Primality-testing Mersenne Numbers (II)

Reports the factor-filtering and primality-testing of Mersenne Numbers Mp for p < 100000, the latter using the ICL 'DAP' Distributed Array Processor.

Using aircraft measurements to determine the refractive index of Saharan dust during the DODO Experiments

Much uncertainty in the value of the imaginary part of the refractive index of mineral dust contributes to uncertainty in the radiative effect of mineral dust in the atmosphere. A synthesis of optical, chemical and physical in-situ aircraft measurements from the DODO experiments during February and August 2006 are used to calculate the refractive index mineral dust encountered over West Africa. Radiative transfer modeling and measurements of broadband shortwave irradiance at a range of altitudes are used to test and validate these calculations for a specific dust event on 23 August 2006 over Mauritania. Two techniques are used to determine the refractive index: firstly a method combining measurements of scattering, absorption, size distributions and Mie code simulations, and secondly a method using composition measured on filter samples to apportion the content of internally mixed quartz, calcite and iron oxide-clay aggregates, where the iron oxide is represented by either hematite or goethite and clay by either illite or kaolinite. The imaginary part of the refractive index at 550 nm (ni550) is found to range between 0.0001 i to 0.0046 i, and where filter samples are available, agreement between methods is found depending on mineral combination assumed. The refractive indices are also found to agree well with AERONET data where comparisons are possible. ni550 is found to vary with dust source, which is investigated with the NAME model for each case. The relationship between both size distribution and ni550 on the accumulation mode single scattering albedo at 550 nm (ω0550) are examined and size distribution is found to have no correlation to ω0550, while ni550 shows a strong linear relationship with ω0550. Radiative transfer modeling was performed with different models (Mie-derived refractive indices, but also filter sampling composition assuming both internal and external mixing). Our calculations indicate that Mie-derived values of ni550 and the externally mixed dust where the iron oxide-clay aggregate corresponds to the goethite-kaolinite combination result in the best agreement with irradiance measurements. The radiative effect of the dust is found to be very sensitive to the mineral combination (and hence refractive index) assumed, and to whether the dust is assumed to be internally or externally mixed.

Mersenne Numbers: consolidated results

This document provides and comments on the results of the Lucas-Lehmer testing and/or partial factorisation of all Mersenne Numbers Mp = 2^p-1 where p is prime and less than 100,000. Previous computations have either been confirmed or corrected. The LLT computations on the ICL DAP is the first implementation of Fast-Fermat-Number-Transform multiplication in connection with Mersenne Number testing. This paper championed the disciplines of systematically testing the Mp, and of double-sourcing results which were not manifestly correct. Both disciplines were adopted by the later GIMPS initiative, the 'Great Internet Mersenne Prime Search, which was itself one of the first web-based distributed-community projects.

Notations and conventions in molecular spectroscopy: part 1. General spectroscopic notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part I in a series, establishes the notations and conventions used for general spectroscopic notations and deals with quantum mechanics, quantum numbers (vibrational states, angular momentum and energy levels), spectroscopic transitions, and miscellaneous notations (e.g. spectroscopic terms). Further parts will follow, dealing inter alia with symmetry notation, permutation and permutation-inversion symmetry notation, vibration-rotation spectroscopy and electronic spectroscopy.

Calculating the exclusion probability and paternity index for X-chromosomal loci in the presence of substructure

There has been recent interest in the use of X-chromosomal loci for forensic and relatedness testing casework, with many authors developing new X-linked short tandem repeat (STR) loci suitable for forensic use. Here we present formulae for two key quantities in paternity testing, the average probability of exclusion and the paternity index, which are suitable for Xchromosomal loci in the presence of population substructure.

Revisiting youden’s index as a useful measure of the misclassification error in meta-analysis of diagnostic studies

The paper considers meta-analysis of diagnostic studies that use a continuous score for classification of study participants into healthy or diseased groups. Classification is often done on the basis of a threshold or cut-off value, which might vary between studies. Consequently, conventional meta-analysis methodology focusing solely on separate analysis of sensitivity and specificity might be confounded by a potentially unknown variation of the cut-off value. To cope with this phenomena it is suggested to use, instead, an overall estimate of the misclassification error previously suggested and used as Youden’s index and; furthermore, it is argued that this index is less prone to between-study variation of cut-off values. A simple Mantel–Haenszel estimator as a summary measure of the overall misclassification error is suggested, which adjusts for a potential study effect. The measure of the misclassification error based on Youden’s index is advantageous in that it easily allows an extension to a likelihood approach, which is then able to cope with unobserved heterogeneity via a nonparametric mixture model. All methods are illustrated at hand of an example on a diagnostic meta-analysis on duplex doppler ultrasound, with angiography as the standard for stroke prevention.

Measuring productivity growth when technological change is biased - a new index and an application to UK agriculture

Productivity growth is conventionally measured by indices representing discreet approximations of the Divisia TFP index under the assumption that technological change is Hicks-neutral. When this assumption is violated, these indices are no longer meaningful because they conflate the effects of factor accumulation and technological change. We propose a way of adjusting the conventional TFP index that solves this problem. The method adopts a latent variable approach to the measurement of technical change biases that provides a simple means of correcting product and factor shares in the standard Tornqvist-Theil TFP index. An application to UK agriculture over the period 1953-2000 demonstrates that technical progress is strongly biased. The implications of that bias for productivity measurement are shown to be very large, with the conventional TFP index severely underestimating productivity growth. The result is explained primarily by the fact that technological change has favoured the rapidly accumulating factors against labour, the factor leaving the sector. (C) 2004 Elsevier B.V. All rights reserved.

