Recent research has shown that interaction effects may often be nonlinear (Hainmueller, Mummolo, and Xu [2019, Political Analysis 27, 163–192]). As standard interaction effect specifications assume a linear interaction effect, that is, the moderator conditions the effect at a constant rate, this can lead to bias. However, allowing nonlinear interaction effects, without accounting for other nonlinearities and nonlinear interaction effects, can also lead to biased estimates. Specifically, researchers can infer nonlinear interaction effects, even though the true interaction effect is linear, when variables used for covariate adjustment that are correlated with the moderator have a nonlinear effect upon the outcome of interest. We illustrate this bias with simulations and show how diagnostic tools recommended in the literature are unable to uncover the issue. We show how using the adaptive Lasso to identify relevant nonlinearities among variables used for covariate adjustment can avoid this issue. Moreover, the use of regularized estimators, which allow for a fuller set of nonlinearities, both independent and interactive, is more generally shown to avoid this bias and more general forms of omitted interaction bias.

Mismatch in the phenology of trophically linked species as a result of climate warming has been shown to have far-reaching effects on animal communities, but implications for disease have so far received limited attention. This paper presents evidence suggestive of phenological asynchrony in a host-parasite system arising from climate change, with impacts on transmission. Diagnostic laboratory data on outbreaks of infection with the pathogenic nematode Nematodirus battus in sheep flocks in the UK were used to validate region-specific models of the effect of spring temperature on parasite transmission. The hatching of parasite eggs to produce infective larvae is driven by temperature, while the availability of susceptible hosts depends on lambing date, which is relatively insensitive to inter-annual variation in spring temperature. In southern areas and in warmer years, earlier emergence of infective larvae in spring was predicted, with decline through mortality before peak availability of susceptible lambs. Data confirmed model predictions, with fewer outbreaks recorded in those years and regions. Overlap between larval peaks and lamb availability was not reduced in northern areas, which experienced no decreases in the number of reported outbreaks. Results suggest that phenological asynchrony arising from climate warming may affect parasite transmission, with non-linear but predictable impacts on disease burden. Improved understanding of complex responses of host-parasite systems to climate change can contribute to effective adaptation of parasite control strategies.

Between 1995 and 2011 a global positioning system survey of 13 boulders and three ablation stakes (long stakes frozen in the ice) on the frozen surface of Lake Hoare was undertaken. Data interpretation illustrates complexities of post-depositional transport dynamics of boulders. Earlier studies on comparable datasets have suggested linear ‘conveyor’ type transport mechanisms for lake surface boulders. Yet explanations for non-linear boulder displacements or ‘walks’ and the mechanisms responsible for movements are inadequate. Two modes of boulder specific movement were observed. First, localized changes in the ice surface promote individual boulder movement (rolling). Second, ice rafting, which indicates the displacement of ‘plates’ of lake ice on which the boulder is located. Ablation stakes used as fixed survey control points support the hypothesis that ice cover moves as discrete plates rather than as a single homogenous mass. Factors that create the conditions to generate either of the two modes of movement may be related to location specific energy budgets. A relationship between average orientations and prevailing wind direction was also observed. The investigation describes the local-scale behaviour of surveyed boulders, and offers methodologies and interpretive frameworks for additional studies of modern and ancient sediment transportation dynamics in Antarctic lacustrine environments.

In this paper we propose and analyze a localized orthogonal decomposition (LOD) methodfor solving semi-linear elliptic problems with heterogeneous and highly variablecoefficient functions. This Galerkin-type method is based on a generalized finite elementbasis that spans a low dimensional multiscale space. The basis is assembled by performinglocalized linear fine-scale computations on small patches that have a diameter of orderH | log (H)| where H is the coarse mesh size. Without any assumptions onthe type of the oscillations in the coefficients, we give a rigorous proof for a linearconvergence of the H1-error with respect to the coarse meshsize even for rough coefficients. To solve the corresponding system of algebraicequations, we propose an algorithm that is based on a damped Newton scheme in themultiscale space.

Non-linear epigenetic processes are a potential underlying source of phenotypic differences in development. Simulation studies of twin pairs using simple non-linear development models characterised by chaotic or near-chaotic behavior are presented. The effect of chaotic processes on correlations is to lower them from their initial values, but high initial correlations are affected much less by chaotic and near-chaotic processes than intermediate correlations. Therefore, we would predict that traits affected by chaotic processes would have high MZ and low DZ twin correlations and this is reminiscent of certain traits such as EEG spectra. However the much more frequent observation of MZ correlations close to twice their DZ counterparts would suggest that the role of chaos in development is quite limited.

Nous nous intéressons dans cette étude à un modèle dynamique non-linéaire d'un engrenage droit à un degré de liberté. Ce modèle permet de prendre en compte la présence du jeu entre dents ainsi que la non-linéarité de la raideur d'engrènement associée à l'évolution instantanée du nombre de dents en prise. Notre étude concerne le cas d'engrenages corrigés par des corrections linéaires en tête de denture ainsi que des engrenages non corrigés. Le but de cette étude a été d'analyser la pertinence de ce modèle vis-à-vis de résultats expérimentaux mettant en œuvre un banc d'essais dont les caractéristiques, notamment aux niveaux de la micro-géométrie des dentures, sont parfaitement contrôlées. En conclusion, les résultats comparatifs sont encourageants, même si nous n'avons pas pu reproduire par simulation certains phénomènes non-linéaires observés. Parmi ceux-ci, on peut citer le cas de la cascade harmonique observée sur un engrenage corrigé et prenant naissance au niveau de la résonance principale.

Il s'agit de prévoir le comportement dynamique d'un démarreur de moteur d'avion dans le cas d'un redémarrage en vol. Une modélisation du système en torsion est réalisée, prenant en compte les raideurs d'engrenages, les jeux, et la non-linéarité de l'embrayage de type roue libre. Trois types d'éléments sont nécessaires à la modélisation du démarreur : arbre en torsion avec amortisseurs, liaison engrenage avec raideur, jeu et amortisseurs, roue libre embrayage avec raideur non-linéaire. Le système est étudié en régime transitoire dans la phase de réengagement (redémarrage en vol). La montée en vitesse de la turbine à air engendre un couple variable en fonction du temps. Un amortissement localisé sur le moteur d'avion permet de simuler le ralentissement du moteur. Les vitesses des différents éléments, ainsi que les couples supportés par l'arbre de transmission sont examinés. La possibilité de glissement entre les bagues de la roue libre au moment de l'embrayage est simulée, faisant apparaître un surcouple important dans l'arbre de transmission.

We consider a general non-linear multivariate time series model which can be parameterized by a finite and fixed number of parameters and which can be rewritten, if necessary, in a form such that the disturbances are stationary martingale differences. Given a series of discrete, equally spaced observations we prove the strong consistency and asymptotic normality of the Gaussian estimators of the parameters, the parameters possibly being subject to non-linear constraints. Because the normal equations are usually highly non-linear it may be difficult to obtain explicit expressions for the Gaussian estimates. To overcome this problem we use a Gauss–Newton type algorithm to obtain a sequence of iterates which converge to, and have the same asymptotic properties as, the Gaussian estimates.