An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm

We establish a correspondence between inverse sumset theorems (which can be viewed as classifications of approximate (abelian) groups) and inverse theorems for the Gowers norms (which can be viewed as classifications of approximate polynomials). In particular, we show that the inverse sumset theorems of Freiman type are equivalent to the known inverse results for the Gowers U^3 norms, and moreover that the conjectured polynomial strengthening of the former is also equivalent to the polynomial strengthening of the latter. We establish this equivalence in two model settings, namely that of the finite field vector spaces F_2^n, and of the cyclic groups Z/NZ. In both cases the argument involves clarifying the structure of certain types of approximate homomorphism.Comment: 23 page

How well do health professionals interpret diagnostic information? A systematic review.

Published onlineResearch Support, Non-U.S. Gov'tOBJECTIVE: To evaluate whether clinicians differ in how they evaluate and interpret diagnostic test information. DESIGN: Systematic review. DATA SOURCES: MEDLINE, EMBASE and PsycINFO from inception to September 2013; bibliographies of retrieved studies, experts and citation search of key included studies. ELIGIBILITY CRITERIA FOR SELECTING STUDIES: Primary studies that provided information on the accuracy of any diagnostic test (eg, sensitivity, specificity, likelihood ratios) to health professionals and that reported outcomes relating to their understanding of information on or implications of test accuracy. RESULTS: We included 24 studies. 6 assessed ability to define accuracy metrics: health professionals were less likely to identify the correct definition of likelihood ratios than of sensitivity and specificity. -25 studies assessed Bayesian reasoning. Most assessed the influence of a positive test result on the probability of disease: they generally found health professionals' estimation of post-test probability to be poor, with a tendency to overestimation. 3 studies found that approaches based on likelihood ratios resulted in more accurate estimates of post-test probability than approaches based on estimates of sensitivity and specificity alone, while 3 found less accurate estimates. 5 studies found that presenting natural frequencies rather than probabilities improved post-test probability estimation and speed of calculations. CONCLUSIONS: Commonly used measures of test accuracy are poorly understood by health professionals. Reporting test accuracy using natural frequencies and visual aids may facilitate improved understanding and better estimation of the post-test probability of disease.This work was partially funded by the UK Medical Research Council (Grant Code G0801405)

Metaphors of Identity: Focus Groups

This set of files contain focus groups data collected for the first phase of the Metaphors of Identity research project. Focus groups involved a small group of people (3 to 6 participants) across different age groups: teenagers (15-17 age group), young adults (19-29 age group) and an older age group (50-60 age group). Focus groups took place between the period March 2012 and March 2013. Each group engaged in a metaphoric discussion that largely arose from a projective technique involving themes pertaining to different levels of abstraction and then subjected to the phenomenological process of 'eidetic' reduction. A visual representation of the metaphor was produced by the participants

How well do health professionals interpret diagnostic information?:A systematic review

OBJECTIVE: To evaluate whether clinicians differ in how they evaluate and interpret diagnostic test information. DESIGN: Systematic review. DATA SOURCES: MEDLINE, EMBASE and PsycINFO from inception to September 2013; bibliographies of retrieved studies, experts and citation search of key included studies. ELIGIBILITY CRITERIA FOR SELECTING STUDIES: Primary studies that provided information on the accuracy of any diagnostic test (eg, sensitivity, specificity, likelihood ratios) to health professionals and that reported outcomes relating to their understanding of information on or implications of test accuracy. RESULTS: We included 24 studies. 6 assessed ability to define accuracy metrics: health professionals were less likely to identify the correct definition of likelihood ratios than of sensitivity and specificity. –25 studies assessed Bayesian reasoning. Most assessed the influence of a positive test result on the probability of disease: they generally found health professionals’ estimation of post-test probability to be poor, with a tendency to overestimation. 3 studies found that approaches based on likelihood ratios resulted in more accurate estimates of post-test probability than approaches based on estimates of sensitivity and specificity alone, while 3 found less accurate estimates. 5 studies found that presenting natural frequencies rather than probabilities improved post-test probability estimation and speed of calculations. CONCLUSIONS: Commonly used measures of test accuracy are poorly understood by health professionals. Reporting test accuracy using natural frequencies and visual aids may facilitate improved understanding and better estimation of the post-test probability of disease

Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

Places of joy : the role of heritage after lockdown

[Abstract not available

Heritage sites, value and wellbeing : learning from the COVID-19 pandemic in England

The COVID-19 lockdown of society in 2020 deprived people of access to many heritage sites. This made the public uniquely aware of why they visited heritage sites and what they valued about the visits, once heritage sites reopened. In particular, regaining access framed visits in terms of personal agency and wellbeing. Notions of capability, social connections, ontological security, and trust–all important elements of wellbeing–were widely shared values. Heritage sites also offered distinct opportunities for combining hedonic (subjective) and eudaimonic (psychological) wellbeing effects. While heritage value cannot be reduced to wellbeing effects, we suggest that constructive awareness of how these effects may be generated can enhance the outcome of visits to heritage sites

Shot noise in mesoscopic systems

This is a review of shot noise, the time-dependent fluctuations in the electrical current due to the discreteness of the electron charge, in small conductors. The shot-noise power can be smaller than that of a Poisson process as a result of correlations in the electron transmission imposed by the Pauli principle. This suppression takes on simple universal values in a symmetric double-barrier junction (suppression factor 1/2), a disordered metal (factor 1/3), and a chaotic cavity (factor 1/4). Loss of phase coherence has no effect on this shot-noise suppression, while thermalization of the electrons due to electron-electron scattering increases the shot noise slightly. Sub-Poissonian shot noise has been observed experimentally. So far unobserved phenomena involve the interplay of shot noise with the Aharonov-Bohm effect, Andreev reflection, and the fractional quantum Hall effect.Comment: 37 pages, Latex, 10 figures (eps). To be published in "Mesoscopic Electron Transport," edited by L. P. Kouwenhoven, G. Schoen, and L. L. Sohn, NATO ASI Series E (Kluwer Academic Publishing, Dordrecht

The Baryon Oscillation Spectroscopic Survey of SDSS-III

The Baryon Oscillation Spectroscopic Survey (BOSS) is designed to measure the scale of baryon acoustic oscillations (BAO) in the clustering of matter over a larger volume than the combined efforts of all previous spectroscopic surveys of large scale structure. BOSS uses 1.5 million luminous galaxies as faint as i=19.9 over 10,000 square degrees to measure BAO to redshifts z<0.7. Observations of neutral hydrogen in the Lyman alpha forest in more than 150,000 quasar spectra (g<22) will constrain BAO over the redshift range 2.15<z<3.5. Early results from BOSS include the first detection of the large-scale three-dimensional clustering of the Lyman alpha forest and a strong detection from the Data Release 9 data set of the BAO in the clustering of massive galaxies at an effective redshift z = 0.57. We project that BOSS will yield measurements of the angular diameter distance D_A to an accuracy of 1.0% at redshifts z=0.3 and z=0.57 and measurements of H(z) to 1.8% and 1.7% at the same redshifts. Forecasts for Lyman alpha forest constraints predict a measurement of an overall dilation factor that scales the highly degenerate D_A(z) and H^{-1}(z) parameters to an accuracy of 1.9% at z~2.5 when the survey is complete. Here, we provide an overview of the selection of spectroscopic targets, planning of observations, and analysis of data and data quality of BOSS.Comment: 49 pages, 16 figures, accepted by A