A cross-taxonomic index for quantifying the health of farmland biodiversity

P>1. The development of sustainable, multi-functional agricultural systems involves reconciling the needs of agricultural production with the objectives for environmental protection, including biodiversity conservation. However, the definition of sustainability remains ambiguous and it has proven difficult to identify suitable indicators for monitoring progress towards, and the successful achievement of, sustainability. 2. In this study, we show that a trait-based approach can be used to assess the detrimental impacts of agricultural change to a broad range of taxonomic groupings and derive a standardised index of farmland biodiversity health, built around an objective of achieving stable or increasing populations in all species associated with agricultural landscapes. 3. To demonstrate its application, we assess the health of UK farmland biodiversity relative to this goal. Our results suggest that the populations of two-thirds of 333 plant and animal species assessed are unsustainable under current UK agricultural practices. 4. We then explore the potential benefits of an agri-environment scheme, Entry Level Stewardship (ELS), to farmland biodiversity in the UK under differing levels of risk mitigation delivery. We show that ELS has the potential to make a significant contribution to progress towards sustainability targets but that this potential is severely restricted by current patterns of scheme deployment. 5.Synthesis and applications: We have developed a cross-taxonomic sustainability index which can be used to assess both the current health of farmland biodiversity and the impacts of future agricultural changes relative to quantitative biodiversity targets. Although biodiversity conservation is just one of a number of factors that must be considered when defining sustainability, we believe our cross-taxonomic index has the potential to be a valuable tool for guiding the development of sustainable agricultural systems.

The relationships of time and temperature to body weight and numbers of endospores in Pasteuria penetrans-infected Meloidogyne javanica females

Tomato plants inoculated with Meloidogyne javanica juveniles infected with Pasteuria penetrans were grown in a glasshouse (20-32degreesC) for 36, 53, 71 and 88 days and in a growth room (26-29degreesC) for 36, 53, 71 and 80 days. Over these periods the numbers of P penetrans endospores in infected M. javanica females and the weights of individual infected females increased. In the growth room, most spores (2.03 x 10(6)) were found after 71 days. However, in the glasshouse the rate of increase was slower and spore numbers were still increasing at the final sampling at 88 days (2.04 x 10(6)), as was the weight of the nematodes (72 mug). Weights of uninfected females reached a maximum of 36.2 and 43.1 mug after 71 days in the growth room and glasshouse, respectively.

Heterosis for yield and its physiological determinants in wheat

Heterosis in hybrid wheat varieties produced using a chemical hybridising agent was assessed in field experiments. Hyno Esta and its parents were compared in factorial combinations of four-seed rates (25-300 seeds m(-2)) and two nitrogen fertilizer rates (0 and 200 kg N ha(-1)) in 2001/02 and again in 2002/03. Hyno Rista and Hyno Renta and their parents were compared at two-seed rates in 2001/02. Hyno Rista and its parents were added factorially to the Hyno Esta experiment in 2002/03, while Hyno Renta and Hybred and their parents were compared at two seed rates in 2002/03. Mid parent heterosis for grain yield was found in three hybrids and two of these showed high parent heterosis. High parent heterosis in Hyno Esta over a range of sowing densities was mostly exhibited in total biomass but also, in one of two years, in harvest index. High parent heterosis in Hyno Renta was associated more with harvest index than with biomass. The heterosis for biomass in Hyno Esta resulted from greater interception of photosynthetically active radiation (PAR) than the male parent, with better radiation use efficiency than the female parent. In both seasons Hyno Esta achieved grain numbers per ear at least as high as the high parent for this trait (Audace), and combined this with mean grain weights at least as heavy as the high parent for mean grain weight (Estica). Much of the increased biomass and grain yield in the hybrid came late in the season as high parent heterosis was expressed for both maximum grain filling rate and grain filling duration. Heterosis was higher when nitrogen was applied than when withheld; only greater at lower seed rates when expressed in proportionate terms (e.g. as a percentage of the parents), rather than in absolute terms (e.g. t ha(-1)); and greater in the year with the cooler and wetter summer.

The agri-environmental Footprint Index

The Agri-Environmental Footprint project is developing a common methodology for assessing the environmental impact of European agri-environment schemes. The Agri-Environmental Footprint Index (AFI) has been constructed as a customisable approach. It is a farm-level index that aggregates the measurement of agri-environmental indicators. Farm-level impact scores can be aggregated at a regional level to track temporal change and/or to provide comparisons of the success (or otherwise) of an agri-environment scheme.

Conceptual development of a harmonised method for tracking change and evaluating policy in the agri-environment: The Agri-environmental Footprint Index

An aggregated farm-level index, the Agri-environmental Footprint Index (AFI), based on multiple criteria methods and representing a harmonised approach to evaluation of EU agri-environmental schemes is described. The index uses a common framework for the design and evaluation of policy that can be customised to locally relevant agri-environmental issues and circumstances. Evaluation can be strictly policy-focused, or broader and more holistic in that context-relevant assessment criteria that are not necessarily considered in the evaluated policy can nevertheless be incorporated. The Index structure is flexible, and can respond to diverse local needs. The process of Index construction is interactive, engaging farmers and other relevant stakeholders in a transparent decision-making process that can ensure acceptance of the outcome, help to forge an improved understanding of local agri-environmental priorities and potentially increase awareness of the critical role of farmers in environmental management. The structure of the AFI facilitates post-evaluation analysis of relative performance in different dimensions of the agri-environment, permitting identification of current strengths and weaknesses, and enabling future improvement in policy design. Quantification of the environmental impact of agriculture beyond the stated aims of policy using an 'unweighted' form of the AFI has potential as the basis of an ongoing system of environmental audit within a specified agricultural context. (C) 2009 Elsevier Ltd. All rights reserved.