Mersenne numbers

These notes have been issued on a small scale in 1983 and 1987 and on request at other times. This issue follows two items of news. First, WaIter Colquitt and Luther Welsh found the 'missed' Mersenne prime M110503 and advanced the frontier of complete Mp-testing to 139,267. In so doing, they terminated Slowinski's significant string of four consecutive Mersenne primes. Secondly, a team of five established a non-Mersenne number as the largest known prime. This result terminated the 1952-89 reign of Mersenne primes. All the original Mersenne numbers with p < 258 were factorised some time ago. The Sandia Laboratories team of Davis, Holdridge & Simmons with some little assistance from a CRAY machine cracked M211 in 1983 and M251 in 1984. They contributed their results to the 'Cunningham Project', care of Sam Wagstaff. That project is now moving apace thanks to developments in technology, factorisation and primality testing. New levels of computer power and new computer architectures motivated by the open-ended promise of parallelism are now available. Once again, the suppliers may be offering free buildings with the computer. However, the Sandia '84 CRAY-l implementation of the quadratic-sieve method is now outpowered by the number-field sieve technique. This is deployed on either purpose-built hardware or large syndicates, even distributed world-wide, of collaborating standard processors. New factorisation techniques of both special and general applicability have been defined and deployed. The elliptic-curve method finds large factors with helpful properties while the number-field sieve approach is breaking down composites with over one hundred digits. The material is updated on an occasional basis to follow the latest developments in primality-testing large Mp and factorising smaller Mp; all dates derive from the published literature or referenced private communications. Minor corrections, additions and changes merely advance the issue number after the decimal point. The reader is invited to report any errors and omissions that have escaped the proof-reading, to answer the unresolved questions noted and to suggest additional material associated with this subject.

Folsomia candida (Collembola): A "standard" soil arthropod

Folsomia candida Willem 1902, a member of the order Collembola (colloquially called springtails), is a common and widespread arthropod that occurs in soils throughout the world. The species is parthenogenetic and is easy to maintain in the laboratory on a diet of granulated dry yeast. F. candida has been used as a "standard" test organism for more than 40 years for estimating the effects of pesticides and environmental pollutants on nontarget soil arthropods. However. it has also been employed as a model for the investigation of numerous other phenomena such as cold tolerance, quality as a prey item, and effects of microarthropod grazing on pathogenic fungi and mycorrhizae of plant roots. In this comprehensive review. aspects of the life history, ecology, and ecotoxicology of F candida are covered. We focus on the recent literature, especially studies that have examined the effects of soil pollutants on reproduction in F candida using the protocol published by the International Standards Organization in 1999.

Study of the lactation curve in dairy cattle on farms in Central Mexico

Accurate knowledge of lactation curves has an important relevance to management and research of dairy production systems. A number of equations have been proposed to describe the lactation curve, the most widely applied being the gamma equation. The objective of this work was to compare and evaluate candidate functions for their predictive ability in describing lactation curves from central Mexican dairy cows reared under 2 contrasting management systems. Five equations were considered: Gaines ( exponential decay), Wood ( gamma equation), Rook ( Michaelis-Menten x exponential), and 2 more mechanistic ones (Dijkstra and Pollott). A database consisting of 701 and 1283 records of cows in small-scale and intensive systems, respectively, was used in the analysis. Before analysis, the database was divided into 6 groups representing first, second, and third and higher parity cows in both systems. In all cases except second and above parity cows in small-scale systems, all models improved on the Gaines equation. The Wood equation explained much of the variation, but its parameters do not have direct biological interpretation. Although the Rook equation fitted the data well, some of the parameter estimates were not significant. The Dijkstra equation consistently gave better predictions, and its parameters were usually statistically significant and lend themselves to physiological interpretation. As such, the differences between systems and parity could be explained due to variations in theoretical initial milk production at parturition, specific rates of secretory cell proliferation and death, and rate of decay, all of which are parameters in the model. The Pollott equation, although containing the most biology, was found to be over-parameterized and resulted in nonsignificant parameter estimates. For central Mexican dairy cows, the Dijkstra equation was the best option to use in describing the lactation curve.

Comparison of sample size formulae for 2x2 cross-over designs applied to bioequivalence studies

We consider the comparison of two formulations in terms of average bioequivalence using the 2 × 2 cross-over design. In a bioequivalence study, the primary outcome is a pharmacokinetic measure, such as the area under the plasma concentration by time curve, which is usually assumed to have a lognormal distribution. The criterion typically used for claiming bioequivalence is that the 90% confidence interval for the ratio of the means should lie within the interval (0.80, 1.25), or equivalently the 90% confidence interval for the differences in the means on the natural log scale should be within the interval (-0.2231, 0.2231). We compare the gold standard method for calculation of the sample size based on the non-central t distribution with those based on the central t and normal distributions. In practice, the differences between the various approaches are likely to be small. Further approximations to the power function are sometimes used to simplify the calculations. These approximations should be used with caution, because the sample size required for a desirable level of power might be under- or overestimated compared to the gold standard method. However, in some situations the approximate methods produce very similar sample sizes to the gold standard method. Copyright © 2005 John Wiley & Sons, Ltd.

