An extension to GUM methodology: degrees-of-freedom calculations for correlated multidimensional estimates

The Guide to the Expression of Uncertainty in Measurement advocates the use of an 'effective number of degrees of freedom' for the calculation of an interval of measurement uncertainty. However, it does not describe how this number is to be calculated when (i) the measurand is a vector quantity or (ii) when the errors in the estimates of the quantities defining the measurand (the 'input quantities') are not incurred independently. An appropriate analysis for a vector-valued measurand has been described (Metrologia 39 (2002) 361-9), and a method for a one-dimensional measurand with dependent errors has also been given (Metrologia 44 (2007) 340-9). This paper builds on those analyses to present a method for the situation where the problem is multidimensional and involves correlated errors. The result is an explicit general procedure that reduces to simpler procedures where appropriate. The example studied is from the field of radio-frequency metrology, where measured quantities are often complex-valued and can be regarded as vectors of two elements.Comment: 30 pages with 2 embedded figure

Effects of hatching timing on red-eyed treefrog tadpoles: relative vulnerability varies among predators but not with hatchling age-structure, growth varies with the presence of more vulnerable tadpoles [poster]

In Gamboa, Panama, undisturbed red-eyed treefrog embryos typically hatch at age 6 days, but they can hatch as early as 4 days if attacked by egg predators. Early hatchlings are less developed and more vulnerable to predatory shrimp and fish. Here we assess the effect of hatching timing on risk of predation by three common insects, with different foraging styles, that prey on red-eyed treefrog larvae. Further, we examine whether the consequences of hatching early vary with the presence of later-hatched tadpoles. We induced hatching at 4 and 6 days and exposed tadpoles to giant water bugs or aeshnid or libellulid dragonfly larvae over 24 hrs, quantifying tadpole behavior and mortality. We used substitutive designs with three treatments: early hatched, late hatched and mixed hatching ages. In no case did presence of the other age class alter mortality. Hatching age did not affect libelullid predation, which was low in both cases. Early-hatched tadpoles had higher mortality than late hatchlings with water bugs, which move throughout the water column. In contrast, early hatchlings had lower mortality than late hatchlings with aeshnids, which cue strongly on movement. Late-hatched tadpoles were more active than early hatchlings, and movement was reduced in the presence of aeshnids. Combining across this and previously published studies, early hatchlings are more vulnerable than late hatchlings to most (3/5) predators. Variation in relative, age-specific hatchling vulnerability to predators with different foraging styles is consistent with developmental changes in tadpole behavior

The Cost of Hatching Early: Vulnerability and Exposure to Predators [poster]

Arboreal red-eyed treefrog embryos can hatch prematurely in response to egg predators. Induced early hatchlings face aquatic predators when less developed and for longer than do later hatchlings; both factors may alter survival through the high-risk early larval period. Prior work focused on developmental effects of induced hatching. In 24 h trials, less developed hatchlings were more vulnerable to three aquatic predators (shrimp, fish, water bugs) but had similar or better survival than full-term hatchlings with libellulid and aeschnid dragonfly nymphs. However, it is unknown how developmental effects and duration of exposure to predators combine to create the net effect of early hatching. Here we measured costs of early hatching over a 72 h period, from first hatching competence past peak spontaneous hatching. Embryos hatched at age 4 or 6 days were exposed to water bugs, aeshnids, or libellulids. Early-hatched tadpoles suffered higher mortality than late hatchlings with all three predators. The longer exposure of early hatchlings to aquatic predators reversed their initial phenotypic advantage with aeshnids and revealed a cost of early hatching with libellulids where none was apparent from phenotypes alone. In other experiments, early-hatched tadpoles reared without predators grew more quickly than those reared with predators cues, which grew more quickly than age-matched embryos, revealing phenotypic effects of both predator cues and the egg vs. aquatic environment. Nonetheless, any potential benefits of predator-induced phenotypes on tadpole survival were insufficient to compensate for the increased duration of predator exposure that is a consequence of hatching early. From the Conference Program at http://www.sicb.org/meetings/2011/schedule/abstractdetails.php3?id=23

