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Polydisperse dust, as in astrophysical observations, occurs in a range of sizes, compositions, charges, and masses, with corresponding changes to linear dispersion laws. At the fluid level the charged dust can be treated as a discrete collection of different fluids or as the continuous limit over a charge range. On the other hand, one global dust fluid needs appropriate model equations, derivable from a Klimontovich or extended Vlasov approach, in which charge, mass, and/or size enter as extra phase space variables. Due to differing charge-to-mass weightings, this is sometimes quite involved. An extended kinetic theory allows for a more correct picture, including possible microscopic damping mechanisms, but quickly becomes very unwieldy. An intermediate procedure is to use results for monodisperse dust and integrate afterwards over dust distributions. This cannot be applied blindly, so that it is necessary to check results on their applicability and consistency. Selected applications have been treated for parallel electromagnetic, oblique electrostatic (and possibly self-gravitational), and fluid dust-Bernstein modes, to illustrate the methodological aspects of this part of dusty plasma physics. Index Terms--Complex plasmas, dust distributions, dust-Bernstein modes, dusty plasmas, electromagnetic waves, electrostatic waves.

Dust-acoustic waves in dusty plasmas are studied in a kinetic context incorporating dust distributions and charge fluctuations, two of the main features that distinguish dusty or complex from ordinary plasmas. This is done by deriving a generalized Vlasov equation in an extended phase space. No specific charging model is used so that the results are generic. Index Terms--Complex plasmas, dust charge fluctuations, dust distributions, dust-acoustic waves, dusty plasmas, generalized Vlasov equation.

Identifying gene-gene interactions or gene-environment interactions in studies of human complex diseases remains a big challenge in genetic epidemiology. An additional challenge, often forgotten, is to account for important lower-order genetic effects. These may hamper the identification of genuine epistasis. If lower-order genetic effects contribute to the genetic variance of a trait, identified statistical interactions may simply be due to a signal boost of these effects. In this study, we restrict attention to quantitative traits and bi-allelic SNPs as genetic markers. Moreover, our interaction study focuses on 2- way SNP-SNP interactions. Via simulations, we assess the performance of different corrective measures for lower-order genetic effects in Model-Based Multifactor Dimensionality Reduction epistasis detection, using additive and co-dominant coding schemes. Performance is evaluated in terms of power and familywise error rate. Our simulations indicate that empirical power estimates are reduced with correction of lower-order effects, likewise familywise error rates. Easy-to-use automatic SNP selection procedures, SNP selection based on ''top'' findings, or SNP selection based on p-value criterion for interesting main effects result in reduced power but also almost zero false positive rates. Always accounting for main effects in the SNP-SNP pair under investigation during Model-Based Multifactor Dimensionality Reduction analysis adequately controls false positive epistasis findings. This is particularly true when adopting a co-dominant corrective coding scheme. In conclusion, automatic search procedures to identify lower-order effects to correct for during epistasis screening should be avoided. The same is true for procedures that adjust for lower-order effects prior to Model-Based Multifactor Dimensionality Reduction and involve using residuals as the new trait. We advocate using ''on-the-fly'' lower-order effects adjusting when screening for SNP-SNP interactions using Model-Based Multifactor Dimensionality Reduction analysis. [ABSTRACT FROM AUTHOR]

In the quest for the missing heritability of most complex diseases, rare variants have received increased attention. Advances in large-scale sequencing have led to a shift from the common disease/common variant hypothesis to the common disease/rare variant hypothesis or have at least reopened the debate about the relevance and importance of rare variants for gene discoveries. The investigation of modeling and testing approaches to identify significant disease/ rare variant associations is in full motion. New methods to better deal with parameter estimation instabilities, convergence problems, or multiple testing corrections in the presence of rare variants or effect modifiers of rare variants are in their infancy. Using a recently developed semiparametric strategy to detect causal variants, we investigate the performance of the model-based multifactor dimensionality reduction (MB-MDR) technique in terms of power and family-wise error rate (FWER) control in the presence of rare variants, using population-based and familybased data (FAM-MDR). We compare family-based results obtained from MB-MDR analyses to screening findings from a quantitative trait Pedigree-based association test (PBAT). Population-based data were further examined using penalized regression models. We restrict attention to all available single-nucleotide polymorphisms on chromosome 4 and consider Q1 as the outcome of interest. The considered family-based methods identified marker C4S4935 in the VEGFC gene with estimated power not exceeding 0.35 (FAM-MDR), when FWER was kept under control. The considered population-based methods gave rise to highly inflated FWERs (up to 90% for PBAT screening). [ABSTRACT FROM AUTHOR]

Earlier systematic nonlinear treatments of parallel propagating electromagnetic waves have been given within a fluid dynamic approach, in a frame where the nonlinear structures are stationary and various constraining first integrals can be obtained. This has lead to the concept of oscillitons that has found application in various space plasmas. The present paper differs in three main aspects from the previous studies: first, the invariants are derived in the plasma frame, as customary in the Sagdeev method, thus retaining in Maxwell’s equations all possible effects. Second, a single differential equation is obtained for the parallel fluid velocity, in a form reminiscent of the Sagdeev integrals, hence allowing a fully nonlinear discussion of the oscilliton properties, at such amplitudes as the underlying Mach number restrictions allow. Third, the transition to weakly nonlinear whistler oscillitons is done in an analytical rather than a numerical fashion. [ABSTRACT FROM AUTHOR]