Conforming and nonconforming virtual element methods for elliptic problems

We present in a unified framework new conforming and nonconforming Virtual Element Methods (VEM) for general second order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and non-symmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal $H^1$- and $L^2$-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable

Towards a mathematical understanding of learning from few examples with nonlinear feature maps

We consider the problem of data classification where the training set consists of just a few data points. We explore this phenomenon mathematically and reveal key relationships between the geometry of an AI model's feature space, the structure of the underlying data distributions, and the model's generalisation capabilities. The main thrust of our analysis is to reveal the influence on the model's generalisation capabilities of nonlinear feature transformations mapping the original data into high, and possibly infinite, dimensional spaces.Comment: 18 pages, 8 figure

Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport

We introduce an $hp$-version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented in an almost identical form to standard multigroup discrete ordinates methods, meaning that solutions can be computed efficiently with high accuracy and in parallel within existing software. This method provides a unified discretisation of the space, angle, and energy domains of the underlying integro-differential equation and naturally incorporates both local mesh and local polynomial degree variation within each of these computational domains. Moreover, general polytopic elements can be handled by the method, enabling efficient discretisations of problems posed on complicated spatial geometries. We study the stability and $hp$-version a priori error analysis of the proposed method, by deriving suitable $hp$-approximation estimates together with a novel inf-sup bound. Numerical experiments highlighting the performance of the method for both polyenergetic and monoenergetic problems are presented.Comment: 27 pages, 2 figure

The Impact of Atmospheric Fluctuations on Degree-scale Imaging of the Cosmic Microwave Background

Fluctuations in the brightness of the Earth's atmosphere originating from water vapor are an important source of noise for ground-based instruments attempting to measure anisotropy in the Cosmic Microwave Background. This paper presents a model for the atmospheric fluctuations and derives simple expressions to predict the contribution of the atmosphere to experimental measurements. Data from the South Pole and from the Atacama Desert in Chile, two of the driest places on Earth, are used to assess the level of fluctuations at each site.Comment: 29 pages, 7 figures, 1 table, appears in The Astrophysical Journa

The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning

In this work, we assess the theoretical limitations of determining guaranteed stability and accuracy of neural networks in classification tasks. We consider classical distribution-agnostic framework and algorithms minimising empirical risks and potentially subjected to some weights regularisation. We show that there is a large family of tasks for which computing and verifying ideal stable and accurate neural networks in the above settings is extremely challenging, if at all possible, even when such ideal solutions exist within the given class of neural architectures

IgE to epitopes of Ara h 2 enhance the diagnostic accuracy of Ara h 2‐specific IgE

© 2020 The Authors. Allergy published by European Academy of Allergy and Clinical Immunology and John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.Background: Understanding the discrepancy between IgE sensitization and allergic reactions to peanut could facilitate diagnosis and lead to novel means of treating peanut allergy. Objective: To identify differences in IgE and IgG4 binding to peanut peptides between peanut-allergic (PA) and peanut-sensitized but tolerant (PS) children. Methods: PA (n = 56), PS (n = 42) and nonsensitized nonallergic (NA, n = 10) patients were studied. Synthetic overlapping 15-mer peptides of peanut allergens (Ara h 1-11) were spotted onto microarray slides, and patients' samples were tested for IgE and IgG4 binding using immunofluorescence. IgE and IgG4 levels to selected peptides were quantified using ImmunoCAP. Diagnostic model comparisons were performed using likelihood-ratio tests between each specified nominal logistic regression models. Results: Seven peptides on Ara h 1, Ara h 2, and Ara h 3 were bound more by IgE of PA compared to PS patients on the microarray. IgE binding to one peptide on Ara h 5 and IgG4 binding to one Ara h 9 peptide were greater in PS than in PA patients. Using ImmunoCAP, IgE to the Ara h 2 peptides enhanced the diagnostic accuracy of Ara h 2-specific IgE. Ratios of IgG4/IgE to 4 out of the 7 peptides were higher in PS than in PA subjects. Conclusions: Ara h 2 peptide-specific IgE added diagnostic value to Ara h 2-specific IgE. Ability of peptide-specific IgG4 to surmount their IgE counterpart seems to be important in established peanut tolerance.This work was supported by the Medical Research Council (MRC Clinical Research Training Fellowship G090218, MRC Centenary Early Career Award and MRC Clinician Scientist Fellowship MR/M008517/1, all awarded to A. F. Santos), the Department of Health via the National Institute for Health Research (NIHR) comprehensive Biomedical Research Centre award to Guy's & St Thomas' NHS Foundation Trust in partnership with King's College London and King's College Hospital NHS Foundation Trust; the US Department of Agriculture, Agricultural Research Service (USDA-ARS6054-43440-046-00D; USDA-NIFA) and the National Peanut Board (GRANT12229460).info:eu-repo/semantics/publishedVersio

Documentation of in-hospital falls on incident reports: Qualitative investigation of an imperfect process

<p>Abstract</p> <p>Background</p> <p>Incident reporting is the prevailing approach to gathering data on accidental falls in hospitals for both research and quality assurance purposes, though is of questionable quality as staff time pressures, perception of blame and other factors are thought to contribute to under-reporting.</p> <p>Methods</p> <p>This research aimed to identify contextual factors influencing recording of in-hospital falls on incident reports. A qualitative multi-centre investigation using an open written response questionnaire was undertaken. Participants were asked to describe any factors that made them feel more or less likely to record a fall on an incident report. 212 hospital staff from 30 wards in 7 hospitals in Queensland, Australia provided a response. A framework approach was employed to identify and understand inter-relationships between emergent categories.</p> <p>Results</p> <p>Three main categories were developed. The first, determinants of reporting, describes a hierarchical structure of primary (principle of reporting), secondary (patient injury), and tertiary determinants that influenced the likelihood that an in-hospital fall would be recorded on an incident report. The tertiary determinants frequently had an inconsistent effect. The second and third main categories described environmental/cultural facilitators and barriers respectively which form a background upon which the determinants of reporting exists.</p> <p>Conclusion</p> <p>A distinctive framework with clear differences to recording of other types of adverse events on incident reports was apparent. Providing information to hospital staff regarding the purpose of incident reporting and the usefulness of incident reporting for preventing future falls may improve incident reporting practices.</p

Upper limits on the strength of periodic gravitational waves from PSR J1939+2134

The first science run of the LIGO and GEO gravitational wave detectors presented the opportunity to test methods of searching for gravitational waves from known pulsars. Here we present new direct upper limits on the strength of waves from the pulsar PSR J1939+2134 using two independent analysis methods, one in the frequency domain using frequentist statistics and one in the time domain using Bayesian inference. Both methods show that the strain amplitude at Earth from this pulsar is less than a few times $10^{-22}$.Comment: 7 pages, 1 figure, to appear in the Proceedings of the 5th Edoardo Amaldi Conference on Gravitational Waves, Tirrenia, Pisa, Italy, 6-11 July 200