Approximating cube roots of integers, after Heron's Metrica III.20

Heron, in Metrica III.20-22, is concerned with the the division of solid figures - pyramids, cones and frustra of cones - to which end there is a need to extract cube roots. We report here on some of our findings on the conjecture by Taisbak in C.M.Taisbak, Cube roots of integers. A conjecture about Heron's method in Metrika III.20. Historia Mathematica, 41 (2014), 103-104

Scintillation detector for carbon-14

Detector consists of plastic, cylindrical double-wall scintillation cell, which is filled with gas to be analyzed. Thin, inner cell wall is isolated optically from outer (guard) scintillator wall by evaporated-aluminum coating. Bonding technique provides mechanical support to cell wall when device is exposed to high temperatures

Genetic correlations among protein yield, productive life, and type traits from the United States and diseases other than mastitis from Denmark and Sweden

Sire genetic evaluations for protein yield, productive life, and selected type traits from the US were correlated with sire evaluations for disease from Denmark and Sweden and were then adjusted to approximate genetic correlations. Disease categories from Denmark included reproductive diseases, foot and leg diseases, metabolic and digestive diseases, and all diseases other than mastitis. Genetic evaluations for Denmark were from separate analyses for each disease category using a multiple-trait sire model with first, second, and third lactations handled as multiple traits. Evaluations from Sweden for all diseases other than mastitis were from a single-trait sire model using only first lactations. In addition, Danish and Swedish genetic evaluations were regressed on US type evaluations to test for quadratic relationships. Relationships were based on 104 bulls with US and Danish evaluations (88 with US type) and 84 bulls with US and Swedish evaluations (83 with US type). Genetic correlations between US protein yield and diseases were unfavorable, but correlations were favorable between productive life and disease. Genetic correlations among US type and diseases were around zero, except for correlations with US dairy form (range -0.34 to -0.73). Genetic correlations calculated from residual correlations (adjusted for predicted transmitting abilities for milk) between productive life and diseases were favorable (range 0.29 to 0.51). Genetic correlations calculated from residual correlations (adjusted for predicted transmitting abilities for milk) between dairy form and diseases ranged from -0.10 to -0.53. Selection for increased productive life may reduce disease occurrences, but selection for higher dairy form scores will increase disease occurrences.</p

Stochastic oscillations of adaptive networks: application to epidemic modelling

Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can radically alter the system's behaviour. In this article we develop a method to predict the effects of stochasticity in adaptive networks by making use of a pair-based proxy model. The technique is developed in the context of an epidemiological model of a disease spreading over an adaptive network of infectious contact. Our analysis reveals that in this model the structure of the network exhibits stochastic oscillations in response to fluctuations in the disease dynamic.Comment: 11 pages, 4 figure