Determination of the characteristic directions of lossless linear optical elements

We show that the problem of finding the primary and secondary characteristic directions of a linear lossless optical element can be reformulated in terms of an eigenvalue problem related to the unimodular factor of the transfer matrix of the optical device. This formulation makes any actual computation of the characteristic directions amenable to pre-implemented numerical routines, thereby facilitating the decomposition of the transfer matrix into equivalent linear retarders and rotators according to the related Poincare equivalence theorem. The method is expected to be useful whenever the inverse problem of reconstruction of the internal state of a transparent medium from optical data obtained by tomographical methods is an issue.Comment: Replaced with extended version as published in JM

Flexible modelling of spatial variation in agricultural field trials with the R package INLA

The objective of this paper was to fit different established spatial models for analysing agricultural field trials using the open-source R package INLA. Spatial variation is common in field trials, and accounting for it increases the accuracy of estimated genetic effects. However, this is still hindered by the lack of available software implementations. We compare some established spatial models and show possibilities for flexible modelling with respect to field trial design and joint modelling over multiple years and locations. We use a Bayesian framework and for statistical inference the integrated nested Laplace approximations (INLA) implemented in the R package INLA. The spatial models we use are the well-known independent row and column effects, separable first-order autoregressive ( AR1⊗AR1 ) models and a Gaussian random field (Matérn) model that is approximated via the stochastic partial differential equation approach. The Matérn model can accommodate flexible field trial designs and yields interpretable parameters. We test the models in a simulation study imitating a wheat breeding programme with different levels of spatial variation, with and without genome-wide markers and with combining data over two locations, modelling spatial and genetic effects jointly. The results show comparable predictive performance for both the AR1⊗AR1 and the Matérn models. We also present an example of fitting the models to a real wheat breeding data and simulated tree breeding data with the Nelder wheel design to show the flexibility of the Matérn model and the R package INLA

Epigenetics, heritability and longitudinal analysis

© 2018 The Author(s). Background: Longitudinal data and repeated measurements in epigenome-wide association studies (EWAS) provide a rich resource for understanding epigenetics. We summarize 7 analytical approaches to the GAW20 data sets that addressed challenges and potential applications of phenotypic and epigenetic data. All contributions used the GAW20 real data set and employed either linear mixed effect (LME) models or marginal models through generalized estimating equations (GEE). These contributions were subdivided into 3 categories: (a) quality control (QC) methods for DNA methylation data; (b) heritability estimates pretreatment and posttreatment with fenofibrate; and (c) impact of drug response pretreatment and posttreatment with fenofibrate on DNA methylation and blood lipids. Results: Two contributions addressed QC and identified large statistical differences with pretreatment and posttreatment DNA methylation, possibly a result of batch effects. Two contributions compared epigenome-wide heritability estimates pretreatment and posttreatment, with one employing a Bayesian LME and the other using a variance-component LME. Density curves comparing these studies indicated these heritability estimates were similar. Another contribution used a variance-component LME to depict the proportion of heritability resulting from a genetic and shared environment. By including environmental exposures as random effects, the authors found heritability estimates became more stable but not significantly different. Two contributions investigated treatment response. One estimated drug-associated methylation effects on triglyceride levels as the response, and identified 11 significant cytosine-phosphate-guanine (CpG) sites with or without adjusting for high-density lipoprotein. The second contribution performed weighted gene coexpression network analysis and identified 6 significant modules of at least 30 CpG sites, including 3 modules with topological differences pretreatment and posttreatment. Conclusions: Four conclusions from this GAW20 working group are: (a) QC measures are an important consideration for EWAS studies that are investigating multiple time points or repeated measurements; (b) application of heritability estimates between time points for individual CpG sites is a useful QC measure for DNA methylation studies; (c) drug intervention demonstrated strong epigenome-wide DNA methylation patterns across the 2 time points; and (d) new statistical methods are required to account for the environmental contributions of DNA methylation across time. These contributions demonstrate numerous opportunities exist for the analysis of longitudinal data in future epigenetic studies

Microsatellite Support for Active Inbreeding in a Cichlid Fish

In wild animal populations, the degree of inbreeding differs between species and within species between populations. Because mating with kin often results in inbreeding depression, observed inbreeding is usually regarded to be caused by limited outbreeding opportunities due to demographic factors like small population size or population substructuring. However, theory predicts inclusive benefits from mating with kin, and thus part of the observed variation in inbreeding might be due to active inbreeding preferences. Although some recent studies indeed report kin mating preferences, the evidence is still highly ambiguous. Here, we investigate inbreeding in a natural population of the West African cichlid fish Pelvicachromis taeniatus which showed clear kin mating preferences in standardized laboratory experiments but no inbreeding depression. The presented microsatellite analysis reveals that the natural population has, in comparison to two reference populations, a reduced allelic diversity (A = 3) resulting in a low heterozygosity (Ho = 0.167) pointing to a highly inbred population. Furthermore, we found a significant heterozygote deficit not only at population (Fis = 0.116) but also at subpopulation level (Fis = 0.081) suggesting that inbreeding is not only a by-product of population substructuring but possibly a consequence of behavioral kin preferences

The Effect of Graded Levels of Exercise on Energy Intake and Balance in Free-Living Women

Assesses the effect of graded increases in exercised-induced energy expenditure (EE) on appetite, daily energy intake (EI), total daily EE and body weight in lean women. Compensations in EI produced by markedly increasing EE through exercise; Accurate adjustments of EI to acute increases in EE that are likely to take weeks rather than days