Local complexity of Delone sets and crystallinity

This paper characterizes when a Delone set X in R-n is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let N-X (T) count the number of translation-inequivalent patches of radius T in X and let M-X (T) be the minimum radius such that every closed ball of radius M-X(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a gap in the spectrum of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal. Explicitly, for N-X (T), if R is the covering radius of X then either N-X (T) is bounded or N-X (T) greater than or equal to T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions. For M-X(T), either M-X(T) is bounded or M-X(T) greater than or equal to T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M-X(T) greater than or equal to c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

Estimating and evaluating the statistics of gapped local-alignment scores

We present a novel maximum-likelihood-based algorithm for estimating the distribution of alignment scores from the scores of unrelated sequences in a database search. Using a new method for measuring the accuracy of p-values, we show that our maximum-likelihood-based algorithm is more accurate than existing regression-based and lookup table methods. We explore a more sophisticated way of modeling and estimating the score distributions (using a two-component mixture model and expectation maximization), but conclude that this does not improve significantly over simply ignoring scores with small E-values during estimation. Finally, we measure the classification accuracy of p-values estimated in different ways and observe that inaccurate p-values can, somewhat paradoxically, lead to higher classification accuracy. We explain this paradox and argue that statistical accuracy, not classification accuracy, should be the primary criterion in comparisons of similarity search methods that return p-values that adjust for target sequence length.

Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitary operations. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.

Simulation of insect movement with respect to plant architecture and morphogenesis

Developments in computer and three dimensional (3D) digitiser technologies have made it possible to keep track of the broad range of data required to simulate an insect moving around or over the highly heterogeneous habitat of a plant's surface. Properties of plant parts vary within a complex canopy architecture, and insect damage can induce further changes that affect an animal's movements, development and likelihood of survival. Models of plant architectural development based on Lindenmayer systems (L-systems) serve as dynamic platforms for simulation of insect movement, providing ail explicit model of the developing 3D structure of a plant as well as allowing physiological processes associated with plant growth and responses to damage to be described and Simulated. Simple examples of the use of the L-system formalism to model insect movement, operating Lit different spatial scales-from insects foraging on an individual plant to insects flying around plants in a field-are presented. Such models can be used to explore questions about the consequences of changes in environmental architecture and configuration on host finding, exploitation and its population consequences. In effect this model is a 'virtual ecosystem' laboratory to address local as well as landscape-level questions pertinent to plant-insect interactions, taking plant architecture into account. (C) 2002 Elsevier Science B.V. All rights reserved.

The devolution of indigenous local government authority in Queensland: Opportunities for statutory planning

Government policy change to self detennination over the past two decades has gradually given rise to various structures of Indigenous self government across Australia. Indigenous Local Government Authorities (LGAs) are the governing structure which receive the greatest devolution of State authority, especially those found in Queensland and the Northern Territory. Their statutory basis has developed over a relatively short period of time and is still very much evolving. This paper explores what opportunities exist for Indigenous LGAs to adopt statutory planning mechanisms.

Cleaner fish drives local fish diversity on coral reefs

Coral reefs are one of the most diverse habitats in the world [1], yet our understanding of the processes affecting their biodiversity is limited [1-3]. At the local scale, cleaner fish are thought to have a disproportionate effect, in relation to their abundance and size, on the activity of many other fish species, but confirmation of this species' effect on local fish diversity has proved elusive. The cleaner fish Labroides dimidiatus has major effects on fish activity patterns [4] and may indirectly affect fish demography through the removal of large numbers of parasites [5, 6]. Here we show that small reefs where L. dimidiatus had been experimentally excluded for 18 months had half the species diversity of fish and one-fourth the abundance of individuals. Only fish that move among reefs, however, were affected. These fish include large species that themselves can affect other reef organisms [2, 7]. In contrast, the distribution of resident fish was not affected by cleaner fish. Thus, many fish appear to choose reefs based on the presence of cleaner fish. Our findings indicate that a single small [8] and not very abundant [9] fish has a strong influence on the movement patterns, habitat choice, activity, and local diversity and abundance of a wide variety of reef fish species.

Fitting genetic models to twin data with binary and ordered categorical responses: A comparison of structural equation modelling and Bayesian hierarchical models

We compare Bayesian methodology utilizing free-ware BUGS (Bayesian Inference Using Gibbs Sampling) with the traditional structural equation modelling approach based on another free-ware package, Mx. Dichotomous and ordinal (three category) twin data were simulated according to different additive genetic and common environment models for phenotypic variation. Practical issues are discussed in using Gibbs sampling as implemented by BUGS to fit subject-specific Bayesian generalized linear models, where the components of variation may be estimated directly. The simulation study (based on 2000 twin pairs) indicated that there is a consistent advantage in using the Bayesian method to detect a correct model under certain specifications of additive genetics and common environmental effects. For binary data, both methods had difficulty in detecting the correct model when the additive genetic effect was low (between 10 and 20%) or of moderate range (between 20 and 40%). Furthermore, neither method could adequately detect a correct model that included a modest common environmental effect (20%) even when the additive genetic effect was large (50%). Power was significantly improved with ordinal data for most scenarios, except for the case of low heritability under a true ACE model. We illustrate and compare both methods using data from 1239 twin pairs over the age of 50 years, who were registered with the Australian National Health and Medical Research Council Twin Registry (ATR) and presented symptoms associated with osteoarthritis occurring in joints of the hand.

