⁸⁷Sr/⁸⁶Sr chemostratigraphy of Neoproterozoic Dalradian limestones of Scotland and Ireland: constraints on depositional ages and time scales

New calcite <sup>87</sup>Sr/<sup>86</sup>Sr data for 47 limestones from the metamorphosed and deformed Neoproterozoic-Cambrian Dalradian Supergroup of Scotland and Ireland are used to identify secular trends in seawater <sup>87</sup>Sr/<sup>86</sup>Sr through the Dalradian succession and to constrain its depositional age. Dalradian limestones commonly have Sr greater than 1000 ppm, indicating primary aragonite and marine diagenesis. Low Mn, Mn/Sr less than 0.6, ë<sup>18</sup>O and trace element data indicate that many <sup>87</sup>Sr/<sup>86</sup>Sr ratios are unaltered since diagenesis despite greenschist- to amphibolite-facies metamorphism, consistent with the documented behaviour of Sr and O during metamorphic fluid-rock interaction. Thus, the <sup>87</sup>Sr/<sup>86</sup>Sr data are interpreted largely to reflect <sup>87</sup>Sr/<sup>86</sup>Sr of coeval seawater. Currently available data show that Neoproterozoic seawater <sup>87</sup>Sr/<sup>86</sup>Sr rose from c. 0.7052 at 850-900 Ma to c. 0.7085 or higher in the latest Neoproterozoic. Temporal changes at c. 800 Ma and c . 600 Ma bracket the range in <sup>87</sup>Sr/<sup>86</sup>Sr values of calcite in Grampian. Appin and lowest Argyll Group (c.0.7064-0.7072) and middle and uppermost Argyll Group (c. 0.7082-0.7095) limestones, consistent with a rise in seawater <sup>87</sup>Sr/<sup>86</sup>Sr around 600 Ma. <sup>87</sup>Sr/<sup>86</sup>Sr data are consistent with the sedimentary affinity of the Islay Subgroup with the underlying Appin Group, and with a possible time interval between deposition of Islay and Easdale Subgroup rocks. They indicate that the Dalradian, as a whole, is younger than c. 800 Ma

Space--Time Tradeoffs for Subset Sum: An Improved Worst Case Algorithm

The technique of Schroeppel and Shamir (SICOMP, 1981) has long been the most efficient way to trade space against time for the SUBSET SUM problem. In the random-instance setting, however, improved tradeoffs exist. In particular, the recently discovered dissection method of Dinur et al. (CRYPTO 2012) yields a significantly improved space--time tradeoff curve for instances with strong randomness properties. Our main result is that these strong randomness assumptions can be removed, obtaining the same space--time tradeoffs in the worst case. We also show that for small space usage the dissection algorithm can be almost fully parallelized. Our strategy for dealing with arbitrary instances is to instead inject the randomness into the dissection process itself by working over a carefully selected but random composite modulus, and to introduce explicit space--time controls into the algorithm by means of a "bailout mechanism"

An active-architecture approach to COTS integration

Commercial off-the-shelf (COTS) software products are increasingly used as standard components within integrated information systems. This creates challenges since both their developers and source code are not usually available, and the ongoing development of COTS cannot be predicted. The ArchWare Framework approach recognises COTS products as part of the ambient environment of an information system and therefore an important part of development is incorporating COTS as effective system components. This integration of COTS components, and the composition of components, is captured by an active architecture model which changes as the system evolves. Indeed the architecture modelling language used enables it to express the monitoring and evolution of a system. This active architecture model is structured using control system principles. By modelling both integration and evolution it can guide the system’s response to both predicted and emergent changes that arise from the use of COTS products.Publisher PDFPeer reviewe

Approximate Deadline-Scheduling with Precedence Constraints

We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence constraints. The goal is to compute a feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan [Annals of Disc. Math., 1977] in their seminal work introduced this problem and showed that it is strongly NP-hard, even when all processing times and weights are 1. We study the approximability of the problem and our main result is an O(log k)-approximation algorithm for instances with k distinct job deadlines

Some extremal functions in Fourier analysis, III

We obtain the best approximation in $L^1(\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.Comment: 26 pages. Submitte

The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes

This work considers the way that quantum loop effects modify the propagation of light in curved space. The calculation of the refractive index for scalar QED is reviewed and then extended for the first time to QED with spinor particles in the loop. It is shown how, in both cases, the low frequency phase velocity can be greater than c, as found originally by Drummond and Hathrell, but causality is respected in the sense that retarded Green functions vanish outside the lightcone. A "phenomenology" of the refractive index is then presented for black holes, FRW universes and gravitational waves. In some cases, some of the polarization states propagate with a refractive index having a negative imaginary part indicating a potential breakdown of the optical theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph

Exploring the Quality of Life of People in North Eastern and Southern Thailand.

The assumption that development brings not only material prosperity but also a better overall quality of life lies at the heart of the development project. Against this, critics assert that development can undermine social cohesion and threaten cultural integrity. Rarely, however, is the impact of development on wellbeing rigourously analysed using empirical data. This is what the Wellbeing in Developing Countries Group at the University of Bath aims to do drawing on fieldwork carried out in four developing countries, which addresses the themes of resources, needs, agency and structure, and subjective Quality of life (QoL). The first phase of the QoL research in Thailand aimed to explore the categories and components of quality of life for people from different backgrounds and locations with the aim of developing methods for QoL assessment in the third phase of the WeD QoL research. The study presents data obtained from rural and peri-urban sites in Southern and Northeastern Thailand (two villages in Songkhla and three in Khon Kaen, Mukdaharn, and Roi-et). Participants were divided into six groups by gender and age, and were divided again by religion (Buddhist and Muslim) and wealth status in the South. Data collection was conducted between October and December 2004 using focus group discussions, semi-structured interviews, and the Person Generated Index. Content analysis was used for data analysis. The use of a qualitative approach enabled the gathering of empirical data that reflects the sources of difficulty and happiness in the lives of participants. Respondents identified 26 aspects to their quality of life, including family relations, health and longevity, income and having money, jobs, housing, education, debt, and so on. The results reveal clear similarities and differences in the role of traditions, religious beliefs, and values in the lives of people living in remote rural or peri-urban areas in Northeastern and Southern Thailand. These results, together with the findings from Peru, Ethiopia, and Bangladesh, will inform the rest of the WeD research and be used to develop measures to assess the quality of life of people living in developing countries

Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations

We show that asymptotically hyperbolic solutions of the Einstein constraint equations with constant mean curvature can be glued in such a way that their asymptotic regions are connected.Comment: 37 pages; 2 figure

Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page