International migration in a sea of islands: Challenges and opportunities for insular Pacific spaces

Our contribution to the International Conference “Connecting Worlds: Emigration, Immigration and Development in Insular Spaces”, held in the Azores between 28 and 30 May 2008, examines contemporary mobility of Pacific peoples in a transnational context with reference to processes of out-migration, return, re-migration and the complex systems of circular mobility between island countries as well as to and from countries on the Pacific rim. There are some significant differences between parts of the Pacific region in terms of the access their peoples have to work and residence opportunities outside their island countries. These are reviewed with reference to some major challenges for development in the region: rapid growth of youthful populations; high levels of unemployment; limited markets for local produce; unsustainable levels of extraction of timber, fish and mineral resources; changing climates; and unstable governance systems in some countries

Cohomology of U(2,1) representation varieties of surface groups

In this paper we use the Morse theory of the Yang-Mills-Higgs functional on the singular space of Higgs bundles on Riemann surfaces to compute the equivariant cohomology of the space of semistable U(2,1) and SU(2,1) Higgs bundles with fixed Toledo invariant. In the non-coprime case this gives new results about the topology of the U(2,1) and SU(2,1) character varieties of surface groups. The main results are a calculation of the equivariant Poincare polynomials, a Kirwan surjectivity theorem in the non-fixed determinant case, and a description of the action of the Torelli group on the equivariant cohomology of the character variety. This builds on earlier work for stable pairs and rank 2 Higgs bundles.Comment: 34 page

Counterfactual Computation

Suppose that we are given a quantum computer programmed ready to perform a computation if it is switched on. Counterfactual computation is a process by which the result of the computation may be learnt without actually running the computer. Such processes are possible within quantum physics and to achieve this effect, a computer embodying the possibility of running the computation must be available, even though the computation is, in fact, not run. We study the possibilities and limitations of general protocols for the counterfactual computation of decision problems (where the result r is either 0 or 1). If p(r) denotes the probability of learning the result r ``for free'' in a protocol then one might hope to design a protocol which simultaneously has large p(0) and p(1). However we prove that p(0)+p(1) never exceeds 1 in any protocol and we derive further constraints on p(0) and p(1) in terms of N, the number of times that the computer is not run. In particular we show that any protocol with p(0)+p(1)=1-epsilon must have N tending to infinity as epsilon tends to 0. These general results are illustrated with some explicit protocols for counterfactual computation. We show that "interaction-free" measurements can be regarded as counterfactual computations, and our results then imply that N must be large if the probability of interaction is to be close to zero. Finally, we consider some ways in which our formulation of counterfactual computation can be generalised.Comment: 19 pages. LaTex, 2 figures. Revised version has some new sections and expanded explanation

How epigenetic evolution can guide genetic evolution (abstract)

The expression level of a gene in future generations can be modified both by genetic mutations and by the attachment of methyl groups to the DNA. Since the DNA methylation pattern along a genome is inherited, methylation patterns constitute a significant epigenetic inheritance mechanism that is subject to evolution by natural selection. The variation rate of methylation patterns is generally higher than that of DNA which suggests that evolution of methylation patterns might be more rapid than that of genetic evolution. But, common consequences of methylation, such as reduced expression of methylated genes, could also be produced by genetic changes and these would have higher heritability. The question we address in this work is how the evolution of epigenetic methylation-dependent phenotypes might interact with the evolution of genetic DNA-determined phenotypes. There is no biological mechanism known to directly transfer methyl groups into equivalent DNA changes. However, in principle an indirect mechanism could cause evolved methylation patterns to enable the subsequent evolution of equivalent genetic patterns in a manner analogous to the Baldwin effect (Baldwin, Am. Nat., 30:441-451, 1896; Jablonka et al, TREE, 13:206-210, 1998). The Baldwin effect describes how non-heritable acquired characteristics can influence the evolution of equivalent genetic characteristics without any direct Lamarckian inheritance of acquired characters. This occurs because the ability to acquire or learn a new behaviour changes the selective pressures acting on genetic changes. Specifically, genetic changes that support this behaviour, e.g. by reducing learning time by making a small part of the behaviour genetically innate, may be selected for when the learning mechanism is present even though these same genetic changes may not be selected for when the learning mechanism is absent. Over generations, the modified selection pressures so produced can cause genetic assimilation of a phenotype that was previously acquired, even to the extent of making the acquisition mechanism subsequently redundant. Thus a learned behaviour can guide the evolution of an equivalent innate behaviour (Hinton & Nowlan, Complex Systems, 1: 495-502, 1987). In the Baldwin effect a rapid mechanism of lifetime adaptation guides the relatively slow genetic evolution of the same behaviour. By analogy, Jablonka et al have suggested that “genetic adaptations may be guided by heritable induced or learnt phenotypic adaptations”. Here we hypothesise that “inherited epigenetic variations may be able to ‘hold’ an adapted state for long enough to allow similar genetic variations to catch up”, as they put it, even if the epigenetic variations are not induced or learnt but simply evolved by natural selection on methylation patterns. We assume that an individual may only express one phenotype in its lifetime, but that a given genome will persist relatively unchanged on a timescale that allows its methylome to adapt by natural selection. Thus, in contrast to the Baldwin effect, in this case two mechanisms of evolution by natural selection are coupled — one acting at a different variation rate from the other. We present a simple model to illustrate how a rapidly evolving methylome can guide a slowly evolving but highly-heritable genome. This is used to show that methylome evolution can enable genetic evolution to cross fitness valleys that would otherwise require multiple genetic changes that were each selected against. This finding suggests that the relatively rapid evolution of methylation patterns can produce novel phenotypes that are subsequently genetically assimilated in DNA evolution without direct transfer or appeal to induced phenotypes. This can enable the genetic evolution of new phenotypes that would not be found by genetic evolution alone, even if methylation is not significant in the ultimate phenotype

High frequency homogenization for travelling waves in periodic media

We consider high frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schr{\"o}dinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wave vector \Bk and frequency $\omega_1$ plus a modulated Bloch carrier wave having crystal wave vector \Bm and frequency $\omega_2$. We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless $\omega_1=\omega_2$ and (\Bk-\Bm)\odot\Lambda \in 2\pi \mathbb Z^d, where $\Lambda=(\lambda_1\lambda_2\dots\lambda_d)$ is the periodicity cell of the medium and for any two vectors $a=(a_1,a_2,\dots,a_d), b=(b_1,b_2,\dots,b_d)\in\mathbb R^d,$ the product $a\odot b$ is defined to be the vector $(a_1b_1,a_2b_2,\dots,a_db_d).$ This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigor as that of Allaire and coworkers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.Comment: 30 pages, Proceedings of the Royal Society A, 201

Maori internal and international migration at the turn of the century: An Australasian perspective

At the beginning of the twenty-first century there were two major national clusters of Maori: New Zealand, the ancestral home for Maori, and Australia, home to a much smaller Maori population from the early years of the nineteenth century. In the 2001 censuses of New Zealand and Australia, the usually resident Maori populations were, respectively, 526,281 (ethnic group classification) and 72,956 (ancestry classification). In this paper we examine four dimensions of Maori population movement between 1996 and 2001 using the census data from New Zealand and Australia: 1) internal migration between rural and urban areas in New Zealand; 2) internal migration between rural and urban areas in Australia; 3) migration into New Zealand of Maori resident overseas in 1996; 4) migration into Australia of Maori resident overseas in 1996. There has never been a comprehensive assessment of Maori migration in an Australasian context before, but in the light of developments in population exchanges between New Zealand and Australia this sort of analysis is critical if one wishes to understand contemporary Maori population dynamics