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

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

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

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

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

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

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

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 $[0,1]^s$ and in $\mathbb{R}^s$, and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension $s$ 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 $s$ 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

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 (Ψpredawn < −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

Vicarious Group Trauma among British Jews

This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s11133-016-9337-4Given that literature on the intra- and inter-generational transmission of traumas is mainly based on secondary literature and focuses on the transmission of trauma memory in terms of the historical knowledge of group trauma, this article develops the theory of vicarious group trauma and tests this theory by exploring vicarious traumatization in the everyday lives of Jews in Britain through the methods of observation and in-depth interviewing. Vicarious group trauma is defined as a life or safety-threatening event or abuse that happened to some members of a social group but is felt by other members as their own experience because of their personal affiliation with the group. The article finds that the vicarious sensation of traumatic group experiences can create anxiety, elicit perceptions of threat and, by extension, hypervigilance among Jews. The findings demonstrate that group traumas of the past interpenetrate and interweave with members’ current lives and in this way can also become constitutive of their group identity. An institutional focus on threats to Jews can inform the construction and reinforcement of traumatization symptoms and accordingly vicarious group trauma. This article suggests an association between the level of involvement of group members in the collective’s social structure and the prominence of vicarious group trauma among them

Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe

High prevalence of bronchiectasis is linked to HTLV-1-associated inflammatory disease.

BACKGROUND: Human T-lymphotropic virus type 1 (HTLV-1), a retrovirus, is the causative agent of HTLV-1-associated myelopathy/tropical spastic paraparesis (HAM/TSP) and adult T-cell leukaemia/lymphoma (ATLL). The reported association with pulmonary disease such as bronchiectasis is less certain. METHODS: A retrospective case review of a HTLV-1 seropositive cohort attending a national referral centre. The cohort was categorised into HTLV-1 symptomatic patients (SPs) (ATLL, HAM/TSP, Strongyloidiasis and HTLV associated inflammatory disease (HAID)) and HTLV-1 asymptomatic carriers (ACs). The cohort was reviewed for diagnosis of bronchiectasis. RESULT: 34/246 ACs and 30/167 SPs had been investigated for respiratory symptoms by computer tomography (CT) with productive cough +/- recurrent chest infections the predominant indications. Bronchiectasis was diagnosed in one AC (1/246) and 13 SPs (2 HAID, 1 ATLL, 10 HAM/TSP) (13/167, RR 19.2 95 % CI 2.5-14.5, p = 0.004) with high resolution CT. In the multivariate analysis ethnicity (p = 0.02) and disease state (p < 0.001) were independent predictors for bronchiectasis. The relative risk of bronchiectasis in SPs was 19.2 (95 % CI 2.5-14.5, p = 0.004) and in HAM/TSP patients compared with all other categories 8.4 (95 % CI 2.7-26.1, p = 0.0002). Subjects not of African/Afro-Caribbean ethnicity had an increased prevalence of bronchiectasis (RR 3.45 95 % 1.2-9.7, p = 0.02). CONCLUSIONS: Bronchiectasis was common in the cohort (3.4 %). Risk factors were a prior diagnosis of HAM/TSP and ethnicity but not HTLV-1 viral load, age and gender. The spectrum of HTLV-associated disease should now include bronchiectasis and HTLV serology should be considered in patients with unexplained bronchiectasis