Premixed hydrogen flames are prone to thermodiffusive instabilities due to strong differential diffusion effects. Reproducing these instabilities in large eddy simulations (LES), where their effects are only partially resolved, is challenging. Combustion models that account for differential diffusion effects have been developed for laminar flames, but to use them in LES, models for the turbulence/flame subfilter interactions are required. Modelling of the subfilter interactions is particularly challenging as instabilities synergistically interact with turbulence resulting in a strong enhancement of the turbulent flame speed. In this work, a combustion model for LES, which accounts for thermodiffusive instabilities and their interactions with turbulence, is presented. In the first part, an a priori analysis based on a direct numerical simulation (DNS) of a turbulent hydrogen/air jet flame is discussed. Progress variable, progress variable variance and mixture fraction are rigorously identified as suitable model input parameters, and an LES combustion model based on pre-tabulated unstretched premixed flamelets with varying equivalence ratio is formulated. Subfilter closure is achieved via a presumed probability density function and a significant reduction of modelling errors is achieved with the presented model. In the second part, LES of the DNS configuration are performed for an a posteriori analysis. The presented combustion model shows significant improvements in predicting the flame length and local phenomena, such as super-adiabatic temperature, compared with combustion models that either neglect differential diffusion effects or consider these effects but neglect the subfilter closure. Two variants of the model formulation with a water- or hydrogen-based progress variable have been tested, yielding overall similar predictions.

Multidimensional item response theory (MIRT) offers psychometric models for various data settings, most popularly for dichotomous and polytomous data. Less attention has been devoted to count responses. A recent growth in interest in count item response models (CIRM)—perhaps sparked by increased occurrence of psychometric count data, e.g., in the form of process data, clinical symptom frequency, number of ideas or errors in cognitive ability assessment—has focused on unidimensional models. Some recent unidimensional CIRMs rely on the Conway–Maxwell–Poisson distribution as the conditional response distribution which allows conditionally over-, under-, and equidispersed responses. In this article, we generalize to the multidimensional case, introducing the Multidimensional Two-Parameter Conway–Maxwell–Poisson Model (M2PCMPM). Using the expectation-maximization (EM) algorithm, we develop marginal maximum likelihood estimation methods, primarily for exploratory M2PCMPMs. The resulting discrimination matrices are rotationally indeterminate. Recently, regularization of the discrimination matrix has been used to obtain a simple structure (i.e., a sparse solution) for dichotomous and polytomous data. For count data, we also (1) rotate or (2) regularize the discrimination matrix. We develop an EM algorithm with lasso ($\ell _1$) regularization for the M2PCMPM and compare (1) and (2) in a simulation study. We illustrate the proposed model with an empirical example using intelligence test data.

Large sample theory states the asymptotic normality of the maximum likelihood estimator of the person parameter in the two parameter logistic (2PL) model. In short tests, however, the assumption of normality can be grossly wrong. As a consequence, intended coverage rates may be exceeded and confidence intervals are revealed to be overly conservative. Methods belonging to the higher-order-theory, more specifically saddlepoint approximations, are a convenient way to deal with small-sample problems. Confidence bounds obtained by these means hold the approximate confidence level for a broad range of the person parameter. Moreover, an approximation to the exact distribution permits to compute median unbiased estimates (MUE) that are as likely to overestimate as to underestimate the true person parameter. Additionally, in small samples, these MUE are less mean-biased than the often-used maximum likelihood estimator.

