First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Generalized Bayesian cloud detection for satellite imagery. part 1: technique and validation for night-time imagery over land and sea

Numerical Weather Prediction (NWP) fields are used to assist the detection of cloud in satellite imagery. Simulated observations based on NWP are used within a framework based on Bayes' theorem to calculate a physically-based probability of each pixel with an imaged scene being clear or cloudy. Different thresholds can be set on the probabilities to create application-specific cloud-masks. Here, this is done over both land and ocean using night-time (infrared) imagery. We use a validation dataset of difficult cloud detection targets for the Spinning Enhanced Visible and Infrared Imager (SEVIRI) achieving true skill scores of 87% and 48% for ocean and land, respectively using the Bayesian technique, compared to 74% and 39%, respectively for the threshold-based techniques associated with the validation dataset.

On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ulti- mately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a non- linear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

Dancing in translation: Irina Brook’s mise en scène of 'Danser à Lughnasa', Jean-Marie Besset’s translation of Brian Friel’s 'Dancing at Lughnasa'

This essay contributes to debates about theatre and cross-cultural encounter through an analysis of Irina Brook’s 1999 Swiss / French co-production of Irish playwright Brian Friel’s Dancing at Lughnasa, in a French translation by Jean-Marie Besset. While the translation and Brook’s mise en scène clearly identified the source text and culture as Irish, they avoided cultural stereotypes, and rendered the play accessible to francophone audiences without entirely assimilating it to a specific Swiss or French cultural context. Drawing on discourses of theatre translation, and concepts of cosmopolitanism and conviviality, the essay focuses on the potential of such textual and theatrical translation to acknowledge specific cultural traces but also to estrange the familiar perceptions and boundaries of both the source and target cultures, offering modes of interconnection across diverse cultural affiliations.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

The description of stencilling by Gilles Filleau des Billettes: transcription and translation

This article presents the description of stencilling by Gilles Filleau des Billettes. The description sets out a method for stencilling letters, words, and texts, and specifies equipment for doing the work; it forms the basis for a reconstruction of the equipment and method, which is presented in a parallel article in this volume of Typography papers (see E. Kindel, 'A reconstruction of stencilling based on the description by Gilles Filleau des Billettes', Typography papers, 9, pp. 28–65). The original French text, approximately 10,000 words in length, is here transcribed and accompanied by a parallel English translation. Introductory notes on the preparation of both texts are provided; images of stencil letters found among the papers of Sébastien Truchet, Des Billettes’s colleague, are shown in an appendix.

Eigenvalues of a one-dimensional Dirac operator pencil

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of the coupling constant for which the kernel of the Dirac operator contains a square integrable function. In physics literature such a function is called a confined zero mode. Several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained. In particular, we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential. Surprisingly, it also depends on the arithmetic properties of certain quantities determined by the potential. We further observe that variable sign potentials may produce complex eigenvalues of the operator pencil. Some examples and numerical calculations illustrating these phenomena are presented.

A decade of plant proteomics and mass spectrometry: translation of technical advancements to food security and safety issues

Tremendous progress in plant proteomics driven by mass spectrometry (MS) techniques has been made since 2000 when few proteomics reports were published and plant proteomics was in its infancy. These achievements include the refinement of existing techniques and the search for new techniques to address food security, safety, and health issues. It is projected that in 2050, the world’s population will reach 9–12 billion people demanding a food production increase of 34–70% (FAO, 2009) from today’s food production. Provision of food in a sustainable and environmentally committed manner for such a demand without threatening natural resources, requires that agricultural production increases significantly and that postharvest handling and food manufacturing systems become more efficient requiring lower energy expenditure, a decrease in postharvest losses, less waste generation and food with longer shelf life. There is also a need to look for alternative protein sources to animal based (i.e., plant based) to be able to fulfill the increase in protein demands by 2050. Thus, plant biology has a critical role to play as a science capable of addressing such challenges. In this review, we discuss proteomics especially MS, as a platform, being utilized in plant biology research for the past 10 years having the potential to expedite the process of understanding plant biology for human benefits. The increasing application of proteomics technologies in food security, analysis, and safety is emphasized in this review. But, we are aware that no unique approach/technology is capable to address the global food issues. Proteomics-generated information/resources must be integrated and correlated with other omics-based approaches, information, and conventional programs to ensure sufficient food and resources for human development now and in the future.

Foreign credit: travel writing and authenticity in the dutch translation of The memoirs and travels of Mauritius Augustus, Count de Benyowsky (1790)

This article explores the translation and reception of the Memoirs and Travels (1790) of Count Mauritius Augustus Benyowsky (1746-86) in the Netherlands, and examines the complications, tensions and problems that transfer between a major and a more minor European language involves. I analyse how the Dutch translator Petrus Loosjes Adriaanszoon positioned himself as a mediator between these very different source and target cultures and ask how he dealt with the problems of plausibility and ‘credit’ which had beleaguered the reception of the Memoirs and Travels from the outset. In this article I am concerned to restore minority languages to the discussion of how travel literature circulated in Western Europe at the close of the eighteenth century and to demonstrate how major/minor language translation was central to the construction of Dutch-language culture in the Low Countries in this period.

Type-1 error inflation in the traditional by-participant analysis to metamemory accuracy: a generalized mixed-effects model perspective

In order to examine metacognitive accuracy (i.e., the relationship between metacognitive judgment and memory performance), researchers often rely on by-participant analysis, where metacognitive accuracy (e.g., resolution, as measured by the gamma coefficient or signal detection measures) is computed for each participant and the computed values are entered into group-level statistical tests such as the t-test. In the current work, we argue that the by-participant analysis, regardless of the accuracy measurements used, would produce a substantial inflation of Type-1 error rates, when a random item effect is present. A mixed-effects model is proposed as a way to effectively address the issue, and our simulation studies examining Type-1 error rates indeed showed superior performance of mixed-effects model analysis as compared to the conventional by-participant analysis. We also present real data applications to illustrate further strengths of mixed-effects model analysis. Our findings imply that caution is needed when using the by-participant analysis, and recommend the mixed-effects model analysis.

Translation and usability of autism screening and diagnostic tools for autism spectrum conditions in India

There is a critical need for screening and diagnostic tools (SDT) for autism spectrum conditions (ASC) in regional languages in South Asia. To address this, we translated four widely used SDT (Social Communication Disorder Checklist, Autism Spectrum Quotient, Social Communication Questionnaire, and Autism Diagnostic Observation Schedule) into Bengali and Hindi, two main regional languages (∼ 360 million speakers), and tested their usability in children with and without ASC. We found a significant difference in scores between children with ASC (n = 45 in Bengali, n = 40 in Hindi) and typically developing children (n = 43 in Bengali, n = 42 in Hindi) on all SDTs. These results demonstrate that these SDTs are usable in South Asia, and constitute an important resource for epidemiology research and clinical diagnosis in the region.

"Just as fragments are part of a vessel": a translation into medieval Occitan of the life of Alexander the Great

This article examines a 14th-c. translation into Old Occitan prose of a late-antique life of Alexander the Great: Justin’s Epitome of the 'Historia Philippicae' of Pompeius Trogus. The article argues that it is the work of translators whose knowledge of pagan Latin materials was incomplete and whose use of their native tongue rested on non-literary bases. This text has not been edited before, and examining its uneven treatment of its source provides important new insights into the work of translators in the later Middle Ages. In conclusion, the article suggests some new approaches to the understanding of translation as a process of reconstruction and adaptation.