Folsomia candida (Collembola): A "standard" soil arthropod

Folsomia candida Willem 1902, a member of the order Collembola (colloquially called springtails), is a common and widespread arthropod that occurs in soils throughout the world. The species is parthenogenetic and is easy to maintain in the laboratory on a diet of granulated dry yeast. F. candida has been used as a "standard" test organism for more than 40 years for estimating the effects of pesticides and environmental pollutants on nontarget soil arthropods. However. it has also been employed as a model for the investigation of numerous other phenomena such as cold tolerance, quality as a prey item, and effects of microarthropod grazing on pathogenic fungi and mycorrhizae of plant roots. In this comprehensive review. aspects of the life history, ecology, and ecotoxicology of F candida are covered. We focus on the recent literature, especially studies that have examined the effects of soil pollutants on reproduction in F candida using the protocol published by the International Standards Organization in 1999.

Responsiveness to change by standard-form contract drafters: A case study of the FIDIC White Book

Purpose – The purpose of this paper is to focus on the Fédération Internationale des Ingénieurs-Conseils (FIDIC) White Book standard form of building contract. It tracks the changes to this contract over its four editions, and seeks to identify their underlying causes. Design/methodology/approach – The changes made to the White Book are quantified using a specific type of quantitative content analysis. The amended clauses are then examined to understand the nature of the changes made. Findings – The length of the contract increased by 34 per cent between 1990 and 2006. A large proportion of the overall increase can be attributed to the clauses dealing with “conflict of interest/corruption” and “dispute resolution”. In both instances, the FIDIC drafting committees have responded to international developments to discourage corruption, and to encourage the use of alternative dispute resolution. Between 1998 and 2006, the average length of the sentences increased slightly, raising the question of whether long sentences are easily understood by users of contracts. Research limitations/implications – Quantification of text appears to be particularly useful for the analysis of documents which are regularly updated because changes can be clearly identified and the length of sentences can be determined, leading to conclusions about the readability of the text. However, caution is needed because changes of great relevance can be made to contract clauses without actually affecting their length. Practical implications – The paper will be instructive for contract drafters and informative for users of FIDIC's White Book. Originality/value – Quantifying text has been rarely used regarding standard-form contracts in the field of construction.

Changing Standards? Children's awareness and knowledge of features of written standard English at ages 10-11

This paper reports the findings of a small-scale research project, which investigated the levels of awareness and knowledge of written standard English of 10- and 11-year-old children in two English primary schools over a six-year period, coinciding with the implementation in the schools of the National Literacy Strategy (NLS). A questionnaire was used to provide quantitative and qualitative data relating to: features of writing which were recognised as standard or non-standard; children's understanding of technical terminology; variations between boys' and girls' performance; and the impact of the NLS over time. The findings reveal variations in levels of recognition of different non-standard features, differences between girls' and boys' recognition, possible examples of language change, but no evidence of a positive impact of the NLS. The implications of these findings are discussed both in terms of changes in educational standards and changes to standard English.

Long-term monounsaturated fatty acid diets reduce platelet aggregation in healthy young subjects

The aim of the present study was to compare the response of a range of atherogenic and thrombogenic risk markers to two dietary levels of saturated fatty acid (SFA) substitution with monounsaturated fatty acids (MUFA) in students living in a university hall of residence. Although the benefits of such diets have been reported for plasma lipoproteins in high-risk groups, more needs to be known about effects of more modest SFA-MUFA substitutions over the long term and in young healthy adults. In a parallel design over 16 weeks, fifty-one healthy young subjects were randomised to one of two diets: (1) a moderate-MUFA diet in which 16 g dietary SFA/100 g total fatty acids were substituted with MUFA (n 25); (2) a high-MUFA diet in which 33 g dietary SFA/100 g total fatty acids were substituted with MUFA (n 26). All subjects followed an 8-week run-in diet (reference diet), with a fatty acid composition close to the UK average values. There were no differences in plasma lipid responses between the two diets over 16 weeks of the study with similar reductions in total cholesterol (P<0.001) and LDL-cholesterol (P<0.01) in both groups; a small but significant reduction in HDL-cholesterol was also observed in both groups (P<0.01). Platelet responses to ADP (P<0.01) and arachidonic acid (P<0.05) differed with time on the two diets; at 16 weeks, platelet aggregatory response to ADP was significantly lower on the high-MUFA than the moderate-MUFA (P<0.01) diet; ADP responses were also significantly lower within this group at 8 (P< 0.05) and 16 (P< 0.01) weeks compared with baseline. There were no differences in fasting factor VII activity (factors VIII and VIIag), fibrinogen concentration or tissue-type plasminogen activator activity between the diets. There were no differences in postprandial factor VIII responses to a standard meal (area under the curve) between the diets after 16 weeks, but postprandial factor VIII response was lower than on the high-MUFA diet compared with baseline (P<0.01). In conclusion, a high-MUFA diet sustains potentially beneficial effects on platelet aggregation and postprandial activation of factor VII. Moderate or high substitution of MUFA for SFA achieves similar reductions in fasting blood lipids in young healthy subjects.

