. Kumashiro shares his reflections on challenges to publishing anti-oppressive research in educational journals. He then invites eight current and former editors of leading educational research journals--William F. Pinar, Elizabeth Graue, Carl A. Grant, Maenette K. P. Benham, Ronald H. Heck, James Joseph Scheurich, Allan Luke, and Carmen Luke--to critique and expand on his analysis. Kumashiro begins the conversation by describing his own experiences submitting manuscripts to educational research journals and receiving comments by anonymous reviewers and journal editors. He suggests three ways to rethink the collaborative potential of the peer-review process: as constructive, as multilensed, and as situated. The eight current and former editors of leading educational research journals then critique and expand Kumashiro's analysis. Kumashiro concludes the conversation with additional reflections on barriers and contradictions involved in advancing anti-oppressive educational research in educational journals. (Contains 3 notes.)

Constraints of nutrient availability on primary production in two alpine tundra communities

A nutrient amendment experiment was conducted for two growing seasons in two alpine tundra communities to test the hypotheses that: (1) primary production is limited by nutrient availability, and (2) physiological and developmental constraints act to limit the responses of plants from a nutrient-poor community more than plants from a more nutrient-rich community to increases in nutrient availability. Experimental treatments consisted of N, P, and N+P amendments applied to plots in two physiognomically similar communities, dry and wet meadows. Extractable N and P from soils in nonfertilized control plots indicated that the wet meadow had higher N and P availability. Photosynthetic, nutrient uptake, and growth responses of the dominants in the two communities showed little difference in the relative capacity of these plants to respond to the nutrient additions. Aboveground production responses of the communities to the treatments indicated N availability was limiting to production in the dry meadow community while N and P availability colimited production in the wet meadow community. There was a greater production response to the N and N+P amendments in the dry meadow relative to the wet meadow, despite equivalent functional responses of the dominant species of both communities. The greater production response in the dry meadow was in part related to changes in community structure, with an increase in the proportion of graminoid and forb biomass, and a decrease in the proportion of community biomass made up by the dominant sedge Kobresia myosuroides. Species richness increased significantly in response to the N+P treatment in the dry meadow. Graminoid biomass increased significantly in the wet meadow N and N+P plots, while forb biomass decreased significantly, suggesting a competitive interaction for light. Thus, the difference in community response to nutrient amendments was not the result of functional changes at the leaf level of the dominant species, but rather was related to changes in community structure in the dry meadow, and to a shift from a nutrient to a light limitation of production in the wet meadow.

James Street market, Brisbane : a subtropical retail case study

Climate change mitigation is driving demand for energy-efficient and environmentally conscious commercial buildings in Australia. In the Australian subtropics, high rainfall, warm weather and humidity present unique challenges and opportunities for the architects tasked with designing eco-sensitive projects. The case of the James Street Market in Brisbane’s Fortitude Valley shows that climate-responsive design is an effective approach for reducing the environmental impact of commercial developments. The James Street Market combines climate-responsiveness, environmentally sensitive design strategies and smart planning to create a more sustainable retail precinct. This paper details the design strategies featured in the James Street Market, the project that kicked off a renaissance in climate-responsive commercial building design in Brisbane.