Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Ice-sheet contributions to future sea-level change

Accurate simulation of ice-sheet surface mass balance requires higher spatial resolution than is afforded by typical atmosphere-ocean general circulation models (AOGCMs), owing, in particular, to the need to resolve the narrow and steep margins where the majority of precipitation and ablation occurs. We have developed a method for calculating mass-balance changes by combining ice-sheet average time-series from AOGCM projections for future centuries, both with information from high-resolution climate models run for short periods and with a 20 km ice-sheet mass-balance model. Antarctica contributes negatively to sea level on account of increased accumulation, while Greenland contributes positively because ablation increases more rapidly. The uncertainty in the results is about 20% for Antarctica and 35% for Greenland. Changes in ice-sheet topography and dynamics are not included, but we discuss their possible effects. For an annual- and area-average warming exceeding 4.5 +/- 0.9 K in Greenland and 3.1 +/- 0.8 K in the global average, the net surface mass balance of the Greenland ice sheet becomes negative, in which case it is likely that the ice sheet would eventually be eliminated, raising global-average sea level by 7 m.

Life and death in a civitas capital: metabolic disease and trauma in the children from late Roman Dorchester, Dorset

The impact that “Romanization” and the development of urban centers had on the health of the Romano-British population is little understood. A re-examination of the skeletal remains of 364 nonadults from the civitas capital at Roman Dorchester (Durnovaria) in Dorset was carried out to measure the health of the children living in this small urban area. The cemetery population was divided into two groups; the first buried their dead organized within an east–west alignment with possible Christian-style graves, and the second with more varied “pagan” graves, aligned north–south. A higher prevalence of malnutrition and trauma was evident in the children from Dorchester than in any other published Romano-British group, with levels similar to those seen in postmedieval industrial communities. Cribra orbitalia was present in 38.5% of the children, with rickets and/or scurvy at 11.2%. Twelve children displayed fractures of the ribs, with 50% of cases associated with rickets and/or scurvy, suggesting that rib fractures should be considered during the diagnosis of these conditions. The high prevalence of anemia, rickets, and scurvy in the Poundbury children, and especially the infants, indicates that this community may have adopted child-rearing practices that involved fasting the newborn, a poor quality weaning diet, and swaddling, leading to general malnutrition and inadequate exposure to sunlight. The Pagan group showed no evidence of scurvy or rib fractures, indicating difference in religious and child-rearing practices but that both burial groups were equally susceptible to rickets and anemia suggests a shared poor standard of living in this urban environment.

Inbreeding depression and founder diversity among captive and free-living populations of the endangered pink pigeon Columba mayeri

The endemic pink pigeon has recovered from less than 20 birds in the mid-1970s to 355 free-living individuals in 2003. A major concern for the species' recovery has been the potential genetic problem of inbreeding. Captive pink pigeons bred for reintroduction were managed to maximise founder representation and minimise inbreeding. In this paper, we quantify the effect of inbreeding on survival and reproductive parameters in captive and wild populations and quantify DNA sequence variation in the mitochondrial d-loop region for pink pigeon founders. Inbreeding affected egg fertility, squab, juvenile and adult survival, but effects were strongest in highly inbred birds (F≥0.25). Inbreeding depression was more apparent in free-living birds where even moderate levels of inbreeding affected survival, although highly inbred birds were equally compromised in both captive and wild populations. Mitochondrial DNA haplotypic diversity in pink pigeon founders is low, suggesting that background inbreeding is contributing to low fertility and depressed productivity in this species, as well as comparable survival of some groups of non-inbred and nominally inbred birds. Management of wild populations has boosted population growth and may be required long-term to offset the negative effects of inbreeding depression and enhance the species' survival.

Describing long-term trends in precipitation using generalized additive models

With the current concern over climate change, descriptions of how rainfall patterns are changing over time can be useful. Observations of daily rainfall data over the last few decades provide information on these trends. Generalized linear models are typically used to model patterns in the occurrence and intensity of rainfall. These models describe rainfall patterns for an average year but are more limited when describing long-term trends, particularly when these are potentially non-linear. Generalized additive models (GAMS) provide a framework for modelling non-linear relationships by fitting smooth functions to the data. This paper describes how GAMS can extend the flexibility of models to describe seasonal patterns and long-term trends in the occurrence and intensity of daily rainfall using data from Mauritius from 1962 to 2001. Smoothed estimates from the models provide useful graphical descriptions of changing rainfall patterns over the last 40 years at this location. GAMS are particularly helpful when exploring non-linear relationships in the data. Care is needed to ensure the choice of smooth functions is appropriate for the data and modelling objectives. (c) 2008 Elsevier B.V. All rights reserved.

