2,755 research outputs found

    Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps

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    Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property

    Moral Framing and Ideological Bias of News

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    News outlets are a primary source for many people to learn what is going on in the world. However, outlets with different political slants, when talking about the same news story, usually emphasize various aspects and choose their language framing differently. This framing implicitly shows their biases and also affects the reader's opinion and understanding. Therefore, understanding the framing in the news stories is fundamental for realizing what kind of view the writer is conveying with each news story. In this paper, we describe methods for characterizing moral frames in the news. We capture the frames based on the Moral Foundation Theory. This theory is a psychological concept which explains how every kind of morality and opinion can be summarized and presented with five main dimensions. We propose an unsupervised method that extracts the framing Bias and the framing Intensity without any external framing annotations provided. We validate the performance on an annotated twitter dataset and then use it to quantify the framing bias and partisanship of news

    Menstrual cycle phase does not predict political conservatism

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    Recent authors have reported a relationship between women's fertility status, as indexed by menstrual cycle phase, and conservatism in moral, social and political values. We conducted a survey to test for the existence of a relationship between menstrual cycle day and conservatism. 2213 women reporting regular menstrual cycles provided data about their political views. Of these women, 2208 provided information about their cycle date, 1260 provided additional evidence of reliability in self-reported cycle date, and of these, 750 also indicated an absence of hormonal disruptors such as recent hormonal contraception use, breastfeeding or pregnancy. Cycle day was used to estimate day-specific fertility rate (probability of conception); political conservatism was measured via direct self-report and via responses to the "Moral Foundations” questionnaire. We also recorded relationship status, which has been reported to interact with menstrual cycle phase in determining political preferences. We found no evidence of a relationship between estimated cyclical fertility changes and conservatism, and no evidence of an interaction between relationship status and cyclical fertility in determining political attitudes. Our findings were robust to multiple inclusion/exclusion criteria and to different methods of estimating fertility and measuring conservatism. In summary, the relationship between cycle-linked reproductive parameters and conservatism may be weaker or less reliable than previously thought

    Soliton pair creation in classical wave scattering

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    We study classical production of soliton-antisoliton pairs from colliding wave packets in (1+1)-dimensional scalar field model. Wave packets represent multiparticle states in quantum theory; we characterize them by energy E and particle number N. Sampling stochastically over the forms of wave packets, we find the entire region in (E,N) plane which corresponds to classical creation of soliton pairs. Particle number is parametrically large within this region meaning that the probability of soliton-antisoliton pair production in few-particle collisions is exponentially suppressed.Comment: 16 pages, 8 figures, journal version; misprint correcte

    Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial

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    This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an accompanying software package which is also briefly discussed here. Embedded in this article is a step-by-step tutorial of the required analysis for the setting known as the uniform case with first order QMC rules. The aim of this article is to provide an easy entry point for QMC experts wanting to start research in this direction and for PDE analysts and practitioners wanting to tap into contemporary QMC theory and methods.Comment: arXiv admin note: text overlap with arXiv:1606.0661

    On renormalization group flows and the a-theorem in 6d

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    We study the extension of the approach to the a-theorem of Komargodski and Schwimmer to quantum field theories in d=6 spacetime dimensions. The dilaton effective action is obtained up to 6th order in derivatives. The anomaly flow a_UV - a_IR is the coefficient of the 6-derivative Euler anomaly term in this action. It then appears at order p^6 in the low energy limit of n-point scattering amplitudes of the dilaton for n > 3. The detailed structure with the correct anomaly coefficient is confirmed by direct calculation in two examples: (i) the case of explicitly broken conformal symmetry is illustrated by the free massive scalar field, and (ii) the case of spontaneously broken conformal symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the latter example, the dilaton is a dynamical field so 4-derivative terms in the action also affect n-point amplitudes at order p^6. The calculation in the (2,0) theory is done by analyzing an M5-brane probe in AdS_7 x S^4. Given the confirmation in two distinct models, we attempt to use dispersion relations to prove that the anomaly flow is positive in general. Unfortunately the 4-point matrix element of the Euler anomaly is proportional to stu and vanishes for forward scattering. Thus the optical theorem cannot be applied to show positivity. Instead the anomaly flow is given by a dispersion sum rule in which the integrand does not have definite sign. It may be possible to base a proof of the a-theorem on the analyticity and unitarity properties of the 6-point function, but our preliminary study reveals some difficulties.Comment: 41 pages, 5 figure

    From everyday conversation to political action: Talking austerity in online ‘third spaces’

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    Taking forward a new agenda for online political deliberation – the study of everyday political talk in non-political, online ‘third spaces’ – this article examines the dynamics of political talk across three general interest UK-based online forums. The quantitative analysis found that discussions about austerity were just as likely to emerge from non-political discussions as they were ones that began as ‘political’, demonstrating the links people made between everyday experiences and public policy. Our qualitative analysis represents the first real attempt to analyse political actions within third spaces, with some striking outcomes. Over half of all political discussions led to at least one political action (with significant variation between forums). The findings demonstrate that while such third spaces remain concerned with the preoccupations of everyday life, they can and do perform a role of mobilizing agent towards political participation

    Hot new directions for quasi-Monte Carlo research in step with applications

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    This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube [0,1]s[0,1]^s and in Rs\mathbb{R}^s, and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension ss under appropriate conditions on the function spaces. Another important feature is that good parameters for these QMC methods can be obtained by fast efficient algorithms even when ss is large. We outline three different applications and explain how they can tap into the different QMC theory. We also discuss three cost saving strategies that can be combined with QMC in these applications. Many of these recent QMC theory and methods are developed not in isolation, but in close connection with applications

    Metabolomics demonstrates divergent responses of two Eucalyptus species to water stress

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    Past studies of water stress in Eucalyptus spp. generally highlighted the role of fewer than five “important” metabolites, whereas recent metabolomic studies on other genera have shown tens of compounds are affected. There are currently no metabolite profiling data for responses of stress-tolerant species to water stress. We used GC–MS metabolite profiling to examine the response of leaf metabolites to a long (2 month) and severe (ιpredawn < −2 MPa) water stress in two species of the perennial tree genus Eucalyptus (the mesic Eucalyptus pauciflora and the semi-arid Eucalyptus dumosa). Polar metabolites in leaves were analysed by GC–MS and inorganic ions by capillary electrophoresis. Pressure–volume curves and metabolite measurements showed that water stress led to more negative osmotic potential and increased total osmotically active solutes in leaves of both species. Water stress affected around 30–40% of measured metabolites in E. dumosa and 10–15% in E. pauciflora. There were many metabolites that were affected in E. dumosa but not E. pauciflora, and some that had opposite responses in the two species. For example, in E. dumosa there were increases in five acyclic sugar alcohols and four low-abundance carbohydrates that were unaffected by water stress in E. pauciflora. Re-watering increased osmotic potential and decreased total osmotically active solutes in E. pauciflora, whereas in E. dumosa re-watering led to further decreases in osmotic potential and increases in total osmotically active solutes. This experiment has added several extra dimensions to previous targeted analyses of water stress responses in Eucalyptus, and highlights that even species that are closely related (e.g. congeners) may respond differently to water stress and re-waterin
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