Osteoarthritis of the hands, hips and knees in an Australian twin sample - Evidence of association with the aggrecan VNTR polymorphism

Age-related changes in the composition of the cartilage matrix may be associated with the development of osteoarthritis, a relatively late-onset disease characterised by the destruction of joint cartilage. In order to investigate whether differences in the VNTR polymorphic region of aggrecan affect cartilage functionality and therefore the development of osteoarthritis, we examined the aggrecan polymorphic genotypes of a sample of 134 Australian twins aged over 50 (including 34 monozygotic and 27 dizygotic twin pairs). Clinical measures of hand, hip and knee osteoarthritis, as well as self-reported bone and joint pain, were tested for association with the aggrecan polymorphism. The results were consistent with either a deleterious effect of allele 27, or a protective effect of alleles 25 and 28, providing some additional evidence for an association between the aggrecan VNTR polymorphism and osteoarthritis of the hands, hips and knees.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study xed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

Special twin environments, genetic influences and their effects on the handedness of twins and their siblings

It has been suggested that twinning may influence handedness through the effects of birth order, intra-uterine crowding and mirror imaging. The influence of these effects on handedness (for writing and throwing) was examined in 3657 Monozygotic (MZ) and 3762 Dizygotic (DZ) twin pairs (born 1893-1992). Maximum likelihood analyses revealed no effects of birth order on the incidence of left-handedness. Twins were no more likely to be left-handed than their singleton siblings (n = 1757), and there were no differences between the DZ co-twin and sibling-twin covariances, suggesting that neither intra-uterine crowding nor the experience of being a twin affects handedness. There was no evidence of mirror imaging; the co-twin correlations of monochorionic and dichorionic MZ twins did not differ. Univariate genetic analyses revealed common environmental factors to be the most parsimonious explanation of familial aggregation for the writing-hand measure, while additive genetic influences provided a better interpretation of the throwing hand data.

The genetics of coronary heart disease: the contribution of twin studies

Despite the decline in coronary heart disease in many European countries, the disease remains an enormous public health problem. Although we know a great deal about environmental risk factors for coronary heart disease, a heritable component was recognized a long time ago. The earliest and best known examples of how our genetic constitution may determine cardiovascular risk relate to lipoprotein(a), familial hypercholesterolaemia and apolipoprotein E. In the past 20 years a fair number of polymorphisms assessed singly have shown strong associations with the disease but most are subject to poor repeatability. Twins constitute a compelling natural experiment to establish the genetic contribution to coronary heart disease and its risk factors. GenomEUtwin, a recently funded Framework 5 Programme of the European Community, affords the opportunity of comparing the heritability of risk factors in different European Twin Registries. As an illustration we present the heritabilities of systolic and diastolic blood pressure, based on data from over 4000 twin pairs from six different European countries and Australia. Heritabilities for systolic blood pressure are between 52 and 66% and for diastolic blood pressure between 44 and 66%. There is no evidence of sex differences in heritability estimates and very little to no evidence for a significant contribution of shared family environment. A non-twin based prospective case/cohort study of coronary heart disease and stroke (MORGAM) will allow hypotheses relating to cardiovascular disease, generated in the twin cohorts, to be tested prospectively in adult populations. Twin studies have also contributed to our understanding of the life course hypothesis, and GenomEUtwin has the potential to add to this.

Genetic and Environmental Influences on Migraine: A Twin Study Across Six Countries

Migraine is a common neurovascular brain disorder that is manifested in recurrent episodes of disabling headache. The aim of the present study was to compare the prevalence and heritability of migraine across six of the countries that participate in GenomEutwin project including a total number of 29,717 twin pairs. Migraine was assessed by questionnaires that differed between most countries. It was most prevalent in Danish and Dutch females (32% and 34%, respectively), whereas the lowest prevalence was found in the younger and older Finnish cohorts (13% and 10%, respectively). The estimated genetic variance (heritability) was significant and the same between sexes in all countries. Heritability ranged from 34% to 57%, with lowest estimates in Australia, and highest estimates in the older cohort of Finland, the Netherlands, and Denmark. There was some indication that part of the genetic variance was non-additive, but this was significant in Sweden only. In addition to genetic factors, environmental effects that are non-shared between members of a twin pair contributed to the liability of migraine. After migraine definitions are homogenized among the participating countries, the GenomEUtwin project will provide a powerful resource to identify the genes involved in migraine.