Many screening tests dichotomize a measurement to classify subjects. Typically a cut-off value is chosen in a way that allows identification of an acceptable number of cases relative to a reference procedure, but does not produce too many false positives at the same time. Thus for the same sample many pairs of sensitivities and false positive rates result as the cut-off is varied. The curve of these points is called the receiver operating characteristic (ROC) curve. One goal of diagnostic meta-analysis is to integrate ROC curves and arrive at a summary ROC (SROC) curve. Holling, Böhning, and Böhning (Psychometrika 77:106–126, 2012a) demonstrated that finite semiparametric mixtures can describe the heterogeneity in a sample of Lehmann ROC curves well; this approach leads to clusters of SROC curves of a particular shape. We extend this work with the help of the $t_{\mathit{\alpha }}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$t_{\alpha }$$\end{document} transformation, a flexible family of transformations for proportions. A collection of SROC curves is constructed that approximately contains the Lehmann family but in addition allows the modeling of shapes beyond the Lehmann ROC curves. We introduce two rationales for determining the shape from the data. Using the fact that each curve corresponds to a natural univariate measure of diagnostic accuracy, we show how covariate adjusted mixtures lead to a meta-regression on SROC curves. Three worked examples illustrate the method.

The paper outlines several approaches for dealing with meta-analyses of count outcome data. These counts are the accumulation of occurred events, and these events might be rare, so a special feature of the meta-analysis is dealing with low counts including zero-count studies. Emphasis is put on approaches which are state of the art for count data modelling including mixed log-linear (Poisson) and mixed logistic (binomial) regression as well as nonparametric mixture models for count data of Poisson and binomial type. A simulation study investigates the performance and capability of discrete mixture models in estimating effect heterogeneity. The approaches are exemplified on a meta-analytic case study investigating the acceptance of bibliotherapy.

In this paper, optimal designs will be derived for estimating the ability parameters of the Rasch model when difficulty parameters are known. It is well established that a design is locally D-optimal if the ability and difficulty coincide. But locally optimal designs require that the ability parameters to be estimated are known. To attenuate this very restrictive assumption, prior knowledge on the ability parameter may be incorporated within a Bayesian approach. Several symmetric weight distributions, e.g., uniform, normal and logistic distributions, will be considered. Furthermore, maximin efficient designs are developed where the minimal efficiency is maximized over a specified range of ability parameters.

The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter θ is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given level of significance in many cases; and, therefore, the corresponding intervals are no longer confidence intervals in terms of the actual definition. In the present work, confidence intervals are defined more precisely by utilizing the relationship between confidence intervals and hypothesis testing. Two approaches to confidence interval construction are explored that are optimal with respect to criteria of smallness and consistency with the standard approach.

This paper develops a theorem that facilitates computing the degrees of freedom of Wald-type chi-square tests for moment restrictions when there is rank deficiency of key matrices involved in the definition of the test. An if and only if (iff) condition is developed for a simple rule of difference of ranks to be used when computing the desired degrees of freedom of the test. The theorem is developed exploiting basics tools of matrix algebra. The theorem is shown to play a key role in proving the asymptotic chi-squaredness of a goodness of fit test in moment structure analysis, and in finding the degrees of freedom of this chi-square statistic.

As an extension of Lastovicka's four-mode components analysis an n-mode components analysis is developed. Using a convenient notation, both a canonical and a least squares solution are derived. The relation between both solutions and their computational aspects are discussed.

Meta-analysis of diagnostic studies experience the common problem that different studies might not be comparable since they have been using a different cut-off value for the continuous or ordered categorical diagnostic test value defining different regions for which the diagnostic test is defined to be positive. Hence specificities and sensitivities arising from different studies might vary just because the underlying cut-off value had been different. To cope with the cut-off value problem interest is usually directed towards the receiver operating characteristic (ROC) curve which consists of pairs of sensitivities and false-positive rates (1-specificity). In the context of meta-analysis one pair represents one study and the associated diagram is called an SROC curve where the S stands for “summary”. In meta-analysis of diagnostic studies emphasis has traditionally been placed on modelling this SROC curve with the intention of providing a summary measure of the diagnostic accuracy by means of an estimate of the summary ROC curve. Here, we focus instead on finding sub-groups or components in the data representing different diagnostic accuracies. The paper will consider modelling SROC curves with the Lehmann family which is characterised by one parameter only. Each single study can be represented by a specific value of that parameter. Hence we focus on the distribution of these parameter estimates and suggest modelling a potential heterogeneous or cluster structure by a mixture of specifically parameterised normal densities. We point out that this mixture is completely nonparametric and the associated mixture likelihood is well-defined and globally bounded. We use the theory and algorithms of nonparametric mixture likelihood estimation to identify a potential cluster structure in the diagnostic accuracies of the collection of studies to be analysed. Several meta-analytic applications on diagnostic studies, including AUDIT and AUDIT-C for detection of unhealthy alcohol use, the mini-mental state examination for cognitive disorders, as well as diagnostic accuracy inspection data on metal fatigue of aircraft spare parts, are discussed to illustrate the methodology.