The reproductive response of rams to thyroidectomy: mediation by impaired inhibin feedback rather than a change in LH pulsatility

A series of experiments was conducted to examine the mechanism by which removal of the thyroid glands in seasonally suppressed rams brings about rapid testicular growth. In the first experiment, thyroidectomy at the nadir of the testicular cycle (late winter) initiated testis growth without any detectable change in the extent of spermatogenesis compared with sham-operated controls. The serum concentration of FSH, but not LH, was also markedly increased by thyroidectomy. In the second experiment, serum FSH concentration was again increased by thyroidectomy in late winter but there was no effect of thyroidectomy on LH concentration, LH pulses (measured in frequent blood samples) or testosterone concentration. Furthermore, there was no evidence of a change in central dopaminergic inhibition of GnRH, as measured by the pulsatile LH response to an i.m. injection of the dopaminergic D-2 agonist bromocriptine or antagonist sulpiride. The rapid increase in FSH concentration occurred despite a markedly increased serum inhibin A concentration in thyroidectomized rams. Therefore, the efficacy of inhibin feedback was examined by testing the FSH-suppressive effect of an inhibin preparation (5 ml charcoal-stripped bovine follicular fluid i.v.) in long-term thyroidectomized and thyroid intact castrated rams. Bovine follicular fluid suppressed FSH concentrations in control rams as expected but in marked contrast, was completely without effect in thyroidectomized animals. In castrated rams, the FSH concentration was only marginally increased by thyroidectomy, indicating that there is a major component of the mediation of the effects of thyroidectomy that is testicular in origin. It was concluded that a reduction in the ability of endogenous inhibin to inhibit FSH release at the pituitary, rather than a hypothalamic mechanism, is the primary cause of the stimulation of testis growth by thyroidectomy.

Pressure-jump X-ray studies of liquid crystal transitions in lipids

In this paper, we give an overview of our studies by static and time-resolved X-ray diffraction of inverse cubic phases and phase transitions in lipids. In 1, we briefly discuss the lyotropic phase behaviour of lipids, focusing attention on non-lamellar structures, and their geometric/topological relationship to fusion processes in lipid membranes. Possible pathways for transitions between different cubic phases are also outlined. In 2, we discuss the effects of hydrostatic pressure on lipid membranes and lipid phase transitions, and describe how the parameters required to predict the pressure dependence of lipid phase transition temperatures can be conveniently measured. We review some earlier results of inverse bicontinuous cubic phases from our laboratory, showing effects such as pressure-induced formation and swelling. In 3, we describe the technique of pressure-jump synchrotron X-ray diffraction. We present results that have been obtained from the lipid system 1:2 dilauroylphosphatidylcholine/lauric acid for cubic-inverse hexagonal, cubic-cubic and lamellar-cubic transitions. The rate of transition was found to increase with the amplitude of the pressure-jump and with increasing temperature. Evidence for intermediate structures occurring transiently during the transitions was also obtained. In 4, we describe an IDL-based 'AXCESS' software package being developed in our laboratory to permit batch processing and analysis of the large X-ray datasets produced by pressure-jump synchrotron experiments. In 5, we present some recent results on the fluid lamellar-Pn3m cubic phase transition of the single-chain lipid 1-monoelaidin, which we have studied both by pressure-jump and temperature-jump X-ray diffraction. Finally, in 6, we give a few indicators of future directions of this research. We anticipate that the most useful technical advance will be the development of pressure-jump apparatus on the microsecond time-scale, which will involve the use of a stack of piezoelectric pressure actuators. The pressure-jump technique is not restricted to lipid phase transitions, but can be used to study a wide range of soft matter transitions, ranging from protein unfolding and DNA unwinding and transitions, to phase transitions in thermotropic liquid crystals, surfactants and block copolymers.