Recent Developments in OCL and Textual Modelling

The panel session of the 16th OCL workshop featured a lightning talk session for discussing recent developments and open questions in the area of OCL and textual modelling. During this session, the OCL community discussed, stimulated through short presentations by OCL experts, tool support, potential future extensions, and suggested initiatives to make the textual modelling community even more successful. This collaborative paper, to which each OCL expert contributed one section, summarises the discussions as well as describes the recent developments and open questions presented in the lightning talks

Temperature drives pre-reproductive selection and shapes the biogeography of a female polymorphism

Acknowledgements We are grateful to the many field assistants, PhD students and postdocs who have participated in the field work and thereby directly and indirectly contributed to this study over many years, since 2000 when it was started. We also wish to thank David and Rosalyn Sparrow who kindly hosted B. Willink during a field trip to Cyprus in 2017 and who provided valuable field work help and guidance, enabling us to gather information about morph frequencies of I. elegans at one of the southernmost localities of this species in Europe. Funding information Funding for this study has been provided by research grants from The Swedish Research Council (VR: grant no. 2016‐03356), Carl Tryggers Foundation (CTS), Gyllenstiernska Krapperupstiftelsen (grant no. KR2018‐0038), Stina Werners Foundation and Erik Philip Sörensens Stiftelse to E.I.S.Peer reviewedPostprin

The Bivariate Normal Copula

We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.Comment: 24 page

Which clinical research questions are the most important? Development and preliminary validation of the Australia & New Zealand Musculoskeletal (ANZMUSC) Clinical Trials Network Research Question Importance Tool (ANZMUSC-RQIT).

Background and aims High quality clinical research that addresses important questions requires significant resources. In resource-constrained environments, projects will therefore need to be prioritized. The Australia and New Zealand Musculoskeletal (ANZMUSC) Clinical Trials Network aimed to develop a stakeholder-based, transparent, easily implementable tool that provides a score for the 'importance' of a research question which could be used to rank research projects in order of importance. Methods Using a mixed-methods, multi-stage approach that included a Delphi survey, consensus workshop, inter-rater reliability testing, validity testing and calibration using a discrete-choice methodology, the Research Question Importance Tool (ANZMUSC-RQIT) was developed. The tool incorporated broad stakeholder opinion, including consumers, at each stage and is designed for scoring by committee consensus. Results The ANZMUSC-RQIT tool consists of 5 dimensions (compared to 6 dimensions for an earlier version of RQIT): (1) extent of stakeholder consensus, (2) social burden of health condition, (3) patient burden of health condition, (4) anticipated effectiveness of proposed intervention, and (5) extent to which health equity is addressed by the research. Each dimension is assessed by defining ordered levels of a relevant attribute and by assigning a score to each level. The scores for the dimensions are then summed to obtain an overall ANZMUSC-RQIT score, which represents the importance of the research question. The result is a score on an interval scale with an arbitrary unit, ranging from 0 (minimal importance) to 1000. The ANZMUSC-RQIT dimensions can be reliably ordered by committee consensus (ICC 0.73-0.93) and the overall score is positively associated with citation count (standardised regression coefficient 0.33, p<0.001) and journal impact factor group (OR 6.78, 95% CI 3.17 to 14.50 for 3rd tertile compared to 1st tertile of ANZMUSC-RQIT scores) for 200 published musculoskeletal clinical trials. Conclusion We propose that the ANZMUSC-RQIT is a useful tool for prioritising the importance of a research question.William J. Taylor, Robin Willink, Denise A. O, Connor, Vinay Patel, Allison Bourne, Ian A. Harris, Samuel L. Whittle, Bethan Richards, Ornella Clavisi, Sally Green, Rana S. Hinman, Chris G. Maher, Ainslie Cahill, Annie McPherson, Charlotte Hewson, Suzie E. May, Bruce Walker, Philip C. Robinson, Davina Ghersi, Jane Fitzpatrick, Tania Winzenberg, Kieran Fallon, Paul Glasziou, Laurent Billot, Rachelle Buchbinde