This study examined associations between pregnancy and infant birth outcomes with child telomere length at age 17 years; and investigated if there are sex differences between pregnancy complications and telomere length. We utilised the population-based prospective Raine cohort study in Western Australia, Australia. 2900 pregnant women were recruited at 16–20 weeks’ gestation (Gen 1), and their children (Gen 2) were followed up over several years. Generalised linear models were used to examine relationships between pregnancy or birth outcomes (gestational diabetes, pre-eclampsia, preterm birth, low birth weight, macrosomia), and as a composite, with telomere length, measured via a DNA sample from blood at 17 years of age. Analyses were adjusted for a range of confounders. Among the 1202 included children, there were no differences in child telomere length for any of the individual maternal or birth weight pregnancy outcomes nor were there any significant interactions between each of the complications (individual or composite) and the sex of the child. However, females born from any of the 5 adverse outcomes had shorter telomeres (estimated mean (SE) = -0.159 (0.061), p = 0.010) than females born in the absence of these complications. Specifically, females born from a pre-eclamptic pregnancy had shorter telomeres than females not born from a pre-eclamptic pregnancy (estimated mean (SE) = -0.166 (0.072), p = 0.022). No relationships were observed in males. Further longitudinal studies are needed to understand mediating factors that are important in predicting offspring telomere length and the necessity to investigate females and males independently.

This work presents the integration of an elemental analyzer (EA) and an isotope ratio mass spectrometer (IRMS) into the 6 MV AMS system at the Institute for Nuclear Physics, University of Cologne. The AMS measurement of δ13C values for IAEA-C6 reference material resulted in –11.39(226)‰, compared to –10.28(32)‰ obtained by IRMS. The EA-IRMS system was also tested with IAEA-C3, IAEA-C5, and IAEA-C7 reference materials, yielding –24.79(9), –25.18(15), and –14.76(18)‰ respectively. Compared to the IAEA information values given as –24.91(49), –25.49(72) and –14.48(21)‰ respectively. To investigate an observed sample mass dependency, environmental samples from Spitzbergen were examined, showing δ13C values of –25.17(55), –25.80(31), and –26.17‰ in Cologne, while Hamburg recorded –24.8(1), –25.5(1), and –26.2(13)‰. In summary, this new setup could enable online analysis and quasi-simultaneous measurements of 14C, δ13C, and δ15N for ultra-small samples, utilizing precise δ13C values from IRMS for fractionation correction of the 14C/14C isotopic ratio.

We applied a Density-Based Clustering algorithm on samples of galaxies and galaxy systems belonging to 53 rich superclusters from the Main SuperCluster Catalogue to identify the presence of “central regions’’, or cores, in these large-scale structures. Cores are defined here as large gravitationally bound galaxy structures, comprised of two or more clusters and groups, with sufficient matter density to survive cosmic expansion and virialize in the future. We identified a total of 105 galaxy structures classified as cores, which exhibit a high density contrast of mass and galaxies. The Density-based Core Catalogue, presented here, includes cores that were previously reported in well-known superclusters of the Local Universe, and also several newly identified ones. We found that 83% of the rich superclusters in our sample have at least one core. While more than three cores with different dynamical state are possible, the presence of a single core in the superclusters is more common. Our work confirms the existence of nucleation regions in the internal structure of most rich superclusters and points to the fact that these cores are the densest and most massive features that can be identified in the cosmic web with high probability for future virialization.