On spectral triples on crossed products arising from equicontinuous actions

The external Kasparov product is used to construct odd and even spectral triples on crossed products of $C^*$-algebras by actions of discrete groups which are equicontinuous in a natural sense. When the group in question is $\Z$ this gives another viewpoint on the spectral triples introduced by Belissard, Marcolli and Reihani. We investigate the properties of this construction and apply it to produce spectral triples on the Bunce-Deddens algebra arising from the odometer action on the Cantor set and some other crossed products of AF-algebras.Comment: 22 pages (v4 corrects a mistake in the discussion of the equicontinuity condition and modifies the terminology used). The paper will appear in Mathematica Scandinavic

Human behavioural ecology, anthropogenic impact and subsistence change at the teouma lapita site, central Vanuatu, 3000-2500 BP

This thesis investigates early human palaeoecological interaction at the Teouma Lapita site on Efate Island, central Vanuatu, and how it changed during a period of cultural transition between 3000-2500 BP. Here I take a quantified approach through an evolutionary ecological theoretical framework using optimal foraging models (Prey Choice, Patch Choice and Central Place Foraging) to generate predictions of optimal economic behaviour in response to temporal variation in prey abundances. These optimal foraging models (OFM) which typically focus on foraging cultures had to be adjusted to the broad spectrum Lapita mixed economy which combined foraging within marine and terrestrial resource patches and horticulture, incorporating pig husbandry and plant cultivation. To this end mammal, bird and reptile vertebrate taxa were divided into three broad resource patches, coastal, terrestrial and the domestic patch. Alternative social theoretical perspectives were also built into the models such as costly signalling theory. OFM predictions were then tested using multiple zooarchaeological datasets to demonstrate changes in foraging efficiency and mobility between resource patches as a result of human induced resource depression. Datasets used include measures of prey diversity, relative abundance, demography, skeletal element representation, and butchery intensity. The results indicate that Lapita foragers focused initially on high ranked fruit bat and large bodied sea turtle resources in concentrated and predictable proximal locations which yielded high post encounter return rates. Giant tortoise exploitation in distant resource patches gained in importance over time as these proximal resource patches became depleted. Domestic patch resources were established and pig abundances increased very quickly but had initially high infant mortality rates due to nutritional deficiency and/or selective culling to reduce associated labour costs. Pigs were closely managed and regulated for a range of purposes which included daily household meat consumption as well as ritualistic feasting events. Faunal abundances peaked during the later post-cemetery period as Lapita settlement and foraging intensified which had a huge impact on the terrestrial and coastal resources due in part to direct foraging, forest clearance. An ecological tipping point followed which saw the disappearance of crocodile and a number of fruit bat and bird species from the record. As encounter rates of high ranked taxa declined so did foraging efficiency and the transition from Lapita to post-Lapita culture saw a dramatic change in subsistence patterns. Tortoise and sea turtle nesting populations were devastated as giant tortoises became extinct around the transition between Lapita to early Erueti, rat demography and the large New Guinea Spiny rat declined likely as a result of human predation as settlement intensity appears to have peaked by the end of the Lapita period. Pig production also declined likely in response to ecological and social developments, and a switch to hunting feral pigs may have occurred. These subsistence changes and declines in foraging efficiency appear to have been associated with changes in settlement patterns which conform to the ideal free distribution model as well as declines in social stratification

Avifauna from the Teouma Lapita Site, Efate Island, Vanuatu, Including a New Genus and Species of Megapode