Chylomicron particle size and number, factor VII activation and dietary monounsaturated fatty acids

This study evaluated the effects of substituting dietary saturated fatty acids (SFAs) with monounsaturated fatty acids (MUFAs) on postprandial chylomicron (triacylglycerol (TAG), apolipoprotein B-48 (apo B-48) and retinyl ester (RE)), chylomicron particle size and factor VII (FVII) response when subjects were given a standard meal. In a controlled sequential design, 51 healthy young subjects followed an SFA-rich diet (Reference diet) for 8 weeks after which half of the subjects followed a moderate MUFA diet (n = 25) and half followed a high MUFA diet (n = 26) for 16 weeks. Fasting lipoprotein and lipid measurements were evaluated at baseline and at 8-week intervals during the Reference and MUFA diets. In 25 of the subjects (n = 12 moderate MUFA, n = 13 high MUFA), postprandial responses to a standard test meal containing RE and 13 C-tripalmitin were investigated at the end of the Reference and the MUFA diet periods. Although there were no differences in the postprandial lipid markers (TAG, RE, C-13-TAG) on the two diets, the postprandial apo B-48 response (incremental area under the curve (IAUC) was reduced by 21% on the moderate MUFA diet (NS) and by 54% on the high MUFA diet (P < 0.01). The postprandial peak concentrations of apo B-48 were reduced by 33% on the moderate MUFA diet (P < 0.01) and 48% on the high MUFA diet (P < 0.001). Fasting values for factor VII activity (FVIIc), activated factor VII (FVIIa) or factor VII antigen (FVIIag) did not differ significantly when subjects were transferred from Reference to MUFA diets. However, the postprandial increases in coagulation FVII activity (FVIIc) were 18% lower and of activated FVII (FVIIa) were 17% lower on the moderate MUFA diet (NS). Postprandial increases in FVIIc and FVIIa were 50% (P < 0.05) and 29% (P < 0.07) lower on the high MUFA diet and the area under the postprandial FVIIc response curve (AUC) was also lower on the high MUFA diet (P < 0.05). Significantly higher ratios of RE:apo B-48 (P < 0.001) and 13 C-palmitic acid:apo B-48 (P < 0.01) during both MUFA diets suggest that the CMs formed carry larger amounts of dietary lipids per particle, reflecting an adaptation to form larger lipid droplets in the enterocyte when increased amounts of dietary MUFAs are fed. Smaller numbers of larger chylomicrons may explain attenuated activation of factor VII during the postprandial state when the background diet is rich in MUFA. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

Assessment of the quality of cottage cheese produced from standard and protein-fortified skim milk

The effects of milk protein fortification on the texture and microstructure of cottage cheese curd were evaluated. Protein powder (92.6% protein) was added to the skim milk at a level of 0.4% (w/w) to produce curds. Control curds with no protein powder addition were also produced. These curds were analysed for differences in yield, total solids, curd size, texture and structure. It was found that the addition of protein powder contributed to a significant yield increase, which can be attributed to increased water retention, with better curd size distribution. Control curds were firmer than the fortified curds and the structure showed less open-pore structure as revealed by electron microscopy. However, the addition of dressing masked the textural differences, and a sensory panel was unable to distinguish between cheeses produced from fortified milk and controls.

Research into anxiety of childhood: playing catch-up (to Olympic standard)

This special issue is the culmination of an ESRC seminar series grant awarded to the authors of this editorial. We named the seminar series CATTS (Child Anxiety, Theory and Treatment Seminars) and it took the form of six highly stimulating, one-day seminars on the subject of child anxiety, with participants from clinical and academic backgrounds and from Great Britain, Europe, the USA and Australia. Most of the authors in this publication, and a sister special issue in Cognitions and Emotion (2008), participated in the CATTS series.