Copyright 2015 University of Hawaii Press. Published version of the article is reproduced here with permission from the publisher.The avifauna of the Teouma archaeological site on Efate in Vanuatu is described. It derives from the Lapita levels (3,000 – 2,800 ybp) and immedi-ately overlying middens extending to ∼2,500 ybp. A total of 30 bird species is represented in the 1,714 identiï¬ ed specimens. Twelve species are new records for the island, which, added to previous records, indicates that minimally 39 land birds exclusive of passerines were in the original avifauna. Three-fourths of the 12 newly recorded species appear to have become extinct by the end of Lapita times, 2,800 ybp. The avifauna is dominated by eight species of columbids (47.5% Minimum Number Individuals [MNI ]) including a large extinct tooth-billed pigeon, Didunculus placopedetes from Tonga, and a giant Ducula sp. cf. D. goliath from New Caledonia. Seabirds are rare despite the coastal location of the site. Fowl are important contributors to the Teouma avifauna, with the human-introduced Red Junglefowl Gallus gallus accounting for 15% MNI and present in all sampled layers. There are two species of megapodes (∼10% of MNI ), with the extant Vanuatu Megapode Megapodius layardi most abundant and represented at all levels in the deposits. A substantially larger extinct megapode, Mwalau walter-linii, n. gen., n. sp., is present only in the Lapita midden area, where it is rela-tively rare. This extinct species was larger than all extant megapodes but smaller than the extinct Progura gallinacea from Australia, with proportions most similar to those of Alectura, and was a volant bird. The remaining signiï¬ cant faunal component is rails, with four species present, of which Porphyrio melanotus was the most abundant. Rare but notable records include an undescribed large rail; a parrot, Eclectus sp. cf. E. infectus; a hornbill, Rhyticeros sp. cf. R. plicatus; and a coucal, Centropus sp. indet., all conservatively considered likely to be conspeciï¬ c with known taxa elsewhere in Melanesia

Sparse preconditioners for dense complex linear systems arising in some radar cross section computations

We present a sparse preconditioner for efficient iterative solution of large dense linear systems that arise in radar cross section computations for a perfectly conducting scatterer using a high-order surface integral equation algorithm. The algorithm allows the linear systems to be assembled efficiently but overall efficiency of the method can only be achieved using iterative solvers with an appropriate preconditioner. We demonstrate the effectiveness and efficiency of our preconditioner for electromagnetic scattering linear systems with tens of thousands of unknowns arising in radar cross section computations for small to medium electromagnetic-sized scatterers

An all-frequency stable surface integral equation algorithm for electromagnetism in 3-D unbounded penetrable media: Continuous and fully-discrete model analysis

We use the time-harmonic Maxwell partial differential equations (PDEs) to model the wave propagation in 3-D space, which comprises a closed penetrable scatterer and its unbounded free-space complement. Surface integral equations (SIEs) that are equivalent to the time-harmonic Maxwell PDEs provide an efficient framework to directly model the surface electromagnetic fields and hence the RCS.The equivalent SIE system on the interface has the advantages that: (a) it avoids truncation of the unbounded region and the solution exactly satisfies the radiation condition; and (b) the surface-fields solution yields the unknowns in the Maxwell PDEs through surface potential representations of the interior and exterior fields. The Maxwell PDE system has been proven (several decades ago) to be stable for all frequencies, that is, (i) it does not possess eigenfrequencies (it is well-posed); and (ii) it does not suffer from low-frequency. However, weakly-singular SIE reformulations of the PDE satisfying these two properties, subject to a stabilization constraint, were derived and mathematically proven only about a decade ago (see {J. Math. Anal. Appl. 412 (2014) 277-300}). The aim of this article is two-fold: (I) To effect a robust coupling of the stabilization constraint to the weakly singular SIE and use mathematical analysis to establish that the resulting continuous weakly-singular second-kind self-adjoint SIE system (without constraints) retains all-frequency stability; and (II) To apply a fully-discrete spectral algorithm for the all-frequency-stable weakly-singular second-kind SIE, and prove spectral accuracy of the algorithm. We numerically demonstrate the high-order accuracy of the algorithm using several dielectric and absorbing benchmark scatterers with curved surfaces

The influence of mussel-modified habitat on Fucus serratus L. a rocky intertidal canopy-forming macroalga

The influence of habitat modification by Mytilus edulis L. on the settlement and development of Fucus serratus populations was investigated on rocky shores of the Isle of Anglesey, North Wales. Settlement of fucoids was higher inside mussel habitat than outside on one of two shores studied. The effect of microhabitat on survival of fucoid germlings was examined by transplanting the germlings into and outside mussel habitats, each with and without the exclusion of grazers. Observation showed that periwinkles and top shells were abundant in mussel habitat, while limpets dominated bare rock. Exclusion of grazers greatly enhanced the survival of fucoid germlings in both habitats, indicating that while mussel habitat supports a different grazer assemblage to bare rock, both assemblages are important in limiting fucoid recruitment. The risk of dislodgement was assessed and compared between fucoids growing on mussel shells and bare rock. In situ pull-tests showed that less force was required to detach large fertile thalli growing on mussel shells than those growing on the rock. Adhesion was generally broken between the mussel and the rock rather than between the holdfast and the mussel. These observations indicate that mussels provide an unstable substrate for mature fucoids. Overall results suggest that a negative effect of mussel-modified habitat on fucoids is profound in adults; but the effect is context-dependent in juveniles and can be positive at settlement. Results from a survey on population structure of fucoids across two shores showed that there were greater numbers of large fertile fucoids growing directly attached to rock than on mussel shells, while there was no difference for juvenile fucoids confirming the experimental results. Moreover thalli larger than 60 cm were found only on the rock but not on shells. This finding suggests that a mussel dominated habitat may have a significant impact on reproductive output in fucoid populations

The computation of eigenvalues of large sparse matrices

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN028558 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A comparative study of water perfusion catheters and microtip transducer catheters for urethral pressure measurements

The aim of this study was to compare the maximum urethral closure pressure (MUCP) measures with two different techniques: water perfused catheter and microtip transducer catheters with respect to reproducibility and comparability for urethral pressure measurements. Eighteen women with stress urinary incontinence had repeat static urethral pressure profilometry on a different day using a dual microtip transducer and water perfused catheter (Brown and Wickham). The investigators were blinded to the results of the other. The microtip measurements were taken in the 45° upright sitting position with the patient at rest at a bladder capacity of 250ml using an 8 Fr Gaeltec® double microtip transducer withdrawn at 1mm/s, and the transducer was orientated in the three o'clock position. Three different measures were taken for each patient. Three water perfusion measurements were performed with the patient at rest in the 45° upright position at a bladder capacity of 250ml using an 8 Fr BARD dual lumen catheter withdrawn at 1mm/s. The mean water perfusion MUCP measure was 26.1cm H20, significantly lower than the mean microtip measure of 35.7cm H20. The correlation coefficient comparing each water perfusion measurement with the other water perfusion measures in the same patient was excellent, at 0.95 (p = 0.01). Correlation coefficient comparing each microtip measure with the other microtip measure in the same patient was also good, ranging from 0.70 to 0.80. This study confirms that both water perfusion catheters and microtip transducers have excellent or very good reproducibility with an acceptable intraindividual variation for both method

Long-term modifications of coastal defences enhance marine biodiversity

Realization that hard coastal infrastructures support lower biodiversity than natural habitats has prompted a wealth of research seeking to identify design enhancements offering ecological benefits. Some studies showed that artificial structures could be modified to increase levels of diversity. Most studies, however, only considered the short-term ecological effects of such modifications, even though reliance on results from short-term studies may lead to serious misjudgements in conservation. In this study, a seven-year experiment examined how the addition of small pits to otherwise featureless seawalls may enhance the stocks of a highly-exploited limpet. Modified areas of the seawall supported enhanced stocks of limpets seven years after the addition of pits. Modified areas of the seawall also supported a community that differed in the abundance of littorinids, barnacles and macroalgae compared to the controls. Responses to different treatments (numbers and size of pits) were species-specific and, while some species responded directly to differences among treatments, others might have responded indirectly via changes in the distribution of competing species. This type of habitat enhancement can have positive long-lasting effects on the ecology of urban seascapes. Understanding of species interactions could be used to develop a rule-based approach to enhance biodiversity